violations-of-regression-models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Violations of Regression Models\n",
    "\n",
    "When using a regression to fit a model to our data, the assumptions of regression analysis must be satisfied in order to ensure good parameter estimates and accurate fit statistics. We would like parameters to be:\n",
    "* unbiased (expected value over different samples is the true value)\n",
    "* consistent (converging to the true value with many samples), and\n",
    "* efficient (minimized variance)\n",
    "\n",
    "Below we investigate the ways in which these assumptions can be violated and the effect on the parameters and fit statistics. We'll be using single-variable linear equations for the examples, but the same considerations apply to other models. We'll also assume that our model is correctly specified; that is, that the functional form we chose is valid. We discuss model specification errors along with the assumption violations and other problems that they cause in another notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Focus on the Residuals\n",
    "\n",
    "Rather than focusing on your model construction, it is possible to gain a huge amount of information from your residuals (errors). Your model may be incredibly complex and impossible to analyze, but as long as you have predictions and observed values, you can compute residuals. Once you have your residuals you can perform many statistical tests.\n",
    "\n",
    "If your residuals do not follow a given distribution (usually normal, but depends on your model), then you know that something is wrong and you should be concerned with the accuracy of your predictions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Residuals not normally-distributed\n",
    "\n",
    "If the error term is not normally distributed, then our tests of statistical significance will be off. Fortunately, the central limit theorem tells us that, for large enough data samples, the coefficient distributions will be close to normal even if the errors are not. Therefore our analysis will still be valid for large data datasets.\n",
    "\n",
    "### Testing for normality\n",
    "\n",
    "A good test for normality is the Jarque-Bera test. It has a python implementation at `statsmodels.stats.stattools.jarque_bera` , we will use it frequently in this notebook.\n",
    "\n",
    "#### Always test for normality!\n",
    "\n",
    "It's incredibly easy and can save you a ton of time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import yfinance as yf\n",
    "from pandas_datareader import data as pdr\n",
    "\n",
    "# Import all other libraries we'll be using\n",
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "from statsmodels import regression, stats\n",
    "import statsmodels\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "yf.pdr_override()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.06795273979699062\n",
      "8.034400745096067e-10\n"
     ]
    }
   ],
   "source": [
    "residuals = np.random.normal(0, 1, 100)\n",
    "\n",
    "_, pvalue, _, _ = statsmodels.stats.stattools.jarque_bera(residuals)\n",
    "print(pvalue)\n",
    "\n",
    "residuals = np.random.poisson(size = 100)\n",
    "\n",
    "_, pvalue, _, _ = statsmodels.stats.stattools.jarque_bera(residuals)\n",
    "print(pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Heteroskedasticity\n",
    "\n",
