Chapter8_exercises.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 775,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from collections import OrderedDict\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.tree import export_graphviz\n",
    "import graphviz\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.ensemble import BaggingRegressor\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.ensemble import GradientBoostingClassifier\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.ensemble import BaggingClassifier\n",
    "from sklearn.ensemble import RandomForestClassifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 8 Exercises\n",
    "\n",
    "## Conceptual\n",
    "\n",
    "**1.** Draw an example (of your own invention) of a partition of two- dimensional feature space that could result from recursive binary splitting. Your example should contain at least six regions. Draw a decision tree corresponding to this partition. Be sure to label all aspects of your figures, including the regions $R1, R2, . . .,$ the cutpoints $t1,t2,...,$ and so forth.\n",
    "\n",
    "*_Hint: Your result should look something like Figures 8.1 and 8.2._*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "                   x1<=5\n",
    "                   |    |\n",
    "             x2<=1.5    x1<=11  \n",
    "             |     |    |    |\n",
    "        x1<=2.5   22    14    x2<=4\n",
    "       |      |              |     | \n",
    "       55    42              25    7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A partition of the predictor space\n",
    "\n",
    "# split lines\n",
    "plt.axhline(y=4, xmin=1, xmax=0.74)\n",
    "plt.axvline(x=5)\n",
    "plt.axvline(x=2.5, ymin=0, ymax=0.29)\n",
    "plt.axvline(x=11)\n",
    "plt.axhline(y=1.5, xmin=0, xmax=0.33)\n",
    "\n",
    "# axis and labels\n",
    "plt.axis([0,15,0,5])\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "\n",
    "# label terminal nodes\n",
    "plt.text(1, 0.7, '55')\n",
    "plt.text(3.4, 0.7, '42')\n",
    "plt.text(2.3, 3.3, '22')\n",
    "plt.text(7.8, 2.5, '14')\n",
    "plt.text(12.7, 2, '25')\n",
    "plt.text(12.7, 4.4, '7')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.** It is mentioned in Section 8.2.3 that boosting using depth-one trees (or stumps) leads to an additive model. Explain why this is the case.\n",
    "\n",
    ">Additive models are a sum of univariate regression functions over the variables (in the regression case). Similarly, boosting using depth-one trees is a sum of single variable models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3.** Consider the Gini index, classification error, and cross-entropy in a simple classification setting with two classes. Create a single plot that displays each of these quantities as a function of ${\\hat p}_{m1}$. The x-axis should display ${\\hat p}_{m1}$, ranging from 0 to 1, and the y-axis should display the value of the Gini index, classification error, and entropy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = np.linspace(0.0001, 0.9999, 100)\n",
    "\n",
    "gini = p*(1-p)*2\n",
    "entropy = -(p * np.log(p) + (1 - p) * np.log(1 - p))\n",
    "class_err = 1 - np.maximum(p, 1 - p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5euUeR6/eIyLmPlfupPzzdTtrK8p7OOHt7kTDcsUoXcyR4s72FHOyxa2IHc72NmQY7vP50feIvHvqn/fVL96IcQ0+xxonEtOyuJeSQXxKBnGJ6cQkpHEjPpWLt5PZeTaWzGzt21kIqOBRhNqlXWlYzo1G5d2oVdoVW2u1duE/HN20HayLu8CawVpdJLX6y2hyktyjAe8HXpcFYh68QEp554GXC4Av8h6aws7P4Mo+eGE+eNXQOxqLYTBITsUksDfqNvuibhN6+R7pWQYAvN0dqVumKC83Kkut0q5U9XKhdDFHrK0efcdzM/kmg7cOJyYphoDaAdha25KWlcbPkT8zMfRN5nacS01Hj0e+PyvbwPX4VM7dSuLMjfucjrnPsavxbDihFcxytLWmcUV3WlbxoEUVT2qVckWoOzBNmYbaGviN72jPlVq/o3dEBYaQT3haLYSwQZtq6QBcB44AvaWUEQ9cU0pKeeOv/34BeE9K2fRx7fr6+srQ0NA8hl+ARW2DZS9BwwDoPlPvaHSXlpnN7nNxbD8Ty/bIWG4npQNQo6QLLap40riCOw3LF8PLxeGp2r1y/wqDtwzmfsZ9vu/wPY1KNPrna/uu72PMzjGULFKS+Z3mU8q51FO1fTMhjaNX73H40l32X7jNuVtJAJRwtadDzRJ0rOlFiyqe2NsU8vl7KbU71IjfIHAjlG+md0QWTQgRJqX0feJ1T0rufzX2DPAtYA0sllJOEUJMAkKllOuEEFOB7kAWcBcYJqWMfFybKrk/RlIs/NBcO65s8E7t4OFCKCPLwO5zcWw4EcPW07dIzsjGxd6GNtWL07FmCVpU8aS4S+7r1p+9e5YhW4dgkAbmdppLLY//LgI7FnuMEdtGUMSuCAs6LaBC0Qq57u/W/TT2nL/N9jO32H0uTvv7ONjQuVZJnq1filZVPLEprNM3afdhXiutuNjQPdqUjfJQRk3upqCS+yMYDFqJ1Mt7YdBOKPGwVacF2+mY+6wMu8bv4THcTc6gqKMt/rVL0q1eKZpW8sDOJu8JMDw2nOHbh+Nk48T8zvOpVLTSI6+NvBvJkK1DAJjXaR413PM+RZaelc3+qDtsOHGDLRE3SUzPwtPZnhcbluHlRmWpWqIQ1uSPDoPFnaH6M/DKUrV44BFUcs+v9n+v1Y3pNh0aD9A7GrNJy8xm/fEYlh28wvHoBOysrehYy4uXGpalVdXiRknofzsQc4DRO0dT3LE4CzovoLRz6Se+53LCZQZtHURyRjKzO86mgVcDo8WTnpXNrrNxrA6LZkdkLFkGSaPybvRtVp6udUoZ9e9u8fZ+C9s+hee+g0aBekdjkVRyz49uHIcFHaBaF+2ovEIwcom9n0bQ/sv8fPgq8SmZVPFypk+TcjzvUwa3InZG72/7le28u/tdKhatyLxO8/B09Mzxe28k3WDw1sHcSrnFt22/pXkZ45dZvp2Uztpj11l28AqX76Tg6WxHnybleaNZeTydC8HRiQYDLHsBrh7Spmc8q+odkcVRyT2/yUyD+W0gNR6GHyjwa37P30pk3u6L/B5+nWyDpHOtkvRtXp5mlTxMtpJk3YV1fLLvE2p71mZOhzkUtS/61G3cSb3D0G1DiYqP4otWX9C5QmcTRKqtCNoTdZul+y+zPTIWexsrXmxYlsGtK1HRs4DXFEq8CXOagltFGLBFq6Wk/EMl9/xm84davevXV0OVjnpHYzJnbtxn1o7zbDx5EwdbK17x9WZAy4qU9zBtwvr5zM9MPTyVJqWaMLPdTJxsnXLd1v2M+4zcPpLjcceZ0GwCL1R9wYiR/ldUbBKL9l5i9dFosrINdK9fmpHtq1DFqwDPy0eshZUB0PZ9aPufclaFmkru+cml3RD8HDQeCN2+0Tsak4iKTeSbLefYdOomzvY2BDQvz4CWlXA3wdTLg6SUzD8xn+/Dv6e9d3u+bPMl9tZ5n95IyUxh7K6x7I/Zz7jG43ij1htGiPbxYhPTWLjnEj8euEJaVjbP1SvNW52qUaGgjuTXDIGTK2HAVijb6MnXFxIquecXaQkwpznYOsCQ3QWujO/1+FS+3XqO1UejcbKzoX/LigxoUZGiTqa/1ZZS8nXo1yw9vZTulbszsflEbKyMVxogIzuD8XvGs/XKVobWH8rw+sPNsjnpTlI6C/ZcImj/JbKyJa829mZ0h6p4uT7dGn+L9/9+NvaAXe7vtgoSldzzi3VvwrFlf41OnvjvlW8kpWfxw64oFu65hJTwRrPyDG9bGQ8zPRTMNmQz6eAk1pxfQ+8avXnP7z2shPFXnWQZsph4YCJro9bSp2YfxjUeZ5J+Hib2fhqzdkTxy+Gr2NlYMbRNZQa1qoSjXQHaFPX3XW2zkdBlit7RWIScJndV4UhPUdu1c1BbjCkwid1gkKw+Gs2Xm88Sl5hOD5/SvNulOmXdzDfqyszOZPye8Wy5ssXkI2obKxsmNp+Ii50LP57+kcSMRKPfITyKl6sDk5+vw8BWFZm2KZLpW8+x/PBV3utag+71SxeMEgcVW2vTlQdmQ83uUO5hNQuVh1Ejd72k3Yc5zbRbzSF7tFvPfC4iJoGP157i6NV4GpQrxifP1qJBOfPuNEzNSmXsrrHsu76Pd3zfIaB2gFn6lVIy98Rc5oTPoUO5DnzZ+kvsrE37POHfDl68w2d/nObU9fs0q+TBpB61C8ZmqPQk7WfFxg6G7i20O7b/ltOReyHaHWFhtn4CiTHQY06+T+xJ6VlMXB/Bc7P2cuVOCl/1rMfqoc3NntjvZ9xnyNYhHIg5wKTmk8yW2AGEEAyrP4zxfuPZfnU7I7ePJCUz5clvNKKmlTz4fURLPnu+Dqdv3Kfrd3uYtimS1Ixss8ZhdPbO0GOWdgrZTjU1k1Nq5K6Hi3/C0u7Q/E3o/Jne0eTJzshYPvztJDfup9GnSTne7VzDLA9L/81c689z4veo3/lk/yfU9azL7A6zc7WePq/uJKUzbVMkK8OiKe/hxNQX6tK8Ss43bFmk9aMhLBgGbisw05i5oR6oWqrMVK0oGMCw/fn2FvNecgYT10ewNjyGKl7OfPFSPRqV16fY083kmwzaMoibyTeZ0W4GLcu01CWOB227so1xu8flaiesMe2/cJv315zkyp0UXvX15qNna+LikE83BaXdh9lNtKJiQ/4stJub1LSMpfrzS7h7EZ79Nt8m9h2Rt+j87W42nLjB6A5V+WNUS90S++WEy/Td1JfbqbeZ12meRSR2gI7lO/J9h++5lniNgE0BxCTFPPlNJtC8siebx7RmSJtKrAy7hv+3e9gfdVuXWPLMwRW6fQ2xEbB/lt7RWDyV3M3p5inYPxN8+kClNnpH89SS0rN4b9UJ+geF4lHEjt9HtmBsp2q61SM/e/csASEBpGens7jLYhqWaKhLHI/SvHRz5neaz730e/Td1JeLCRd1icPB1pr3u9Zk9bDm2NtY0XvhISasiyAtMx/OxdfoBjWfgz+/gDsX9I7Goqnkbi6GbFg/ChyK5ct59uPX4nl25h5WhF1jWNvK/D6yBbVLm38u+W/hseH0C+mHrZUtQf5B1PSoqVssj+Pj5cOSLkvINGTSL6Qfp+/od658g3Ju/DGqFYHNKxC0/zLdv99L5M37usWTa12/Ams72DBGO+hDeSiV3M0ldDFcDwP/qfmqKJjBIJn75wVe+mE/6VkGlg9qynv+NXQ9PWh/zH4Gbx2Mu6M7S7supWLRirrFkhPV3asT7B+MnbUdAzYPIOxWmG6xONpZM6F7bYL7+3E3OZPu3+8jaN8l9Hr2liuupaDjBG2D04lf9Y7GYqnkbg5JsbB9MlRqC3Vf1juaHLubnEG/oCNM2xRJ59olCBndmiaVHn2WqDlsu7KNkdtH4u3iTZB/UI5qsVuCCkUr8GPXH/F09GTo1qHsvb5X13jaVCtOyJhWtKjswYT1pxm6LIyE1ExdY3oqjfpBGV/Y8pFWSVX5D5XczWHrJ5CZAs98nW9qtIdduUu3mXs4cOEOnz1fh9m9G+qyxPFBa6PW8vafb1PLoxaLuyzWbQVKbpUsUpIg/yAqFK3AmzveZPPlzbrG4+lsz+LAxnzUrSbbz8Ty3Ky9nLqeoGtMOWZlpRXZS7mj1r4/gkrupnZ5Hxz/RVvTng8OHpBSsmTfJV6ddxBbayvWDG/O603L676VfdnpZXy872OalGzC/E7zdVk7bgwejh4s6rKIup51Gbd7HGvOr9E1HiEEA1tV4tchTcnMNvDinP0sP3xV15hyrLQP+A6AIwshJlzvaCxOjpK7EMJfCHFWCBElhHhkcWUhRE8hhBRCFN4dBg/KzoQ/3oai3tD6Hb2jeaLUjGzeWnGcietP07a6FxtGtaROGX2TqJSSOeFz+OLIF3Qspy0vzEstdkvgaufKvE7zaFaqGZ/u/5TgiGC9Q6JReXf+GNWKJpXcGb/mJB/8dpL0rHywmqb9R+Dkof2cGQx6R2NRnpjchRDWwGygK1AL6CWE+M+pzUIIF2AUcMjYQeZbh+dD3Bnwn2bxpXyj76XQc+5+1oZf5+1O1Zj/RiNcdd7sYpAGvjzyJT8c/4EelXvwVZuvzF6vxVQcbRyZ1X4Wncp34uvQr5l1bJbuDzXdi9gR1M+PYW0r8/Ohq7w2/yCx99N0jemJHItBp8lwPRTCl+kdjUXJycjdD4iSUl6UUmYAy4EeD7luMvAlYOHfDWaSFAe7voDKHbS1uRYs9PJdeny/j6t3U1gc0Jg3O1TFykrfaZgsQxaf7PuEZWeW0admHya1mGSWSovmZGtty1etv+KFKi8w/8R8ph6eikHqO/q0thK851+DOX0acvZmIt2/32f58/D1XwPvprB9klYDXgFyltzLANceeB391+f+IYRoAHhLKTcYMbb8bednkJmsLX204Ieoq8Ki6b3gEC4ONvw2vAXtanjpHRIZ2Rm8++e7/H7hd4bVH8Z7jU1Ti90SWFtZM7H5RPrW6ssvkb/w0d6PyDJk6R0Wz9QtxaqhzbG2EvScu5+NJ2/oHdKjCQFdp0Hybdj9ld7RWIyc/MQ8LDP9c/8ohLACZgBvP7EhIQYLIUKFEKFxcXE5jzK/uXFCK3DkNxiKV9c7mocyGCRfbY7knZXH8a3gxtoRLaji5ax3WKRkpjBy+0i2Xd3GuMbjGO5jntON9CSE4B3fdxjpM5L1F9fz9q63Sc9O1zssapV2Ze2IFtQq5crwn47y/Y7zuk8dPVLpBtCgDxycC7ej9I7GIuQkuUcD3g+8Lgs8WCjDBagD7BJCXAaaAuse9lBVSjlfSukrpfQtXrx47qO2ZFJCyHituFGbcXpH81DpWdmM+TWc2Tsv8Fpjb4L7+1HMSf+57IT0BIZsHcKhm4eY1HySWc4ltRRCCIbUH8J4v/HsuLaDEdtHmL1k8MMUd7Hn50FN6eFTmq+3nOP9NSfJzLbQB5ftPwEbB9jyod6RWIScJPcjQFUhREUhhB3wGrDu7y9KKROklJ5SygpSygrAQaC7lLIQlnwETq+FK/u0p/iO+hTTepz4lAzeWHSYdcdjGOdfnakv1sXWWv8pj9uptxmweQCn7pzi6zZf80LVF/QOSRd9avZhSsspHLl5hEFbB5GQrv8csoOtNd++6sPIdlVYfuQaA4JDSUyzwA1PLiW0VWnnQiBqm97R6O6JP9VSyixgJLAZOAOskFJGCCEmCSG6mzrAfCUrHbZNAK9a0ChQ72j+40ZCKi/PPUD41Xi+e82H4W2rWMSUx42kGwSGBHI18Sqz28+mU/lOeoekq+6VuzO9zXTO3DlDYEggcSn6T2EKIXinS3WmvViXfVG36bXgIHGJ+k8d/UfTYeBWAbZ8rNVzKsRyNGSTUm6UUlaTUlaWUk7563OfSCnXPeTatoV21H5kEdy7rC3NsrKsQ4qjYhN5ac5+biakEdzfjx4+ZZ78JjO4lHCJviF9uZt6l/md5tO8THO9Q7IIHcp3YHaH2VxPuk5ASADXk67rHRIAr/mVY2FfX6Jik+g5dz9X7+g/dfT/2NhrdWdiT0P4T3pHoyv978cLitR7sPtLqNQOqnTQO5r/59jVe/Sce4CMbMnyIU1pVlnf+jB/i7wbSWBIIBnZGSz2X4yPl4/eIVmUZqWbMb/TfOLT47WSwfH6lAyYYUwEAAAgAElEQVT+t3Y1vPh5UFMSUjN58Yf9RMToP3X0/9R6Hso2hh1TICNZ72h0o5K7sez5Ritg1HmyRS193B91mz4LD1HU0ZY1w5rrWqb3Qcdij9E/pD921nYE+wdTw72G3iFZpL9LBmcbsgkMCdS1ZPCDGpZzY9XQZthZC3rNP0jYlXt6h/Q/QmhltZNuwoHZekejG5XcjeHeFTg0D+r3gpJ19Y7mH9vP3CIw6Ajebk6sHNKMch6WsW1/3/V9DN4yGA9HD5b6L6VC0Qp6h2TRqrtXJ7hrMI42jgzYPIDQm5Yx61nFy4WVw5rjXsSONxYdYp8lnfBUrql2qMfebyHxlt7R6EIld2PYOQWElbZCxkKsPx7DkB/DqFnSheWDm+Ll6qB3SABsubyFkTtGUqFoBYL8gyjlXErvkPKF8q7lCe4aTHGn4gzdNpTd0bv1DgmAMsUcWTG0Gd5uTvQLOsL2MxaUSDtOhOx07dSmQkgl97y6FQEnVkCTIVDUMh5Srj12ndHLj9GwvBvLBjbBrYj+a9gBfjv/G+/ufpe6nnVZ1GURHo6WMfefX/xdMrhS0UqM3jGakEsheocEgJeLA78OaUrNki4MXRbG5oibeoek8agMDQPgaLB2bnEho5J7Xu2YAvau0GKM3pEAWjmBsSvCaVrJg6B+jS3mpPulEUv5ZP8nNC3VlLkd5+Jq56p3SPmSu4M7i7osol7xeozbPY5V51bpHRIAxZzs+HFgE+qUKcqIn45aTrmCNuPAyhZ2TdM7ErNTyT0vrh2Bs39Aizct4ui8FUeu8e6q47Ss4smigMY42elfaEtKyezw2XwV+hWdyndiVvtZ+b5kr95c7FyY22kuLcq0YOKBiQSdCtI7JABcHWxZ2t8PH+9ivPnLMdYfj3nym0zNpSQ0GazdXd+K0Dsas1LJPS92TIIixaHJML0jYVVYNO+tOUGrqsVZ0NcXRzv919kbpIEvjnzB3ONzeb7K83zZ+ssCU7JXb442jsxsNxP/Cv58E/YNM4/OtIi6Ly4OtgT396NROTfG/BrOJksYwbcYo91d7yhcJzap5J5bF3ZqB/S2egfs9S249Xv4dd5ddZwWlT2Z/0YjHGz1T+xZhiw+3vcxP535iddrvs7E5hMLXMlevdla2zKt1TReqvoSC04u4PNDn+teMhigiL0Ni/s1/mcEv0XvOXgnd+3u+uwf2t12IaGSe25ICTs+005Y8u2naygbT97grRXHaVLRnQV9fS0isWdkZ/D2rrdZd2EdI3xGMK7xuAJbsldv1lbWfNrsUwJrB7L87HI+3PshmQb9674429sQ1K+xNgf/81F2ROq8iqbJMO0ue+dn+sZhRuonLjeitmsnv7R+R9vurJMdkbcY9csxGpYrxqKAxhYxFZOSmcKI7SPYcW0H4/3GM7T+UIuoX1OQCSF4q9FbjGowig0XN/DWrrcsomTw31M0NUq6MnTZUfZf0HEdvL0ztBgNF3fBlQP6xWFGKrk/LSlh11QoWg7q99YtjAMX7jBs2VFqlnJlcWBjitjrP+WRkJ7AoK2DOHzzMJNbTKZPzT56h1RoCCEYVG8QHzT5gF3XdjFi2wiSM/Xfel/UUXvIWt7diUHBoRy7quNOVt/+2uj9z8KxckYl96f1z6j9bbDR5+Fg+LV4BgYfoZy7E8H9/SxiuePt1Nv039yfM3fOML3NdJ6v8rzeIRVKvWr04vOWnxN6K5TBWwZbRMlgtyJ2LBvYBA9newKXHCHy5n19ArErUqhG7yq5Pw0pYdfnUEy/UXtUbCKBSw7j4WzPsoFNcLeADUoxSTEEbArgWuI1ZneYTYfyllU4rbB5rvJzzGg745/CbJZQMriEqwM/DWyCo601byw6rF81Sd8BhWb0rpL704jaBtfDtBUyOozaY+JTeWPRYWytrVg2oAklLKCkwMWEi/Td1Jd76feY32k+zUo30zskBWhXrh1zOs7hetJ1+m7qS3RitN4h4e3uxI8D/MjMNtB38SF96sHbOWlLIwvB6F0l95ySUqtRUbScViDMzO4lZ/DGokMkpWUR3M/PIoqAnb5zmsBNgWQaMlnSZYkq2WthmpRqwsLOC7mfcZ+ATQFciL+gd0hULeHCooDG3LyfRuCSw/qc6PTP3HvBrjmjkntOXd4D0Ueg5Rizj9pTM7LpH3yEa/dSWRDgS63S+m/dD7sVxoDNA3CwcWBp16VUd7fMg8ALu3rF6xHkH4REEhgSSMRt/XdpNirvxg+vN+LszUSG/BhGepaZT0yyc4JmI+HiTrh+1Lx9m5FK7jm15xtwLgE+5l0Bkm2QjFp+jPBr8cx8rQFNK+lfbGtP9B6GbB2Cp6MnS7supbxreb1DUh6jqltVgv2DKWJbhAFbBnDkpv4bedpV9+LLnvXYf+EO7606Yf7dtb79waEo7J1u3n7NSCX3nIgO0+bomo0AW/PNc0spmbAugq2nbzHhudr41ylptr4fJeRyCKN2jKJS0UoEdw2mZBH9Y1KezNvVm2D/YEo6lWTYtmEWUTL4xYZlebdLddaGx/DV5rPm7dzBFfyGwJn1EBtp3r7NRCX3nNg7Xfst79vfrN3O232RHw9eYXDrSgQ0r2DWvh9m9bnVjPtzHPWK12NRl0W4O+hfLE3JuRJFSrDEfwlVilVh9I7RbLy4Ue+QGN62Mr38yjFn1wV+PHjFvJ03GQq2TrDvW/P2ayY5Su5CCH8hxFkhRJQQYvxDvj5UCHFSCBEuhNgrhKhl/FB1EnsGIjdo3wj2Lmbr9o8TN5i2KZJn65VivL/+R9AFRwQz4cAEmpdpztxOc3GxM9//C8V43BzcWNh5IT5ePozfM54VZ1foGo8Qgsk9atO+hhef/n6KnZGx5uu8iAc06qdVjLxn5l8sZvDE5C6EsAZmA12BWkCvhyTvn6WUdaWUPsCXQMGZyNo7Q/vt3mSo2bo8dvUeb60Ip1F5N75+uT5WVvpt35dSMuvYLL4O/ZrO5Tszq90sHG0cdYtHyTtnO2d+6PgDrcq2YvLBySw+tVjXeGysrZjVqwE1Sroy8uejnLlhxk1OzUZop6jtn2m+Ps0kJyN3PyBKSnlRSpkBLAd6PHiBlPLBf40igP61R40hIRpOrdZOczFTvfZrd1MYtDSUEq4Ould4NEgDUw9PZf6J+bxY9UW+bP0lttb674ZV8s7BxoFv231L1wpdmRE2g2/DvtW1ZHARexsWBfri7GDDgKAjxN5PM0/HRctA/dfg2DJIvmOePs0kJ8m9DHDtgdfRf33u/xFCjBBCXEAbuY96WENCiMFCiFAhRGhcnP675p7o0FxtfXtT89RrT0zLZGBwKOlZBhYHNsbDWb+iZFmGLD7a+xG/RP5CQK0AJjSbgLWV/oXJFOOxtbJlaqupvFztZRadWsRnBz/TtWRwqaKOLApozL2UTAYuDSU1w0xLJJuNhKw0CF1knv7MJCfJ/WFzAv/5FS+lnC2lrAy8Bzz0pGgp5Xwppa+U0rd48eJPF6m5pd2HsGCo1QPcTL/UL9sgGb08nKi4JOa+3ogqXvrViE/PTuetXW+x/uJ63mzwJm/7vq0qOxZQ1lbWfNz0Y/rX6c+Kcyt4f8/7upYMrlOmKDN7NeDk9QTeXXXcPHcTXjWgamc4PB8yzXTHYAY5Se7RgPcDr8sCjzs/azmQ/6tGHV0K6feh+Ztm6e7LzZHsiIxlwnO1aFHF0yx9PkxKZgojto1g57WdfNDkAwbXG6wSewEnhGBso7GMbjiajZc28tbOt0jL0i/JdapVgne7VGfDiRt8vyPKPJ02GwnJcXDiV/P0ZwY5Se5HgKpCiIpCCDvgNWDdgxcIIao+8LIbcN54IeogO0ubkinfEso0NHl3q8OimffnRV5vWo43mlUweX+PkpCewKAtgwi9FcrnLT+nVw3zl1lQ9DOw7kA+avIRf0b/yfDtw3UtGTysTWWe9ynNN1vPEXLKDCc5VWwNJevBge/BoP9pVsbwxOQupcwCRgKbgTPACillhBBikhCi+1+XjRRCRAghwoG3gACTRWwOp9dCwjVoPtLkXYVfi+f9NSdpVsmDT5+rbfL+HuV26m36be7HmbtnmN52Os9Vfk63WBT9vFrjVaa2msrRW0cZuHkg8WnxusQhhGDaS/Wo712Mt1aEm75MsBDaXfrtcxC11bR9mYnQ6wm5r6+vDA0N1aXvx5ISFrSD9CQYcRisTLfPKzYxjedm7cXW2or1I1viplP53utJ1xm0ZRC3U28zs/1MmpZqqksciuXYdW0Xb+96G28Xb+Z3no+Xk5cucdy6r/2MONhas25kC4o5mfBnJDsTvqsP7pUgcIPp+skjIUSYlNL3SdepHar/Fn0EYo5B06EmTewZWQaGLztKQmom89/w1S2xX4zXSvYmpCewsPNCldgVANp6t+WHjj9wI/kGfTf15VritSe/yQRKuDrww+uNuJGQypu/HCPbYMLBqLUt+A3WigTe0r/AWl6p5P5vh+aCfVGo95pJu5m84TShV+7xZc/6ulV5jLgTQUBIAAZpYIn/EuoVr6dLHIpl8ivlx8LOC0nKTCJgUwBR98z0cPNfGpV3Y1KPOuw5f5uvt5i4Bk3DvmDjoK2cyedUcn/Q/Rtw+ndo8Lp2oK6JrAy9xo8HrzCkdSW61y9tsn4eJ/RmKAM2D8DJxolg/2CquVXTJQ7FstUtXpegLkEABG4O5GTcSV3i6OVXjt5NyvHDrgtsOnnDdB05uUPdl+H4r5By13T9mIFK7g8KWwKGbPAbaLIuImIS+GjtKZpX9uDdLvrUQN8dvZuh24bi5eRFcNdgyrmW0yUOJX+o4laF4K7BuNi6MHDLQA7fOKxLHBOeq42PdzHeXXWCC3FJpuuoyRDIStV2reZjKrn/LSsdQpdomxncK5mki4SUTIYuC8PNyY6ZvRpgY23+//0hl0IYvWM0lYtV1krAqpK9Sg54u3gT3DWY0s6lGbZtGLuu7TJ7DHY2Vszp0xA7GyuG/hhGcnqWaToqWRfKNYcjC7TBXj6lkvvfItZCcqz2W9sEDAbJ2BXh3ExIY87rDfHUobTAynMrGbd7HPW96rOo8yLcHNzMHoOSf3k5ebGkyxKqulVlzM4xbLho/hUlpYs5MqtXAy7EJTF+zUnT7WBtMgTir8K5zaZp3wxUcv/b4XngURUqtTNJ8z/8eYEdkbF8/GwtGpYzf1JdfGoxkw5MomWZlsztOBdnO/3KGyj5VzGHYizsvJAGXg34YM8HLI9cbvYYWlTx5O3O1Vl/PIalB0xUqrfGs+BaRssL+ZRK7gAx4XA9DBoPNMnyx4MX7/DNlrN0r1+aN5qa90g6KSXfHf2OGWEz8K/gz3ftvsPBxnynSSkFz98lg9uUbcOUQ1NYeHKh2WMY1qYyHWp48dkfpzl+zQQbraxtwLefdgLbHf0PFs8NldxBe5Bq46CV/jSyuMR0Rv1yjAoeRfj8xbpmrdNikIZ/fvh6VuvJtFbTVMlexSgcbByY3m46z1R85p/Bgzk3RFpZCb55pT5eLg6M+PkoCSkmKHbW4A0Q1lp+yIdUck9PhJOroPaL4FjMqE1nGyRjfw0nITWT2X0a4mxvY9T2HyfTkMkHez/g17O/0q92Pz5p+okq2asY1d8lg1+t/iqLTy1m8sHJZJvxAWQxJztm9W7AzYQ03jFFBUmXklC9K4T/rC24yGdUcj+5EjKStFswI5uzM4q9UbeZ1KM2NUuZb6PS3yV7/7j4B6MbjmZso7GqsqNiElbCig+bfMjAugNZeW4l7+81b8nghuXceP+Zmmw9fYvF+y4bvwPffpByRztIO58p3MldSm35o1dtKNvYqE0fvnSXGdvO0cOnNK/4ej/5DUaSnJnM8G3D2XVt1z8/dCqxK6YkhGB0w9GMaTiGTZc2MWbnGLOWDO7fogIda5Zg2qYznIxOMG7jldpDsfJanshnCndyjzkKN09ov52NmADjUzIYvfwY5dydmPKC+ebZ49PiGbRlEGG3wpjaaiqv1TBtCQVFedCAugP4uOnH7Inew7Btw0jKMOFGowcIIfiqZz08ne1585ejJBlz/buVFTQKgCt7Ie6c8do1g8Kd3EOXaIdf13vFaE1KKXln5QluJ6Uzq5f55tljU2Lpt7kfZ++e5dt23/JspWfN0q+iPOiV6q/wResvCI8NZ8CWAdxLu2eWft2K2PHdaw24ejeFj34z8vp3n9fBygbCgozXphkU3uSenqgdfl3nRXAoarRmlx64wrYztxjftSZ1yxqv3ceJTowmYFMAMUkx/NDxB9p6tzVLv4ryMF0rduW79t9xIf4CgSGB3Eq+ZZZ+/Sq6M7pDNdaGx7D66HXjNexSAmp0g+P568Fq4U3uEWshMwUaGu9ckbM3E5my8Qztqhenf4sKRmv3cS7EXyBgUwCJmYks7LwQv1J+ZulXUR6nddnW/NDxB26l3CIgJIBr981TMnhk+yo0qejOp7+f4vJtI54k1bAvpN6Ds5uM16aJFd7kHv6ztiPVSA9S0zKzGfXLMVwdbPjq5fpmmWePuB1BYEggEsmSLkuoW7yuyftUlJxqXLIxizovIjkzmb4hfTl3z/Rz1tZWghmv+mBtJRjzaziZ2UY6Mq9SO3ApreWNfKJwJvc7F+DqfvDpbbQHqdM2RXL2ViJfvVzfLHVjjtw8woAtAyhiW4Rg/2CqulV98psUxcxqe9YmyD8IK6zoF9KPE3EnTN5n6WKOTH2xHuHX4pm53UjHOVtZa5sco7ZCohnOdDWCwpncj/8CwspoO1J3nY0laP9lAptXoF110x9H9ue1Pxm2bRglnUoS7B+Mt6v5lloqytOqXKwywV2DcbVzZeCWgRy8cdDkfXarV4qXG5Vl9s4oDl8yUl12n94gDXDiV+O0Z2I5Su5CCH8hxFkhRJQQYvxDvv6WEOK0EOKEEGK7EMK8BVSehsEA4b9ot1mueT8o425yBu+uOkH1Ei6M71rDCAE+3saLGxmzcwxVilUhyD+IEkVKmLxPRcmrsi5lWdp1KWWcyzB823B2XN1h8j4/7V4bb3cnxv4aTmKaETZWeVaFsn7a1IxOZ08/jScmdyGENTAb6ArUAnoJIWr967JjgK+Ush6wCvjS2IEazaU/4X40NOiT56aklHyw5iTxKRnMeNUHB1vTbu9fcXYF4/eMx8fLh4WdF1LMwbjlEhTFlIo7FSfIP4ga7jV4a9dbrL9g2l2fzvY2TH/FhxsJqUxcf9o4jTboA3GRcP2ocdozoZyM3P2AKCnlRSllBrAc6PHgBVLKnVLKlL9eHgTKGjdMIwr/WVv6WL1bnptac/Q6IRE3ebtzdZOfg7ro5CImH5z8zyoEVbJXyY+K2hdlQecF+Jbw5YO9H/BL5C8m7a9ReTdGtKvCqrBoQk4Z4Xi+2i+AjSOE/5T3tkwsJ8m9DPDgOqbovz73KAMAy1wvlHZfqxFRpyfY5q3s7bW7KXy6LgK/Cu4MamWak5tAuzuYETaDb49+yzMVn2FGuxmqZK+SrxWxLcLsjrNp692Wzw99zoITC0xaUXJUh6rUKePK+2tOEpuYx7IIDkWh5nNwahVkmq/EQm7kJLk/bDnJQ/8lhBCvA77AV4/4+mAhRKgQIjQuLi7nURpL5B/a2Yj1Xs1TMwaD5N1VxwH45pX6WFuZZtmjQRr47OBnLD61mFeqvcLUVlOxtVIle5X8z97anultp9OtUjdmHpvJ9LDpJkvwttZWfPuqDykZ2by/2gi7V+u/CmkJELXNOAGaSE6SezTw4HKMskDMvy8SQnQEPgS6Sykfuo1LSjlfSukrpfQtXrx4buLNm5MroVg58M7bRp/gA5c5ePEuHz9bE293J+PE9i+Zhkze3/M+K86tYECdAXzU9COsROFc3KQUTLZWtnze8nNeq/4aQRFBTDww0WQlg6t4ufBul+psj4xlVVh03hqr2BacPLV8YsFyki2OAFWFEBWFEHbAa8C6By8QQjQA5qEl9ljjh2kESbHaqSp1X87T2vaLcUl8ERJJu+rFTVbtMS0rjbE7x7Lx0kat2l6jMaqyo1IgWQkrPmjyAYPqDmL1+dWM3zOezGzTlAzu36IifhXdmbT+NDHxqblvyNpGK1tyLkSb6rVQT0zuUsosYCSwGTgDrJBSRgghJgkhuv912VeAM7BSCBEuhFj3iOb0E7EWZLaW3HMp2yB5Z+Vx7G2smfZSPZMk3KSMJIZtG8bu6N183PRjBtYdaPQ+FMWSCCEY1XAUbzd6m5DLIYzaOYrUrDwk30ewshJ83bM+2VLy3uoTeZueqfsyZKVpU70WKkf3+VLKjVLKalLKylLKKX997hMp5bq//rujlLKElNLnr4/uj29RBydXanXbvWrmuokFey5y9Go8k3rUpoSr8R9q3ku7x8AtAzkWe4yprabySnXjVatUFEsXWCeQT5t9yr7r+xi6dSiJGYlG76OchxMfPFOTPedv89Ohq7lvqGxjbYrXgqdmCsck7r3LEH0Y6vbMdRNRsUlM33oO/9ol6V4/75uf/u1W8i36hfQjKj6K79p9R7dKeV+qqSj5Tc9qPfmy9ZeciDvBgM0DuJtmpN2lD+jTpBytqnoydeMZrt1NefIbHkYIbdXdxV2QpMPikBwoHMn91Grtzzov5ert2X+tjiliZ83k5+sYfTrm2v1rBIQEcCP5hnaqvHcbo7avKPmJf0V/ZrafyaWESwSGBHIz2bi1XIQQTHupHgDvr8nD6pm6L2tTvafXGjE64ykcyf3kKvBuCm65q4qweO8ljl2NZ0L32hR3MW5RsPP3zhMQEkBSZhKLuiyicUnjHvenKPlRq7KtmNtpLnEpcQRsCuDq/TxMoTxEmWKOvP9MTfZG3Wb5kVyWIy5RS5vqtdCpmYKf3G+dhtjTuZ6SuRiXxNdbztKxZgmjT8ecjDtJYEggAEFdgqjjWceo7StKftaoRCMWdVlEalYqfTcZv2Rwb79yNKvkwZQ/znA9t6tn6r4E1w5BvHF/+RhDwU/uZ9YBAmo+/TNeg0EyfvVJ7G2s+PwF407HHLpxiIFbBuJq50pw12CquFUxWtuKUlDU8qhFUNcgrK2s6RfSj+Nxx43WtpWV4IuX6pFt0GpE5Wp6ptbz2p9nTFsnJzcKQXJfD+WaakdlPaWfDl/l8OW7fPxsLbyMuDpm59WdDN82nNLOpVnadSneLqpkr6I8SqWilVjadSnF7IsxaMsgDsQcMFrb5TycGOdfnT/PxbE2PBdH83lUhhJ1VHI3uzsX4NYprRbEU7qRkMoXmyJpVdWTno2MVwdtw8UNjN01lmpu1VjSZQnFnXTYqaso+UwZ5zIEdw2mrEtZRmwfwfar243Wdt9mFWhQrhiT1p/mTlIuzkit+RxcPQiJ5jkrNqcKdnL/+7fpUyZ3KSUf/XaKbIPk8xfqGm06Znnkcj7Y8wGNSjRiYRdVsldRnoanoydLuiyhpkdN3t71NusuGGevpPVf0zNJ6VlM2pCL0sA1uwMSIi1r9F7Ak/s6KN1A22zwFNafuMH2yFje7lzNKLVjpJQsPLmQKYem0KZsG+Z0nEMR2yJ5bldRCpui9kVZ0GkBviV9+XDvh/x0xjild6uVcGFEuyr8Hh7DjsinHIF71QSPKhY3NWOjdwAmkxAN18OgwydP9bb4lAwmrougftmi9GtRMc9hSCmZcXQGS04toVulbkxuMdmiKztmZmYSHR1NWppllzNVTMvBwYGyZctia2t536tOtk7M7jCbcX+OY9rhaSRlJDG43uA832EPb1uFjSdv8NFvp9j6lgdF7HOYHoXQZgf2zYSUu+Dknqc4jKXgJvczG7Q/a/Z4/HX/8vnGM8SnZrJsYJM8l/LNNmTz2aHPWHVuFa9Wf5UPmnxg8ZUdo6OjcXFxoUKFCqpYWSElpeTOnTtER0dTsWLeBzimYG9tzzdtv+HT/Z/yffj33M+4zzu+7+Tpe9bOxoqpL9blpR8O8M2Wc3zy3L8PnHuMmt1h7ww4uxEavJ7rGIzJsjNNXpxZD8VrgmfOlxgevHiHFaHRDGxVkZql8nayUmZ2JuP3jGfVuVUMqjuID5t8aPGJHSAtLQ0PDw+V2AsxIQQeHh4Wf/dmY2XD5BaT6V2jN0tPL+XT/Z/muWRwo/Lu9GlSjqD9lzgZnZDzN5ZuAEW9LWpqxvKzTW4kxcHV/VAr52vb07Oy+eC3k3i7OzKmQ7U8dZ+alcronaMJuRzC2EZjGdVwVL5KlvkpVsU08sv3gJWwYrzfeIbUG8JvUb8xbve4PJcMHudfA09ne8avOUFWtiFnb/p7aubCDospA1wwk/v5zSANUCPnxbfm7LzAxbhkpjxfF0e73B90/XfJ3r3X9/JJs0/oX6d/rtsqrG7dukXv3r2pVKkSjRo1olmzZvz2228AhIaGMmrUqCe20bx586f6/KPs2rWLZ5999qneo5iXEIKRDUbyju87bLmyhTd3vpmnksFFHW2Z0L02ETH3Cdp/OedvrPEsZGdoCd4CFMzkfm4zuJSGkvVydPnFuCR+2HWBHj6laV0t9+vO76XdY8CWARyPPc4Xrb/g5Wq5rx1fWEkpef7552ndujUXL14kLCyM5cuXEx2tnZ7j6+vLzJkzn9jO/v37n+rzSv4XUDuACc0msP/6/jyXDO5apyQdangxfeu5nB/s4d1EO2P1/NZc92tMBS+5Z2fChZ1QtVOOTlySUvLx76ewt7Xio25P8QDlX24m3yQwJJAL8Rf4rv13dK3YNddtFWY7duzAzs6OoUOH/vO58uXL8+abbwL/fyQ9YcIE+vfvT9u2balUqdL/S/rOzs4Pbf/vz+/atYu2bdvSs2dPatSoQZ8+ff7Zfh4SEkKNGjVo2bIla9as+ee9ycnJ9O/fn8aNG9OgQQN+//13AKZPn07//tod2smTJ6lTpw4pKbksJavkyUvVXuKrNl9x4rZWMvhO6p1ctSOEYEL32hikZOL6iJy9ydoGKneA802jOFkAAB0aSURBVFvAkMPpHBMqeKtlrh6AjESo2jlHl687HsO+qDtM7pH7io9X719l0JZBJGQkMLfjXHxL+uaqHUszcX0Ep2OMO39Yq7Qrnz5X+5Ffj4iIoGHDhjluLzIykp07d5KYmEj16tUZNmxYjpfvHTt2jIiICEqXLk2LFi3Yt28fvr6+DBo0iB07dlClShVeffV/h6lPmTKF9u3bs3jxYuLj4/Hz86Njx46MGTOGtm3b8ttvvzFlyhTmzZuHk5NpztZVnqxLhS4UsS3C2J1jCQwJZEHnBZQsUvKp2/F2d2JUh6p8GXKW7Wdu0aFmDkqYVO0MEWvgRjiUyfn3sSkUvJH7uc1gbQeV2j7x0oTUTCZvOEP9skXp3SR35YDP3TtH3019SclKYVGXRQUmsVuKESNGUL9+fRo3fngp5G7dumFvb4+npydeXl7cupXzDSh+fn6ULVsWKysrfHx8uHz5MpGRkVSsWJGqVasihOD11/+3rG3Lli1MmzYNHx8f2rZtS1paGlevXsXKyoqgoCDeeOMN2rRpQ4sWLfL891bypmWZlszrNI/bqbfpu6kvlxMu56qdgS0rUdXLmU/XRZCakYOVOFU7AcIipmYK3sj9/BYo3wLsH35b/qBvtpzlbnI6Qf0a52pN+/G44wzfNhwHawcWdVlE5WKVcxOxxXrcCNtUateuzerVq/95PXv2bG7fvo2v78N/adrb/+9uy9ramqysrBz39aj3PmqliJSS1atXU7169f987fz58zg7OxMTE5Pj/hXTaliiIYu6LGLo1qEEhAQwv9N8qrv/X3vnHhdVtfbx7+ImKGoiaSgKaBoi4ICA1ElEU6G0vKTvsTwomXqI9HQ5KnZByfKkHs1zMk3xbpm+vfZqvnbSQMP7jRRMMRUFzLtCYoLIbb1/bJwEuYw4DAyu7+czH2b2XnvvZ81snlnzrGf9nns/u8qwsbLgo4Ge/Dl2H/O2nWJSqHvlBzRyhNZdtaSO4KgHsP7BqV8j96w0uHYSOoZU2fTnc9l8sS+DEU+64tm66X1fat/FfYz5YQxNGzRl5bMr651jry169epFXl4en3/+uX6bKePX7u7upKWlcfr0aQDWrFmj3xcSEsK8efP0sfnDhw8DkJ2dzRtvvMGOHTvIzMxk3bp1JrNXUTl3JIOtLax5ZcsrJF1Juu9zdGvXnBd9nYndcYbUKzerPqBjCJw/VOvl9wxy7kKIUCHECSFEqhBicjn7g4QQh4QQhUKI6hcqfVDu/BSqIt5eXKxNojZv1IC3+tx/TvvWs1uJjI/UlOpCNaU6hXEQQrBhwwa2b9+Om5sbAQEBjBw5kpkzZ5rk+ra2tsTGxtKvXz+efvppXFz+CNdFR0dTUFCAt7c3np6eREdHA/DWW28RGRlJx44dWbp0KZMnT+bKlSsmsVdRNXckg5s1aMbYuLHsuXD/GVPvPOeOnY0lMRuPVa373qEvICE1vnoGGwspZaUPwBI4DbQDbIBkwKNMG1fAG1gFDKnqnFJKunbtKo3OF4Ol/LdPlc3WHsiQLlGb5Dc//Xrfl9iYulF2WdlFvrzpZXk973p1rKzTpKSk1LYJijpCfbsXruZelYO/HSx9VvnIuPS4+z5+5Z406RK1SW5KvlB5w6IiKf/ZQcqvR1bP0CoAEqUBPtaQkXsAkCqlPCOlzAfWAqUEW6SU6VLKI0Dt5f/k50DazipDMtdz85nx/S/4uzZjkE/r+7rEV8e/4t1d7+LX0o/FfRfTtMH9h3MUCkXt4GjnyLKQZXg09+Dv2//OhtT7K2w9vJsLHk5N+HBTCjm3K5nbsbDQJlZTt2mp2bWEIc69NXB3BdlzJdvuGyHEWCFEohAi8epVI8ej0ndB0e0qQzKzfzjBjbxCpg0wvGyelJLYI7F8fOBjerbpyfze82lorVLdFApzo2mDpsT2iSXgsQCid0fzZcqXBh9raSH4cGBnLt3IY9621MobdwiB29lw7uADWlx9DHHu5XnAahQbBCllrJTST0rp9+ijRq5AlLYDLBtA2ycrbHL0fDar958lLNDFYGEwKSVzEucw7/A8+rfrz5zgOTSwrF4+vEKhqH3uSAY/0/YZZh6cyedJnxtcP7WriwNDuzqzZGcVk6tuQSAsNL9USxji3M8Bdxf5dAbqXr5X2g5oEwDW5dc6lVIydeMxmjey4e2+hk2iFhUX8cHeD1iZspJhTwxj+tPT67QWu0KhMAwbSxtm95jNC+1fYEHyAmYdnEWxNCyqHPWsO3bWlkzblFLxl4LdI5r8SR137geBDkIINyGEDTAMME59K2ORmwWXfta+LSvg26QL/JTxG5NC3GliW7WDLigqYNKOSXxz6hvGeI0xCy12hUJhOHckg4d3Gs6Xx79k6p6pFBZXvU7C0b4Bb/bpyI6TV9l6vJKsKLfuWlimoPoiZg9Cld5KSlkIjAO2AMeBr6WUx4QQ04QQLwAIIfyFEOeAocAiIYSBYgxGImM3IMG1e7m7b94u5B//OY63c1ODil3fKrzF+B/H80PGD/y969/NTrJXoVAYhoWwIMo/ite6vMaG1A1M2jGJ/KL8Ko8b8aQLj7ewZ9qmFPIKKli56tZDU4n8db+RrTYMg4aiUsr/SCk7SinbSymnl2ybIqXcWPL8oJTSWUrZSErZXEpp2qWNaTvBuqG2MqwcPtuWypXfb/PBC52xqGIl6u/5vxMRF8Ge83uY+uRUwj3Da8BgRWVYWlqi0+n0jxkzZlTaPiEhQak9KqqNEIJIXSST/CcRlxHH+G3jyS2ofOGctaUFMc935mxWLkt3pZXfqG0gCMtaC83UD/mB9J3aG2llc8+utGs5LN11hiFdnfFp26zS02TeyuS1+Nc4df0Us3rMItQ1tKYsVlSCnZ0dSUmGryRMSEjA3t6+XK32wsJCrKzqx22uqFnCPMKwt7YnZm8Mf437K/N7z6eJTcWJF093cCS082N8ti2Vwb6tcWpqV7pBg8aaeFjazhq2vHzMP4h88ypcSakwJDP9u+PYWFowKbRyTYk7kr1p2Wl82vNT5djrIK6urkydOhVfX1+8vLz45ZdfSE9PZ+HChcydOxedTsfOnTsJDw/n7bffpmfPnkRFRZGVlcXAgQPx9vYmMDCQI0eOAJpkcFhYGL169aJDhw4sXrwYgLCwML2cL8Dw4cPZuLFuTTMpaoZBHQYxp8ccjmYeZdTmUVy7da3S9u/160SRlMzafKL8Bq7d4cIhuG2AbIGRMf8hTXrJt2I5k6m7Tl0j/vhlokLdadG4/CwagIwbGYz9YSw38m+wsM9CurYsP7zz0PH9ZG2i2pg85gXPVh5muXXrFjqdTv/6nXfe0UvvOjo6cujQIRYsWMDs2bNZsmQJERER2NvbM2HCBACWLl3KyZMniY+Px9LSkvHjx+Pj48OGDRvYtm0bI0aM0P8yOHLkCPv27SMnJwcfHx/69evH6NGjmTt3LgMGDCA7O5s9e/awcuVK474PijpLb5fezO81nzcT3tQkg/ssxsneqdy2bRwaMqa7G/N/PE3Yky74lo0OuAXBrk/g7D7o0NsE1v+B+Y/c03eCTWNw0pXaXFhUzLRNx2jr0JBRT7tWePiJrBOM/H4ktwpvsTRkqXLsdYA7YZk7j7s11QcPHgxA165dSU9Pr/AcQ4cOxdJSK5e4a9cuwsLCAE2YLDMzk+xsrfjxgAEDsLOzw9HRkZ49e3LgwAF69OhBamoqV65cYc2aNbz44osqtPOQ8VTrp4jtE0vWrSxGbB5BWnYFcXUgMvhxWjRuwLT/S6G4uExqZJtuYGENadtr2OJ7Mf87Nm0nuDypVUG5izUHznLy8k0W/qUrDazKr4madCWJyK2R2FnZsazvMto1bWcKi82HKkbYtcEdmd6q5H0bNWqkf15eLvKd7KeyWVB3XoeFhbF69WrWrl3LsmXLHthuhfmha6FjWegy/hr3V8I3h7OozyLcHe6V/G3UwIpJoe5M+J9kvk0+zyCfuzLybBqCs/8fEQYTYt4j9xsXIfPUPfH27NwC5sSd5Ml2zQnpXH71lL0X9jI2bizNGjRj1bOrlGM3Yxo3bszvv1dcLzMoKIjVq1cD2uSro6MjTZpoE2XffvsteXl5ZGZmkpCQoC8KEh4ezr/+9S9A05hXPJy4O7izMnQlNpY2jNo8isNXDpfbbrBPa7o4N2XG97+Qm19m0OHWHS4mw63rJrD4D8zbuWfs1v66lXbun247RfatAqL7e5Sbn741Yyuvb30d58bOrHx2Ja3tqyWVo6gh7sTc7zwmT75HZboUzz//POvXr9dPqJYlJiaGxMREvL29mTx5cqn4eUBAAP369SMwMJDo6GhatWoFQMuWLenUqROvvPKKcTunMDtcm7qyKnQVze2aM/aHsew+v/ueNhYWginPe3D5xm0WbT9TeqdbEMhirQSoCTHvsMyFw2BlCy299JvSruWwam86f/Zrg0ere9OYvk39lil7puDp6MmCZxYoZcc6SFFR+YtC7o6x+/n5kZCQAEDHjh31GTAA3buX/rJ3cHAolf1yNx07diQ2Nvae7bm5uZw6dYqXXnrpPq1X1Eec7J1YEbqCiPgIxm0bx8zuM+nrWlqksKuLA/28nVi04zQvBbTlsaYlSRytfAABF5LgiWdNZrN5j9wvJkMLj1Lx9hnfH8fa0qJc/ZjVx1fz/u738X/Mn8V9lGSvonzi4+Nxd3dn/PjxNG2q7hGFRnO75iwNWYqXoxcTd0xk/an197SZHOpOcTH8c8tdqZE2jcCxA1w6ck/7msR8R+5Sam9W58H6TfvOZLLl2GUm9O1YKvVRSsmiI4uYn6Qpwc0KmoWN5b0LnhQPFzExMeVu7927N2fPnjWtMQqzoIlNExb2XsjbCW8zZc8UbhbcJMwjTL+/jUNDXnnalUXbzxD+lCteziWDA6cukGHaVdTmO3K/ngF52eDkDWil8z76LoVWTW0Z3f2PyVEpJbMTZzM/aT4vtH+B2T1mK8euUCiqTUPrhszrNY8+Ln2YdXAW85Pml8rIer3n4zg0suGj7+5SjXzMG26ch5xMk9lpvs79YslPHKcuAGxIOs/R8zeYGPoEttZa6mNRcRFT90xlVcoqhncazod/+hArC/P9saJQKOoG1pbWzAqaxaDHB7EweSEzD87USwY3sbXmrT4d2Z+WRVzKZe2AkkEol5JNZqMZO/dkTZSnRWfyCoqYveUEnq2bMKCLlvmSX5SvxcVS1/Nal9eI8o9Skr0KhcJoWFlY8cFTHxDmEcbq46uJ3h2tlwwe5t+Gdo82YsbmXygoKtZG7qD5LRNhvt7u0hF41B2sbVm+O50L2Xm8+1wnLCwEuQW5/G3b34jLiGOi30QidZFKslehUBgdIQQT/Sbyuu51Np7eyITtE8gvysfa0oLJoe6cuZrD2oO/QkMHaNr2j4iDCTBf534xGZy8ycrJZ8GPqfRyb8FT7R25kX+DiPgI9l7cy7SnpjGi84jatlRxn1y6dIlhw4bRvn17PDw8eO655zh58iTp6el4enoa7TpTpkwhPj4egJ07d9K5c2d0Oh3nz59nyJAh1TrnihUruHDhj0Jlo0ePJiUlxSj2KuomQggiukQwOWAyW89uZdzWceQW5NLHoyUBrg78O/4kN28XaqEZE2bMmKdz//0y3LwMj3nz6dZT5OQX8s6z7mTeyuTVLa/y87Wf+WfQPxnUYVBtW6q4T6SUDBo0iODgYE6fPk1KSgr/+Mc/uHz5stGvNW3aNHr31sScVq9ezYQJE0hKSqJ169asW7euWucs69yXLFmCh4eHUeytirJyDBWtFyiLlJLiYsNKzCkqZnin4Xz0p4/Yf2k/Y+LGcCP/Bu/268S1m/ks2n5amx/MTIXbFa+mNibm6dxLvv0uNnyCL/dl8Gf/Ntg3ukn45nDSs9P5rNdn9ywwUJgHP/74I9bW1kREROi36XS6exYmpaen0717d3x9ffH19dUX67h48SJBQUHodDo8PT3ZuXMnRUVFhIeH4+npiZeXF3PnzgU0iYF169axZMkSvv76a6ZNm8bw4cNL/UIoKipiwoQJeHl54e3tzbx58wDti8Hf3x9PT0/Gjh2LlJJ169aRmJjI8OHD0el03Lp1i+DgYBITEwFYs2YNXl5eeHp6EhUVpe+Lvb097733Hl26dCEwMLDcL7KcnBxGjRqFv78/Pj4++kVZK1asYOjQoTz//PP07duXhIQEevbsycsvv4yXl7a475NPPsHT0xNPT0+9pEJ6ejqdOnUiMjISX19ffv311wf/8BQMeHwAc3rM4XjmcUZtGYWzYyH9vZ1YvPMMvzUp0aW5dNQktphn6shFTa51zhEbrC0LGNKtASM2j+Bm/k0W9VmEb0vfWjawfjDzwEx+yfrFqOd0d3AnKiCqwv1Hjx6la9eqlTlbtGhBXFwctra2+pWkiYmJfPXVV4SEhPDee+9RVFREbm4uSUlJnD9/nqNHtX+q69dLa3yMHj2aXbt20b9/f4YMGVJqJWxsbCxpaWkcPnwYKysrsrKyABg3bhxTpkwBNJGxTZs2MWTIED777DNmz56Nn59fqWtcuHCBqKgofvrpJ5o1a0bfvn3ZsGEDAwcOJCcnh8DAQKZPn86kSZNYvHgx77//fqnjp0+fTq9evVi2bBnXr18nICBA/6tj7969HDlyBAcHBxISEjhw4ABHjx7Fzc2Nn376ieXLl7N//36klHTr1o0ePXrQrFkzTpw4wfLly1mwYEGV77fCcHq79OazZz7jzR/fZOT3I/mg+6dsOXaJz0/a8y5og1OXJ2vcDvMcuV88wu0mrqw7doPBgfD2rrHkF+WzLGSZcuwPCQUFBYwZMwYvLy+GDh2qj2v7+/uzfPlyYmJi+Pnnn2ncuDHt2rXjzJkzjB8/ns2bN+tFwwwhPj6eiIgIveSvg4MDoP3C6NatG15eXmzbto1jxyovG3zw4EGCg4N59NFHsbKyYvjw4ezYoZVfs7GxoX///kDFUsY//PADM2bMQKfTERwcTF5enn6hVZ8+ffR2gaaX4+bmBmhyx4MGDaJRo0bY29szePBgvf6Oi4sLgYGBBr8XCsN5qpUmGfzb7d+I2jeWF/ytWJKUS6Gdo8kyZgwauQshQoF/A5bAEinljDL7GwCrgK5AJvBnKWW6cU39A3kxmcMFbXmk2Xm2ZS+nkXUjYvvGKmVHI1PZCLum6Ny5s0Hx7rlz59KyZUuSk5MpLi7G1lZbkRwUFMSOHTv47rvvCAsLY+LEiYwYMYLk5GS2bNnC/Pnz+frrrw2W8ZVS3pNplZeXR2RkJImJibRp04aYmBjy8vKqPE9FWFtb669RkZSxlJJvvvmGJ54oXVFs//79peSNoWq54/LaKYyProWO5SHLGRs3lv23PqShfTgncKOziTJmqhy5CyEsgfnAs4AH8JIQouwM0avAb1LKx4G5wExjG6rn1nXE9QzWFjZEOMXS3K65kuytR/Tq1Yvbt2/rS96BNurdvr10sYPs7GycnJywsLDgiy++0E8eZmRk0KJFC8aMGcOrr77KoUOHuHbtGsXFxbz44ot8+OGHHDp0yGB7+vbty8KFC/UONysrS+/IHR0duXnzZqkvo4rkh7t168b27du5du0aRUVFrFmzhh49ehhsR0hICPPmzdM768OHy5eeLUtQUBAbNmwgNzeXnJwc1q9ff8/8haLmeMLhCVaGrqShtR02bWJZU9AYeeU4FN6u8WsbEpYJAFKllGeklPnAWmBAmTYDgDs6quuAZ0QNJZYXXzxCXEM7trU+QbtHXFgRuoJW9q1q4lKKWkAIwfr164mLi6N9+/Z07tyZmJgYvRTvHSIjI1m5ciWBgYGcPHlSPwpNSEhAp9Ph4+PDN998wxtvvMH58+cJDg5Gp9MRHh7Oxx9/bLA9o0ePpm3btnh7e9OlSxe++uorHnnkEX1IaODAgXoNeNAmaSMiIvQTqndwcnLi448/pmfPnnTp0gVfX18GDCj7b1Qx0dHRFBQU4O3tjaenJ9HR0QYd5+vrS3h4OAEBAXTr1o3Ro0fj4+Nj8HUVD45rU1dWPbuKVvYt+L/Waey2tUJervn0WFHZzzYAIcQQIFRKObrkdRjQTUo57q42R0vanCt5fbqkTYXVZf38/OSdLIL74fM1o1l4ex9tGnZk9YDlStnRyBw/fpxOnTrVthmKOoC6F4xLVl4Ww/73L1zNP8sbjfsS/uIn1TqPEOInKaVfVe0MGbmXNwIv+41gSBuEEGOFEIlCiMSrV68acOl7aebUnQ5FrVg74Avl2BUKhdngYOvA2oGrcStsySOP1Xy2jCETqueANne9dgYuVNDmnBDCCmgKZJU9kZQyFogFbeReHYOHBY9kWPDI6hyqUCgUtYpDw2b87+itJrmWISP3g0AHIYSbEMIGGAZsLNNmI3DH4w4Btsmq4j0KhUKhqDGqHLlLKQuFEOOALWipkMuklMeEENOARCnlRmAp8IUQIhVtxD6sJo1W1Czlpf8pHi7U2Mz8MSjPXUr5H+A/ZbZNuet5HjDUuKYpagNbW1syMzNp3ry5cvAPKVJKMjMz9WsHFOaJecoPKGoMZ2dnzp07R3UnvBX1A1tbW5ydnWvbDMUDoJy7ohTW1tb6pesKhcJ8MU9tGYVCoVBUinLuCoVCUQ9Rzl2hUCjqIVXKD9TYhYW4CmRU83BHoEJpg3qK6vPDgerzw8GD9NlFSvloVY1qzbk/CEKIREO0FeoTqs8PB6rPDwem6LMKyygUCkU9RDl3hUKhqIeYq3OPrW0DagHV54cD1eeHgxrvs1nG3BUKhUJROeY6clcoFApFJdRp5y6ECBVCnBBCpAohJpezv4EQ4r9L9u8XQria3krjYkCf3xZCpAghjgghtgohXGrDTmNSVZ/vajdECCGFEGafWWFIn4UQ/1XyWR8TQnxlahuNjQH3dlshxI9CiMMl9/dztWGnsRBCLBNCXCmpVFfefiGE+LTk/TgihPA1qgFSyjr5QJMXPg20A2yAZMCjTJtIYGHJ82HAf9e23Sboc0+gYcnz1x6GPpe0awzsAPYBfrVttwk+5w7AYaBZyesWtW23CfocC7xW8twDSK9tux+wz0GAL3C0gv3PAd+jVbILBPYb8/p1eeRepwpzm4gq+yyl/FFKmVvych9aZSxzxpDPGeBDYBaQZ0rjaghD+jwGmC+l/A1ASnnFxDYaG0P6LIEmJc+bcm/FN7NCSrmDcirS3cUAYJXU2Ac8IoRwMtb167Jzbw38etfrcyXbym0jpSwEsoHmJrGuZjCkz3fzKto3vzlTZZ+FED5AGynlJlMaVoMY8jl3BDoKIXYLIfYJIUJNZl3NYEifY4C/CCHOodWPGG8a02qN+/1/vy/qsuSv0QpzmxEG90cI8RfAD+hRoxbVPJX2WQhhAcwFwk1lkAkw5HO2QgvNBKP9OtsphPCUUl6vYdtqCkP6/BKwQko5RwjxJFp1N08pZXHNm1cr1Kj/qssj9/spzE1lhbnNCEP6jBCiN/Ae8IKU8raJbKspqupzY8ATSBBCpKPFJjea+aSqoff2t1LKAillGnACzdmbK4b0+VXgawAp5V7AFk2Dpb5i0P97danLzv1hLMxdZZ9LQhSL0By7ucdhoYo+SymzpZSOUkpXKaUr2jzDC1LKxNox1ygYcm9vQJs8RwjhiBamOWNSK42LIX0+CzwDIITohObc63NJsI3AiJKsmUAgW0p50Whnr+0Z5Spmm58DTqLNsr9Xsm0a2j83aB/+/wCpwAGgXW3bbII+xwOXgaSSx8batrmm+1ymbQJmni1j4OcsgE+AFOBnYFht22yCPnsAu9EyaZKAvrVt8wP2dw1wEShAG6W/CkQAEXd9xvNL3o+fjX1fqxWqCoVCUQ+py2EZhUKhUFQT5dwVCoWiHqKcu0KhUNRDlHNXKBSKeohy7gqFQlEPUc5doVAo6iHKuSsUCkU9RDl3hUKhqIf8P8Uw8pk/lrXyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(p, gini)\n",
    "plt.plot(p, entropy)\n",
    "plt.plot(p, class_err)\n",
    "plt.legend(('Gini index', 'Entropy', 'Classification error'),loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4.** See answer to question 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**5.** Suppose we produce ten bootstrapped samples from a data set containing red and green classes. We then apply a classification tree to each bootstrapped sample and, for a specific value of X, produce 10 estimates of P(Class is Red|X).\n",
    "\n",
    "There are two common ways to combine these results together into a single class prediction. One is the majority vote approach discussed in this chapter. The second approach is to classify based on the average probability. In this example, what is the final classification under each of these two approaches?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6\n",
      "0.45\n"
     ]
    }
   ],
   "source": [
    "p_red = [0.1, 0.15, 0.2, 0.2, 0.55, 0.6, 0.6, 0.65, 0.7, 0.75]\n",
    "\n",
    "# majority vote\n",
    "print(sum(1 for i in p_red if i>=0.5)/len(p_red))\n",
    "\n",
    "# average\n",
    "print(np.average(p_red))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**6.** Provide a detailed explanation of the algorithm that is used to fit a regression tree.\n",
    "\n",
    "First, we select the predictor $X_j$ and the cutpoint $s$ such that splitting the predictor space into the regions ${X|X_j<s}$ and ${X|X_j>=s}$ leads to the greatest possible reduction in RSS.\n",
    "\n",
    "Next, we repeat the process, looking for the best predictor and best cutpoint in order to split the data further so as to minimize the RSS within each of the resulting regions.\n",
    "\n",
    "This process continues until a stopping point is reached; for instance, we may continue until no region contains more that five observations.\n",
    "\n",
    "Once the regions have been created, we predict the response for a given test observation using the mean of the training observations in the region to which that test observation belongs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applied\n",
    "\n",
    "**7.** In the lab, we applied random forests to the `Boston` data using `mtry=6` and using `ntree=25` and `ntree=500`. Create a plot displaying the test error resulting from random forests on this data set for a more com-prehensive range of values for `mtry` and `ntree`. You can model your plot after Figure 8.10. Describe the results obtained.\n",
    "\n",
    ">m=p/2 and m=sqrt(p) perform the best."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 509,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>crim</th>\n",
       "      <th>zn</th>\n",
       "      <th>indus</th>\n",
       "      <th>chas</th>\n",
       "      <th>nox</th>\n",
       "      <th>rm</th>\n",
       "      <th>age</th>\n",
       "      <th>dis</th>\n",
       "      <th>rad</th>\n",
       "      <th>tax</th>\n",
       "      <th>ptratio</th>\n",
       "      <th>black</th>\n",
       "      <th>lstat</th>\n",
       "      <th>medv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      crim    zn  indus  chas    nox     rm   age     dis  rad  tax  ptratio  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575  65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421  78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185  61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998  45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147  54.2  6.0622    3  222     18.7   \n",
       "\n",
       "    black  lstat  medv  \n",
       "0  396.90   4.98  24.0  \n",
       "1  396.90   9.14  21.6  \n",
       "2  392.83   4.03  34.7  \n",
       "3  394.63   2.94  33.4  \n",
