model-evaluation-and-refinement.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "    <a href=\"https://cocl.us/corsera_da0101en_notebook_top\">\n",
    "         <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/TopAd.png\" width=\"750\" align=\"center\">\n",
    "    </a>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.bigdatauniversity.com\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/CCLog.png\" width=300, align=\"center\"></a>\n",
    "\n",
    "<h1 align=center><font size=5>Data Analysis with Python</font></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Module 5: Model Evaluation and Refinement</h1>\n",
    "\n",
    "We have built models and made predictions of vehicle prices. Now we will determine how accurate these predictions are. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Table of content</h1>\n",
    "<ul>\n",
    "    <li><a href=\"#ref1\">Model Evaluation </a></li>\n",
    "    <li><a href=\"#ref2\">Over-fitting, Under-fitting and Model Selection </a></li>\n",
    "    <li><a href=\"#ref3\">Ridge Regression </a></li>\n",
    "    <li><a href=\"#ref4\">Grid Search</a></li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Import clean data \n",
    "path = 'https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/module_5_auto.csv'\n",
    "df = pd.read_csv(path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_csv('module_5_auto.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " First lets only use numeric data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Unnamed: 0.1</th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>...</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>0.909722</td>\n",
       "      <td>52.4</td>\n",
       "      <td>2823</td>\n",
       "      <td>152</td>\n",
       "      <td>...</td>\n",
       "      <td>3.47</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <td>164</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>0.919444</td>\n",
       "      <td>54.3</td>\n",
       "      <td>2337</td>\n",
       "      <td>109</td>\n",
       "      <td>...</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
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       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
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       "      <td>54.3</td>\n",
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       "      <td>3.40</td>\n",
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       "   Unnamed: 0  Unnamed: 0.1  symboling  normalized-losses  wheel-base  \\\n",
       "0           0             0          3                122        88.6   \n",
       "1           1             1          3                122        88.6   \n",
       "2           2             2          1                122        94.5   \n",
       "3           3             3          2                164        99.8   \n",
       "4           4             4          2                164        99.4   \n",
       "\n",
       "     length     width  height  curb-weight  engine-size  ...  stroke  \\\n",
       "0  0.811148  0.890278    48.8         2548          130  ...    2.68   \n",
       "1  0.811148  0.890278    48.8         2548          130  ...    2.68   \n",
       "2  0.822681  0.909722    52.4         2823          152  ...    3.47   \n",
       "3  0.848630  0.919444    54.3         2337          109  ...    3.40   \n",
       "4  0.848630  0.922222    54.3         2824          136  ...    3.40   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm  city-mpg  highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0        21           27  13495.0   \n",
       "1                9.0       111.0    5000.0        21           27  16500.0   \n",
       "2                9.0       154.0    5000.0        19           26  16500.0   \n",
       "3               10.0       102.0    5500.0        24           30  13950.0   \n",
       "4                8.0       115.0    5500.0        18           22  17450.0   \n",
       "\n",
       "   city-L/100km  diesel  gas  \n",
       "0     11.190476       0    1  \n",
       "1     11.190476       0    1  \n",
       "2     12.368421       0    1  \n",
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       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df=df._get_numeric_data()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Libraries for plotting "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "! pip install ipywidgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/IPython/html.py:14: ShimWarning: The `IPython.html` package has been deprecated since IPython 4.0. You should import from `notebook` instead. `IPython.html.widgets` has moved to `ipywidgets`.\n",
      "  \"`IPython.html.widgets` has moved to `ipywidgets`.\", ShimWarning)\n"
     ]
    }
   ],
   "source": [
    "from IPython.display import display\n",
    "from IPython.html import widgets \n",
    "from IPython.display import display\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Functions for plotting</h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "def DistributionPlot(RedFunction, BlueFunction, RedName, BlueName, Title):\n",
    "    width = 12\n",
    "    height = 10\n",
    "    plt.figure(figsize=(width, height))\n",
    "\n",
    "    ax1 = sns.distplot(RedFunction, hist=False, color=\"r\", label=RedName)\n",
    "    ax2 = sns.distplot(BlueFunction, hist=False, color=\"b\", label=BlueName, ax=ax1)\n",
    "\n",
    "    plt.title(Title)\n",
    "    plt.xlabel('Price (in dollars)')\n",