    "Heteroskedasticity means that the variance of the error terms is not constant across observations. Intuitively, this means that the observations are not uniformly distributed along the regression line. It often occurs in cross-sectional data where the differences in the samples we are measuring lead to differences in the variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": [
    "# Artificially create dataset with constant variance around a line\n",
    "xs = np.arange(100)\n",
    "y1 = xs + 3*np.random.randn(100)\n",
    "\n",
    "# Get results of linear regression\n",
    "slr1 = regression.linear_model.OLS(y1, sm.add_constant(xs)).fit()\n",
    "\n",
    "# Construct the fit line\n",
    "fit1 = slr1.params[0] + slr1.params[1]*xs\n",
    "\n",
    "# Plot data and regression line\n",
    "plt.scatter(xs, y1)\n",
    "plt.plot(xs, fit1)\n",
    "plt.title('Homoskedastic errors');\n",
    "plt.legend(['Predicted', 'Observed'])\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.598</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.594</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   145.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 08 Jun 2020</td> <th>  Prob (F-statistic):</th> <td>4.12e-21</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>23:05:21</td>     <th>  Log-Likelihood:    </th> <td> -451.39</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   100</td>      <th>  AIC:               </th> <td>   906.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    98</td>      <th>  BIC:               </th> <td>   912.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    1.5371</td> <td>    4.429</td> <td>    0.347</td> <td> 0.729</td> <td>   -7.252</td> <td>   10.326</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.9334</td> <td>    0.077</td> <td>   12.077</td> <td> 0.000</td> <td>    0.780</td> <td>    1.087</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 9.008</td> <th>  Durbin-Watson:     </th> <td>   1.964</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.011</td> <th>  Jarque-Bera (JB):  </th> <td>  19.721</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.114</td> <th>  Prob(JB):          </th> <td>5.22e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.164</td> <th>  Cond. No.          </th> <td>    114.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.598\n",
       "Model:                            OLS   Adj. R-squared:                  0.594\n",
       "Method:                 Least Squares   F-statistic:                     145.9\n",
       "Date:                Mon, 08 Jun 2020   Prob (F-statistic):           4.12e-21\n",
       "Time:                        23:05:21   Log-Likelihood:                -451.39\n",
       "No. Observations:                 100   AIC:                             906.8\n",
       "Df Residuals:                      98   BIC:                             912.0\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          1.5371      4.429      0.347      0.729      -7.252      10.326\n",
       "x1             0.9334      0.077     12.077      0.000       0.780       1.087\n",
       "==============================================================================\n",
       "Omnibus:                        9.008   Durbin-Watson:                   1.964\n",
       "Prob(Omnibus):                  0.011   Jarque-Bera (JB):               19.721\n",
       "Skew:                          -0.114   Prob(JB):                     5.22e-05\n",