       "4  396.90   5.33  36.2  "
      ]
     },
     "execution_count": 509,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"https://vincentarelbundock.github.io/Rdatasets/csv/MASS/Boston.csv\").drop('Unnamed: 0', axis=1)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 510,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.iloc[:, :-1]\n",
    "y = df['medv']\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 511,
   "metadata": {},
   "outputs": [],
   "source": [
    "err_rate1 = OrderedDict()\n",
    "err_rate2 = OrderedDict()\n",
    "err_rate3 = OrderedDict()\n",
    "\n",
    "# m=p\n",
    "for i in range(1, 506, 5):\n",
    "    rf = RandomForestRegressor(random_state=1,\n",
    "                              n_estimators=i).fit(X_train, y_train)\n",
    "    err_rate1[i] = mean_squared_error(y_test, rf.predict(X_test))\n",
    "\n",
    "# m=p/2\n",
    "for i in range(1, 506, 5):\n",
    "    rf = RandomForestRegressor(random_state=1, max_features=int(len(X_train.columns)/2),\n",
    "                              n_estimators=i).fit(X_train, y_train)\n",
    "    err_rate2[i] = mean_squared_error(y_test, rf.predict(X_test))\n",
    "\n",
    "# m=sqrt(p)\n",
    "for i in range(1, 506, 5):\n",
    "    rf = RandomForestRegressor(random_state=1, max_features='sqrt',\n",
    "                              n_estimators=i).fit(X_train, y_train)\n",
    "    err_rate3[i] = mean_squared_error(y_test, rf.predict(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 512,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot our dictionaries of results\n",
    "plt.plot(*zip(*sorted(err_rate1.items())))\n",
    "plt.plot(*zip(*sorted(err_rate2.items())))\n",
    "plt.plot(*zip(*sorted(err_rate3.items())))\n",
    "plt.xlabel('Number of Trees')\n",
    "plt.ylabel('Test MSE')\n",
    "plt.legend(('m=p', 'm=p/2', 'm=sqrt(p)'),loc='best');\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 518,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# of trees and error rate for each split method.\n",
      "(281, 15.899361810826397)\n",
      "(26, 14.61327642257408)\n",
      "(66, 14.828831941404708)\n"
     ]
    }
   ],
   "source": [
    "print(\"# of trees and error rate for each split method.\")\n",
    "print(min(err_rate1.items(), key=lambda x: x[1]))\n",
    "print(min(err_rate2.items(), key=lambda x: x[1]))\n",
    "print(min(err_rate3.items(), key=lambda x: x[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [],
   "source": [
    "# another approach for this problem could be gridsearch\n",
    "# m (max_features) and # of trees (n_estimators)\n",
    "# this example is not complete\n",
    "\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "rff = GridSearchCV(RandomForestRegressor(random_state=1),\n",
    "                  param_grid={'max_features': ['auto','sqrt'],\n",
    "                             'n_estimators': range(1,11)},\n",
    "                   scoring='neg_mean_squared_error',\n",
    "                  return_train_score=True)\n",
    "\n",
    "rff.fit(X_train, y_train)\n",
    "results = rff.cv_results_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**8.** In the lab, a classification tree was applied to the `Carseats` data set after converting `Sales` into a qualitative response variable. Now we will seek to predict `Sales` using regression trees and related approaches, treating the response as a quantitative variable.\n",
    "\n",
    "**(a)** Split the data set into a training set and a test set.\n",
    "\n",
    "**(b)** Fit a regression tree to the training set. Plot the tree, and interpret the results. What test error rate do you obtain?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of df: (400, 11)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sales</th>\n",
       "      <th>CompPrice</th>\n",
       "      <th>Income</th>\n",
       "      <th>Advertising</th>\n",
       "      <th>Population</th>\n",
       "      <th>Price</th>\n",
       "      <th>ShelveLoc</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Urban</th>\n",
       "      <th>US</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9.50</td>\n",
       "      <td>138</td>\n",
       "      <td>73</td>\n",
       "      <td>11</td>\n",
       "      <td>276</td>\n",
       "      <td>120</td>\n",
       "      <td>Bad</td>\n",
       "      <td>42</td>\n",
       "      <td>17</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11.22</td>\n",
       "      <td>111</td>\n",
       "      <td>48</td>\n",
       "      <td>16</td>\n",
       "      <td>260</td>\n",
       "      <td>83</td>\n",
       "      <td>Good</td>\n",
       "      <td>65</td>\n",
       "      <td>10</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10.06</td>\n",
       "      <td>113</td>\n",
       "      <td>35</td>\n",
       "      <td>10</td>\n",
       "      <td>269</td>\n",
       "      <td>80</td>\n",
       "      <td>Medium</td>\n",
       "      <td>59</td>\n",
       "      <td>12</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.40</td>\n",
       "      <td>117</td>\n",
       "      <td>100</td>\n",
       "      <td>4</td>\n",
       "      <td>466</td>\n",
       "      <td>97</td>\n",
       "      <td>Medium</td>\n",
       "      <td>55</td>\n",
       "      <td>14</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.15</td>\n",
       "      <td>141</td>\n",
       "      <td>64</td>\n",
       "      <td>3</td>\n",
       "      <td>340</td>\n",
       "      <td>128</td>\n",
       "      <td>Bad</td>\n",
       "      <td>38</td>\n",
       "      <td>13</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Sales  CompPrice  Income  Advertising  Population  Price ShelveLoc  Age  \\\n",
       "0   9.50        138      73           11         276    120       Bad   42   \n",
       "1  11.22        111      48           16         260     83      Good   65   \n",
       "2  10.06        113      35           10         269     80    Medium   59   \n",
       "3   7.40        117     100            4         466     97    Medium   55   \n",
       "4   4.15        141      64            3         340    128       Bad   38   \n",
       "\n",
       "   Education Urban   US  \n",
       "0         17   Yes  Yes  \n",
       "1         10   Yes  Yes  \n",
       "2         12   Yes  Yes  \n",
       "3         14   Yes  Yes  \n",
       "4         13   Yes   No  "
      ]
     },
     "execution_count": 284,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"https://vincentarelbundock.github.io/Rdatasets/csv/ISLR/Carseats.csv\")\n",
    "\n",
    "df=df.drop(columns=['Unnamed: 0'])\n",
    "print(\"Shape of df: \" + str(df.shape))\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 400 entries, 0 to 399\n",
      "Data columns (total 11 columns):\n",
      "CompPrice           400 non-null float64\n",
      "Income              400 non-null float64\n",
      "Advertising         400 non-null float64\n",
      "Population          400 non-null float64\n",
      "Price               400 non-null float64\n",
      "Age                 400 non-null float64\n",
      "Education           400 non-null float64\n",
      "ShelveLoc_Good      400 non-null float64\n",
      "ShelveLoc_Medium    400 non-null float64\n",
      "Urban_Yes           400 non-null float64\n",
      "US_Yes              400 non-null float64\n",
      "dtypes: float64(11)\n",
      "memory usage: 34.5 KB\n"
     ]
    }
   ],
   "source": [
    "# create our categorical variables with pd.get_dummies\n",
    "\n",
    "# looks like you don't need to pass column list of categorical, so don't need this\n",
    "# df = pd.get_dummies(df, columns=['ShelveLoc', 'Urban', 'US'], drop_first=True)\n",
    "\n",
    "# use this instead. it's more simple\n",
    "df = pd.get_dummies(df, drop_first=True)\n",
    "\n",
    "\n",
    "X = df.drop(['Sales'], axis=1).astype('float64')\n",
    "y = df.Sales\n",
    "\n",
    "X.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split data into train and test\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5, random_state=17)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.668220999999999"
      ]
     },
     "execution_count": 367,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit tree and get test mse\n",
    "\n",
    "dtr = DecisionTreeRegressor(random_state=17).fit(X_train, y_train)\n",
    "\n",
    "mean_squared_error(y_test, dtr.predict(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {},
   "outputs": [
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       "<path fill=\"none\" stroke=\"#000000\" d=\"M282.352,-1237.1978C261.7574,-1224.9587 237.7643,-1210.6999 216.3459,-1197.9713\"/>\n",
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       "<!-- 8 -->\n",
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       "<title>8</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"385.5,-1197 279.5,-1197 279.5,-1129 385.5,-1129 385.5,-1197\"/>\n",
       "<text text-anchor=\"middle\" x=\"332.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 77.5</text>\n",
       "<text text-anchor=\"middle\" x=\"332.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.359</text>\n",
       "<text text-anchor=\"middle\" x=\"332.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"332.5\" y=\"-1136.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 12.57</text>\n",
       "</g>\n",
       "<!-- 4&#45;&gt;8 -->\n",
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       "<title>4&#45;&gt;8</title>\n",
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       "<!-- 6 -->\n",
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       "<title>6</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"93,-1085.5 0,-1085.5 0,-1032.5 93,-1032.5 93,-1085.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"46.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"46.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"46.5\" y=\"-1040.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.66</text>\n",
       "</g>\n",
       "<!-- 5&#45;&gt;6 -->\n",
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       "<title>5&#45;&gt;6</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M121.1544,-1128.9465C108.6928,-1117.2707 94.7626,-1104.219 82.3412,-1092.5809\"/>\n",
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       "<!-- 7 -->\n",
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       "<title>7</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"204,-1085.5 111,-1085.5 111,-1032.5 204,-1032.5 204,-1085.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"157.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"157.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"157.5\" y=\"-1040.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.19</text>\n",
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       "<!-- 5&#45;&gt;7 -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>5&#45;&gt;7</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M157.5,-1128.9465C157.5,-1118.2621 157.5,-1106.4254 157.5,-1095.5742\"/>\n",
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       "<!-- 9 -->\n",
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       "<title>9</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"315,-1085.5 222,-1085.5 222,-1032.5 315,-1032.5 315,-1085.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"268.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"268.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"268.5\" y=\"-1040.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 13.36</text>\n",
       "</g>\n",
       "<!-- 8&#45;&gt;9 -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>8&#45;&gt;9</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M311.544,-1128.9465C304.6978,-1117.8215 297.0829,-1105.4473 290.1843,-1094.237\"/>\n",
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       "<!-- 10 -->\n",
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       "<title>10</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"439.5,-1093 333.5,-1093 333.5,-1025 439.5,-1025 439.5,-1093\"/>\n",
       "<text text-anchor=\"middle\" x=\"386.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 86.0</text>\n",
       "<text text-anchor=\"middle\" x=\"386.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.07</text>\n",
       "<text text-anchor=\"middle\" x=\"386.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"386.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 12.175</text>\n",
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       "<!-- 8&#45;&gt;10 -->\n",
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       "<title>8&#45;&gt;10</title>\n",
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       "<!-- 11 -->\n",
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       "<title>11</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"377,-981.5 284,-981.5 284,-928.5 377,-928.5 377,-981.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"330.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"330.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"330.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.91</text>\n",
       "</g>\n",
       "<!-- 10&#45;&gt;11 -->\n",
       "<g id=\"edge11\" class=\"edge\">\n",
       "<title>10&#45;&gt;11</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M368.1635,-1024.9465C362.2324,-1013.9316 355.6419,-1001.6922 349.6532,-990.5703\"/>\n",
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       "</g>\n",
       "<!-- 12 -->\n",
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       "<title>12</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"488,-981.5 395,-981.5 395,-928.5 488,-928.5 488,-981.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"441.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"441.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"441.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 12.44</text>\n",
       "</g>\n",
       "<!-- 10&#45;&gt;12 -->\n",
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       "<title>10&#45;&gt;12</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M404.5091,-1024.9465C410.3342,-1013.9316 416.807,-1001.6922 422.6888,-990.5703\"/>\n",
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       "<title>14</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"650,-1197 529,-1197 529,-1129 650,-1129 650,-1197\"/>\n",
       "<text text-anchor=\"middle\" x=\"589.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 11.5</text>\n",
       "<text text-anchor=\"middle\" x=\"589.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"589.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"589.5\" y=\"-1136.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.34</text>\n",
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       "<!-- 13&#45;&gt;14 -->\n",
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       "<title>13&#45;&gt;14</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M636.5794,-1232.9465C630.7174,-1224.2373 624.3402,-1214.7626 618.227,-1205.6801\"/>\n",
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       "<title>17</title>\n",
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       "<text text-anchor=\"middle\" x=\"728.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 13.5</text>\n",
       "<text text-anchor=\"middle\" x=\"728.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.103</text>\n",
       "<text text-anchor=\"middle\" x=\"728.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
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       "<!-- 13&#45;&gt;17 -->\n",
       "<g id=\"edge17\" class=\"edge\">\n",
       "<title>13&#45;&gt;17</title>\n",
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       "<!-- 15 -->\n",
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       "<title>15</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"543.5,-1085.5 457.5,-1085.5 457.5,-1032.5 543.5,-1032.5 543.5,-1085.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"500.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"500.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"500.5\" y=\"-1040.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.35</text>\n",
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       "<!-- 14&#45;&gt;15 -->\n",
       "<g id=\"edge15\" class=\"edge\">\n",
       "<title>14&#45;&gt;15</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M560.3581,-1128.9465C550.5548,-1117.491 539.6181,-1104.711 529.8025,-1093.2412\"/>\n",
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       "<title>16</title>\n",
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       "<text text-anchor=\"middle\" x=\"604.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"604.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"604.5\" y=\"-1040.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.33</text>\n",
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       "<!-- 14&#45;&gt;16 -->\n",
       "<g id=\"edge16\" class=\"edge\">\n",
       "<title>14&#45;&gt;16</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M594.4116,-1128.9465C595.9526,-1118.2621 597.6598,-1106.4254 599.2249,-1095.5742\"/>\n",
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       "<!-- 18 -->\n",
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       "<title>18</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"759,-1085.5 666,-1085.5 666,-1032.5 759,-1032.5 759,-1085.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"712.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"712.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"712.5\" y=\"-1040.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.06</text>\n",
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       "<!-- 17&#45;&gt;18 -->\n",
       "<g id=\"edge18\" class=\"edge\">\n",
       "<title>17&#45;&gt;18</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M723.261,-1128.9465C721.6172,-1118.2621 719.7962,-1106.4254 718.1268,-1095.5742\"/>\n",
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       "<title>19</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"898,-1093 777,-1093 777,-1025 898,-1025 898,-1093\"/>\n",
       "<text text-anchor=\"middle\" x=\"837.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Urban_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"837.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.007</text>\n",
       "<text text-anchor=\"middle\" x=\"837.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"837.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.725</text>\n",
       "</g>\n",
       "<!-- 17&#45;&gt;19 -->\n",
       "<g id=\"edge19\" class=\"edge\">\n",
       "<title>17&#45;&gt;19</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M764.1907,-1128.9465C773.7891,-1119.7884 784.2747,-1109.7838 794.2366,-1100.2788\"/>\n",
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       "<title>20</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"773,-981.5 680,-981.5 680,-928.5 773,-928.5 773,-981.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"726.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"726.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"726.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.81</text>\n",
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       "<!-- 19&#45;&gt;20 -->\n",
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       "<title>19&#45;&gt;20</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M801.1544,-1024.9465C788.6928,-1013.2707 774.7626,-1000.219 762.3412,-988.5809\"/>\n",
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       "<title>21</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"884,-981.5 791,-981.5 791,-928.5 884,-928.5 884,-981.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"837.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"837.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"837.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.64</text>\n",
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       "<!-- 19&#45;&gt;21 -->\n",
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       "<title>19&#45;&gt;21</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M837.5,-1024.9465C837.5,-1014.2621 837.5,-1002.4254 837.5,-991.5742\"/>\n",
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       "<title>23</title>\n",
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       "<text text-anchor=\"middle\" x=\"1336.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 93.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1336.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.938</text>\n",
       "<text text-anchor=\"middle\" x=\"1336.5\" y=\"-1255.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 13</text>\n",
       "<text text-anchor=\"middle\" x=\"1336.5\" y=\"-1240.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.653</text>\n",
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       "<!-- 22&#45;&gt;23 -->\n",
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       "<title>22&#45;&gt;23</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M1443.4375,-1336.9465C1426.8556,-1326.1005 1408.4586,-1314.0673 1391.665,-1303.0828\"/>\n",
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       "<title>48</title>\n",
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       "<text text-anchor=\"middle\" x=\"1550.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 12.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1550.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 2.115</text>\n",
       "<text text-anchor=\"middle\" x=\"1550.5\" y=\"-1255.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 7</text>\n",
       "<text text-anchor=\"middle\" x=\"1550.5\" y=\"-1240.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.953</text>\n",
       "</g>\n",
       "<!-- 22&#45;&gt;48 -->\n",
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       "<title>22&#45;&gt;48</title>\n",
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       "<title>24</title>\n",
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       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 86.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.061</text>\n",
       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 11</text>\n",
       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-1136.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.052</text>\n",
       "</g>\n",
       "<!-- 23&#45;&gt;24 -->\n",
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       "<title>23&#45;&gt;24</title>\n",
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       "<title>45</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1397,-1197 1276,-1197 1276,-1129 1397,-1129 1397,-1197\"/>\n",
       "<text text-anchor=\"middle\" x=\"1336.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 13.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1336.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.082</text>\n",
       "<text text-anchor=\"middle\" x=\"1336.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"1336.5\" y=\"-1136.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.46</text>\n",
       "</g>\n",
       "<!-- 23&#45;&gt;45 -->\n",
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       "<title>23&#45;&gt;45</title>\n",
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       "<title>25</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1081.5,-1093 975.5,-1093 975.5,-1025 1081.5,-1025 1081.5,-1093\"/>\n",
       "<text text-anchor=\"middle\" x=\"1028.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 78.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1028.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.462</text>\n",
       "<text text-anchor=\"middle\" x=\"1028.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"1028.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.36</text>\n",
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       "<!-- 24&#45;&gt;25 -->\n",
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       "<title>24&#45;&gt;25</title>\n",
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       "<!-- 28 -->\n",
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       "<title>28</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1223.5,-1093 1099.5,-1093 1099.5,-1025 1223.5,-1025 1223.5,-1093\"/>\n",
       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 30.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.729</text>\n",
       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 9</text>\n",
       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.761</text>\n",
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       "<!-- 24&#45;&gt;28 -->\n",
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       "<title>24&#45;&gt;28</title>\n",
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       "<title>26</title>\n",
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       "<text text-anchor=\"middle\" x=\"945.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"945.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"945.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.68</text>\n",
       "</g>\n",
       "<!-- 25&#45;&gt;26 -->\n",
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       "<title>25&#45;&gt;26</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M1001.3227,-1024.9465C992.2682,-1013.6012 982.177,-1000.9567 973.0914,-989.5724\"/>\n",
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       "<title>27</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1100,-981.5 1007,-981.5 1007,-928.5 1100,-928.5 1100,-981.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"1053.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1053.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1053.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.04</text>\n",
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       "<!-- 25&#45;&gt;27 -->\n",
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       "<title>25&#45;&gt;27</title>\n",
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       "<!-- 29 -->\n",
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       "<title>29</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1204.5,-981.5 1118.5,-981.5 1118.5,-928.5 1204.5,-928.5 1204.5,-981.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1161.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.64</text>\n",
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       "<!-- 28&#45;&gt;29 -->\n",
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       "<title>28&#45;&gt;29</title>\n",
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       "<title>30</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1354,-989 1223,-989 1223,-921 1354,-921 1354,-989\"/>\n",
       "<text text-anchor=\"middle\" x=\"1288.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 417.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1288.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.323</text>\n",
       "<text text-anchor=\"middle\" x=\"1288.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 8</text>\n",
       "<text text-anchor=\"middle\" x=\"1288.5\" y=\"-928.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.526</text>\n",
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       "<!-- 28&#45;&gt;30 -->\n",
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       "<title>28&#45;&gt;30</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M1203.0845,-1024.9465C1214.4873,-1015.6088 1226.9647,-1005.3911 1238.7743,-995.7203\"/>\n",
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       "<title>31</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1296,-885 1125,-885 1125,-817 1296,-817 1296,-885\"/>\n",
       "<text text-anchor=\"middle\" x=\"1210.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">ShelveLoc_Medium &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1210.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.139</text>\n",
       "<text text-anchor=\"middle\" x=\"1210.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 6</text>\n",
       "<text text-anchor=\"middle\" x=\"1210.5\" y=\"-824.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.265</text>\n",
       "</g>\n",
       "<!-- 30&#45;&gt;31 -->\n",
       "<g id=\"edge31\" class=\"edge\">\n",
       "<title>30&#45;&gt;31</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M1262.9599,-920.9465C1256.3607,-912.1475 1249.1754,-902.5672 1242.2995,-893.3993\"/>\n",
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       "<title>42</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1417,-885 1314,-885 1314,-817 1417,-817 1417,-885\"/>\n",
       "<text text-anchor=\"middle\" x=\"1365.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">US_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1365.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.058</text>\n",
       "<text text-anchor=\"middle\" x=\"1365.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"1365.5\" y=\"-824.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.31</text>\n",
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       "<!-- 30&#45;&gt;42 -->\n",
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       "<title>30&#45;&gt;42</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M1313.7127,-920.9465C1320.2273,-912.1475 1327.3205,-902.5672 1334.1082,-893.3993\"/>\n",
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       "<title>32</title>\n",
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       "<text text-anchor=\"middle\" x=\"1098.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 17.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1098.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.017</text>\n",
       "<text text-anchor=\"middle\" x=\"1098.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"1098.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.77</text>\n",
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       "<!-- 31&#45;&gt;32 -->\n",
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       "<title>31&#45;&gt;32</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M1173.827,-816.9465C1163.8677,-807.6986 1152.9789,-797.5876 1142.6532,-787.9994\"/>\n",
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       "<title>35</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1283.5,-781 1177.5,-781 1177.5,-713 1283.5,-713 1283.5,-781\"/>\n",
       "<text text-anchor=\"middle\" x=\"1230.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 82.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1230.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.016</text>\n",
       "<text text-anchor=\"middle\" x=\"1230.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
       "<text text-anchor=\"middle\" x=\"1230.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.512</text>\n",
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       "<!-- 31&#45;&gt;35 -->\n",
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       "<title>31&#45;&gt;35</title>\n",
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       "<title>33</title>\n",
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       "<text text-anchor=\"middle\" x=\"1000.5\" y=\"-654.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1000.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1000.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.64</text>\n",
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       "<!-- 32&#45;&gt;33 -->\n",
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       "<title>32&#45;&gt;33</title>\n",
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       "<title>34</title>\n",
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       "<text text-anchor=\"middle\" x=\"1103.5\" y=\"-654.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1103.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1103.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.9</text>\n",
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       "<title>32&#45;&gt;34</title>\n",
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       "<title>36</title>\n",
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       "<text text-anchor=\"middle\" x=\"1225.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 48.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1225.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.005</text>\n",
       "<text text-anchor=\"middle\" x=\"1225.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"1225.5\" y=\"-616.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.63</text>\n",
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       "<text text-anchor=\"middle\" x=\"1355.5\" y=\"-743.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"1459.5\" y=\"-728.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.55</text>\n",
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       "<!-- 45&#45;&gt;46 -->\n",
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       "<title>45&#45;&gt;47</title>\n",
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       "<title>49</title>\n",
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       "<text text-anchor=\"middle\" x=\"1550.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">US_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1550.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.07</text>\n",
       "<text text-anchor=\"middle\" x=\"1550.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<!-- 48&#45;&gt;49 -->\n",
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       "<title>48&#45;&gt;49</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M1550.5,-1232.9465C1550.5,-1224.776 1550.5,-1215.9318 1550.5,-1207.3697\"/>\n",