    "    plt.ylabel('Proportion of Cars')\n",
    "\n",
    "    plt.show()\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "def PollyPlot(xtrain, xtest, y_train, y_test, lr,poly_transform):\n",
    "    width = 12\n",
    "    height = 10\n",
    "    plt.figure(figsize=(width, height))\n",
    "    \n",
    "    \n",
    "    #training data \n",
    "    #testing data \n",
    "    # lr:  linear regression object \n",
    "    #poly_transform:  polynomial transformation object \n",
    " \n",
    "    xmax=max([xtrain.values.max(), xtest.values.max()])\n",
    "\n",
    "    xmin=min([xtrain.values.min(), xtest.values.min()])\n",
    "\n",
    "    x=np.arange(xmin, xmax, 0.1)\n",
    "\n",
    "\n",
    "    plt.plot(xtrain, y_train, 'ro', label='Training Data')\n",
    "    plt.plot(xtest, y_test, 'go', label='Test Data')\n",
    "    plt.plot(x, lr.predict(poly_transform.fit_transform(x.reshape(-1, 1))), label='Predicted Function')\n",
    "    plt.ylim([-10000, 60000])\n",
    "    plt.ylabel('Price')\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 id=\"ref1\">Part 1: Training and Testing</h1>\n",
    "\n",
    "<p>An important step in testing your model is to split your data into training and testing data. We will place the target data <b>price</b> in a separate dataframe <b>y</b>:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "y_data = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "drop price data in x data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_data=df.drop('price',axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we randomly split our data into training and testing data  using the function <b>train_test_split</b>. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 31\n",
      "number of training samples: 170\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.15, random_state=1)\n",
    "\n",
    "\n",
    "print(\"number of test samples :\", x_test.shape[0])\n",
    "print(\"number of training samples:\",x_train.shape[0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The <b>test_size</b> parameter sets the proportion of data that is split into the testing set. In the above, the testing set is set to 10% of the total dataset. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #1):</h1>\n",
    "\n",
    "<b>Use the function \"train_test_split\" to split up the data set such that 40% of the data samples will be utilized for testing, set the parameter \"random_state\" equal to zero. The output of the function should be the following:  \"x_train_1\" , \"x_test_1\", \"y_train_1\" and  \"y_test_1\".</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.4, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0) \n",
    "print(\"number of test samples :\", x_test1.shape[0])\n",
    "print(\"number of training samples:\",x_train1.shape[0])\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import <b>LinearRegression</b> from the module <b>linear_model</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We create a Linear Regression object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "lre=LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we fit the model using the feature horsepower "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lre.fit(x_train[['horsepower']], y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's Calculate the R^2 on the test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7139364665406973"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lre.score(x_test[['horsepower']], y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can see the R^2 is much smaller using the test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5754067463583004"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lre.score(x_train[['horsepower']], y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #2): </h1>\n",
    "<b> \n",
    "Find the R^2  on the test data using 90% of the data for training data\n",
    "</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7340722810055448"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.1, random_state=0)\n",
    "lre.fit(x_train1[['horsepower']],y_train1)\n",
    "lre.score(x_test1[['horsepower']],y_test1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.1, random_state=0)\n",
    "lre.fit(x_train1[['horsepower']],y_train1)\n",
    "lre.score(x_test1[['horsepower']],y_test1)\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Sometimes you do not have sufficient testing data; as a result, you may want to perform Cross-validation. Let's  go over several methods that you can use for  Cross-validation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Cross-validation Score</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets import <b>model_selection</b> from the module <b>cross_val_score</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We input the object, the feature in this case ' horsepower', the target data (y_data). The parameter 'cv'  determines the number of folds; in this case 4. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Rcross = cross_val_score(lre, x_data[['horsepower']], y_data, cv=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The default scoring is R^2; each element in the array has the average  R^2 value in the fold:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.7746232 , 0.51716687, 0.74785353, 0.04839605])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rcross"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can calculate the average and standard deviation of our estimate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the folds are 0.522009915042119 and the standard deviation is 0.291183944475603\n"
     ]
    }
   ],
   "source": [
    "print(\"The mean of the folds are\", Rcross.mean(), \"and the standard deviation is\" , Rcross.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use negative squared error as a score by setting the parameter  'scoring' metric to 'neg_mean_squared_error'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20254142.84026702, 43745493.2650517 , 12539630.34014931,\n",
       "       17561927.72247591])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-1 * cross_val_score(lre,x_data[['horsepower']], y_data,cv=4,scoring='neg_mean_squared_error')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #3): </h1>\n",
    "<b> \n",
    "Calculate the average R^2 using two folds, find the average R^2 for the second fold utilizing the horsepower as a feature : \n",
    "</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the folds are 0.5166761697127429 and the standard deviation is 0.07348004195771388\n"
     ]
    }
   ],
   "source": [
    "Rcross1 = cross_val_score(lre, x_data[['horsepower']], y_data, cv=2)\n",
    "print(\"The mean of the folds are\", Rcross1.mean(), \"and the standard deviation is\" , Rcross1.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "Rc=cross_val_score(lre,x_data[['horsepower']], y_data,cv=2)\n",
    "Rc.mean()\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also use the function 'cross_val_predict' to predict the output. The function splits up the data into the specified number of folds, using one fold to get a prediction while the rest of the folds are used as test data. First import the function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_predict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We input the object, the feature in this case <b>'horsepower'</b> , the target data <b>y_data</b>. The parameter 'cv' determines the number of folds; in this case 4. We can produce an output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([14141.63807508, 14141.63807508, 20814.29423473, 12745.03562306,\n",
       "       14762.35027598])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = cross_val_predict(lre,x_data[['horsepower']], y_data,cv=4)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 id=\"ref2\">Part 2: Overfitting, Underfitting and Model Selection</h1>\n",
    "\n",
    "<p>It turns out that the test data sometimes referred to as the out of sample data is a much better measure of how well your model performs in the real world.  One reason for this is overfitting; let's go over some examples. It turns out these differences are more apparent in Multiple Linear Regression and Polynomial Regression so we will explore overfitting in that context.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create Multiple linear regression objects and train the model using <b>'horsepower'</b>, <b>'curb-weight'</b>, <b>'engine-size'</b> and <b>'highway-mpg'</b> as features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LinearRegression()\n",
    "lr.fit(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction using training data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([38237.3225152 ,  8757.67570728, 16832.43125207, 16093.28264058,\n",
       "       14757.89820098])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat_train = lr.predict(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "yhat_train[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction using test data: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5114.7345989 , 10941.98915173, 20956.19697977, 20968.65125706,\n",
       "       19966.75504097])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat_test = lr.predict(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "yhat_test[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's perform some model evaluation using our training and testing data separately. First  we import the seaborn and matplotlibb library for plotting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine the distribution of the predicted values of the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Title = 'Distribution  Plot of  Predicted Value Using Training Data vs Training Data Distribution'\n",
    "DistributionPlot(y_train, yhat_train, \"Actual Values (Train)\", \"Predicted Values (Train)\", Title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 1: Plot of predicted values using the training data compared to the training data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far the model seems to be doing well in learning from the training dataset. But what happens when the model encounters new data from the testing dataset? When the model generates new values from the test data, we see the distribution of the predicted values is much different from the actual target values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n",
    "DistributionPlot(y_test,yhat_test,\"Actual Values (Test)\",\"Predicted Values (Test)\",Title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figur 2: Plot of predicted value using the test data compared to the test data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing Figure 1 and Figure 2; it is evident the distribution of the test data in Figure 1 is much better at fitting the data. This difference in Figure 2 is apparent where the ranges are from 5000 to 15 000. This is where the distribution shape is exceptionally different. Let's see if polynomial regression also exhibits a drop in the prediction accuracy when analysing the test dataset.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Overfitting</h4>\n",