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       "<title>52</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1789,-1197 1686,-1197 1686,-1129 1789,-1129 1789,-1197\"/>\n",
       "<text text-anchor=\"middle\" x=\"1737.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">US_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"1737.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.134</text>\n",
       "<text text-anchor=\"middle\" x=\"1737.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 5</text>\n",
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       "<!-- 48&#45;&gt;52 -->\n",
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       "<title>48&#45;&gt;52</title>\n",
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       "<title>49&#45;&gt;50</title>\n",
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       "<text text-anchor=\"middle\" x=\"1605.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1605.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1605.5\" y=\"-1040.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.48</text>\n",
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       "<text text-anchor=\"middle\" x=\"1737.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 137.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1737.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.511</text>\n",
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       "<text text-anchor=\"middle\" x=\"1883.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.018</text>\n",
       "<text text-anchor=\"middle\" x=\"1883.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"1883.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.345</text>\n",
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       "<title>52&#45;&gt;58</title>\n",
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       "<title>53&#45;&gt;54</title>\n",
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       "<text text-anchor=\"middle\" x=\"1737.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1737.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.5</text>\n",
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       "<text text-anchor=\"middle\" x=\"1558.5\" y=\"-862.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1558.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1558.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.85</text>\n",
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       "<title>54&#45;&gt;55</title>\n",
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       "<text text-anchor=\"middle\" x=\"1662.5\" y=\"-862.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1662.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1662.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.14</text>\n",
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       "<title>54&#45;&gt;56</title>\n",
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       "<text text-anchor=\"middle\" x=\"1844.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1844.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.21</text>\n",
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       "<text text-anchor=\"middle\" x=\"1955.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1955.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.48</text>\n",
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       "<title>58&#45;&gt;60</title>\n",
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       "<text text-anchor=\"middle\" x=\"3038.5\" y=\"-1389.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 144.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3038.5\" y=\"-1374.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 4.202</text>\n",
       "<text text-anchor=\"middle\" x=\"3038.5\" y=\"-1359.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 35</text>\n",
       "<text text-anchor=\"middle\" x=\"3038.5\" y=\"-1344.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.936</text>\n",
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       "<title>61&#45;&gt;62</title>\n",
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       "<polygon fill=\"none\" stroke=\"#000000\" points=\"4796.5,-1405 4662.5,-1405 4662.5,-1337 4796.5,-1337 4796.5,-1405\"/>\n",
       "<text text-anchor=\"middle\" x=\"4729.5\" y=\"-1389.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 124.5</text>\n",
       "<text text-anchor=\"middle\" x=\"4729.5\" y=\"-1374.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 4.349</text>\n",
       "<text text-anchor=\"middle\" x=\"4729.5\" y=\"-1359.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 93</text>\n",
       "<text text-anchor=\"middle\" x=\"4729.5\" y=\"-1344.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.972</text>\n",
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       "<title>61&#45;&gt;131</title>\n",
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       "<text text-anchor=\"middle\" x=\"2547.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 38.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2547.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 3.235</text>\n",
       "<text text-anchor=\"middle\" x=\"2547.5\" y=\"-1255.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 31</text>\n",
       "<text text-anchor=\"middle\" x=\"2547.5\" y=\"-1240.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.575</text>\n",
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       "<title>62&#45;&gt;63</title>\n",
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       "<title>124</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"3105.5,-1301 2971.5,-1301 2971.5,-1233 3105.5,-1233 3105.5,-1301\"/>\n",
       "<text text-anchor=\"middle\" x=\"3038.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 147.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3038.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 2.842</text>\n",
       "<text text-anchor=\"middle\" x=\"3038.5\" y=\"-1255.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
       "<text text-anchor=\"middle\" x=\"3038.5\" y=\"-1240.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.738</text>\n",
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       "<!-- 62&#45;&gt;124 -->\n",
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       "<title>62&#45;&gt;124</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M3038.5,-1336.9465C3038.5,-1328.776 3038.5,-1319.9318 3038.5,-1311.3697\"/>\n",
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       "<title>64</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2248.5,-1197 2124.5,-1197 2124.5,-1129 2248.5,-1129 2248.5,-1197\"/>\n",
       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 15.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 4.517</text>\n",
       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-1136.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 2.352</text>\n",
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       "<!-- 63&#45;&gt;64 -->\n",
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       "<title>63&#45;&gt;64</title>\n",
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       "<text text-anchor=\"middle\" x=\"2547.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 31.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2547.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 2.205</text>\n",
       "<text text-anchor=\"middle\" x=\"2547.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 27</text>\n",
       "<text text-anchor=\"middle\" x=\"2547.5\" y=\"-1136.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.904</text>\n",
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       "<!-- 63&#45;&gt;71 -->\n",
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       "<title>63&#45;&gt;71</title>\n",
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       "<text text-anchor=\"middle\" x=\"2065.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2065.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2065.5\" y=\"-1040.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.9</text>\n",
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       "<title>64&#45;&gt;65</title>\n",
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       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2247,-1093 2126,-1093 2126,-1025 2247,-1025 2247,-1093\"/>\n",
       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Urban_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.429</text>\n",
       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 1.17</text>\n",
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       "<title>64&#45;&gt;66</title>\n",
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       "<title>67</title>\n",
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       "<text text-anchor=\"middle\" x=\"2063.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2063.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2063.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 2.07</text>\n",
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       "<title>66&#45;&gt;67</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M2146.2252,-1024.9465C2132.2861,-1013.1606 2116.6888,-999.9726 2102.8268,-988.2519\"/>\n",
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       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 29.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.036</text>\n",
       "<text text-anchor=\"middle\" x=\"2186.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<title>66&#45;&gt;68</title>\n",
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       "<text text-anchor=\"middle\" x=\"2157.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2157.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 0.53</text>\n",
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       "<!-- 68&#45;&gt;70 -->\n",
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       "<title>68&#45;&gt;70</title>\n",
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       "<text text-anchor=\"middle\" x=\"2476.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 131.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2476.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.092</text>\n",
       "<text text-anchor=\"middle\" x=\"2476.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"2476.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.953</text>\n",
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       "<title>71&#45;&gt;72</title>\n",
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       "<text text-anchor=\"middle\" x=\"2618.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 102.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2618.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.036</text>\n",
       "<text text-anchor=\"middle\" x=\"2618.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 24</text>\n",
       "<text text-anchor=\"middle\" x=\"2618.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.523</text>\n",
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       "<text text-anchor=\"middle\" x=\"2358.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Urban_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2358.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.119</text>\n",
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       "<text text-anchor=\"middle\" x=\"2480.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2480.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2480.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.53</text>\n",
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       "<title>74</title>\n",
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       "<text text-anchor=\"middle\" x=\"2261.5\" y=\"-862.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2261.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2261.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.01</text>\n",
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       "<title>73&#45;&gt;74</title>\n",
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       "<title>75</title>\n",
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       "<text text-anchor=\"middle\" x=\"2365.5\" y=\"-862.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2365.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2365.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.32</text>\n",
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       "<!-- 73&#45;&gt;75 -->\n",
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       "<title>73&#45;&gt;75</title>\n",
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       "<title>78</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2678.5,-989 2544.5,-989 2544.5,-921 2678.5,-921 2678.5,-989\"/>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 111.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.854</text>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 20</text>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-928.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.326</text>\n",
       "</g>\n",
       "<!-- 77&#45;&gt;78 -->\n",
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       "<title>77&#45;&gt;78</title>\n",
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       "<title>117</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2848,-989 2725,-989 2725,-921 2848,-921 2848,-989\"/>\n",
       "<text text-anchor=\"middle\" x=\"2786.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 6.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2786.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.79</text>\n",
       "<text text-anchor=\"middle\" x=\"2786.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
       "<text text-anchor=\"middle\" x=\"2786.5\" y=\"-928.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.505</text>\n",
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       "<!-- 77&#45;&gt;117 -->\n",
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       "<title>77&#45;&gt;117</title>\n",
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       "<title>79</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2532.5,-885 2426.5,-885 2426.5,-817 2532.5,-817 2532.5,-885\"/>\n",
       "<text text-anchor=\"middle\" x=\"2479.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 78.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2479.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.109</text>\n",
       "<text text-anchor=\"middle\" x=\"2479.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"2479.5\" y=\"-824.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.61</text>\n",
       "</g>\n",
       "<!-- 78&#45;&gt;79 -->\n",
       "<g id=\"edge79\" class=\"edge\">\n",
       "<title>78&#45;&gt;79</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M2568.2783,-920.9465C2556.3126,-911.519 2543.2085,-901.1946 2530.8296,-891.4415\"/>\n",
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       "<title>82</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2672,-885 2551,-885 2551,-817 2672,-817 2672,-885\"/>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 15.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.734</text>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 18</text>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-824.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.184</text>\n",
       "</g>\n",
       "<!-- 78&#45;&gt;82 -->\n",
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       "<title>78&#45;&gt;82</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M2611.5,-920.9465C2611.5,-912.776 2611.5,-903.9318 2611.5,-895.3697\"/>\n",
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       "<title>80</title>\n",
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       "<text text-anchor=\"middle\" x=\"2237.5\" y=\"-758.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2237.5\" y=\"-743.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2237.5\" y=\"-728.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.28</text>\n",
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       "<!-- 79&#45;&gt;80 -->\n",
       "<g id=\"edge80\" class=\"edge\">\n",
       "<title>79&#45;&gt;80</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M2426.4437,-820.9043C2423.4487,-819.52 2420.4547,-818.2072 2417.5,-817 2362.7941,-794.648 2343.2992,-805.4538 2289.5,-781 2287.7325,-780.1966 2285.9565,-779.3381 2284.1818,-778.4362\"/>\n",
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       "<title>81</title>\n",
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       "<text text-anchor=\"middle\" x=\"2341.5\" y=\"-758.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2341.5\" y=\"-743.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2341.5\" y=\"-728.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.94</text>\n",
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       "<title>79&#45;&gt;81</title>\n",
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       "<title>83</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2526,-781 2403,-781 2403,-713 2526,-713 2526,-781\"/>\n",
       "<text text-anchor=\"middle\" x=\"2464.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2464.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.553</text>\n",
       "<text text-anchor=\"middle\" x=\"2464.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 14</text>\n",
       "<text text-anchor=\"middle\" x=\"2464.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 3.914</text>\n",
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       "<title>82&#45;&gt;83</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M2563.3667,-816.9465C2549.9144,-807.4293 2535.17,-796.9978 2521.2688,-787.163\"/>\n",
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       "<title>110</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2678.5,-781 2544.5,-781 2544.5,-713 2678.5,-713 2678.5,-781\"/>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 122.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.215</text>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
       "<text text-anchor=\"middle\" x=\"2611.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.13</text>\n",
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       "<title>82&#45;&gt;110</title>\n",
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       "<text text-anchor=\"middle\" x=\"2126.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.524</text>\n",
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       "<title>83&#45;&gt;84</title>\n",
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       "<title>93</title>\n",
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       "<text text-anchor=\"middle\" x=\"2464.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 295.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2464.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.38</text>\n",
       "<text text-anchor=\"middle\" x=\"2464.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 9</text>\n",
       "<text text-anchor=\"middle\" x=\"2464.5\" y=\"-616.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 3.653</text>\n",
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       "<text text-anchor=\"middle\" x=\"1944.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 120.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1944.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.003</text>\n",
       "<text text-anchor=\"middle\" x=\"1944.5\" y=\"-527.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<title>88</title>\n",
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       "<text text-anchor=\"middle\" x=\"2126.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Urban_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2126.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.29</text>\n",
       "<text text-anchor=\"middle\" x=\"2126.5\" y=\"-527.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"2126.5\" y=\"-512.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 3.9</text>\n",
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       "<text text-anchor=\"middle\" x=\"1840.5\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1840.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1840.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.16</text>\n",
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       "<title>85&#45;&gt;86</title>\n",
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       "<title>87</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"1987.5,-461.5 1901.5,-461.5 1901.5,-408.5 1987.5,-408.5 1987.5,-461.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"1944.5\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"1944.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"1944.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.05</text>\n",
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       "<title>85&#45;&gt;87</title>\n",
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       "<title>89</title>\n",
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       "<text text-anchor=\"middle\" x=\"2048.5\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2048.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2048.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 3.24</text>\n",
       "</g>\n",
       "<!-- 88&#45;&gt;89 -->\n",
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       "<title>88&#45;&gt;89</title>\n",
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       "<!-- 90 -->\n",
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       "<title>90</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2215.5,-469 2109.5,-469 2109.5,-401 2215.5,-401 2215.5,-469\"/>\n",
       "<text text-anchor=\"middle\" x=\"2162.5\" y=\"-453.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 73.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2162.5\" y=\"-438.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.109</text>\n",
       "<text text-anchor=\"middle\" x=\"2162.5\" y=\"-423.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"2162.5\" y=\"-408.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.23</text>\n",
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       "<title>88&#45;&gt;90</title>\n",
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       "<title>91</title>\n",
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       "<text text-anchor=\"middle\" x=\"2066.5\" y=\"-342.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2066.5\" y=\"-327.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2066.5\" y=\"-312.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.56</text>\n",
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       "<!-- 90&#45;&gt;91 -->\n",
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       "<title>90&#45;&gt;91</title>\n",
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       "<title>92</title>\n",
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       "<text text-anchor=\"middle\" x=\"2169.5\" y=\"-342.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2169.5\" y=\"-327.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2169.5\" y=\"-312.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 3.9</text>\n",
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       "<!-- 90&#45;&gt;92 -->\n",
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       "<title>90&#45;&gt;92</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M2164.7921,-400.9465C2165.5112,-390.2621 2166.3079,-378.4254 2167.0383,-367.5742\"/>\n",
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       "<title>94</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2445.5,-573 2345.5,-573 2345.5,-505 2445.5,-505 2445.5,-573\"/>\n",
       "<text text-anchor=\"middle\" x=\"2395.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 130.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2395.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.046</text>\n",
       "<text text-anchor=\"middle\" x=\"2395.5\" y=\"-527.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"2395.5\" y=\"-512.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 2.96</text>\n",
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       "<!-- 93&#45;&gt;94 -->\n",
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       "<title>93&#45;&gt;94</title>\n",
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       "<title>99</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2585,-573 2464,-573 2464,-505 2585,-505 2585,-573\"/>\n",
       "<text text-anchor=\"middle\" x=\"2524.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 13.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2524.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.186</text>\n",
       "<text text-anchor=\"middle\" x=\"2524.5\" y=\"-527.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 6</text>\n",
       "<text text-anchor=\"middle\" x=\"2524.5\" y=\"-512.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.0</text>\n",
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       "<!-- 93&#45;&gt;99 -->\n",
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       "<title>95</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"2355,-469 2234,-469 2234,-401 2355,-401 2355,-469\"/>\n",
       "<text text-anchor=\"middle\" x=\"2294.5\" y=\"-453.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 10.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2294.5\" y=\"-438.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.002</text>\n",
       "<text text-anchor=\"middle\" x=\"2294.5\" y=\"-423.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"2294.5\" y=\"-408.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 3.11</text>\n",
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       "<title>94&#45;&gt;95</title>\n",
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       "<title>98</title>\n",
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       "<text text-anchor=\"middle\" x=\"2416.5\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2416.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2416.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 2.66</text>\n",
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       "<!-- 94&#45;&gt;98 -->\n",
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       "<title>94&#45;&gt;98</title>\n",
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       "<title>96</title>\n",
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       "<text text-anchor=\"middle\" x=\"2286.5\" y=\"-342.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2286.5\" y=\"-327.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2286.5\" y=\"-312.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 3.07</text>\n",
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       "<!-- 95&#45;&gt;96 -->\n",
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       "<title>95&#45;&gt;96</title>\n",
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       "<text text-anchor=\"middle\" x=\"2390.5\" y=\"-327.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<!-- 95&#45;&gt;97 -->\n",
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       "<title>95&#45;&gt;97</title>\n",
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       "<text text-anchor=\"middle\" x=\"2524.5\" y=\"-453.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 36.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2524.5\" y=\"-438.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.042</text>\n",
       "<text text-anchor=\"middle\" x=\"2524.5\" y=\"-423.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 5</text>\n",
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       "<title>99&#45;&gt;100</title>\n",
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       "<!-- 99&#45;&gt;109 -->\n",
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       "<text text-anchor=\"middle\" x=\"2643.5\" y=\"-119.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2643.5\" y=\"-104.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.1</text>\n",
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       "<!-- 110&#45;&gt;111 -->\n",
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       "<title>112</title>\n",
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       "<text text-anchor=\"middle\" x=\"2720.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">US_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2720.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.062</text>\n",
       "<text text-anchor=\"middle\" x=\"2720.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"2720.5\" y=\"-616.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.367</text>\n",
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       "<title>113</title>\n",
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       "<text text-anchor=\"middle\" x=\"2646.5\" y=\"-550.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
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       "<title>114</title>\n",
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       "<text text-anchor=\"middle\" x=\"2760.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 74.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2760.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.02</text>\n",
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       "<text text-anchor=\"middle\" x=\"2739.5\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
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       "<text text-anchor=\"middle\" x=\"2786.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 114.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2786.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.245</text>\n",
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       "<text text-anchor=\"middle\" x=\"4729.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 138.5</text>\n",
       "<text text-anchor=\"middle\" x=\"4729.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 3.415</text>\n",
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       "<text text-anchor=\"middle\" x=\"3504.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 99.5</text>\n",
       "<text text-anchor=\"middle\" x=\"3504.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.392</text>\n",
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       "<text text-anchor=\"middle\" x=\"4206.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.717</text>\n",
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       "<text text-anchor=\"middle\" x=\"3280.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 100.5</text>\n",
       "<text text-anchor=\"middle\" x=\"3280.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 2.096</text>\n",
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       "<text text-anchor=\"middle\" x=\"3504.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 15.5</text>\n",
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       "<text text-anchor=\"middle\" x=\"3280.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 286.5</text>\n",
       "<text text-anchor=\"middle\" x=\"3280.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.116</text>\n",
       "<text text-anchor=\"middle\" x=\"3280.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
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       "<text text-anchor=\"middle\" x=\"2856.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2856.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.98</text>\n",
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       "<text text-anchor=\"middle\" x=\"2978.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Urban_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"2978.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.02</text>\n",
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       "<text text-anchor=\"middle\" x=\"2978.5\" y=\"-616.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.66</text>\n",
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       "<text text-anchor=\"middle\" x=\"2873.5\" y=\"-550.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
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       "<text text-anchor=\"middle\" x=\"2873.5\" y=\"-520.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.8</text>\n",
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       "<title>140&#45;&gt;141</title>\n",
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       "<text text-anchor=\"middle\" x=\"2976.5\" y=\"-550.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"2976.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2976.5\" y=\"-520.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.52</text>\n",
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       "<!-- 140&#45;&gt;142 -->\n",
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       "<title>140&#45;&gt;142</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M2977.8451,-608.9465C2977.6397,-598.2621 2977.412,-586.4254 2977.2034,-575.5742\"/>\n",
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       "<title>144</title>\n",
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       "<text text-anchor=\"middle\" x=\"3425.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 12.5</text>\n",
       "<text text-anchor=\"middle\" x=\"3425.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.274</text>\n",
       "<text text-anchor=\"middle\" x=\"3425.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 12</text>\n",
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       "<title>143&#45;&gt;144</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M3478.6324,-816.9465C3471.8804,-808.0578 3464.5226,-798.3716 3457.4941,-789.1188\"/>\n",