    "<p>Overfitting occurs when the model fits the noise, not the underlying process. Therefore when testing your model using the test-set, your model does not perform as well as it is modelling noise, not the underlying process that generated the relationship. Let's create a degree 5 polynomial model.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use 55 percent of the data for testing and the rest for training:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.45, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will perform a degree 5 polynomial transformation on the feature <b>'horse power'</b>. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=5, include_bias=True, interaction_only=False)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr = PolynomialFeatures(degree=5)\n",
    "x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "x_test_pr = pr.fit_transform(x_test[['horsepower']])\n",
    "pr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's create a linear regression model \"poly\" and train it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly = LinearRegression()\n",
    "poly.fit(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the output of our model using the method  \"predict.\" then assign the values to \"yhat\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6728.65561887,  7307.98782321, 12213.78770965, 18893.24804015,\n",
       "       19995.95195136])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = poly.predict(x_test_pr)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take the first five predicted values and compare it to the actual targets. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted values: [ 6728.65561887  7307.98782321 12213.78770965 18893.24804015]\n",
      "True values: [ 6295. 10698. 13860. 13499.]\n"
     ]
    }
   ],
   "source": [
    "print(\"Predicted values:\", yhat[0:4])\n",
    "print(\"True values:\", y_test[0:4].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the function \"PollyPlot\" that we defined at the beginning of the lab to display the training data, testing data, and the predicted function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train, y_test, poly,pr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figur 4 A polynomial regression model, red dots represent training data, green dots represent test data, and the blue line represents the model prediction. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the estimated function appears to track the data but around 200 horsepower, the function begins to diverge from the data points. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " R^2 of the training data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.556771690212023"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly.score(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " R^2 of the test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-29.871340302044153"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly.score(x_test_pr, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see the R^2 for the training data is 0.5567 while the R^2 on the test data was -29.87.  The lower the R^2, the worse the model, a Negative R^2 is a sign of overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how the R^2 changes on the test data for different order polynomials and plot the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(3, 0.75, 'Maximum R^2 ')"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "Rsqu_test = []\n",
    "\n",
    "order = [1, 2, 3, 4]\n",
    "for n in order:\n",
    "    pr = PolynomialFeatures(degree=n)\n",
    "    \n",
    "    x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "    \n",
    "    x_test_pr = pr.fit_transform(x_test[['horsepower']])    \n",
    "    \n",
    "    lr.fit(x_train_pr, y_train)\n",
    "    \n",
    "    Rsqu_test.append(lr.score(x_test_pr, y_test))\n",
    "\n",
    "plt.plot(order, Rsqu_test)\n",
    "plt.xlabel('order')\n",
    "plt.ylabel('R^2')\n",
    "plt.title('R^2 Using Test Data')\n",
    "plt.text(3, 0.75, 'Maximum R^2 ')    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see the R^2 gradually increases until an order three polynomial is used. Then the  R^2 dramatically decreases at four."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function will be used in the next section; please run the cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(order, test_data):\n",
    "    x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=test_data, random_state=0)\n",
    "    pr = PolynomialFeatures(degree=order)\n",
    "    x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "    x_test_pr = pr.fit_transform(x_test[['horsepower']])\n",
    "    poly = LinearRegression()\n",
    "    poly.fit(x_train_pr,y_train)\n",
    "    PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train,y_test, poly, pr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following interface allows you to experiment with different polynomial orders and different amounts of data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f20431cf8a3e4fa5ad13f0031483a3a7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=3, description='order', max=6), FloatSlider(value=0.45, description='tes…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.f(order, test_data)>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interact(f, order=(0, 6, 1), test_data=(0.05, 0.95, 0.05))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #4a):</h1>\n",