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       "<text text-anchor=\"middle\" x=\"3576.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 113.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3576.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.097</text>\n",
       "<text text-anchor=\"middle\" x=\"3576.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
       "<text text-anchor=\"middle\" x=\"3576.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.192</text>\n",
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       "<title>143&#45;&gt;167</title>\n",
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       "<title>145</title>\n",
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       "<text text-anchor=\"middle\" x=\"3209.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 466.5</text>\n",
       "<text text-anchor=\"middle\" x=\"3209.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.155</text>\n",
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       "<title>144&#45;&gt;145</title>\n",
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       "<text text-anchor=\"middle\" x=\"3425.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 120.5</text>\n",
       "<text text-anchor=\"middle\" x=\"3425.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.274</text>\n",
       "<text text-anchor=\"middle\" x=\"3425.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
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       "<title>144&#45;&gt;160</title>\n",
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       "<text text-anchor=\"middle\" x=\"3084.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 55.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3084.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.054</text>\n",
       "<text text-anchor=\"middle\" x=\"3084.5\" y=\"-527.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 6</text>\n",
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       "<text text-anchor=\"middle\" x=\"3209.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 11.5</text>\n",
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       "<text text-anchor=\"middle\" x=\"2956.5\" y=\"-423.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
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       "<text text-anchor=\"middle\" x=\"3081.5\" y=\"-453.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Urban_Yes &lt;= 0.5</text>\n",
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       "<text text-anchor=\"middle\" x=\"2959.5\" y=\"-319.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<text text-anchor=\"middle\" x=\"2907.5\" y=\"-223.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"2907.5\" y=\"-208.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.97</text>\n",
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       "<text text-anchor=\"middle\" x=\"3011.5\" y=\"-208.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.98</text>\n",
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       "<text text-anchor=\"middle\" x=\"3078.5\" y=\"-327.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"3078.5\" y=\"-312.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.64</text>\n",
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       "<title>152&#45;&gt;153</title>\n",
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       "<title>154</title>\n",
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       "<text text-anchor=\"middle\" x=\"3186.5\" y=\"-349.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 64.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3186.5\" y=\"-334.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.003</text>\n",
       "<text text-anchor=\"middle\" x=\"3186.5\" y=\"-319.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<title>152&#45;&gt;154</title>\n",
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       "<text text-anchor=\"middle\" x=\"3179.5\" y=\"-223.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<!-- 154&#45;&gt;155 -->\n",
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       "<title>154&#45;&gt;155</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M3184.2079,-296.9465C3183.4888,-286.2621 3182.6921,-274.4254 3181.9617,-263.5742\"/>\n",
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       "<text text-anchor=\"middle\" x=\"3283.5\" y=\"-238.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3283.5\" y=\"-223.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"3283.5\" y=\"-208.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.47</text>\n",
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       "<!-- 154&#45;&gt;156 -->\n",
       "<g id=\"edge156\" class=\"edge\">\n",
       "<title>154&#45;&gt;156</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M3218.2614,-296.9465C3229.0486,-285.3809 3241.095,-272.4652 3251.8718,-260.9107\"/>\n",
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       "<title>158</title>\n",
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       "<text text-anchor=\"middle\" x=\"3203.5\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3203.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"3203.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.33</text>\n",
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       "<!-- 157&#45;&gt;158 -->\n",
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       "<title>157&#45;&gt;158</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M3207.5354,-504.9465C3206.919,-494.2621 3206.2361,-482.4254 3205.6101,-471.5742\"/>\n",
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       "<text text-anchor=\"middle\" x=\"3307.5\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3307.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"3307.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.67</text>\n",
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       "<title>157&#45;&gt;159</title>\n",
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       "<title>161</title>\n",
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       "<text text-anchor=\"middle\" x=\"3338.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 110.5</text>\n",
       "<text text-anchor=\"middle\" x=\"3338.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.084</text>\n",
       "<text text-anchor=\"middle\" x=\"3338.5\" y=\"-527.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"3338.5\" y=\"-512.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.18</text>\n",
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       "<title>160&#45;&gt;161</title>\n",
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       "<text text-anchor=\"middle\" x=\"3449.5\" y=\"-550.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3449.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"3411.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"3657.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"3761.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"3865.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"3865.5\" y=\"-520.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 2.67</text>\n",
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       "<title>171&#45;&gt;173</title>\n",
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       "<title>175</title>\n",
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       "<text text-anchor=\"middle\" x=\"4115.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 184.5</text>\n",
       "<text text-anchor=\"middle\" x=\"4115.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.721</text>\n",
       "<text text-anchor=\"middle\" x=\"4115.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 5</text>\n",
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       "<text text-anchor=\"middle\" x=\"4342.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 115.5</text>\n",
       "<text text-anchor=\"middle\" x=\"4342.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.602</text>\n",
       "<text text-anchor=\"middle\" x=\"4342.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 5</text>\n",
       "<text text-anchor=\"middle\" x=\"4342.5\" y=\"-824.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.462</text>\n",
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       "<polygon fill=\"none\" stroke=\"#000000\" points=\"3993.5,-781 3887.5,-781 3887.5,-713 3993.5,-713 3993.5,-781\"/>\n",
       "<text text-anchor=\"middle\" x=\"3940.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 46.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3940.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.383</text>\n",
       "<text text-anchor=\"middle\" x=\"3940.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"3940.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.967</text>\n",
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       "<title>175&#45;&gt;176</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M4058.1985,-816.9465C4040.3802,-806.3574 4020.6577,-794.6366 4002.5323,-783.8649\"/>\n",
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       "<title>181</title>\n",
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       "<text text-anchor=\"middle\" x=\"4115.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 31.0</text>\n",
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       "<text text-anchor=\"middle\" x=\"3940.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 16.0</text>\n",
       "<text text-anchor=\"middle\" x=\"3940.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.029</text>\n",
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       "<text text-anchor=\"middle\" x=\"3969.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"3969.5\" y=\"-520.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.37</text>\n",
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       "<title>178&#45;&gt;179</title>\n",
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       "<text text-anchor=\"middle\" x=\"4073.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"4073.5\" y=\"-520.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.71</text>\n",
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       "<title>190&#45;&gt;192</title>\n",
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       "<text text-anchor=\"middle\" x=\"4667.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 92.5</text>\n",
       "<text text-anchor=\"middle\" x=\"4667.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.188</text>\n",
       "<text text-anchor=\"middle\" x=\"4667.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
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       "<title>201</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"5020,-989 4889,-989 4889,-921 5020,-921 5020,-989\"/>\n",
       "<text text-anchor=\"middle\" x=\"4954.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 428.5</text>\n",
       "<text text-anchor=\"middle\" x=\"4954.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.328</text>\n",
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       "<text text-anchor=\"middle\" x=\"4722.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 122.5</text>\n",
       "<text text-anchor=\"middle\" x=\"4722.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.152</text>\n",
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       "<text text-anchor=\"middle\" x=\"4671.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 4.0</text>\n",
       "<text text-anchor=\"middle\" x=\"4671.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.02</text>\n",
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       "<text text-anchor=\"middle\" x=\"4946.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"5050.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"5050.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.47</text>\n",
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       "<text text-anchor=\"middle\" x=\"5255.5\" y=\"-728.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.23</text>\n",
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       "<text text-anchor=\"middle\" x=\"4894.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
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       "<text text-anchor=\"middle\" x=\"5750.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Urban_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"5750.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.872</text>\n",
       "<text text-anchor=\"middle\" x=\"5750.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 32</text>\n",
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       "<text text-anchor=\"middle\" x=\"7520.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 14.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7520.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 2.902</text>\n",
       "<text text-anchor=\"middle\" x=\"7520.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 20</text>\n",
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       "<text text-anchor=\"middle\" x=\"5618.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.91</text>\n",
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       "<text text-anchor=\"middle\" x=\"5618.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 67.5</text>\n",
       "<text text-anchor=\"middle\" x=\"5618.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.152</text>\n",
       "<text text-anchor=\"middle\" x=\"5618.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"5618.5\" y=\"-928.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.75</text>\n",
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       "<text text-anchor=\"middle\" x=\"5398.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"5506.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 53.0</text>\n",
       "<text text-anchor=\"middle\" x=\"5506.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.699</text>\n",
       "<text text-anchor=\"middle\" x=\"5506.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 6</text>\n",
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       "<text text-anchor=\"middle\" x=\"5369.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 86.0</text>\n",
       "<text text-anchor=\"middle\" x=\"5369.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.156</text>\n",
       "<text text-anchor=\"middle\" x=\"5369.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
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       "<text text-anchor=\"middle\" x=\"5506.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 283.5</text>\n",
       "<text text-anchor=\"middle\" x=\"5506.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.046</text>\n",
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       "<text text-anchor=\"middle\" x=\"5173.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 1.5</text>\n",
       "<text text-anchor=\"middle\" x=\"5173.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.005</text>\n",
       "<text text-anchor=\"middle\" x=\"5173.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<title>219&#45;&gt;220</title>\n",
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       "<polygon fill=\"none\" stroke=\"#000000\" points=\"5387.5,-677 5253.5,-677 5253.5,-609 5387.5,-609 5387.5,-677\"/>\n",
       "<text text-anchor=\"middle\" x=\"5320.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 128.5</text>\n",
       "<text text-anchor=\"middle\" x=\"5320.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.062</text>\n",
       "<text text-anchor=\"middle\" x=\"5320.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<title>219&#45;&gt;223</title>\n",
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       "<text text-anchor=\"middle\" x=\"5184.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<!-- 220&#45;&gt;222 -->\n",
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       "<title>220&#45;&gt;222</title>\n",
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       "<text text-anchor=\"middle\" x=\"5309.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<title>223&#45;&gt;224</title>\n",
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       "<title>223&#45;&gt;225</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M5350.9517,-608.9465C5361.1955,-597.491 5372.6238,-584.711 5382.8805,-573.2412\"/>\n",
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       "<text text-anchor=\"middle\" x=\"5448.5\" y=\"-654.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
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       "<!-- 226&#45;&gt;227 -->\n",
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       "<title>226&#45;&gt;227</title>\n",
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       "<text text-anchor=\"middle\" x=\"5552.5\" y=\"-654.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"5552.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"5552.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.97</text>\n",
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       "<!-- 226&#45;&gt;228 -->\n",
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       "<title>226&#45;&gt;228</title>\n",
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       "<title>229&#45;&gt;230</title>\n",
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       "<text text-anchor=\"middle\" x=\"5720.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"5883.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.558</text>\n",
       "<text text-anchor=\"middle\" x=\"5883.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 7</text>\n",
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       "<title>232&#45;&gt;233</title>\n",
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       "<text text-anchor=\"middle\" x=\"6279.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 11.5</text>\n",
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       "<text text-anchor=\"middle\" x=\"6279.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 16</text>\n",
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       "<text text-anchor=\"middle\" x=\"5939.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">US_Yes &lt;= 0.5</text>\n",
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       "<text text-anchor=\"middle\" x=\"5939.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 6</text>\n",
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       "<text text-anchor=\"middle\" x=\"5807.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.018</text>\n",
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       "<text text-anchor=\"middle\" x=\"5939.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 13.0</text>\n",
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       "<text text-anchor=\"middle\" x=\"5680.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 137.5</text>\n",
       "<text text-anchor=\"middle\" x=\"5680.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.002</text>\n",
       "<text text-anchor=\"middle\" x=\"5680.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<title>236&#45;&gt;237</title>\n",
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       "<text text-anchor=\"middle\" x=\"5808.5\" y=\"-654.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"5808.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"5808.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.54</text>\n",
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       "<text text-anchor=\"middle\" x=\"5628.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"5732.5\" y=\"-550.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"5732.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"5732.5\" y=\"-520.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.86</text>\n",
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       "<!-- 237&#45;&gt;239 -->\n",
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       "<title>237&#45;&gt;239</title>\n",
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       "<title>242</title>\n",
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       "<text text-anchor=\"middle\" x=\"5912.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"5912.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.01</text>\n",
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       "<!-- 241&#45;&gt;242 -->\n",
       "<g id=\"edge242\" class=\"edge\">\n",
       "<title>241&#45;&gt;242</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M5930.6592,-712.9465C5927.8567,-702.1519 5924.749,-690.1813 5921.9082,-679.2389\"/>\n",
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       "<title>243</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"6097,-677 5974,-677 5974,-609 6097,-609 6097,-677\"/>\n",
       "<text text-anchor=\"middle\" x=\"6035.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 7.5</text>\n",
       "<text text-anchor=\"middle\" x=\"6035.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6035.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"6035.5\" y=\"-616.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.79</text>\n",
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       "<!-- 241&#45;&gt;243 -->\n",
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       "<title>241&#45;&gt;243</title>\n",
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       "<title>244</title>\n",
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       "<text text-anchor=\"middle\" x=\"5932.5\" y=\"-550.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"5932.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<!-- 243&#45;&gt;244 -->\n",
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       "<title>243&#45;&gt;244</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M6001.7739,-608.9465C5990.3195,-597.3809 5977.528,-584.4652 5966.0846,-572.9107\"/>\n",
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       "<title>245</title>\n",
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       "<text text-anchor=\"middle\" x=\"6035.5\" y=\"-550.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6035.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"6035.5\" y=\"-520.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.8</text>\n",
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       "<text text-anchor=\"middle\" x=\"6279.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 139.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6279.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.866</text>\n",
       "<text text-anchor=\"middle\" x=\"6279.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 5</text>\n",
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       "<title>246&#45;&gt;247</title>\n",
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       "<text text-anchor=\"middle\" x=\"6480.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 36.5</text>\n",
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       "<text text-anchor=\"middle\" x=\"6480.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 11</text>\n",
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       "<text text-anchor=\"middle\" x=\"6260.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.001</text>\n",
       "<text text-anchor=\"middle\" x=\"6260.5\" y=\"-527.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<text text-anchor=\"middle\" x=\"6316.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"6316.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.07</text>\n",
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       "<title>257</title>\n",
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       "<text text-anchor=\"middle\" x=\"6480.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 25.5</text>\n",
       "<text text-anchor=\"middle\" x=\"6480.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.076</text>\n",
       "<text text-anchor=\"middle\" x=\"6480.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"6480.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.09</text>\n",
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       "<title>256&#45;&gt;257</title>\n",
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       "<title>262</title>\n",
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       "<text text-anchor=\"middle\" x=\"6682.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 13.5</text>\n",
       "<text text-anchor=\"middle\" x=\"6682.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.021</text>\n",
       "<text text-anchor=\"middle\" x=\"6682.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 8</text>\n",
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       "<!-- 256&#45;&gt;262 -->\n",
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       "<title>256&#45;&gt;262</title>\n",
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       "<title>258</title>\n",
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       "<title>257&#45;&gt;258</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M6447.4288,-712.9465C6436.1968,-701.3809 6423.6537,-688.4652 6412.4325,-676.9107\"/>\n",
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       "<title>259</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"6569.5,-677 6439.5,-677 6439.5,-609 6569.5,-609 6569.5,-677\"/>\n",
       "<text text-anchor=\"middle\" x=\"6504.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 11.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6504.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.001</text>\n",
       "<text text-anchor=\"middle\" x=\"6504.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"6504.5\" y=\"-616.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.285</text>\n",
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       "<!-- 257&#45;&gt;259 -->\n",
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       "<title>257&#45;&gt;259</title>\n",
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       "<title>260</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"6425,-565.5 6332,-565.5 6332,-512.5 6425,-512.5 6425,-565.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"6378.5\" y=\"-550.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6378.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<title>259&#45;&gt;260</title>\n",
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       "<polygon fill=\"none\" stroke=\"#000000\" points=\"6536,-565.5 6443,-565.5 6443,-512.5 6536,-512.5 6536,-565.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"6489.5\" y=\"-550.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
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       "<title>259&#45;&gt;261</title>\n",
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       "<text text-anchor=\"middle\" x=\"6682.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 57.5</text>\n",
       "<text text-anchor=\"middle\" x=\"6682.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.003</text>\n",
       "<text text-anchor=\"middle\" x=\"6682.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
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       "<text text-anchor=\"middle\" x=\"6869.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 153.5</text>\n",
       "<text text-anchor=\"middle\" x=\"6869.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.019</text>\n",
       "<text text-anchor=\"middle\" x=\"6869.5\" y=\"-631.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 5</text>\n",
       "<text text-anchor=\"middle\" x=\"6869.5\" y=\"-616.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.92</text>\n",
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       "<title>262&#45;&gt;268</title>\n",
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       "<text text-anchor=\"middle\" x=\"6596.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"6596.5\" y=\"-520.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.8</text>\n",
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       "<title>263&#45;&gt;264</title>\n",
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       "<text text-anchor=\"middle\" x=\"6723.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 127.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6723.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.001</text>\n",
       "<text text-anchor=\"middle\" x=\"6723.5\" y=\"-527.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"6723.5\" y=\"-512.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.7</text>\n",
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       "<title>263&#45;&gt;265</title>\n",
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       "<title>266</title>\n",
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       "<text text-anchor=\"middle\" x=\"6622.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"6622.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.67</text>\n",
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       "<title>265&#45;&gt;266</title>\n",
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       "<text text-anchor=\"middle\" x=\"6726.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"6726.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.73</text>\n",
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       "<title>265&#45;&gt;267</title>\n",
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       "<text text-anchor=\"middle\" x=\"6869.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 16.5</text>\n",
       "<text text-anchor=\"middle\" x=\"6869.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.014</text>\n",
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       "<text text-anchor=\"middle\" x=\"6991.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"6991.5\" y=\"-520.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.74</text>\n",
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       "<text text-anchor=\"middle\" x=\"6860.5\" y=\"-453.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 3.5</text>\n",
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       "<text text-anchor=\"middle\" x=\"6860.5\" y=\"-423.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
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       "<text text-anchor=\"middle\" x=\"6983.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"6983.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.77</text>\n",
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       "<text text-anchor=\"middle\" x=\"6796.5\" y=\"-342.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6796.5\" y=\"-327.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"6796.5\" y=\"-312.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.08</text>\n",
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       "<title>272</title>\n",
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       "<text text-anchor=\"middle\" x=\"6924.5\" y=\"-349.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 127.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6924.5\" y=\"-334.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6924.5\" y=\"-319.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"6924.5\" y=\"-304.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.005</text>\n",
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       "<text text-anchor=\"middle\" x=\"6872.5\" y=\"-238.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6872.5\" y=\"-223.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"6872.5\" y=\"-208.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.01</text>\n",
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       "<title>274</title>\n",
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       "<text text-anchor=\"middle\" x=\"6975.5\" y=\"-238.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"6975.5\" y=\"-223.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<title>272&#45;&gt;274</title>\n",
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       "<title>278</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"7586,-1093 7455,-1093 7455,-1025 7586,-1025 7586,-1093\"/>\n",
       "<text text-anchor=\"middle\" x=\"7520.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 498.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7520.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.928</text>\n",
       "<text text-anchor=\"middle\" x=\"7520.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 17</text>\n",
       "<text text-anchor=\"middle\" x=\"7520.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.002</text>\n",
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       "<!-- 277&#45;&gt;278 -->\n",
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       "<title>277&#45;&gt;278</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M7520.5,-1128.9465C7520.5,-1120.776 7520.5,-1111.9318 7520.5,-1103.3697\"/>\n",
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       "<polygon fill=\"none\" stroke=\"#000000\" points=\"7775.5,-1093 7645.5,-1093 7645.5,-1025 7775.5,-1025 7775.5,-1093\"/>\n",
       "<text text-anchor=\"middle\" x=\"7710.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 15.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7710.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.611</text>\n",
       "<text text-anchor=\"middle\" x=\"7710.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"7710.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.033</text>\n",
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       "<title>277&#45;&gt;311</title>\n",
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       "<title>279</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"7544,-989 7413,-989 7413,-921 7544,-921 7544,-989\"/>\n",