    "\n",
    "<b>We can perform polynomial transformations with more than one feature. Create a \"PolynomialFeatures\" object \"pr1\" of degree two?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "pr1=PolynomialFeatures(degree=2)\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #4b): </h1>\n",
    "\n",
    "<b> \n",
    " Transform the training and testing samples for the features 'horsepower', 'curb-weight', 'engine-size' and 'highway-mpg'. Hint: use the method \"fit_transform\" \n",
    "?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "x_train_pr1=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "\n",
    "x_test_pr1=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- The answer is below:\n",
    "\n",
    "x_train_pr1=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "x_test_pr1=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #4c): </h1>\n",
    "<b> \n",
    "How many dimensions does the new feature have? Hint: use the attribute \"shape\"\n",
    "</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "There are now 15 features: x_train_pr1.shape \n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #4d): </h1>\n",
    "\n",
    "<b> \n",
    "Create a linear regression model \"poly1\" and train the object using the method \"fit\" using the polynomial features?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "poly1=linear_model.LinearRegression().fit(x_train_pr1,y_train)\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #4e): </h1>\n",
    "<b>Use the method  \"predict\" to predict an output on the polynomial features, then use the function \"DistributionPlot\"  to display the distribution of the predicted output vs the test data?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "yhat_test1=poly1.predict(x_test_pr1)\n",
    "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n",
    "DistributionPlot(y_test, yhat_test1, \"Actual Values (Test)\", \"Predicted Values (Test)\", Title)\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #4f): </h1>\n",
    "\n",
    "<b>Use the distribution plot to determine the two regions were the predicted prices are less accurate than the actual prices.</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "The predicted value is lower than actual value for cars where the price  $ 10,000 range, conversely the predicted price is larger than the price cost in the $30, 000 to $40,000 range. As such the model is not as accurate in these ranges .\n",
    "    \n",
    "-->\n",
    "\n",
    "<img src = \"https://ibm.box.com/shared/static/c35ipv9zeanu7ynsnppb8gjo2re5ugeg.png\" width = 700, align = \"center\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref3\">Part 3: Ridge regression</h2> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " In this section, we will review Ridge Regression we will see how the parameter Alfa changes the model. Just a note here our test data will be used as validation data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's perform a degree two polynomial transformation on our data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "x_train_pr=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])\n",
    "x_test_pr=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's import  <b>Ridge</b>  from the module <b>linear models</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a Ridge regression object, setting the regularization parameter to 0.1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "RigeModel=Ridge(alpha=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Like regular regression, you can fit the model using the method <b>fit</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/linear_model/ridge.py:125: LinAlgWarning: Ill-conditioned matrix (rcond=1.02972e-16): result may not be accurate.\n",
      "  overwrite_a=True).T\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RigeModel.fit(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Similarly, you can obtain a prediction: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "yhat = RigeModel.predict(x_test_pr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare the first five predicted samples to our test set "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted: [ 6567.83081933  9597.97151399 20836.22326843 19347.69543463]\n",
      "test set : [ 6295. 10698. 13860. 13499.]\n"
     ]
    }
   ],
   "source": [
    "print('predicted:', yhat[0:4])\n",
    "print('test set :', y_test[0:4].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We select the value of Alfa that minimizes the test error, for example, we can use a for loop. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Rsqu_test = []\n",
    "Rsqu_train = []\n",
    "dummy1 = []\n",
    "ALFA = 10 * np.array(range(0,1000))\n",
    "for alfa in ALFA:\n",
    "    RigeModel = Ridge(alpha=alfa) \n",
    "    RigeModel.fit(x_train_pr, y_train)\n",
    "    Rsqu_test.append(RigeModel.score(x_test_pr, y_test))\n",
    "    Rsqu_train.append(RigeModel.score(x_train_pr, y_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot out the value of R^2 for different Alphas "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8bfd5e17f0>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "\n",
    "plt.plot(ALFA,Rsqu_test, label='validation data  ')\n",