       "<text text-anchor=\"middle\" x=\"7478.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 339.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7478.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.179</text>\n",
       "<text text-anchor=\"middle\" x=\"7478.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 16</text>\n",
       "<text text-anchor=\"middle\" x=\"7478.5\" y=\"-928.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.776</text>\n",
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       "<text text-anchor=\"middle\" x=\"7605.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7605.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7605.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.62</text>\n",
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       "<title>278&#45;&gt;310</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M7548.3322,-1024.9465C7557.6048,-1013.6012 7567.9392,-1000.9567 7577.2437,-989.5724\"/>\n",
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       "<polygon fill=\"none\" stroke=\"#000000\" points=\"7531.5,-885 7425.5,-885 7425.5,-817 7531.5,-817 7531.5,-885\"/>\n",
       "<text text-anchor=\"middle\" x=\"7478.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 68.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7478.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.686</text>\n",
       "<text text-anchor=\"middle\" x=\"7478.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 12</text>\n",
       "<text text-anchor=\"middle\" x=\"7478.5\" y=\"-824.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.162</text>\n",
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       "<title>279&#45;&gt;280</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M7478.5,-920.9465C7478.5,-912.776 7478.5,-903.9318 7478.5,-895.3697\"/>\n",
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       "<text text-anchor=\"middle\" x=\"7694.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 132.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7694.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.871</text>\n",
       "<text text-anchor=\"middle\" x=\"7694.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
       "<text text-anchor=\"middle\" x=\"7694.5\" y=\"-824.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.618</text>\n",
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       "<title>279&#45;&gt;303</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M7544.1869,-923.373C7567.5191,-912.1389 7593.981,-899.398 7618.1291,-887.7712\"/>\n",
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       "<text text-anchor=\"middle\" x=\"7334.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 108.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7334.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.352</text>\n",
       "<text text-anchor=\"middle\" x=\"7334.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 7</text>\n",
       "<text text-anchor=\"middle\" x=\"7334.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.597</text>\n",
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       "<text text-anchor=\"middle\" x=\"7478.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 118.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7478.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.083</text>\n",
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       "<text text-anchor=\"middle\" x=\"7188.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 90.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7188.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.084</text>\n",
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       "<text text-anchor=\"middle\" x=\"7334.5\" y=\"-661.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 214.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7334.5\" y=\"-646.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.073</text>\n",
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       "<text text-anchor=\"middle\" x=\"7099.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 45.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7099.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.046</text>\n",
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       "<text text-anchor=\"middle\" x=\"7207.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7207.5\" y=\"-520.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.53</text>\n",
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       "<text text-anchor=\"middle\" x=\"7087.5\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7087.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7087.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.3</text>\n",
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       "<title>283&#45;&gt;284</title>\n",
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       "<text text-anchor=\"middle\" x=\"7197.5\" y=\"-453.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 146.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7197.5\" y=\"-438.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.009</text>\n",
       "<text text-anchor=\"middle\" x=\"7197.5\" y=\"-423.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"7197.5\" y=\"-408.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.875</text>\n",
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       "<title>283&#45;&gt;285</title>\n",
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       "<text text-anchor=\"middle\" x=\"7145.5\" y=\"-342.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7145.5\" y=\"-327.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7145.5\" y=\"-312.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.78</text>\n",
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       "<title>285&#45;&gt;286</title>\n",
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       "<title>285&#45;&gt;287</title>\n",
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       "<title>290</title>\n",
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       "<text text-anchor=\"middle\" x=\"7315.5\" y=\"-557.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 60.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7315.5\" y=\"-542.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.027</text>\n",
       "<text text-anchor=\"middle\" x=\"7315.5\" y=\"-527.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"7315.5\" y=\"-512.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.365</text>\n",
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       "<text text-anchor=\"middle\" x=\"7423.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"7313.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7313.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.53</text>\n",
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       "<text text-anchor=\"middle\" x=\"7416.5\" y=\"-446.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
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       "<text text-anchor=\"middle\" x=\"7416.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.2</text>\n",
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       "<text text-anchor=\"middle\" x=\"7675.5\" y=\"-535.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"7541.5\" y=\"-438.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7541.5\" y=\"-423.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"7541.5\" y=\"-408.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.86</text>\n",
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       "<text text-anchor=\"middle\" x=\"7655.5\" y=\"-431.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7655.5\" y=\"-416.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.93</text>\n",
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       "<text text-anchor=\"middle\" x=\"7489.5\" y=\"-327.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7489.5\" y=\"-312.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.85</text>\n",
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       "<text text-anchor=\"middle\" x=\"7593.5\" y=\"-327.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7593.5\" y=\"-312.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.87</text>\n",
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       "<title>297&#45;&gt;299</title>\n",
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       "<title>304</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"7762,-781 7631,-781 7631,-713 7762,-713 7762,-781\"/>\n",
       "<text text-anchor=\"middle\" x=\"7696.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 476.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7696.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.156</text>\n",
       "<text text-anchor=\"middle\" x=\"7696.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"7696.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.475</text>\n",
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       "<title>303&#45;&gt;304</title>\n",
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       "<title>307</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"7953.5,-781 7853.5,-781 7853.5,-713 7953.5,-713 7953.5,-781\"/>\n",
       "<text text-anchor=\"middle\" x=\"7903.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 149.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7903.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.116</text>\n",
       "<text text-anchor=\"middle\" x=\"7903.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"7903.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 3.76</text>\n",
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       "<title>303&#45;&gt;307</title>\n",
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       "<title>305</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"7739.5,-669.5 7653.5,-669.5 7653.5,-616.5 7739.5,-616.5 7739.5,-669.5\"/>\n",
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       "<text text-anchor=\"middle\" x=\"7696.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7696.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.87</text>\n",
       "</g>\n",
       "<!-- 304&#45;&gt;305 -->\n",
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       "<title>304&#45;&gt;305</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M7696.5,-712.9465C7696.5,-702.2621 7696.5,-690.4254 7696.5,-679.5742\"/>\n",
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       "<title>306</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"7843.5,-669.5 7757.5,-669.5 7757.5,-616.5 7843.5,-616.5 7843.5,-669.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"7800.5\" y=\"-654.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7800.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7800.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 5.08</text>\n",
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       "<!-- 304&#45;&gt;306 -->\n",
       "<g id=\"edge306\" class=\"edge\">\n",
       "<title>304&#45;&gt;306</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M7730.5535,-712.9465C7742.1191,-701.3809 7755.0348,-688.4652 7766.5893,-676.9107\"/>\n",
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       "<title>308</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"7945.5,-669.5 7861.5,-669.5 7861.5,-616.5 7945.5,-616.5 7945.5,-669.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"7903.5\" y=\"-654.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7903.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7903.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.1</text>\n",
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       "<!-- 307&#45;&gt;308 -->\n",
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       "<title>307&#45;&gt;308</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M7903.5,-712.9465C7903.5,-702.2621 7903.5,-690.4254 7903.5,-679.5742\"/>\n",
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       "<title>309</title>\n",
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       "<text text-anchor=\"middle\" x=\"8006.5\" y=\"-654.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8006.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8006.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 3.42</text>\n",
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       "<!-- 307&#45;&gt;309 -->\n",
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       "<title>307&#45;&gt;309</title>\n",
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       "<title>312</title>\n",
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       "<text text-anchor=\"middle\" x=\"7710.5\" y=\"-966.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"7710.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7710.5\" y=\"-936.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.1</text>\n",
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       "<title>311&#45;&gt;312</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M7710.5,-1024.9465C7710.5,-1014.2621 7710.5,-1002.4254 7710.5,-991.5742\"/>\n",
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       "<title>313</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"7872.5,-989 7772.5,-989 7772.5,-921 7872.5,-921 7872.5,-989\"/>\n",
       "<text text-anchor=\"middle\" x=\"7822.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 143.5</text>\n",
       "<text text-anchor=\"middle\" x=\"7822.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.062</text>\n",
       "<text text-anchor=\"middle\" x=\"7822.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"7822.5\" y=\"-928.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.5</text>\n",
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       "<title>311&#45;&gt;313</title>\n",
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       "<text text-anchor=\"middle\" x=\"7822.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"7822.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.25</text>\n",
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       "<title>313&#45;&gt;314</title>\n",
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       "<text text-anchor=\"middle\" x=\"7926.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<title>316&#45;&gt;317</title>\n",
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       "<text text-anchor=\"middle\" x=\"9374.5\" y=\"-1493.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 81.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9374.5\" y=\"-1478.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 3.939</text>\n",
       "<text text-anchor=\"middle\" x=\"9374.5\" y=\"-1463.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 8</text>\n",
       "<text text-anchor=\"middle\" x=\"9374.5\" y=\"-1448.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.676</text>\n",
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       "<!-- 316&#45;&gt;384 -->\n",
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       "<title>316&#45;&gt;384</title>\n",
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       "<!-- 318 -->\n",
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       "<title>318</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"8663.5,-1405 8529.5,-1405 8529.5,-1337 8663.5,-1337 8663.5,-1405\"/>\n",
       "<text text-anchor=\"middle\" x=\"8596.5\" y=\"-1389.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 116.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8596.5\" y=\"-1374.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.409</text>\n",
       "<text text-anchor=\"middle\" x=\"8596.5\" y=\"-1359.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
       "<text text-anchor=\"middle\" x=\"8596.5\" y=\"-1344.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 14.702</text>\n",
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       "<title>317&#45;&gt;318</title>\n",
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       "<title>325</title>\n",
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       "<text text-anchor=\"middle\" x=\"8782.5\" y=\"-1389.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 12.5</text>\n",
       "<text text-anchor=\"middle\" x=\"8782.5\" y=\"-1374.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 2.963</text>\n",
       "<text text-anchor=\"middle\" x=\"8782.5\" y=\"-1359.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 30</text>\n",
       "<text text-anchor=\"middle\" x=\"8782.5\" y=\"-1344.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.902</text>\n",
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       "<title>317&#45;&gt;325</title>\n",
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       "<title>319</title>\n",
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       "<text text-anchor=\"middle\" x=\"8407.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 60.5</text>\n",
       "<text text-anchor=\"middle\" x=\"8407.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.053</text>\n",
       "<text text-anchor=\"middle\" x=\"8407.5\" y=\"-1255.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"8407.5\" y=\"-1240.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 14.14</text>\n",
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       "<title>318&#45;&gt;319</title>\n",
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       "<title>322</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"8658,-1301 8535,-1301 8535,-1233 8658,-1233 8658,-1301\"/>\n",
       "<text text-anchor=\"middle\" x=\"8596.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 2.5</text>\n",
       "<text text-anchor=\"middle\" x=\"8596.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.133</text>\n",
       "<text text-anchor=\"middle\" x=\"8596.5\" y=\"-1255.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"8596.5\" y=\"-1240.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 15.265</text>\n",
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       "<title>318&#45;&gt;322</title>\n",
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       "<title>320</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"8343,-1189.5 8250,-1189.5 8250,-1136.5 8343,-1136.5 8343,-1189.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"8296.5\" y=\"-1174.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8296.5\" y=\"-1159.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8296.5\" y=\"-1144.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 14.37</text>\n",
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       "<!-- 319&#45;&gt;320 -->\n",
       "<g id=\"edge320\" class=\"edge\">\n",
       "<title>319&#45;&gt;320</title>\n",
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       "<title>321</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"8454,-1189.5 8361,-1189.5 8361,-1136.5 8454,-1136.5 8454,-1189.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"8407.5\" y=\"-1174.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8407.5\" y=\"-1159.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8407.5\" y=\"-1144.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 13.91</text>\n",
       "</g>\n",
       "<!-- 319&#45;&gt;321 -->\n",
       "<g id=\"edge321\" class=\"edge\">\n",
       "<title>319&#45;&gt;321</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8407.5,-1232.9465C8407.5,-1222.2621 8407.5,-1210.4254 8407.5,-1199.5742\"/>\n",
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       "<title>323</title>\n",
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       "<text text-anchor=\"middle\" x=\"8515.5\" y=\"-1174.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8515.5\" y=\"-1159.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8515.5\" y=\"-1144.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 14.9</text>\n",
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       "<!-- 322&#45;&gt;323 -->\n",
       "<g id=\"edge323\" class=\"edge\">\n",
       "<title>322&#45;&gt;323</title>\n",
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       "<title>324</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"8670,-1189.5 8577,-1189.5 8577,-1136.5 8670,-1136.5 8670,-1189.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"8623.5\" y=\"-1174.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8623.5\" y=\"-1159.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8623.5\" y=\"-1144.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 15.63</text>\n",
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       "<!-- 322&#45;&gt;324 -->\n",
       "<g id=\"edge324\" class=\"edge\">\n",
       "<title>322&#45;&gt;324</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8605.3408,-1232.9465C8608.1433,-1222.1519 8611.251,-1210.1813 8614.0918,-1199.2389\"/>\n",
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       "<title>326</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"8832.5,-1301 8732.5,-1301 8732.5,-1233 8832.5,-1233 8832.5,-1301\"/>\n",
       "<text text-anchor=\"middle\" x=\"8782.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 110.5</text>\n",
       "<text text-anchor=\"middle\" x=\"8782.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 2.857</text>\n",
       "<text text-anchor=\"middle\" x=\"8782.5\" y=\"-1255.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 23</text>\n",
       "<text text-anchor=\"middle\" x=\"8782.5\" y=\"-1240.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.45</text>\n",
       "</g>\n",
       "<!-- 325&#45;&gt;326 -->\n",
       "<g id=\"edge326\" class=\"edge\">\n",
       "<title>325&#45;&gt;326</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8782.5,-1336.9465C8782.5,-1328.776 8782.5,-1319.9318 8782.5,-1311.3697\"/>\n",
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       "<title>371</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"9501.5,-1301 9401.5,-1301 9401.5,-1233 9501.5,-1233 9501.5,-1301\"/>\n",
       "<text text-anchor=\"middle\" x=\"9451.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 63.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9451.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.432</text>\n",
       "<text text-anchor=\"middle\" x=\"9451.5\" y=\"-1255.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 7</text>\n",
       "<text text-anchor=\"middle\" x=\"9451.5\" y=\"-1240.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 12.387</text>\n",
       "</g>\n",
       "<!-- 325&#45;&gt;371 -->\n",
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       "<title>325&#45;&gt;371</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8847.5592,-1360.8862C8977.0651,-1340.7537 9265.434,-1295.9251 9391.059,-1276.3959\"/>\n",
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       "<title>327</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"8822.5,-1197 8688.5,-1197 8688.5,-1129 8822.5,-1129 8822.5,-1197\"/>\n",
       "<text text-anchor=\"middle\" x=\"8755.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 124.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8755.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.822</text>\n",
       "<text text-anchor=\"middle\" x=\"8755.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 11</text>\n",
       "<text text-anchor=\"middle\" x=\"8755.5\" y=\"-1136.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.495</text>\n",
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       "<!-- 326&#45;&gt;327 -->\n",
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       "<title>326&#45;&gt;327</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8773.6592,-1232.9465C8771.5147,-1224.6863 8769.1914,-1215.7374 8766.9458,-1207.0875\"/>\n",
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       "<text text-anchor=\"middle\" x=\"8953.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 13.5</text>\n",
       "<text text-anchor=\"middle\" x=\"8953.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.884</text>\n",
       "<text text-anchor=\"middle\" x=\"8953.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 12</text>\n",
       "<text text-anchor=\"middle\" x=\"8953.5\" y=\"-1136.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.491</text>\n",
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       "<title>326&#45;&gt;348</title>\n",
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       "<text text-anchor=\"middle\" x=\"8480.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.216</text>\n",
       "<text text-anchor=\"middle\" x=\"8480.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 8</text>\n",
       "<text text-anchor=\"middle\" x=\"8480.5\" y=\"-1032.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.936</text>\n",
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       "<title>327&#45;&gt;328</title>\n",
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       "<text text-anchor=\"middle\" x=\"8729.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 9.5</text>\n",
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       "<text text-anchor=\"middle\" x=\"8729.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
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       "<title>327&#45;&gt;343</title>\n",
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       "<text text-anchor=\"middle\" x=\"8352.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 116.0</text>\n",
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       "<text text-anchor=\"middle\" x=\"8263.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 5.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8263.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.3</text>\n",
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       "<text text-anchor=\"middle\" x=\"8144.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 0.5</text>\n",
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       "<title>330&#45;&gt;334</title>\n",
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       "<text text-anchor=\"middle\" x=\"8110.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8110.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.0</text>\n",
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       "<text text-anchor=\"middle\" x=\"8218.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8218.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.26</text>\n",
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       "<!-- 331&#45;&gt;333 -->\n",
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       "<title>331&#45;&gt;333</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8168.7304,-712.9465C8176.7246,-701.7113 8185.6254,-689.2021 8193.6642,-677.9043\"/>\n",
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       "<title>336</title>\n",
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       "<text text-anchor=\"middle\" x=\"8393.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">US_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"8393.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.096</text>\n",
       "<text text-anchor=\"middle\" x=\"8393.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"8393.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 12.3</text>\n",
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       "<!-- 335&#45;&gt;336 -->\n",
       "<g id=\"edge336\" class=\"edge\">\n",
       "<title>335&#45;&gt;336</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8393.5,-816.9465C8393.5,-808.776 8393.5,-799.9318 8393.5,-791.3697\"/>\n",
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       "<title>339</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"8604.5,-781 8498.5,-781 8498.5,-713 8604.5,-713 8604.5,-781\"/>\n",
       "<text text-anchor=\"middle\" x=\"8551.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 76.5</text>\n",
       "<text text-anchor=\"middle\" x=\"8551.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.002</text>\n",
       "<text text-anchor=\"middle\" x=\"8551.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"8551.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.235</text>\n",
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       "<!-- 335&#45;&gt;339 -->\n",
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       "<title>335&#45;&gt;339</title>\n",
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       "<title>337</title>\n",
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       "<!-- 336&#45;&gt;337 -->\n",
       "<g id=\"edge337\" class=\"edge\">\n",
       "<title>336&#45;&gt;337</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8372.544,-712.9465C8365.6978,-701.8215 8358.0829,-689.4473 8351.1843,-678.237\"/>\n",
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       "<title>338</title>\n",
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       "<text text-anchor=\"middle\" x=\"8440.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8440.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 12.61</text>\n",
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       "<!-- 336&#45;&gt;338 -->\n",
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       "<title>336&#45;&gt;338</title>\n",
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       "<title>340</title>\n",
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       "<text text-anchor=\"middle\" x=\"8551.5\" y=\"-654.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8551.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8551.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.19</text>\n",
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       "<!-- 339&#45;&gt;340 -->\n",
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       "<title>339&#45;&gt;340</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8551.5,-712.9465C8551.5,-702.2621 8551.5,-690.4254 8551.5,-679.5742\"/>\n",
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       "<text text-anchor=\"middle\" x=\"8603.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 3.5</text>\n",
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       "<title>344&#45;&gt;345</title>\n",
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       "<text text-anchor=\"middle\" x=\"8619.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8619.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 13.28</text>\n",
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       "<!-- 344&#45;&gt;346 -->\n",
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       "<title>344&#45;&gt;346</title>\n",
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       "<text text-anchor=\"middle\" x=\"8953.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 12.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8953.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.448</text>\n",
       "<text text-anchor=\"middle\" x=\"8953.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
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       "<title>348&#45;&gt;349</title>\n",
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       "<text text-anchor=\"middle\" x=\"9186.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 61.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9186.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.162</text>\n",
       "<text text-anchor=\"middle\" x=\"9186.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 8</text>\n",
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       "<text text-anchor=\"middle\" x=\"8847.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 91.5</text>\n",
       "<text text-anchor=\"middle\" x=\"8847.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.144</text>\n",
       "<text text-anchor=\"middle\" x=\"8847.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<title>349&#45;&gt;350</title>\n",
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       "<title>353</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"9040,-989 8919,-989 8919,-921 9040,-921 9040,-989\"/>\n",
       "<text text-anchor=\"middle\" x=\"8979.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Urban_Yes &lt;= 0.5</text>\n",
       "<text text-anchor=\"middle\" x=\"8979.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.02</text>\n",
       "<text text-anchor=\"middle\" x=\"8979.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<text text-anchor=\"middle\" x=\"8727.5\" y=\"-862.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8727.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8727.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.09</text>\n",
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       "<title>352</title>\n",
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       "<text text-anchor=\"middle\" x=\"8831.5\" y=\"-862.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8831.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8831.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 8.33</text>\n",
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       "<title>350&#45;&gt;352</title>\n",
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       "<title>354</title>\n",
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       "<text text-anchor=\"middle\" x=\"8935.5\" y=\"-862.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"8935.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"8935.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.64</text>\n",
       "</g>\n",
       "<!-- 353&#45;&gt;354 -->\n",
       "<g id=\"edge354\" class=\"edge\">\n",
       "<title>353&#45;&gt;354</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8965.0928,-920.9465C8960.4792,-910.0418 8955.3579,-897.9368 8950.6903,-886.9043\"/>\n",
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       "<title>355</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"9082.5,-877.5 8996.5,-877.5 8996.5,-824.5 9082.5,-824.5 9082.5,-877.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"9039.5\" y=\"-862.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9039.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"9039.5\" y=\"-832.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.36</text>\n",
       "</g>\n",
       "<!-- 353&#45;&gt;355 -->\n",
       "<g id=\"edge355\" class=\"edge\">\n",
       "<title>353&#45;&gt;355</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M8999.1462,-920.9465C9005.5645,-909.8215 9012.7035,-897.4473 9019.171,-886.237\"/>\n",
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       "<title>357</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"9248,-989 9125,-989 9125,-921 9248,-921 9248,-989\"/>\n",
       "<text text-anchor=\"middle\" x=\"9186.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 8.5</text>\n",
       "<text text-anchor=\"middle\" x=\"9186.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.795</text>\n",
       "<text text-anchor=\"middle\" x=\"9186.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 5</text>\n",
       "<text text-anchor=\"middle\" x=\"9186.5\" y=\"-928.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 10.804</text>\n",
       "</g>\n",
       "<!-- 356&#45;&gt;357 -->\n",
       "<g id=\"edge357\" class=\"edge\">\n",
       "<title>356&#45;&gt;357</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M9186.5,-1024.9465C9186.5,-1016.776 9186.5,-1007.9318 9186.5,-999.3697\"/>\n",
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       "<title>366</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"9417,-989 9286,-989 9286,-921 9417,-921 9417,-989\"/>\n",
       "<text text-anchor=\"middle\" x=\"9351.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 375.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9351.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.063</text>\n",
       "<text text-anchor=\"middle\" x=\"9351.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"9351.5\" y=\"-928.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.15</text>\n",
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       "<!-- 356&#45;&gt;366 -->\n",
       "<g id=\"edge366\" class=\"edge\">\n",
       "<title>356&#45;&gt;366</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M9236.902,-1027.2315C9253.2043,-1016.9561 9271.4877,-1005.432 9288.5809,-994.6581\"/>\n",
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       "<title>358</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"9232,-885 9101,-885 9101,-817 9232,-817 9232,-885\"/>\n",
       "<text text-anchor=\"middle\" x=\"9166.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 139.5</text>\n",
       "<text text-anchor=\"middle\" x=\"9166.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.031</text>\n",
       "<text text-anchor=\"middle\" x=\"9166.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"9166.5\" y=\"-824.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.503</text>\n",
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       "<!-- 357&#45;&gt;358 -->\n",
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       "<title>357&#45;&gt;358</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M9179.9513,-920.9465C9178.3627,-912.6863 9176.6418,-903.7374 9174.9784,-895.0875\"/>\n",
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       "<title>363</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"9343,-885 9250,-885 9250,-817 9343,-817 9343,-885\"/>\n",
       "<text text-anchor=\"middle\" x=\"9296.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 48.5</text>\n",
       "<text text-anchor=\"middle\" x=\"9296.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.106</text>\n",
       "<text text-anchor=\"middle\" x=\"9296.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"9296.5\" y=\"-824.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 9.755</text>\n",
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       "<!-- 357&#45;&gt;363 -->\n",
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       "<title>357&#45;&gt;363</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M9222.5181,-920.9465C9232.2046,-911.7884 9242.7864,-901.7838 9252.8397,-892.2788\"/>\n",
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       "<text text-anchor=\"middle\" x=\"9000.5\" y=\"-758.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9000.5\" y=\"-743.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"9000.5\" y=\"-728.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.27</text>\n",
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       "<!-- 358&#45;&gt;359 -->\n",
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       "<title>358&#45;&gt;359</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M9112.1454,-816.9465C9092.6299,-804.72 9070.7063,-790.9847 9051.4871,-778.9437\"/>\n",
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       "<text text-anchor=\"middle\" x=\"9125.5\" y=\"-765.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 15.5</text>\n",
       "<text text-anchor=\"middle\" x=\"9125.5\" y=\"-750.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.006</text>\n",
       "<text text-anchor=\"middle\" x=\"9125.5\" y=\"-735.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"9125.5\" y=\"-720.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.62</text>\n",
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       "<title>358&#45;&gt;360</title>\n",
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       "<text text-anchor=\"middle\" x=\"9071.5\" y=\"-639.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"9071.5\" y=\"-624.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.54</text>\n",
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       "<text text-anchor=\"middle\" x=\"9451.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Age &lt;= 56.5</text>\n",
       "<text text-anchor=\"middle\" x=\"9451.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.159</text>\n",
       "<text text-anchor=\"middle\" x=\"9451.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 5</text>\n",
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       "<text text-anchor=\"middle\" x=\"9624.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">CompPrice &lt;= 123.5</text>\n",
       "<text text-anchor=\"middle\" x=\"9624.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.099</text>\n",
       "<text text-anchor=\"middle\" x=\"9624.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<title>371&#45;&gt;381</title>\n",
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       "<polygon fill=\"none\" stroke=\"#000000\" points=\"9457.5,-1093 9351.5,-1093 9351.5,-1025 9457.5,-1025 9457.5,-1093\"/>\n",
       "<text text-anchor=\"middle\" x=\"9404.5\" y=\"-1077.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Income &lt;= 55.5</text>\n",
       "<text text-anchor=\"middle\" x=\"9404.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.04</text>\n",
       "<text text-anchor=\"middle\" x=\"9404.5\" y=\"-1047.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
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       "<title>372&#45;&gt;373</title>\n",
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       "<text text-anchor=\"middle\" x=\"9522.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<!-- 372&#45;&gt;380 -->\n",
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       "<title>372&#45;&gt;380</title>\n",
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       "<text text-anchor=\"middle\" x=\"9481.5\" y=\"-951.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<title>373&#45;&gt;374</title>\n",
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       "<text text-anchor=\"middle\" x=\"9651.5\" y=\"-973.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Advertising &lt;= 15.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9651.5\" y=\"-958.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.014</text>\n",
       "<text text-anchor=\"middle\" x=\"9651.5\" y=\"-943.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
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       "<text text-anchor=\"middle\" x=\"9651.5\" y=\"-862.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9651.5\" y=\"-847.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<title>375&#45;&gt;376</title>\n",
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       "<title>377</title>\n",
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       "<text text-anchor=\"middle\" x=\"9781.5\" y=\"-869.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 292.5</text>\n",
       "<text text-anchor=\"middle\" x=\"9781.5\" y=\"-854.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.002</text>\n",
       "<text text-anchor=\"middle\" x=\"9781.5\" y=\"-839.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
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       "<title>377&#45;&gt;378</title>\n",
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       "<title>379</title>\n",
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       "<text text-anchor=\"middle\" x=\"9838.5\" y=\"-758.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9838.5\" y=\"-743.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"9838.5\" y=\"-728.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 12.49</text>\n",
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       "<text text-anchor=\"middle\" x=\"9633.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"9633.5\" y=\"-1040.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.22</text>\n",
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       "<text text-anchor=\"middle\" x=\"9744.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"middle\" x=\"9744.5\" y=\"-1040.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 11.85</text>\n",
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       "<text text-anchor=\"middle\" x=\"9811.5\" y=\"-1389.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Education &lt;= 13.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9811.5\" y=\"-1374.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.975</text>\n",
       "<text text-anchor=\"middle\" x=\"9811.5\" y=\"-1359.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 7</text>\n",
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       "<text text-anchor=\"middle\" x=\"9811.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Price &lt;= 143.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9811.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 1.145</text>\n",
       "<text text-anchor=\"middle\" x=\"9811.5\" y=\"-1255.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
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       "<title>392</title>\n",
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       "<text text-anchor=\"middle\" x=\"10004.5\" y=\"-1285.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 127.0</text>\n",
       "<text text-anchor=\"middle\" x=\"10004.5\" y=\"-1270.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.543</text>\n",
       "<text text-anchor=\"middle\" x=\"10004.5\" y=\"-1255.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 4</text>\n",
       "<text text-anchor=\"middle\" x=\"10004.5\" y=\"-1240.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 7.052</text>\n",
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       "<text text-anchor=\"middle\" x=\"9751.5\" y=\"-1174.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
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       "<text text-anchor=\"middle\" x=\"9751.5\" y=\"-1144.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.2</text>\n",
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       "<text text-anchor=\"middle\" x=\"9877.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 195.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9877.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.378</text>\n",
       "<text text-anchor=\"middle\" x=\"9877.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"middle\" x=\"9877.5\" y=\"-1136.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 4.195</text>\n",
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       "<title>389&#45;&gt;390</title>\n",
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       "<text text-anchor=\"middle\" x=\"9973.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = &#45;0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"9973.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"10004.5\" y=\"-1159.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<title>392&#45;&gt;393</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M10004.5,-1232.9465C10004.5,-1222.2621 10004.5,-1210.4254 10004.5,-1199.5742\"/>\n",
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       "<title>394</title>\n",
       "<polygon fill=\"none\" stroke=\"#000000\" points=\"10197,-1197 10066,-1197 10066,-1129 10197,-1129 10197,-1197\"/>\n",
       "<text text-anchor=\"middle\" x=\"10131.5\" y=\"-1181.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Population &lt;= 174.5</text>\n",
       "<text text-anchor=\"middle\" x=\"10131.5\" y=\"-1166.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.149</text>\n",
       "<text text-anchor=\"middle\" x=\"10131.5\" y=\"-1151.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"middle\" x=\"10131.5\" y=\"-1136.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">value = 6.673</text>\n",
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       "<text text-anchor=\"middle\" x=\"10100.5\" y=\"-1070.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
       "<text text-anchor=\"middle\" x=\"10100.5\" y=\"-1055.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
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       "<text text-anchor=\"middle\" x=\"10205.5\" y=\"-1062.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mse = 0.0</text>\n",
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       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.files.Source at 0x1a1a8e0cf8>"
      ]
     },
     "execution_count": 368,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# massive tree. completely unpruned\n",
    "\n",
    "# plot tree\n",
    "\n",
    "export_graphviz(dtr, out_file=\"mytree.dot\", feature_names=X.columns)\n",
    "with open(\"mytree.dot\") as f:\n",
    "    dot_graph = f.read()\n",
    "graphviz.Source(dot_graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 369,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# number of terminal nodes\n",
    "len(np.unique(dtr.apply(X)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(c)** Use cross-validation in order to determine the optimal level of tree complexity. Does pruning the tree improve the test error rate?\n",
    "\n",
    ">Yes, pruning improves test mse from 6.67 to 5.16\n",
    "\n",
    "NOTE: pruning is not available in `sklearn` like the `tree` package in `R`. But you can tweak some paramaters within the package to get something similar. Check out [this issue discussion](https://github.com/scikit-learn/scikit-learn/issues/8399) in the sklearn github. In the below example, we evaluated a number of `max_leaf_nodes` via cross-validation (through GridSearch). From there we are able to find the best model via CV and evaluate on our test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "metadata": {},
   "outputs": [],
   "source": [
    "# examine max_leaf_nodes for CV\n",
    "# pruning not really in sklearn.tree\n",
    "# https://github.com/scikit-learn/scikit-learn/issues/8399\n",
    "\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "# 'max_depth' : range(1, 21) #could use max_depth to prune as well                       \n",
    "\n",
    "dtr_cv = GridSearchCV(DecisionTreeRegressor(random_state=17),\n",
    "                  param_grid={'max_leaf_nodes' : range(2, 51)},\n",
    "                  return_train_score=True)\n",
    "\n",
    "dtr_cv.fit(X_train, y_train)\n",
    "results = dtr_cv.cv_results_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(criterion='mse', max_depth=None, max_features=None,\n",
       "           max_leaf_nodes=12, min_impurity_decrease=0.0,\n",
       "           min_impurity_split=None, min_samples_leaf=1,\n",
       "           min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "           presort=False, random_state=17, splitter='best')"
      ]
     },
     "execution_count": 371,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# best model has max_leaf_nodes=12\n",
    "dtr_cv.best_estimator_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 372,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.163770420742659"
      ]
     },
     "execution_count": 372,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit our best model from CV and get test mse\n",
    "\n",
    "dtr_cv_best = dtr_cv.best_estimator_.fit(X_train, y_train)\n",
    "\n",
    "mean_squared_error(y_test, dtr_cv_best.predict(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 373,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# number of terminal nodes\n",
    "len(np.unique(dtr_cv_best.apply(X)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {},
   "outputs": [
    {
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     },
     "execution_count": 374,
     "metadata": {},
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   ],
   "source": [
    "# plot cv selected tree\n",
    "\n",
    "export_graphviz(dtr_cv_best, out_file=\"mytree.dot\", feature_names=X.columns)\n",
    "with open(\"mytree.dot\") as f:\n",
    "    dot_graph = f.read()\n",
    "graphviz.Source(dot_graph)"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(d)** Use the bagging approach in order to analyze this data. What test error rate do you obtain? Use the `importance()` function to determine which variables are most important."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 383,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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     "execution_count": 383,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "bag_reg = BaggingRegressor(random_state=17).fit(X_train, y_train)\n",
    "\n",
    "mean_squared_error(y_test, bag_reg.predict(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Price               0.379421\n",
       "ShelveLoc_Good      0.211286\n",
       "CompPrice           0.110055\n",
       "Age                 0.061230\n",
       "Advertising         0.055010\n",
       "ShelveLoc_Medium    0.049553\n",
       "Population          0.042714\n",
       "Income              0.039262\n",
       "Education           0.033377\n",
       "Urban_Yes           0.014380\n",
       "US_Yes              0.003711\n",
       "dtype: float64"
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     },
     "execution_count": 388,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "feature_imp = np.mean([tree.feature_importances_ for tree in bag_reg.estimators_], axis=0)\n",
    "    \n",
    "pd.Series(feature_imp, X_train.columns).sort_values(ascending=False)"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(e)** Use random forests to analyze this data. What test error rate do you obtain? Use the `importance()` function to determine which variables are most important. Describe the effect of $m$, the number of variables considered at each split, on the error rate obtained.\n",
    "\n",
    ">Limiting the number of $m$ in random forests (where m=sqrt(p)) improves on the test error relative to bagging (m=p). This is because random forest split consideration allows the aggregated trees to be more decorrelated from each other, compared to bagging. Selecting a smaller number of predictors on which to split leads to less variance and therefore (typically) smaller test mse."
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  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 396,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "rf = RandomForestRegressor(random_state=1).fit(X_train, y_train)\n",
    "\n",
    "mean_squared_error(y_test, rf.predict(X_test))"
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  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Price               0.329167\n",
       "ShelveLoc_Good      0.230911\n",
       "CompPrice           0.125805\n",
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       "Population          0.049253\n",
       "ShelveLoc_Medium    0.036232\n",
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       "dtype: float64"
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     "execution_count": 397,
     "metadata": {},
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   "source": [
    "pd.Series(rf.feature_importances_, X.columns).sort_values(ascending=False)"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**9.** This problem involves the OJ data set which is part of the ISLR package.\n",
    "\n",
    "**(a)** Create a training set containing a random sample of 800 observations, and a test set containing the remaining observations."
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  },
  {
   "cell_type": "code",
   "execution_count": 519,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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       "      <td>0.091398</td>\n",
       "      <td>0.23</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>MM</td>\n",
       "      <td>227</td>\n",
       "      <td>1</td>\n",
       "      <td>1.69</td>\n",
       "      <td>1.69</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.400000</td>\n",
       "      <td>1.69</td>\n",
       "      <td>1.69</td>\n",
       "      <td>0.00</td>\n",
       "      <td>No</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>CH</td>\n",
       "      <td>228</td>\n",
       "      <td>7</td>\n",
       "      <td>1.69</td>\n",
       "      <td>1.69</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.956535</td>\n",
       "      <td>1.69</td>\n",
       "      <td>1.69</td>\n",
       "      <td>0.00</td>\n",
       "      <td>Yes</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Purchase  WeekofPurchase  StoreID  PriceCH  PriceMM  DiscCH  DiscMM  \\\n",
       "0       CH             237        1     1.75     1.99    0.00     0.0   \n",
       "1       CH             239        1     1.75     1.99    0.00     0.3   \n",
       "2       CH             245        1     1.86     2.09    0.17     0.0   \n",
       "3       MM             227        1     1.69     1.69    0.00     0.0   \n",
       "4       CH             228        7     1.69     1.69    0.00     0.0   \n",
       "\n",
       "   SpecialCH  SpecialMM   LoyalCH  SalePriceMM  SalePriceCH  PriceDiff Store7  \\\n",
       "0          0          0  0.500000         1.99         1.75       0.24     No   \n",
       "1          0          1  0.600000         1.69         1.75      -0.06     No   \n",
       "2          0          0  0.680000         2.09         1.69       0.40     No   \n",
       "3          0          0  0.400000         1.69         1.69       0.00     No   \n",
       "4          0          0  0.956535         1.69         1.69       0.00    Yes   \n",
       "\n",
       "   PctDiscMM  PctDiscCH  ListPriceDiff  STORE  \n",
       "0   0.000000   0.000000           0.24      1  \n",
       "1   0.150754   0.000000           0.24      1  \n",
       "2   0.000000   0.091398           0.23      1  \n",
       "3   0.000000   0.000000           0.00      1  \n",
       "4   0.000000   0.000000           0.00      0  "
      ]
     },
     "execution_count": 519,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"https://vincentarelbundock.github.io/Rdatasets/csv/ISLR/OJ.csv\").drop('Unnamed: 0', axis=1)\n",
    "print(df.shape)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 520,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Purchase</th>\n",
       "      <th>Store7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1070</td>\n",
       "      <td>1070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>CH</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>653</td>\n",
       "      <td>714</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Purchase Store7\n",
       "count      1070   1070\n",
       "unique        2      2\n",
       "top          CH     No\n",
       "freq        653    714"
      ]
     },
     "execution_count": 520,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check for categoricals\n",
    "df.describe(include='object')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 521,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 1070 entries, 0 to 1069\n",
      "Data columns (total 17 columns):\n",
      "WeekofPurchase    1070 non-null float64\n",
      "StoreID           1070 non-null float64\n",
      "PriceCH           1070 non-null float64\n",
      "PriceMM           1070 non-null float64\n",
      "DiscCH            1070 non-null float64\n",
      "DiscMM            1070 non-null float64\n",
      "SpecialCH         1070 non-null float64\n",
      "SpecialMM         1070 non-null float64\n",
      "LoyalCH           1070 non-null float64\n",
      "SalePriceMM       1070 non-null float64\n",
      "SalePriceCH       1070 non-null float64\n",
      "PriceDiff         1070 non-null float64\n",
      "PctDiscMM         1070 non-null float64\n",
      "PctDiscCH         1070 non-null float64\n",
      "ListPriceDiff     1070 non-null float64\n",
      "STORE             1070 non-null float64\n",
      "Store7_Yes        1070 non-null float64\n",
      "dtypes: float64(17)\n",
      "memory usage: 142.2 KB\n"
     ]
    },
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>WeekofPurchase</th>\n",
       "      <th>StoreID</th>\n",
       "      <th>PriceCH</th>\n",
       "      <th>PriceMM</th>\n",
       "      <th>DiscCH</th>\n",
       "      <th>DiscMM</th>\n",
       "      <th>SpecialCH</th>\n",
       "      <th>SpecialMM</th>\n",
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       "      <th>SalePriceMM</th>\n",
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       "      <th>PriceDiff</th>\n",
       "      <th>PctDiscMM</th>\n",
       "      <th>PctDiscCH</th>\n",
       "      <th>ListPriceDiff</th>\n",
       "      <th>STORE</th>\n",
       "      <th>Purchase_MM</th>\n",
       "      <th>Store7_Yes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>237</td>\n",
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       "      <td>227</td>\n",
       "      <td>1</td>\n",
       "      <td>1.69</td>\n",
       "      <td>1.69</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.400000</td>\n",
       "      <td>1.69</td>\n",
       "      <td>1.69</td>\n",
       "      <td>0.00</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>228</td>\n",
       "      <td>7</td>\n",
       "      <td>1.69</td>\n",
       "      <td>1.69</td>\n",
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      ],
      "text/plain": [
       "   WeekofPurchase  StoreID  PriceCH  PriceMM  DiscCH  DiscMM  SpecialCH  \\\n",
       "0             237        1     1.75     1.99    0.00     0.0          0   \n",
       "1             239        1     1.75     1.99    0.00     0.3          0   \n",
       "2             245        1     1.86     2.09    0.17     0.0          0   \n",
       "3             227        1     1.69     1.69    0.00     0.0          0   \n",
       "4             228        7     1.69     1.69    0.00     0.0          0   \n",
       "\n",
       "   SpecialMM   LoyalCH  SalePriceMM  SalePriceCH  PriceDiff  PctDiscMM  \\\n",
       "0          0  0.500000         1.99         1.75       0.24   0.000000   \n",
       "1          1  0.600000         1.69         1.75      -0.06   0.150754   \n",
       "2          0  0.680000         2.09         1.69       0.40   0.000000   \n",
       "3          0  0.400000         1.69         1.69       0.00   0.000000   \n",
       "4          0  0.956535         1.69         1.69       0.00   0.000000   \n",
       "\n",
       "   PctDiscCH  ListPriceDiff  STORE  Purchase_MM  Store7_Yes  \n",
       "0   0.000000           0.24      1            0           0  \n",
       "1   0.000000           0.24      1            0           0  \n",
       "2   0.091398           0.23      1            0           0  \n",
       "3   0.000000           0.00      1            1           0  \n",
       "4   0.000000           0.00      0            0           1  "
      ]
     },
     "execution_count": 521,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get dummies\n",
    "df = pd.get_dummies(df, drop_first=True)\n",
    "\n",
    "\n",
    "X = df.drop(['Purchase_MM'], axis=1).astype('float64')\n",
    "y = df.Purchase_MM\n",
    "\n",
    "X.info()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 522,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(800, 17)\n",
      "(800,)\n",
      "(270, 17)\n",
      "(270,)\n"
     ]
    }
   ],
   "source": [
    "# split data into 800 train obs. remaining as test obs\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=len(X)-800, random_state=17)\n",
    "\n",
    "# confirm shapes\n",
    "print(X_train.shape)\n",
    "print(y_train.shape)\n",
    "print(X_test.shape)\n",
    "print(y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(b)** Fit a tree to the training data, with `Purchase` as the response and the other variables as predictors. Use the `summary()` function to produce summary statistics about the tree, and describe the results obtained. What is the training error rate? How many terminal nodes does the tree have?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 523,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 523,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# I selected max_depth and max_leaf_nodes to match the R output\n",
    "# this is bc there is no pruning in sklearn trees\n",
    "\n",
    "dtc = DecisionTreeClassifier(random_state=17,\n",
    "                            max_depth=4,\n",
    "                            max_leaf_nodes=7).fit(X_train, y_train)\n",
    "\n",
    "# number of terminal nodes\n",
    "len(np.unique(dtc.apply(X)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 524,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of terminal nodes: 7\n",
      "Error rate (misclassification): 0.15625 = 125 / 800\n",
      "Accuracy: 0.84375\n"
     ]
    },
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Actual</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Predicted</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>431</td>\n",
       "      <td>66</td>\n",
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       "      <th>1</th>\n",
       "      <td>59</td>\n",
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       "      <td>303</td>\n",
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       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>490</td>\n",
       "      <td>310</td>\n",
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      "text/plain": [
       "Actual       0    1  All\n",
       "Predicted               \n",
       "0          431   66  497\n",
       "1           59  244  303\n",
       "All        490  310  800"
      ]
     },
     "execution_count": 524,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# evaluated on the training data\n",
    "\n",
    "conf_matrix = pd.crosstab(dtc.predict(X_train), y_train, rownames=['Predicted'],\n",
    "           colnames=['Actual'], margins=True)\n",
    "\n",
    "TN = conf_matrix.iloc[0][0]\n",
    "TP = conf_matrix.iloc[1][1]\n",
    "FN = conf_matrix.iloc[0][1]\n",
    "FP = conf_matrix.iloc[1][0]\n",
    "ALL = conf_matrix.iloc[2][2]\n",
    "accuracy = (TP+TN)/ALL\n",
    "error_rate = (FP+FN)/ALL\n",
    "terminal_nodes = len(np.unique(dtc.apply(X)))\n",
    "\n",
    "print(\"Number of terminal nodes: \" + str(terminal_nodes))\n",
    "print(\"Error rate (misclassification): \" + str(error_rate) + \n",
    "     \" = \" + str(FP+FN) + \" / \" + str(ALL))\n",
    "print(\"Accuracy: \" + str(accuracy))\n",
    "conf_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(c)** Type in the name of the tree object in order to get a detailed text output. Pick one of the terminal nodes, and interpret the information displayed.\n",
    "\n",
    ">Come back to this one. Command not as easily available in Python as in R. See pg.325 in ISLR for how to do it in R."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(d)** Create a plot of the tree, and interpret the results.\n",
    "\n",
    ">Brand loyalty and price difference are the most imporant predictors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "metadata": {},
   "outputs": [
    {
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       "<text text-anchor=\"middle\" x=\"229.5\" y=\"-245.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">PriceDiff &lt;= 0.195</text>\n",
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       "<text text-anchor=\"middle\" x=\"381.5\" y=\"-245.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">ListPriceDiff &lt;= 0.235</text>\n",
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      "text/plain": [
       "<graphviz.files.Source at 0x1179199b0>"
      ]
     },
     "execution_count": 434,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "export_graphviz(dtc, out_file=\"mytree.dot\", feature_names=X.columns)\n",
    "with open(\"mytree.dot\") as f:\n",
    "    dot_graph = f.read()\n",
    "graphviz.Source(dot_graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(e)** Predict the response on the test data, and produce a confusion matrix comparing the test labels to the predicted test labels. What is the test error rate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 525,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of terminal nodes: 7\n",