    "plt.plot(ALFA,Rsqu_train, 'r', label='training Data ')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('R^2')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 6:The blue line represents the R^2 of the test data, and the red line represents the R^2 of the training data. The x-axis represents the different values of Alfa "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The red line in figure 6 represents the  R^2 of the test data, as Alpha increases the R^2 decreases; therefore as Alfa increases the model performs worse on the test data.  The blue line represents the R^2 on the validation data, as the value for Alfa increases the R^2 decreases.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #5): </h1>\n",
    "\n",
    "Perform Ridge regression and calculate the R^2 using the polynomial features, use the training data to train the model and test data to test the model. The parameter alpha should be set to  10.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47098333063511094"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "RigeModel = Ridge(alpha=0) \n",
    "RigeModel.fit(x_train_pr, y_train)\n",
    "RigeModel.score(x_test_pr, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "RigeModel = Ridge(alpha=0) \n",
    "RigeModel.fit(x_train_pr, y_train)\n",
    "RigeModel.score(x_test_pr, y_test)\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref4\">Part 4: Grid Search</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The term Alfa is a hyperparameter, sklearn has the class  <b>GridSearchCV</b> to make the process of finding the best hyperparameter simpler."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import <b>GridSearchCV</b> from  the module <b>model_selection</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a dictionary of parameter values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000, 100000]}]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parameters1= [{'alpha': [0.001,0.1,1, 10, 100, 1000, 10000, 100000, 100000]}]\n",
    "parameters1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a ridge regions object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RR=Ridge()\n",
    "RR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a ridge grid search object "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Grid1 = GridSearchCV(RR, parameters1,cv=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/model_selection/_search.py:841: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
      "  DeprecationWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=4, error_score='raise-deprecating',\n",
       "       estimator=Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001),\n",
       "       fit_params=None, iid='warn', n_jobs=None,\n",
       "       param_grid=[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000, 100000]}],\n",
       "       pre_dispatch='2*n_jobs', refit=True, return_train_score='warn',\n",
       "       scoring=None, verbose=0)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Grid1.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The object finds the best parameter values on the validation data. We can obtain the estimator with the best parameters and assign it to the variable BestRR as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=10000, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BestRR=Grid1.best_estimator_\n",
    "BestRR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We now test our model on the test data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8411649831036152"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BestRR.score(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #6): </h1>\n",
    "Perform a grid search for the alpha parameter and the normalization parameter, then find the best values of the parameters\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "parameters2= [{'alpha': [0.001,0.1,1, 10, 100, 1000,10000,100000,100000],'normalize':[True,False]} ]\n",
    "Grid2 = GridSearchCV(Ridge(), parameters2,cv=4)\n",
    "Grid2.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']],y_data)\n",
    "Grid2.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "parameters2= [{'alpha': [0.001,0.1,1, 10, 100, 1000,10000,100000,100000],'normalize':[True,False]} ]\n",
    "Grid2 = GridSearchCV(Ridge(), parameters2,cv=4)\n",
    "Grid2.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']],y_data)\n",
    "Grid2.best_estimator_\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Thank you for completing this notebook!</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "\n",
    "    <p><a href=\"https://cocl.us/corsera_da0101en_notebook_bottom\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/BottomAd.png\" width=\"750\" align=\"center\"></a></p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>About the Authors:</h3>\n",
    "\n",
    "This notebook was written by <a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>, <a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>, Bahare Talayian, Eric Xiao, Steven Dong, Parizad, Hima Vsudevan and <a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a> and <a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "<p><a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a> is a Data Scientist at IBM, and holds a PhD in Electrical Engineering. His research focused on using Machine Learning, Signal Processing, and Computer Vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "<p>Copyright &copy; 2018 IBM Developer Skills Network. This notebook and its source code are released under the terms of the <a href=\"https://cognitiveclass.ai/mit-license/\">MIT License</a>.</p>"
   ]
  }
 ],
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