      "Error rate (misclassification): 0.23333333333333334 = 63 / 270\n",
      "Accuracy: 0.7666666666666667\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th>Actual</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Predicted</th>\n",
       "      <th></th>\n",
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       "      <td>135</td>\n",
       "      <td>35</td>\n",
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      "text/plain": [
       "Actual       0    1  All\n",
       "Predicted               \n",
       "0          135   35  170\n",
       "1           28   72  100\n",
       "All        163  107  270"
      ]
     },
     "execution_count": 525,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# evaluated on the test data\n",
    "\n",
    "conf_matrix = pd.crosstab(dtc.predict(X_test), y_test, rownames=['Predicted'],\n",
    "           colnames=['Actual'], margins=True)\n",
    "\n",
    "TN = conf_matrix.iloc[0][0]\n",
    "TP = conf_matrix.iloc[1][1]\n",
    "FN = conf_matrix.iloc[0][1]\n",
    "FP = conf_matrix.iloc[1][0]\n",
    "ALL = conf_matrix.iloc[2][2]\n",
    "accuracy = (TP+TN)/ALL\n",
    "error_rate = (FP+FN)/ALL\n",
    "terminal_nodes = len(np.unique(dtc.apply(X)))\n",
    "\n",
    "print(\"Number of terminal nodes: \" + str(terminal_nodes))\n",
    "print(\"Error rate (misclassification): \" + str(error_rate) + \n",
    "     \" = \" + str(FP+FN) + \" / \" + str(ALL))\n",
    "print(\"Accuracy: \" + str(accuracy))\n",
    "conf_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(f)** Apply the `cv.tree()` function to the training set in order to determine the optimal tree size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 526,
   "metadata": {},
   "outputs": [],
   "source": [
    "dtc_cv = GridSearchCV(DecisionTreeClassifier(random_state=17),\n",
    "                  param_grid={'max_leaf_nodes' : range(2, 51),\n",
    "                             'max_depth': range(2, 51)},\n",
    "                  return_train_score=True)\n",
    "\n",
    "dtc_cv.fit(X_train, y_train)\n",
    "results = dtr_cv.cv_results_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 527,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=4,\n",
       "            max_features=None, max_leaf_nodes=9, min_impurity_decrease=0.0,\n",
       "            min_impurity_split=None, min_samples_leaf=1,\n",
       "            min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "            presort=False, random_state=17, splitter='best')"
      ]
     },
     "execution_count": 527,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dtc_cv.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(g)** Produce a plot with tree size on the x-axis and cross-validated classification error rate on the y-axis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Evaluated using CV**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 528,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "err_rate_cv = OrderedDict()\n",
    "\n",
    "for i in range(2, 150):\n",
    "    dtc_b = DecisionTreeClassifier(random_state=17,\n",
    "                              max_leaf_nodes=i).fit(X_train, y_train)\n",
    "    err_rate_cv[i] = 1-cross_val_score(dtc_b, X_train, y_train, cv=10).mean() # cv misclassification rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 530,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "plt.plot(*zip(*sorted(err_rate_cv.items())))\n",
    "plt.xlabel('Number of Trees')\n",
    "plt.ylabel('CV misclassification rate')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(h)** Which tree size corresponds to the lowest cross-validated classification error rate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 534,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 534,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# number of trees with lowest CV error rate\n",
    "min(err_rate_cv, key=err_rate_cv.get)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Evaluated using test set**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 531,
   "metadata": {},
   "outputs": [],
   "source": [
    "err_rate = OrderedDict()\n",
    "\n",
    "for i in range(2, 300):\n",
    "    dtc_b = DecisionTreeClassifier(random_state=17,\n",
    "                              max_leaf_nodes=i).fit(X_train, y_train)\n",
    "    err_rate[i] = 1-dtc_b.score(X_test, y_test) # test misclassification rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 532,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "plt.plot(*zip(*sorted(err_rate.items())))\n",
    "plt.xlabel('Number of Trees')\n",
    "plt.ylabel('Test misclassification rate')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 533,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 533,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# number of trees with lowest test error rate\n",
    "min(err_rate, key=err_rate.get)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(i)** Produce a pruned tree corresponding to the optimal tree size obtained using cross-validation. If cross-validation does not lead to selection of a pruned tree, then create a pruned tree with five terminal nodes.\n",
    "\n",
    ">in `sklearn.tree.DecisionTreeClassifier` the parameter `max_leaf_nodes` equals terminal nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 535,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=4,\n",
       "            max_features=None, max_leaf_nodes=9, min_impurity_decrease=0.0,\n",
       "            min_impurity_split=None, min_samples_leaf=1,\n",
       "            min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "            presort=False, random_state=17, splitter='best')"
      ]
     },
     "execution_count": 535,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# model summary\n",
    "\n",
    "dtc_cv.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(j)** Compare the training error rates between the pruned and unpruned trees. Which is higher?\n",
    "\n",
    ">Slightly better training error rate. **0.1487** for pruned and **0.1562** for unpruned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 536,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of terminal nodes: 9\n",
      "Error rate (misclassification): 0.14875 = 119 / 800\n",
      "Accuracy: 0.85125\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Actual</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Predicted</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>454</td>\n",
       "      <td>83</td>\n",
       "      <td>537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>36</td>\n",
       "      <td>227</td>\n",
       "      <td>263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>490</td>\n",
       "      <td>310</td>\n",
       "      <td>800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Actual       0    1  All\n",
       "Predicted               \n",
       "0          454   83  537\n",
       "1           36  227  263\n",
       "All        490  310  800"
      ]
     },
     "execution_count": 536,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# best (pruned) model on the training data\n",
    "\n",
    "conf_matrix = pd.crosstab(dtc_cv.best_estimator_.predict(X_train), y_train, rownames=['Predicted'],\n",
    "           colnames=['Actual'], margins=True)\n",
    "\n",
    "TN = conf_matrix.iloc[0][0]\n",
    "TP = conf_matrix.iloc[1][1]\n",
    "FN = conf_matrix.iloc[0][1]\n",
    "FP = conf_matrix.iloc[1][0]\n",
    "ALL = conf_matrix.iloc[2][2]\n",
    "accuracy = (TP+TN)/ALL\n",
    "error_rate = (FP+FN)/ALL\n",
    "terminal_nodes = len(np.unique(dtc_cv.best_estimator_.apply(X)))\n",
    "\n",
    "print(\"Number of terminal nodes: \" + str(terminal_nodes))\n",
    "print(\"Error rate (misclassification): \" + str(error_rate) + \n",
    "     \" = \" + str(FP+FN) + \" / \" + str(ALL))\n",
    "print(\"Accuracy: \" + str(accuracy))\n",
    "conf_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(k)** Compare the test error rates between the pruned and unpruned trees. Which is higher?\n",
    "\n",
    ">Pruned model performed better on test data. **0.1963** for pruned and **0.2333** for unpruned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 537,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of terminal nodes: 9\n",
      "Error rate (misclassification): 0.1962962962962963 = 53 / 270\n",
      "Accuracy: 0.8037037037037037\n"
     ]
    },
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Actual</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Predicted</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>147</td>\n",
       "      <td>37</td>\n",
       "      <td>184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>16</td>\n",
       "      <td>70</td>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>163</td>\n",
       "      <td>107</td>\n",
       "      <td>270</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Actual       0    1  All\n",
       "Predicted               \n",
       "0          147   37  184\n",
       "1           16   70   86\n",
       "All        163  107  270"
      ]
     },
     "execution_count": 537,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# best (pruned) model on the test data\n",
    "\n",
    "conf_matrix = pd.crosstab(dtc_cv.best_estimator_.predict(X_test), y_test, rownames=['Predicted'],\n",
    "           colnames=['Actual'], margins=True)\n",
    "\n",
    "TN = conf_matrix.iloc[0][0]\n",
    "TP = conf_matrix.iloc[1][1]\n",
    "FN = conf_matrix.iloc[0][1]\n",
    "FP = conf_matrix.iloc[1][0]\n",
    "ALL = conf_matrix.iloc[2][2]\n",
    "accuracy = (TP+TN)/ALL\n",
    "error_rate = (FP+FN)/ALL\n",
    "terminal_nodes = len(np.unique(dtc_cv.best_estimator_.apply(X)))\n",
    "\n",
    "print(\"Number of terminal nodes: \" + str(terminal_nodes))\n",
    "print(\"Error rate (misclassification): \" + str(error_rate) + \n",
    "     \" = \" + str(FP+FN) + \" / \" + str(ALL))\n",
    "print(\"Accuracy: \" + str(accuracy))\n",
    "conf_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**10.** We now use boosting to predict `Salary` in the `Hitters` data set.\n",
    "\n",
    "**(a)** Remove the observations for whom the salary information is unknown, and then log-transform the salaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 556,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of dataframe: (263, 20)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AtBat</th>\n",
       "      <th>Hits</th>\n",
       "      <th>HmRun</th>\n",
       "      <th>Runs</th>\n",
       "      <th>RBI</th>\n",
       "      <th>Walks</th>\n",
       "      <th>Years</th>\n",
       "      <th>CAtBat</th>\n",
       "      <th>CHits</th>\n",
       "      <th>CHmRun</th>\n",
       "      <th>CRuns</th>\n",
       "      <th>CRBI</th>\n",
       "      <th>CWalks</th>\n",
       "      <th>League</th>\n",
       "      <th>Division</th>\n",
       "      <th>PutOuts</th>\n",
       "      <th>Assists</th>\n",
       "      <th>Errors</th>\n",
       "      <th>Salary</th>\n",
       "      <th>NewLeague</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Player</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-Alan Ashby</th>\n",
       "      <td>315</td>\n",
       "      <td>81</td>\n",
       "      <td>7</td>\n",
       "      <td>24</td>\n",
       "      <td>38</td>\n",
       "      <td>39</td>\n",
       "      <td>14</td>\n",
       "      <td>3449</td>\n",
       "      <td>835</td>\n",
       "      <td>69</td>\n",
       "      <td>321</td>\n",
       "      <td>414</td>\n",
       "      <td>375</td>\n",
       "      <td>N</td>\n",
       "      <td>W</td>\n",
       "      <td>632</td>\n",
       "      <td>43</td>\n",
       "      <td>10</td>\n",
       "      <td>475.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alvin Davis</th>\n",
       "      <td>479</td>\n",
       "      <td>130</td>\n",
       "      <td>18</td>\n",
       "      <td>66</td>\n",
       "      <td>72</td>\n",
       "      <td>76</td>\n",
       "      <td>3</td>\n",
       "      <td>1624</td>\n",
       "      <td>457</td>\n",
       "      <td>63</td>\n",
       "      <td>224</td>\n",
       "      <td>266</td>\n",
       "      <td>263</td>\n",
       "      <td>A</td>\n",
       "      <td>W</td>\n",
       "      <td>880</td>\n",
       "      <td>82</td>\n",
       "      <td>14</td>\n",
       "      <td>480.0</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andre Dawson</th>\n",
       "      <td>496</td>\n",
       "      <td>141</td>\n",
       "      <td>20</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>37</td>\n",
       "      <td>11</td>\n",
       "      <td>5628</td>\n",
       "      <td>1575</td>\n",
       "      <td>225</td>\n",
       "      <td>828</td>\n",
       "      <td>838</td>\n",
       "      <td>354</td>\n",
       "      <td>N</td>\n",
       "      <td>E</td>\n",
       "      <td>200</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>500.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andres Galarraga</th>\n",
       "      <td>321</td>\n",
       "      <td>87</td>\n",
       "      <td>10</td>\n",
       "      <td>39</td>\n",
       "      <td>42</td>\n",
       "      <td>30</td>\n",
       "      <td>2</td>\n",
       "      <td>396</td>\n",
       "      <td>101</td>\n",
       "      <td>12</td>\n",
       "      <td>48</td>\n",
       "      <td>46</td>\n",
       "      <td>33</td>\n",
       "      <td>N</td>\n",
       "      <td>E</td>\n",
       "      <td>805</td>\n",
       "      <td>40</td>\n",
       "      <td>4</td>\n",
       "      <td>91.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alfredo Griffin</th>\n",
       "      <td>594</td>\n",
       "      <td>169</td>\n",
       "      <td>4</td>\n",
       "      <td>74</td>\n",
       "      <td>51</td>\n",
       "      <td>35</td>\n",
       "      <td>11</td>\n",
       "      <td>4408</td>\n",
       "      <td>1133</td>\n",
       "      <td>19</td>\n",
       "      <td>501</td>\n",
       "      <td>336</td>\n",
       "      <td>194</td>\n",
       "      <td>A</td>\n",
       "      <td>W</td>\n",
       "      <td>282</td>\n",
       "      <td>421</td>\n",
       "      <td>25</td>\n",
       "      <td>750.0</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   AtBat  Hits  HmRun  Runs  RBI  Walks  Years  CAtBat  CHits  \\\n",
       "Player                                                                          \n",
       "-Alan Ashby          315    81      7    24   38     39     14    3449    835   \n",
       "-Alvin Davis         479   130     18    66   72     76      3    1624    457   \n",
       "-Andre Dawson        496   141     20    65   78     37     11    5628   1575   \n",
       "-Andres Galarraga    321    87     10    39   42     30      2     396    101   \n",
       "-Alfredo Griffin     594   169      4    74   51     35     11    4408   1133   \n",
       "\n",
       "                   CHmRun  CRuns  CRBI  CWalks League Division  PutOuts  \\\n",
       "Player                                                                    \n",
       "-Alan Ashby            69    321   414     375      N        W      632   \n",
       "-Alvin Davis           63    224   266     263      A        W      880   \n",
       "-Andre Dawson         225    828   838     354      N        E      200   \n",
       "-Andres Galarraga      12     48    46      33      N        E      805   \n",
       "-Alfredo Griffin       19    501   336     194      A        W      282   \n",
       "\n",
       "                   Assists  Errors  Salary NewLeague  \n",
       "Player                                                \n",
       "-Alan Ashby             43      10   475.0         N  \n",
       "-Alvin Davis            82      14   480.0         A  \n",
       "-Andre Dawson           11       3   500.0         N  \n",
       "-Andres Galarraga       40       4    91.5         N  \n",
       "-Alfredo Griffin       421      25   750.0         A  "
      ]
     },
     "execution_count": 556,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/ISLR/Hitters.csv', index_col=0).dropna()\n",
    "df.index.name = 'Player'\n",
    "print(\"Shape of dataframe: \" + str(df.shape))\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 558,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AtBat</th>\n",
       "      <th>Hits</th>\n",
       "      <th>HmRun</th>\n",
       "      <th>Runs</th>\n",
       "      <th>RBI</th>\n",
       "      <th>Walks</th>\n",
       "      <th>Years</th>\n",
       "      <th>CAtBat</th>\n",
       "      <th>CHits</th>\n",
       "      <th>CHmRun</th>\n",
       "      <th>CRuns</th>\n",
       "      <th>CRBI</th>\n",
       "      <th>CWalks</th>\n",
       "      <th>League</th>\n",
       "      <th>Division</th>\n",
       "      <th>PutOuts</th>\n",
       "      <th>Assists</th>\n",
       "      <th>Errors</th>\n",
       "      <th>Salary</th>\n",
       "      <th>NewLeague</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Player</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-Alan Ashby</th>\n",
       "      <td>315</td>\n",
       "      <td>81</td>\n",
       "      <td>7</td>\n",
       "      <td>24</td>\n",
       "      <td>38</td>\n",
       "      <td>39</td>\n",
       "      <td>14</td>\n",
       "      <td>3449</td>\n",
       "      <td>835</td>\n",
       "      <td>69</td>\n",
       "      <td>321</td>\n",
       "      <td>414</td>\n",
       "      <td>375</td>\n",
       "      <td>N</td>\n",
       "      <td>W</td>\n",
       "      <td>632</td>\n",
       "      <td>43</td>\n",
       "      <td>10</td>\n",
       "      <td>6.163315</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alvin Davis</th>\n",
       "      <td>479</td>\n",
       "      <td>130</td>\n",
       "      <td>18</td>\n",
       "      <td>66</td>\n",
       "      <td>72</td>\n",
       "      <td>76</td>\n",
       "      <td>3</td>\n",
       "      <td>1624</td>\n",
       "      <td>457</td>\n",
       "      <td>63</td>\n",
       "      <td>224</td>\n",
       "      <td>266</td>\n",
       "      <td>263</td>\n",
       "      <td>A</td>\n",
       "      <td>W</td>\n",
       "      <td>880</td>\n",
       "      <td>82</td>\n",
       "      <td>14</td>\n",
       "      <td>6.173786</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andre Dawson</th>\n",
       "      <td>496</td>\n",
       "      <td>141</td>\n",
       "      <td>20</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>37</td>\n",
       "      <td>11</td>\n",
       "      <td>5628</td>\n",
       "      <td>1575</td>\n",
       "      <td>225</td>\n",
       "      <td>828</td>\n",
       "      <td>838</td>\n",
       "      <td>354</td>\n",
       "      <td>N</td>\n",
       "      <td>E</td>\n",
       "      <td>200</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>6.214608</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andres Galarraga</th>\n",
       "      <td>321</td>\n",
       "      <td>87</td>\n",
       "      <td>10</td>\n",
       "      <td>39</td>\n",
       "      <td>42</td>\n",
       "      <td>30</td>\n",
       "      <td>2</td>\n",
       "      <td>396</td>\n",
       "      <td>101</td>\n",
       "      <td>12</td>\n",
       "      <td>48</td>\n",
       "      <td>46</td>\n",
       "      <td>33</td>\n",
       "      <td>N</td>\n",
       "      <td>E</td>\n",
       "      <td>805</td>\n",
       "      <td>40</td>\n",
       "      <td>4</td>\n",
       "      <td>4.516339</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alfredo Griffin</th>\n",
       "      <td>594</td>\n",
       "      <td>169</td>\n",
       "      <td>4</td>\n",
       "      <td>74</td>\n",
       "      <td>51</td>\n",
       "      <td>35</td>\n",
       "      <td>11</td>\n",
       "      <td>4408</td>\n",
       "      <td>1133</td>\n",
       "      <td>19</td>\n",
       "      <td>501</td>\n",
       "      <td>336</td>\n",
       "      <td>194</td>\n",
       "      <td>A</td>\n",
       "      <td>W</td>\n",
       "      <td>282</td>\n",
       "      <td>421</td>\n",
       "      <td>25</td>\n",
       "      <td>6.620073</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   AtBat  Hits  HmRun  Runs  RBI  Walks  Years  CAtBat  CHits  \\\n",
       "Player                                                                          \n",
       "-Alan Ashby          315    81      7    24   38     39     14    3449    835   \n",
       "-Alvin Davis         479   130     18    66   72     76      3    1624    457   \n",
       "-Andre Dawson        496   141     20    65   78     37     11    5628   1575   \n",
       "-Andres Galarraga    321    87     10    39   42     30      2     396    101   \n",
       "-Alfredo Griffin     594   169      4    74   51     35     11    4408   1133   \n",
       "\n",
       "                   CHmRun  CRuns  CRBI  CWalks League Division  PutOuts  \\\n",
       "Player                                                                    \n",
       "-Alan Ashby            69    321   414     375      N        W      632   \n",
       "-Alvin Davis           63    224   266     263      A        W      880   \n",
       "-Andre Dawson         225    828   838     354      N        E      200   \n",
       "-Andres Galarraga      12     48    46      33      N        E      805   \n",
       "-Alfredo Griffin       19    501   336     194      A        W      282   \n",
       "\n",
       "                   Assists  Errors    Salary NewLeague  \n",
       "Player                                                  \n",
       "-Alan Ashby             43      10  6.163315         N  \n",
       "-Alvin Davis            82      14  6.173786         A  \n",
       "-Andre Dawson           11       3  6.214608         N  \n",
       "-Andres Galarraga       40       4  4.516339         N  \n",
       "-Alfredo Griffin       421      25  6.620073         A  "
      ]
     },
     "execution_count": 558,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# log salary\n",
    "\n",
    "df['Salary'] = np.log(df.Salary)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(b)** Create a training set consisting of the first 200 observations, and a test set consisting of the remaining observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 559,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 263 entries, -Alan Ashby to -Willie Wilson\n",
      "Data columns (total 19 columns):\n",
      "AtBat          263 non-null float64\n",
      "Hits           263 non-null float64\n",
      "HmRun          263 non-null float64\n",
      "Runs           263 non-null float64\n",
      "RBI            263 non-null float64\n",
      "Walks          263 non-null float64\n",
      "Years          263 non-null float64\n",
      "CAtBat         263 non-null float64\n",
      "CHits          263 non-null float64\n",
      "CHmRun         263 non-null float64\n",
      "CRuns          263 non-null float64\n",
      "CRBI           263 non-null float64\n",
      "CWalks         263 non-null float64\n",
      "PutOuts        263 non-null float64\n",
      "Assists        263 non-null float64\n",
      "Errors         263 non-null float64\n",
      "League_N       263 non-null float64\n",
      "Division_W     263 non-null float64\n",
      "NewLeague_N    263 non-null float64\n",
      "dtypes: float64(19)\n",
      "memory usage: 41.1+ KB\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
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       "      <th>Hits</th>\n",
       "      <th>HmRun</th>\n",
       "      <th>Runs</th>\n",
       "      <th>RBI</th>\n",
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       "      <th>PutOuts</th>\n",
       "      <th>Assists</th>\n",
       "      <th>Errors</th>\n",
       "      <th>Salary</th>\n",
       "      <th>League_N</th>\n",
       "      <th>Division_W</th>\n",
       "      <th>NewLeague_N</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Player</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-Alan Ashby</th>\n",
       "      <td>315</td>\n",
       "      <td>81</td>\n",
       "      <td>7</td>\n",
       "      <td>24</td>\n",
       "      <td>38</td>\n",
       "      <td>39</td>\n",
       "      <td>14</td>\n",
       "      <td>3449</td>\n",
       "      <td>835</td>\n",
       "      <td>69</td>\n",
       "      <td>321</td>\n",
       "      <td>414</td>\n",
       "      <td>375</td>\n",
       "      <td>632</td>\n",
       "      <td>43</td>\n",
       "      <td>10</td>\n",
       "      <td>6.163315</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alvin Davis</th>\n",
       "      <td>479</td>\n",
       "      <td>130</td>\n",
       "      <td>18</td>\n",
       "      <td>66</td>\n",
       "      <td>72</td>\n",
       "      <td>76</td>\n",
       "      <td>3</td>\n",
       "      <td>1624</td>\n",
       "      <td>457</td>\n",
       "      <td>63</td>\n",
       "      <td>224</td>\n",
       "      <td>266</td>\n",
       "      <td>263</td>\n",
       "      <td>880</td>\n",
       "      <td>82</td>\n",
       "      <td>14</td>\n",
       "      <td>6.173786</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andre Dawson</th>\n",
       "      <td>496</td>\n",
       "      <td>141</td>\n",
       "      <td>20</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>37</td>\n",
       "      <td>11</td>\n",
       "      <td>5628</td>\n",
       "      <td>1575</td>\n",
       "      <td>225</td>\n",
       "      <td>828</td>\n",
       "      <td>838</td>\n",
       "      <td>354</td>\n",
       "      <td>200</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>6.214608</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Andres Galarraga</th>\n",
       "      <td>321</td>\n",
       "      <td>87</td>\n",
       "      <td>10</td>\n",
       "      <td>39</td>\n",
       "      <td>42</td>\n",
       "      <td>30</td>\n",
       "      <td>2</td>\n",
       "      <td>396</td>\n",
       "      <td>101</td>\n",
       "      <td>12</td>\n",
       "      <td>48</td>\n",
       "      <td>46</td>\n",
       "      <td>33</td>\n",
       "      <td>805</td>\n",
       "      <td>40</td>\n",
       "      <td>4</td>\n",
       "      <td>4.516339</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-Alfredo Griffin</th>\n",
       "      <td>594</td>\n",
       "      <td>169</td>\n",
       "      <td>4</td>\n",
       "      <td>74</td>\n",
       "      <td>51</td>\n",
       "      <td>35</td>\n",
       "      <td>11</td>\n",
       "      <td>4408</td>\n",
       "      <td>1133</td>\n",
       "      <td>19</td>\n",
       "      <td>501</td>\n",
       "      <td>336</td>\n",
       "      <td>194</td>\n",
       "      <td>282</td>\n",
       "      <td>421</td>\n",
       "      <td>25</td>\n",
       "      <td>6.620073</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   AtBat  Hits  HmRun  Runs  RBI  Walks  Years  CAtBat  CHits  \\\n",
       "Player                                                                          \n",
       "-Alan Ashby          315    81      7    24   38     39     14    3449    835   \n",
       "-Alvin Davis         479   130     18    66   72     76      3    1624    457   \n",
       "-Andre Dawson        496   141     20    65   78     37     11    5628   1575   \n",
       "-Andres Galarraga    321    87     10    39   42     30      2     396    101   \n",
       "-Alfredo Griffin     594   169      4    74   51     35     11    4408   1133   \n",
       "\n",
       "                   CHmRun  CRuns  CRBI  CWalks  PutOuts  Assists  Errors  \\\n",
       "Player                                                                     \n",
       "-Alan Ashby            69    321   414     375      632       43      10   \n",
       "-Alvin Davis           63    224   266     263      880       82      14   \n",
       "-Andre Dawson         225    828   838     354      200       11       3   \n",
       "-Andres Galarraga      12     48    46      33      805       40       4   \n",
       "-Alfredo Griffin       19    501   336     194      282      421      25   \n",
       "\n",
       "                     Salary  League_N  Division_W  NewLeague_N  \n",
       "Player                                                          \n",
       "-Alan Ashby        6.163315         1           1            1  \n",
       "-Alvin Davis       6.173786         0           1            0  \n",
       "-Andre Dawson      6.214608         1           0            1  \n",
       "-Andres Galarraga  4.516339         1           0            1  \n",
       "-Alfredo Griffin   6.620073         0           1            0  "
      ]
     },
     "execution_count": 559,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# first we've got to get dummies for our categorical variables\n",
    "\n",
    "# get dummies\n",
    "df = pd.get_dummies(df, drop_first=True)\n",
    "\n",
    "\n",
    "X = df.drop(['Salary'], axis=1).astype('float64')\n",
    "y = df.Salary\n",
    "\n",
    "X.info()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 560,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 19)\n",
      "(200,)\n",
      "(63, 19)\n",
      "(63,)\n"
     ]
    }
   ],
   "source": [
    "# next\n",
    "# split data into 200 train obs. remaining as test obs\n",
    "# here, we take random sample. not first 200 (ordinal)\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=len(X)-200, random_state=17)\n",
    "\n",
    "# confirm shapes\n",
    "print(X_train.shape)\n",
    "print(y_train.shape)\n",
    "print(X_test.shape)\n",
    "print(y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(c)** Perform boosting on the training set with 1,000 trees for a range of values of the shrinkage parameter λ. Produce a plot with different shrinkage values on the x-axis and the corresponding training set MSE on the y-axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 599,
   "metadata": {},
   "outputs": [],
   "source": [
    "err_rate_gbr = OrderedDict()\n",
    "\n",
    "for i in np.linspace(10e-10, 0.5, 100):\n",
    "    gbrv = GradientBoostingRegressor(learning_rate=i,\n",
    "                                random_state=17,\n",
    "                                n_estimators=1000).fit(X_train, y_train)\n",
    "    err_rate_gbr[i] = mean_squared_error(y_train, gbrv.predict(X_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 600,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WsizPwXHfq2BmNk3SJbAjYiews2ffNYXX70/5+WWWuKZgZlapn2UujivdmoJPH5mZTdO4UGhnnimYmVVpXChkrXzIvvrIzGy6xoWC71MwM6vW2FAYn/TVR2ZmvZoXCq4pmJlValwouKZgZlatcaHgmoKZWbXGhUJxlVQzM3u2xoXCksw3r5mZVWlcKEzVFHz6yMxsusaFQttLZ5uZVWpcKGTdQrNrCmZmvRoXCp4pmJlVa14odJ6n4EKzmdl0zQsFzxTMzCo1LhRcUzAzq5Y0FCStl7RP0oikK0vev0LSXkl3SfpbSWek7A94pmBmVidZKEjKgG3ARcBa4BJJa3ua/RAYjIhXADcCH07VnymZl7kwM6uUcqawDhiJiP0RcQjYAWwsNoiIWyPiV53N24EVCfsDQLtz89q4C81mZtOkDIXlwIHC9mhnX5XLgJvL3pC0WdKwpOGxsbE5derI0tmuKZiZ9UoZCirZV/rruaQ/AgaBj5S9HxHbI2IwIgYHBgbm1KnMNQUzs0rthMceBVYWtlcAB3sbSboA+BBwXkQ8k7A/QGHpbJ8+MjObJuVMYTewRtJqSUuBTcBQsYGkc4DPABsi4uGEfenyTMHMrFqyUIiICWALsAu4B7ghIvZI2ippQ6fZR4CTgS9JulPSUMXhjhlJZC356iMzsxIpTx8RETuBnT37rim8viDl51dpt8S4C81mZtM07o5myEPBNQUzs+kaGQpZS64pmJmVaGQotLOWawpmZiUaGQqeKZiZlWtkKCxpiYlJF5rNzHo1MhSyzJekmpmVaWQotFstnz4yMyvRyFDwzWtmZuUaGQrtlpjwzWtmZtM0MxQyMeGb18zMpmlkKGSuKZiZlWpkKLRdUzAzK9XIUMhcUzAzK9XIUPBMwcysXCNDwctcmJmVa2QoLMlavvrIzKxE0lCQtF7SPkkjkq4sef8Nkn4gaULSxSn7UuSZgplZuWShICkDtgEXAWuBSySt7Wn2U+BS4PpU/SiT1xRcaDYz65XycZzrgJGI2A8gaQewEdg71SAi7uu8N68/oT1TMDMrl/L00XLgQGF7tLNvwfnqIzOzcilDQSX7ZvWTWNJmScOShsfGxubYrfzJay40m5lNlzIURoGVhe0VwMHZHCgitkfEYEQMDgwMzLljXhDPzKxcylDYDayRtFrSUmATMJTw8/rmpbPNzMolC4WImAC2ALuAe4AbImKPpK2SNgBIeo2kUeD3gc9I2pOqP0VtF5rNzEqlvPqIiNgJ7OzZd03h9W7y00rzKmu1mHRNwcxsmobe0SzGXVMwM5umkaHgmoKZWblGhoJrCmZm5RoZClmrRQQcdjCYmT1LI0OhneX31Xm2YGb2bM0MhdZUKLjYbGZW1MhQyFqeKZiZlWlkKEzNFHyvgpnZszUyFLIsH7ZnCmZmz9bIUJiaKRyadE3BzKyokaHw0l9/AQC3/PjBBe6JmdlzSyND4ZzTX8S61f+Ez/7dfg5NeLZgZjalkaEA8CdvPIufPf40X77zgYXuipnZc0ZjQ+G8swdY+5JT+PQ37/U6SGZmHY0NBUm8941nsX/sSb62x7UFMzNocCgAXPTyX+eM057Pp267lwjPFszMkoaCpPWS9kkakXRlyfsnSPpi5/07JK1K2Z9e7azFe887i7sfeJx3fW6YBx9/ej4/3szsOSdZKEjKgG3ARcBa4BJJa3uaXQY8FhG/AXwM+K+p+lPl7YMrufqtv8l37v05F370m3zhjvt5enxyvrthZvacoFSnTSS9Drg2In6ns30VQET8eaHNrk6b70pqAw8CA1HTqcHBwRgeHj7m/b3/kSe56v/czf+79xFOXNLidWeexnlnD3DmwMm8+JQTefEpJ3DyCW3aWaPPuJnZIiXp+xExOFO7lM9oXg4cKGyPAudWtYmICUmPA6cBP0/Yr1JnnHYSX3jXuXzrJz/n1r9/mNv2Pcyt+8amtVuSiRPbGUvaLVoSWQsyiVZLZC3RUn63tLr/OaK4KfW8WdLGzKzo8vPX8LZX/tOkn5EyFMp+vvXOAPppg6TNwGaA008/fe49qyCJ884e4LyzB4CX8cAvnuLgL57iwcef5qEnnuZXhyZ5anySpw5NMnk4mDgcHD4cTMaRPyPyAfROdqJyo7jbxW4zq3bq85Yk/4yUoTAKrCxsrwAOVrQZ7Zw+OhV4tPdAEbEd2A756aMkvS2x/IXPY/kLnzdfH2dmtuBSniDfDayRtFrSUmATMNTTZgh4Z+f1xcA36uoJZmaWVrKZQqdGsAXYBWTAdRGxR9JWYDgihoC/Aj4vaYR8hrApVX/MzGxmKU8fERE7gZ09+64pvH4a+P2UfTAzs/75+kozM+tyKJiZWZdDwczMuhwKZmbW5VAwM7OuZGsfpSJpDLh/ln99GQuwhMYC85ibwWNuhrmM+YyIGJip0aILhbmQNNzPglDHE4+5GTzmZpiPMfv0kZmZdTkUzMysq2mhsH2hO7AAPOZm8JibIfmYG1VTMDOzek2bKZiZWY3jMhQkrZe0T9KIpCtL3j9B0hc7798hadX89/LY6mPMb5D0A0kTki5eiD4ea32M+QpJeyXdJelvJZ2xEP08lvoY83sk3S3pTknfLnku+qIz05gL7S6WFJIW9RVJfXyPL5U01vke3ynpXce0AxFxXH2RL9N9L3AmsBT4EbC2p82fAJ/uvN4EfHGh+z0PY14FvAL4n8DFC93neRrzm4Dnd16/tyHf51MKrzcAtyx0v1OPudPuBcC3gNuBwYXud+Lv8aXAJ1P14XicKawDRiJif0QcAnYAG3vabAQ+13l9I3C+qh6avDjMOOaIuC8i7gIOL0QHE+hnzLdGxK86m7eTP/1vMetnzE8UNk+i8uGvi0Y//z8D/BnwYeDp+excAv2ON5njMRSWAwcK26OdfaVtImICeBw4bV56l0Y/Yz7eHO2YLwNuTtqj9Poas6T3SbqX/Ifk5fPUt1RmHLOkc4CVEfHV+exYIv3+u/69zmnRGyWtLHl/1o7HUCj7jb/3t6V+2iwmx9t4+tH3mCX9ETAIfCRpj9Lra8wRsS0izgL+A3B18l6lVTtmSS3gY8AH5q1HafXzPf4KsCoiXgF8nSNnPY6J4zEURoFicq4ADla1kdQGTiV/HOhi1c+Yjzd9jVnSBcCHgA0R8cw89S2Vo/0+7wB+N2mP0ptpzC8AXg7cJuk+4LXA0CIuNs/4PY6IRwr/lv8SePWx7MDxGAq7gTWSVktaSl5IHuppMwS8s/P6YuAb0angLFL9jPl4M+OYO6cVPkMeCA8vQB+PtX7GvKaw+VbgJ/PYvxRqxxwRj0fEsohYFRGryGtHGyJieGG6O2f9fI9fUtjcANxzTHuw0NX2RBX8twD/QF7F/1Bn31byfywAJwJfAkaA7wFnLnSf52HMryH/LeRJ4BFgz0L3eR7G/HXgIeDOztfQQvd5Hsb8cWBPZ7y3Ai9b6D6nHnNP29tYxFcf9fk9/vPO9/hHne/xS4/l5/uOZjMz6zoeTx+ZmdksORTMzKzLoWBmZl0OBTMz63IomJlZl0PBGk3SLxMc8z5Jyxbis83myqFgZmZd7YXugNlzjaS3ka8ZtJT8Rr8/jIiHJF0LrAZeApwNXEG+rMJFwAPA2yJivHOYD0p6U+f1H0TEiKTVwPXk/9/dUvi8k4GbgBcBS4CrI+KmtKM0K+eZgtl03wZeGxHnkK8f9O8L751FvnzERuB/AbdGxG8BT3X2T3kiItYBnwT+W2ffx4H/HhGvAR4stH0a+FcR8SryZ0D8xSJfyt0WMYeC2XQrgF2S7gY+CLys8N7NndnA3eQPRJn6jf9u8gcZTfmbwp+v67x+fWH/5wttBfxnSXeRL82xHHjxMRmJ2VFyKJhN9wnyJ1v9FvBvyNfKmvIMQEQcBsbjyDoxh3n26djo4/WUPwQGgFdHxD8nX6/pxJJ2Zsk5FMymO5W8RgBHVtM9Wu8o/PndzuvvkK96CXkQFD/v4YgY79QhFv2zpG3xcqHZmu75kkYL2x8FrgW+JOkB8qWYV8/iuCdIuoP8F69LOvveD1wv6f3A/y60/QLwFUnD5Kub/v0sPs/smPAqqWZm1uXTR2Zm1uVQMDOzLoeCmZl1ORTMzKzLoWBmZl0OBTMz63IomJlZl0PBzMy6/j80RmNEjNx+xQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot\n",
    "plt.plot(*zip(*sorted(err_rate_gbr.items())))\n",
    "plt.xlabel('Lambda')\n",
    "plt.ylabel('Train MSE')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(d)** Produce a plot with different shrinkage values on the x-axis and the corresponding test set MSE on the y-axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 602,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "err_rate_gbr_t = OrderedDict()\n",
    "\n",
    "for i in np.linspace(10e-10, 0.5, 100):\n",
    "    gbrv_t = GradientBoostingRegressor(learning_rate=i,\n",
    "                                random_state=17,\n",
    "                                n_estimators=1000).fit(X_train, y_train)\n",
    "    # use test sets here\n",
    "    err_rate_gbr_t[i] = mean_squared_error(y_test, gbrv_t.predict(X_test))\n",
    "    \n",
    "# plot\n",
    "plt.plot(*zip(*sorted(err_rate_gbr_t.items())))\n",
    "plt.xlabel('Lambda')\n",
    "plt.ylabel('Train MSE')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 604,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.373737373989899, 0.11730132633933925)\n"
     ]
    }
   ],
   "source": [
    "# minimum test error is 0.117\n",
    "print(min(err_rate_gbr_t.items(), key=lambda x: x[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(e)** Compare the test MSE of boosting to the test MSE that results from applying two of the regression approaches seen in Chapters 3 and 6.\n",
    "\n",
    ">Both LR and LR+lasso have worse test MSE than our Gradient Boosting Regressor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 606,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3627832254546815"
      ]
     },
     "execution_count": 606,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plain 'ol linear regression\n",
    "\n",
    "lr = LinearRegression().fit(X_train, y_train)\n",
    "\n",
    "mean_squared_error(y_test, lr.predict(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 610,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4252851493261184"
      ]
     },
     "execution_count": 610,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# linear reg with lasso\n",
    "\n",
    "lr_las = Lasso(alpha=1).fit(X_train, y_train)\n",
    "\n",
    "mean_squared_error(y_test, lr_las.predict(X_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(f)** Which variables appear to be the most important predictors in the boosted model?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 616,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's GridSearchCV api to get our best model from a search of lambdas\n",
    "\n",
    "gbr_cv = GridSearchCV(GradientBoostingRegressor(random_state=17,\n",
    "                                                max_depth=4,\n",
    "                                                n_estimators=1000),\n",
    "                    param_grid={'learning_rate' : np.linspace(10e-10, 0.5, 100)},\n",
    "                  return_train_score=True)\n",
    "\n",
    "gbr_cv.fit(X_train, y_train)\n",
    "results = gbr_cv.cv_results_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 617,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,\n",
       "             learning_rate=0.21212121269696968, loss='ls', max_depth=4,\n",
       "             max_features=None, max_leaf_nodes=None,\n",
       "             min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "             min_samples_leaf=1, min_samples_split=2,\n",
       "             min_weight_fraction_leaf=0.0, n_estimators=1000,\n",
       "             presort='auto', random_state=17, subsample=1.0, verbose=0,\n",
       "             warm_start=False)"
      ]
     },
     "execution_count": 617,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# model summary\n",
    "\n",
    "gbr_cv.best_estimator_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 623,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1515630218079566"
      ]
     },
     "execution_count": 623,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test MSE from or best model select via CV\n",
    "\n",
    "mean_squared_error(y_test, gbr_cv.best_estimator_.predict(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 618,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RBI            0.017449\n",
       "CWalks         0.016170\n",
       "Assists        0.016013\n",
       "CHmRun         0.015508\n",
       "CRuns          0.014853\n",
       "PutOuts        0.014363\n",
       "Hits           0.012883\n",
       "AtBat          0.012269\n",
       "CHits          0.011898\n",
       "Walks          0.011270\n",
       "Runs           0.011179\n",
       "CAtBat         0.010984\n",
       "HmRun          0.009821\n",
       "Errors         0.009600\n",
       "CRBI           0.009552\n",
       "Years          0.008430\n",
       "Division_W     0.001172\n",
       "League_N       0.000882\n",
       "NewLeague_N    0.000702\n",
       "dtype: float64"
      ]
     },
     "execution_count": 618,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(gbr_cv.best_estimator_.feature_importances_, X.columns).sort_values(ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 620,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# variable importance plotted\n",
    "\n",
    "Importance = pd.DataFrame({'Importance':gbr_cv.best_estimator_.feature_importances_*100}, index=X.columns)\n",
    "Importance.sort_values('Importance', axis=0, ascending=True).plot(kind='barh', color='r', )\n",
    "plt.xlabel('Variable Importance')\n",
    "plt.gca().legend_ = None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(g)** Now apply bagging to the training set. What is the test set MSE for this approach?\n",
    "\n",
    ">The test MSE is slightly worse than Boosting, but better than both LR and LR+lasso."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 622,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1579178149785341"
      ]
     },
     "execution_count": 622,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bag_reg = BaggingRegressor(random_state=17,\n",
    "                           max_features=13).fit(X_train, y_train)\n",
    "\n",
    "mean_squared_error(y_test, bag_reg.predict(X_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**11.** This question uses the `Caravan` data set.\n",
    "\n",
    "**(a)** Create a training set consisting of the first 1,000 observations,\n",
    "and a test set consisting of the remaining observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 781,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of df: (5822, 86)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MOSTYPE</th>\n",
       "      <th>MAANTHUI</th>\n",
       "      <th>MGEMOMV</th>\n",
       "      <th>MGEMLEEF</th>\n",
       "      <th>MOSHOOFD</th>\n",
       "      <th>MGODRK</th>\n",
       "      <th>MGODPR</th>\n",
       "      <th>MGODOV</th>\n",
       "      <th>MGODGE</th>\n",
       "      <th>MRELGE</th>\n",
       "      <th>...</th>\n",
       "      <th>APERSONG</th>\n",
       "      <th>AGEZONG</th>\n",
       "      <th>AWAOREG</th>\n",
       "      <th>ABRAND</th>\n",
       "      <th>AZEILPL</th>\n",
       "      <th>APLEZIER</th>\n",
       "      <th>AFIETS</th>\n",
       "      <th>AINBOED</th>\n",
       "      <th>ABYSTAND</th>\n",
       "      <th>Purchase_Yes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>33</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>37</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>37</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>40</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 86 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   MOSTYPE  MAANTHUI  MGEMOMV  MGEMLEEF  MOSHOOFD  MGODRK  MGODPR  MGODOV  \\\n",
       "1       33         1        3         2         8       0       5       1   \n",
       "2       37         1        2         2         8       1       4       1   \n",
       "3       37         1        2         2         8       0       4       2   \n",
       "4        9         1        3         3         3       2       3       2   \n",
       "5       40         1        4         2        10       1       4       1   \n",
       "\n",
       "   MGODGE  MRELGE      ...       APERSONG  AGEZONG  AWAOREG  ABRAND  AZEILPL  \\\n",
       "1       3       7      ...              0        0        0       1        0   \n",
       "2       4       6      ...              0        0        0       1        0   \n",
       "3       4       3      ...              0        0        0       1        0   \n",
       "4       4       5      ...              0        0        0       1        0   \n",
       "5       4       7      ...              0        0        0       1        0   \n",
       "\n",
       "   APLEZIER  AFIETS  AINBOED  ABYSTAND  Purchase_Yes  \n",
       "1         0       0        0         0             0  \n",
       "2         0       0        0         0             0  \n",
       "3         0       0        0         0             0  \n",
       "4         0       0        0         0             0  \n",
       "5         0       0        0         0             0  \n",
       "\n",
       "[5 rows x 86 columns]"
      ]
     },
     "execution_count": 781,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"https://vincentarelbundock.github.io/Rdatasets/csv/ISLR/Caravan.csv\", index_col=0)#.drop('Unnamed: 0', axis=1)\n",
    "# convert our categorical\n",
    "df = pd.get_dummies(df, drop_first=True)\n",
    "print(\"Shape of df: \" + str(df.shape))\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, were are not taking a random sample to create our test and train sets. But, rather, as directed in the question, we are taking the first 1000 rows as our train set and the remainder as our test set. Normally we would use `sklearn.train_test_split` or `pd.sample` to get sampled train and test sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 782,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 86)\n",
      "(4822, 86)\n"
     ]
    }
   ],
   "source": [
    "train = df.iloc[:1000,:]\n",
    "test = df.drop(train.index)\n",
    "\n",
    "print(train.shape)\n",
    "print(test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 783,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 85)\n",
      "(1000,)\n",
      "(4822, 85)\n",
      "(4822,)\n"
     ]
    }
   ],
   "source": [
    "X_train = train.drop(['Purchase_Yes'], axis=1).astype('float64')\n",
    "y_train = train.Purchase_Yes\n",
    "X_test = test.drop(['Purchase_Yes'], axis=1).astype('float64')\n",
    "y_test = test.Purchase_Yes\n",
    "\n",
    "print(X_train.shape)\n",
    "print(y_train.shape)\n",
    "print(X_test.shape)\n",
    "print(y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(b)** Fit a boosting model to the training set with `Purchase` as the response and the other variables as predictors. Use 1,000 trees, and a shrinkage value of 0.01. Which predictors appear to be the most important?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 784,
   "metadata": {},
   "outputs": [],
   "source": [
    "gbc = GradientBoostingClassifier(random_state=17,\n",
    "                                n_estimators=1000,\n",
    "                                learning_rate=0.01).fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 785,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MOSTYPE     7.461566e+00\n",
       "MGODGE      4.558420e+00\n",
       "PPERSAUT    4.245581e+00\n",
       "ABRAND      4.062608e+00\n",
       "MKOOPKLA    4.039378e+00\n",
       "MOPLHOOG    3.996630e+00\n",
       "PLEVEN      3.670544e+00\n",
       "PWAPART     3.273668e+00\n",
       "MBERARBG    3.047556e+00\n",
       "AMOTSCO     3.007705e+00\n",
       "MSKB1       2.945327e+00\n",
       "PGEZONG     2.464978e+00\n",
       "PBRAND      2.410583e+00\n",
       "MGODPR      2.182047e+00\n",
       "MBERMIDD    2.161161e+00\n",
       "MINKM30     1.884654e+00\n",
       "MSKA        1.872444e+00\n",
       "MINK3045    1.784942e+00\n",
       "PPLEZIER    1.760985e+00\n",
       "MFGEKIND    1.745220e+00\n",
       "MFWEKIND    1.731099e+00\n",
       "MOSHOOFD    1.728677e+00\n",
       "PBYSTAND    1.682273e+00\n",
       "MRELGE      1.677448e+00\n",
       "MGODRK      1.651958e+00\n",
       "MFALLEEN    1.623035e+00\n",
       "AFIETS      1.446264e+00\n",
       "MINK7512    1.442373e+00\n",
       "APLEZIER    1.431756e+00\n",
       "MZFONDS     1.239791e+00\n",
       "                ...     \n",
       "MGEMLEEF    3.478810e-01\n",
       "PZEILPL     3.205353e-01\n",
       "ALEVEN      2.979555e-01\n",
       "MOPLLAAG    2.887450e-01\n",
       "PWALAND     2.539706e-01\n",
       "AGEZONG     2.351313e-01\n",
       "AZEILPL     2.218867e-01\n",
       "AWALAND     2.128371e-01\n",
       "MAUT0       2.088694e-01\n",
       "MAANTHUI    1.598815e-01\n",
       "ATRACTOR    8.909764e-02\n",
       "PTRACTOR    4.992124e-02\n",
       "MINK123M    3.416377e-02\n",
       "PFIETS      3.023469e-02\n",
       "PWABEDR     2.090577e-02\n",
       "AINBOED     1.608680e-03\n",
       "AAANHANG    1.311129e-03\n",
       "PINBOED     9.670966e-04\n",
       "PAANHANG    6.226732e-04\n",
       "ABESAUT     5.704675e-05\n",
       "PBESAUT     2.256031e-07\n",
       "ABROM       0.000000e+00\n",
       "APERSONG    0.000000e+00\n",
       "PWERKT      0.000000e+00\n",
       "PVRAAUT     0.000000e+00\n",
       "AWERKT      0.000000e+00\n",
       "PBROM       0.000000e+00\n",
       "AWABEDR     0.000000e+00\n",
       "PPERSONG    0.000000e+00\n",
       "AVRAAUT     0.000000e+00\n",
       "Length: 85, dtype: float64"
      ]
     },
     "execution_count": 785,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(gbc.feature_importances_*100, X_train.columns).sort_values(ascending=False)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 787,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# variable importance plotted\n",
    "\n",
    "Importance = pd.DataFrame({'Importance':gbc.feature_importances_*100}, index=X_train.columns)\n",
    "Importance.sort_values('Importance', axis=0, ascending=True).plot(kind='barh', color='b', )\n",
    "plt.rcParams['figure.figsize'] = [10, 10]\n",
    "plt.xlabel('Variable Importance')\n",
    "plt.gca().legend_ = None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(c)** Use the boosting model to predict the response on the test data. Predict that a person will make a purchase if the estimated probability of purchase is greater than 20%. Form a confusion matrix. What fraction of the people predicted to make a purchase do in fact make one? How does this compare with the results obtained from applying KNN or logistic regression to this data set?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 788,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, ..., 0, 0, 0])"
      ]
     },
     "execution_count": 788,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get 0's and 1's prediction based on threshold\n",
    "\n",
    "np.where(gbc.predict_proba(X_test)[:,1] > 0.2, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 789,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get our predictions to be loaded for our cofusion matrix\n",
    "\n",
    "pred = np.where(gbc.predict_proba(X_test)[:,1] > 0.2, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 790,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error rate (misclassification): 0.09332227291580257 = 450 / 4822\n",
      "Accuracy: 0.9066777270841975\n",
      "Recall: 0.1314878892733564\n",
      "Precision: 0.16033755274261605\n",
      "F1 score: 0.1444866920152091\n"
     ]
    },
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Actual</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Predicted</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4334</td>\n",
       "      <td>251</td>\n",
       "      <td>4585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>199</td>\n",
       "      <td>38</td>\n",
       "      <td>237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>4533</td>\n",
       "      <td>289</td>\n",
       "      <td>4822</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Actual        0    1   All\n",
       "Predicted                 \n",
       "0          4334  251  4585\n",
       "1           199   38   237\n",
       "All        4533  289  4822"
      ]
     },
     "execution_count": 790,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# confusion matrix with 20% treshold\n",
    "\n",
    "conf_matrix = pd.crosstab(pred, y_test, rownames=['Predicted'],\n",
    "           colnames=['Actual'], margins=True)\n",
    "\n",
    "TN = conf_matrix.iloc[0][0]\n",
    "TP = conf_matrix.iloc[1][1]\n",
    "FN = conf_matrix.iloc[0][1]\n",
    "FP = conf_matrix.iloc[1][0]\n",
    "ALL = conf_matrix.iloc[2][2]\n",
    "accuracy = (TP+TN)/ALL\n",
    "error_rate = (FP+FN)/ALL\n",
    "recall = TP/(TP+FN)\n",
    "precision = TP/(TP+FP)\n",
    "f1 = 2*(precision*recall)/(precision+recall)\n",
    "\n",
    "print(\"Error rate (misclassification): \" + str(error_rate) + \n",
    "     \" = \" + str(FP+FN) + \" / \" + str(ALL))\n",
    "print(\"Accuracy: \" + str(accuracy))\n",
    "print(\"Recall: \" + str(recall))\n",
    "print(\"Precision: \" + str(precision))\n",
    "print(\"F1 score: \" + str(f1))\n",
    "conf_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What fraction of the people predicted to make a purchase do in fact make one?\n",
    "\n",
    "This metric is also known as recall, sensitivity or True Positive Rate (TPR). And is calculated by TP/(TP+FN).\n",
    "\n",
    "Of all those that were positive, what % did your model capture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 791,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.148788927335639 of people predicted to make a purchase in fact do make one.\n"
     ]
    }
   ],
   "source": [
    "print(str(conf_matrix.iloc[1][1]/conf_matrix.iloc[2][1]*100) + \n",
    "     \" of people predicted to make a purchase in fact do make one.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How does this compare with the results obtained from applying KNN or logistic regression to this data set?\n",
    "\n",
    ">Recall = 17% for logistic regression. This is not as good as our Boosting classifier recall of 13%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 792,
   "metadata": {},
   "outputs": [],
   "source": [
    "# logistic regression\n",
    "\n",
    "logr = LogisticRegression(random_state=17).fit(X_train, y_train)\n",
    "\n",
    "pred = np.where(logr.predict_proba(X_test)[:,1] > 0.2, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 793,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error rate (misclassification): 0.09850684363334716 = 475 / 4822\n",
      "Accuracy: 0.9014931563666528\n",
      "Recall: 0.17301038062283736\n",
      "Precision: 0.17482517482517482\n",
      "F1 score: 0.17391304347826086\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Actual</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Predicted</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4297</td>\n",
       "      <td>239</td>\n",
       "      <td>4536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>236</td>\n",
       "      <td>50</td>\n",
       "      <td>286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>4533</td>\n",
       "      <td>289</td>\n",
       "      <td>4822</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Actual        0    1   All\n",
       "Predicted                 \n",
       "0          4297  239  4536\n",
       "1           236   50   286\n",
       "All        4533  289  4822"
      ]
     },
     "execution_count": 793,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# logistic regression confusion matrix with 20% treshold\n",
    "\n",
    "conf_matrix = pd.crosstab(pred, y_test, rownames=['Predicted'],\n",
    "           colnames=['Actual'], margins=True)\n",
    "\n",
    "TN = conf_matrix.iloc[0][0]\n",
    "TP = conf_matrix.iloc[1][1]\n",
    "FN = conf_matrix.iloc[0][1]\n",
    "FP = conf_matrix.iloc[1][0]\n",
    "ALL = conf_matrix.iloc[2][2]\n",
    "accuracy = (TP+TN)/ALL\n",
    "error_rate = (FP+FN)/ALL\n",
    "recall = TP/(TP+FN)\n",
    "precision = TP/(TP+FP)\n",
    "f1 = 2*(precision*recall)/(precision+recall)\n",
    "\n",
    "print(\"Error rate (misclassification): \" + str(error_rate) + \n",
    "     \" = \" + str(FP+FN) + \" / \" + str(ALL))\n",
    "print(\"Accuracy: \" + str(accuracy))\n",
    "print(\"Recall: \" + str(recall))\n",
    "print(\"Precision: \" + str(precision))\n",
    "print(\"F1 score: \" + str(f1))\n",
    "conf_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**12.** Apply boosting, bagging, and random forests to a data set of your choice. Be sure to fit the models on a training set and to evaluate their performance on a test set. How accurate are the results compared to simple methods like linear or logistic regression? Which of these approaches yields the best performance?\n",
    "\n",
    ">We will use the `Smarket` data to predict and build a classifier of wether the market will be up or down.\n",
    "\n",
    ">Using misclassification rate as your metric the order is as follows:\n",
    "1. Boosting: 42.49 = 133 / 313\n",
    "2. Random Forest: 46.96 = 147 / 313\n",
    "3. Bagging: 49.20 = 154 / 313\n",
    "4. Logistic Regression: 51.11 = 160 / 313"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 794,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Lag1</th>\n",
       "      <th>Lag2</th>\n",
       "      <th>Lag3</th>\n",
       "      <th>Lag4</th>\n",
       "      <th>Lag5</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Today</th>\n",
       "      <th>Direction_Up</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2001</td>\n",
       "      <td>0.381</td>\n",
       "      <td>-0.192</td>\n",
       "      <td>-2.624</td>\n",
       "      <td>-1.055</td>\n",
       "      <td>5.010</td>\n",
       "      <td>1.1913</td>\n",
       "      <td>0.959</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2001</td>\n",
       "      <td>0.959</td>\n",
       "      <td>0.381</td>\n",
       "      <td>-0.192</td>\n",
       "      <td>-2.624</td>\n",
       "      <td>-1.055</td>\n",
       "      <td>1.2965</td>\n",
       "      <td>1.032</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2001</td>\n",
       "      <td>1.032</td>\n",
       "      <td>0.959</td>\n",
       "      <td>0.381</td>\n",
       "      <td>-0.192</td>\n",
       "      <td>-2.624</td>\n",
       "      <td>1.4112</td>\n",
       "      <td>-0.623</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2001</td>\n",
       "      <td>-0.623</td>\n",
       "      <td>1.032</td>\n",
       "      <td>0.959</td>\n",
       "      <td>0.381</td>\n",
       "      <td>-0.192</td>\n",
       "      <td>1.2760</td>\n",
       "      <td>0.614</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2001</td>\n",
       "      <td>0.614</td>\n",
       "      <td>-0.623</td>\n",
       "      <td>1.032</td>\n",
       "      <td>0.959</td>\n",
       "      <td>0.381</td>\n",
       "      <td>1.2057</td>\n",
       "      <td>0.213</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Year   Lag1   Lag2   Lag3   Lag4   Lag5  Volume  Today  Direction_Up\n",
       "1  2001  0.381 -0.192 -2.624 -1.055  5.010  1.1913  0.959             1\n",
       "2  2001  0.959  0.381 -0.192 -2.624 -1.055  1.2965  1.032             1\n",
       "3  2001  1.032  0.959  0.381 -0.192 -2.624  1.4112 -0.623             0\n",
       "4  2001 -0.623  1.032  0.959  0.381 -0.192  1.2760  0.614             1\n",
       "5  2001  0.614 -0.623  1.032  0.959  0.381  1.2057  0.213             1"
      ]
     },
     "execution_count": 794,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"https://vincentarelbundock.github.io/Rdatasets/csv/ISLR/Smarket.csv\", index_col=0)\n",
    "# get dummies\n",
    "df = pd.get_dummies(df, drop_first=True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 795,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.drop(['Direction_Up', 'Year', 'Today'], axis=1).astype('float64')\n",
    "y = df.Direction_Up\n",
    "\n",
    "# split data into train and test\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=17)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Boosting**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 797,
   "metadata": {},
   "outputs": [],
   "source": [
    "gbc = GradientBoostingClassifier(random_state=17,\n",
    "                                max_depth=4,\n",
    "                                n_estimators=5000).fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 798,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error rate (misclassification): 0.4249201277955272 = 133 / 313\n",
      "Accuracy: 0.5750798722044729\n",
      "Recall: 0.64\n",
      "Precision: 0.5485714285714286\n",
      "F1 score: 0.5907692307692308\n"
     ]
    },
    {
     "data": {
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       "</style>\n",
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       "Actual       0    1  All\n",
       "Predicted               \n",
       "0           84   54  138\n",
       "1           79   96  175\n",
       "All        163  150  313"
      ]
     },
     "execution_count": 798,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_matrix = pd.crosstab(gbc.predict(X_test), y_test, rownames=['Predicted'],\n",
    "           colnames=['Actual'], margins=True)\n",
    "\n",
    "TN = conf_matrix.iloc[0][0]\n",
    "TP = conf_matrix.iloc[1][1]\n",
    "FN = conf_matrix.iloc[0][1]\n",
    "FP = conf_matrix.iloc[1][0]\n",
    "ALL = conf_matrix.iloc[2][2]\n",
    "accuracy = (TP+TN)/ALL\n",
    "error_rate = (FP+FN)/ALL\n",
    "recall = TP/(TP+FN)\n",
    "precision = TP/(TP+FP)\n",
    "f1 = 2*(precision*recall)/(precision+recall)\n",
    "\n",
    "print(\"Error rate (misclassification): \" + str(error_rate) + \n",
    "     \" = \" + str(FP+FN) + \" / \" + str(ALL))\n",
    "print(\"Accuracy: \" + str(accuracy))\n",
    "print(\"Recall: \" + str(recall))\n",
    "print(\"Precision: \" + str(precision))\n",
    "print(\"F1 score: \" + str(f1))\n",
    "conf_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Bagging**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 773,
   "metadata": {},
   "outputs": [],
   "source": [
    "bag = BaggingClassifier(random_state=17,\n",
    "                        max_features=len(X_train.columns)).fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 774,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error rate (misclassification): 0.49201277955271566 = 154 / 313\n",
      "Accuracy: 0.5079872204472844\n",
      "Recall: 0.5\n",
      "Precision: 0.487012987012987\n",
      "F1 score: 0.4934210526315789\n"
     ]
    },
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
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       "      <th>Actual</th>\n",
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       "      <td>84</td>\n",
       "      <td>75</td>\n",
       "      <td>159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>79</td>\n",
       "      <td>75</td>\n",
       "      <td>154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>All</th>\n",
       "      <td>163</td>\n",
       "      <td>150</td>\n",
       "      <td>313</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Actual       0    1  All\n",
       "Predicted               \n",
       "0           84   75  159\n",
       "1           79   75  154\n",
       "All        163  150  313"
      ]
     },
     "execution_count": 774,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_matrix = pd.crosstab(bag.predict(X_test), y_test, rownames=['Predicted'],\n",
    "           colnames=['Actual'], margins=True)\n",
    "\n",
    "TN = conf_matrix.iloc[0][0]\n",
    "TP = conf_matrix.iloc[1][1]\n",
    "FN = conf_matrix.iloc[0][1]\n",
    "FP = conf_matrix.iloc[1][0]\n",
    "ALL = conf_matrix.iloc[2][2]\n",
    "accuracy = (TP+TN)/ALL\n",
    "error_rate = (FP+FN)/ALL\n",
    "recall = TP/(TP+FN)\n",
    "precision = TP/(TP+FP)\n",
    "f1 = 2*(precision*recall)/(precision+recall)\n",
    "\n",
    "print(\"Error rate (misclassification): \" + str(error_rate) + \n",
    "     \" = \" + str(FP+FN) + \" / \" + str(ALL))\n",
    "print(\"Accuracy: \" + str(accuracy))\n",
    "print(\"Recall: \" + str(recall))\n",
    "print(\"Precision: \" + str(precision))\n",
    "print(\"F1 score: \" + str(f1))\n",
    "conf_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Random Forest**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 776,
   "metadata": {},
   "outputs": [],
   "source": [
    "rf = RandomForestClassifier(random_state=17).fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 777,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error rate (misclassification): 0.4696485623003195 = 147 / 313\n",
      "Accuracy: 0.5303514376996805\n",
      "Recall: 0.5133333333333333\n",
      "Precision: 0.5099337748344371\n",
      "F1 score: 0.5116279069767442\n"
     ]
    },
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
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       "      <th>All</th>\n",
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       "    <tr>\n",
       "      <th>Predicted</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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      "text/plain": [
       "Actual       0    1  All\n",
       "Predicted               \n",
       "0           89   73  162\n",
       "1           74   77  151\n",
       "All        163  150  313"
      ]
     },
     "execution_count": 777,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_matrix = pd.crosstab(rf.predict(X_test), y_test, rownames=['Predicted'],\n",
    "           colnames=['Actual'], margins=True)\n",
    "\n",
    "TN = conf_matrix.iloc[0][0]\n",
    "TP = conf_matrix.iloc[1][1]\n",
    "FN = conf_matrix.iloc[0][1]\n",
    "FP = conf_matrix.iloc[1][0]\n",
    "ALL = conf_matrix.iloc[2][2]\n",
    "accuracy = (TP+TN)/ALL\n",
    "error_rate = (FP+FN)/ALL\n",
    "recall = TP/(TP+FN)\n",
    "precision = TP/(TP+FP)\n",
    "f1 = 2*(precision*recall)/(precision+recall)\n",
    "\n",
    "print(\"Error rate (misclassification): \" + str(error_rate) + \n",
    "     \" = \" + str(FP+FN) + \" / \" + str(ALL))\n",
    "print(\"Accuracy: \" + str(accuracy))\n",
    "print(\"Recall: \" + str(recall))\n",
    "print(\"Precision: \" + str(precision))\n",
    "print(\"F1 score: \" + str(f1))\n",
    "conf_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Logistic Regression**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 778,
   "metadata": {},
   "outputs": [],
   "source": [
    "logreg = LogisticRegression(random_state=17).fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 779,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error rate (misclassification): 0.5111821086261981 = 160 / 313\n",
      "Accuracy: 0.48881789137380194\n",
      "Recall: 0.86\n",
      "Precision: 0.48134328358208955\n",
      "F1 score: 0.6172248803827751\n"
     ]
    },
    {
     "data": {
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Actual</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>All</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Predicted</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "    <tr>\n",
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       "      <td>163</td>\n",
       "      <td>150</td>\n",
       "      <td>313</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Actual       0    1  All\n",
       "Predicted               \n",
       "0           24   21   45\n",
       "1          139  129  268\n",
       "All        163  150  313"
      ]
     },
     "execution_count": 779,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conf_matrix = pd.crosstab(logreg.predict(X_test), y_test, rownames=['Predicted'],\n",
    "           colnames=['Actual'], margins=True)\n",
    "\n",
    "TN = conf_matrix.iloc[0][0]\n",
    "TP = conf_matrix.iloc[1][1]\n",
    "FN = conf_matrix.iloc[0][1]\n",
    "FP = conf_matrix.iloc[1][0]\n",
    "ALL = conf_matrix.iloc[2][2]\n",
    "accuracy = (TP+TN)/ALL\n",
    "error_rate = (FP+FN)/ALL\n",
    "recall = TP/(TP+FN)\n",
    "precision = TP/(TP+FP)\n",
    "f1 = 2*(precision*recall)/(precision+recall)\n",
    "\n",
    "print(\"Error rate (misclassification): \" + str(error_rate) + \n",
    "     \" = \" + str(FP+FN) + \" / \" + str(ALL))\n",
    "print(\"Accuracy: \" + str(accuracy))\n",
    "print(\"Recall: \" + str(recall))\n",
    "print(\"Precision: \" + str(precision))\n",
    "print(\"F1 score: \" + str(f1))\n",
    "conf_matrix"
   ]
  }
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