       "Kurtosis:                       5.164   Cond. No.                         114.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEWCAYAAACJ0YulAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nO3deXxU9b34/9c7G0nYAghIEpGoAWQRSJBKUUFwAUWQxVK9rdraYu2i9loUl3vVe13o8q31fr9WL7da7W1/YiWIqKhY0WqxaklAWS0ICDNhD2FLQrb37485iUOYSWaS2ef9fDzyIHPOmZnPnAmf9znvzyaqijHGGAOQEu0CGGOMiR0WFIwxxjSzoGCMMaaZBQVjjDHNLCgYY4xpZkHBGGNMMwsKxgAi8p6IfC8ErzNARFRE0kJRLq/X7S8ix0QkNZSva0xLFhRMyIjIDhG5tMW2m0TkbwE+/0ER+WN4ShdfWp5LVd2pql1UtSGa5TKJz4KCSRihvjpPNr7OX7DnVDysXolj9uWZiBKRXBEpEZH9IrJdRG5ztk8G7gXmOGmST53t3UXkGRHZLSJuEXm4KYXi3IWsEpHHReQg8KCIpIjI/SLypYjsE5E/iEh35/hMEfmjiBwUkUoR+YeI9PVRxn4i8pmIzAugDKki8isROSAi24CrWrzWd0Rkk4gcFZFtInKL177TROQ1pywVIvKBU/7/BfoDrzrn4q6WaSkR6SkivxeRchE5JCJLWznn33XKcEhE3hKRM732qYj8SES2AFta2fZ153wddv79utdrvCcij4jIKqAKOMv5brY5n3u7iPxLYH8hJupU1X7sJyQ/wA7g0hbbbgL+5vyeApQC/w5kAGcB24ArnP0PAn9s8fyXgf8GOgN9gE+AW7xeux74CZAGZAHfBbY6r90FWAL8r3P8LcCrQDaQChQD3Zx97wHfAwqAfwJzAyzDD4DNwBlAT+BdQIE0Z/9VwNmAAOPxVJpFzr7HgKeBdOfnIkB8nUtgQIvXfR14EejhPHe8n+9kunM+znXO0f3Ah177FXjbKXuWr23Ov4eAbzuvcZ3zuJfXudsJDHX2dweOAIOc/f2AodH++7SfAP8fR7sA9pM4P05Fdgyo9Pqp4qug8DVgZ4vn3AP83vn9QbyCAtAXONFUWTnbrgPedX6/ycfrvQP80OvxIKDOqay+C3wInOej7O8Bv3Y+w3VBlGEl8AOvfZd7V94+3mcpcLvz+38ArwDn+DmXPoOCU8k2Aj0C+E7eAG72epzifCdnOo8VmNjiOSdtc4LBJy2O+Ttwk9e5+w+vfZ2d736W93mzn/j4sfSRCbVrVDWn6Qf4ode+M4FcJ11SKSKVeFJGp6RwvI5PB3Z7Hf/feK7Wm+xq8Zxc4Euvx1/iqUj7Av8LvAUsctIuvxCRdK9j/wVwA4uDKENuizJ4vzciMkVEPnLSQ5XAlcBpzu5f4rmKX+GkWub7OQ8tnQFUqOqhAI49E3jCq+wVeO5a8ryOaXkOW25reU5xHvt8DVU9DszBcxe1W0ReF5HBAZTVxAALCiaSdgHbvYOGqnZV1Sud/S2n7N2F5yr9NK/ju6nqUK9jWj6nHE9F2KQ/nhTTXlWtU9WHVHUI8HVgKnCD17EPAgeA/8+r62dbZdiNp5L2fj8ARKQTUAL8CujrBMnleCplVPWoqt6pqmcB04B/FZFJfj5Xy/PSU0RyWjnG+9hbWpzzLFX90OsYX+/lva3lOQXP53T7ew1VfUtVL8NzV7MZ+J8AympigAUFE0mfAEdF5G4RyXIaaYeJyPnO/r3AgKbeK6q6G1gB/B8R6eY0wp4tIuNbeY8XgJ+KSIGIdAEeBV5U1XoRuUREhjsV/hE8aaVGr+fWAdfiSX/8QURSAijDn4HbRCRfRHoA3lf7GUAnYD9QLyJT8KSXABCRqSJyjogIcBho8CrPXjztIqdwyvQG8FsR6SEi6SJysZ/z8TRwj4gMdd6zu4hc28r582U5MFBErheRNBGZAwwBXvN1sIj0FZHpItIZT0A9xsnn2cQwCwomYtTTx34qMBLYjueq/Hd4GiYBXnL+PSgiZc7vN+CpXDfiadxcjOfq059n8aSJ3nfeowZPQzTA6c7zjwCbgL86x3qXsRaYiSfd9KwToForw//gSUl9CpThadhueq2jwG14Asch4HpgmdfbFQJ/wVNp/h34raq+6+x7DLjfSfv8zMfn/DaeILYZ2Afc4etkqOrLwM/xpMyOAOuBKb6O9UdVD+L53u4EDgJ3AVNV9YCfp6QA/4rnDqMCTwP7rcG8p4mepp4OxhhjjN0pGGOM+YoFBWOMMc0sKBhjjGlmQcEYY0yzuJ5A7LTTTtMBAwZEuxjGGBNXSktLD6hqb1/74jooDBgwgNWrV0e7GMYYE1dEpOUI9WaWPjLGGNPMgoIxxphmFhSMMcY0i+s2BV/q6upwuVzU1NREuyhxLzMzk/z8fNLT09s+2BiTEBIuKLhcLrp27cqAAQPwzDNm2kNVOXjwIC6Xi4KCgmgXxxgTIQkXFGpqaiwghICI0KtXL/bv3x/tohgT95aucfPLtz6nvLKa3Jws5l0xiGtG5bX9xChIuKAAWEAIETuPxnTc0jVu7lmyjuq6BgDcldXcs2QdQEwGBmtoNsaYMPrlW583B4Qm1XUN/PKtz6NUotZZUAiD1NRURo4cybBhw7j22mupqqpq92u99957TJ06FYBly5axYMECv8dWVlby29/+Nuj3ePDBB/nVr37V7jIaY/wrr6wOanu0WVAIg6ysLNauXcv69evJyMjg6aefPmm/qtLYGPxCVNOmTWP+fP/L+LY3KBhjwic3Jyuo7dFmQSHMLrroIrZu3cqOHTsYNGgQN9xwA8OGDWPXrl2sWLGCsWPHUlRUxLXXXsuxY8cAePPNNxk8eDBFRUUsWdK8kBfPPfccP/7xjwHYu3cvM2bMYMSIEYwYMYIPP/yQ+fPn88UXXzBy5EjmzZsHwC9/+UvOP/98zjvvPB544IHm13rkkUcYOHAgF154IZ9/Hpu3scYkgnlXDCIrPfWkbVnpqcy7YlCUStS6hGxobvLQqxvYWH4kpK85JLcbD1w9tO0Dgfr6et544w0mT54MwJYtW3j++ee54IILOHDgAA8//DB/+ctf6Ny5Mz//+c/59a9/zV133cX3v/99Vq5cyTnnnMOcOXN8vvZtt93G+PHjefnll2loaODYsWMsWLCA9evXs3btWgBWrFjBli1b+OSTT1BVpk2bxvvvv0/nzp1ZtGgRa9eupb6+nqKiIoqLi0NzgowxJ2lqTLbeR0msurqakSNHAp47hZtvvpny8nLOPPNMLrjgAgA++ugjNm7cyLhx4wCora1l7NixbN68mYKCAgoLCwH41re+xcKFC095j5UrV/KHP/wB8LRhdO/enUOHDp10zIoVK1ixYgWjRo0C4NixY2zZsoWjR48yY8YMsrOzAU9ayhgTPteMyovZINBSQgeFQK/oQ62pTaGlzp07N/+uqlx22WW88MILJx3j63ntparcc8893HLLLSdt/81vfhOy9zDGJBZrU4iSCy64gFWrVrF161YAjh8/zj//+U8GDx7Mjh07+OKLLwBOCRpNJk2axFNPPQVAQ0MDhw8fpmvXrhw9erT5mCuuuIJnn322ua3C7Xazb98+Lr74YpYuXUp1dTVHjx7l1VdfDedHNcbEEQsKUdK7d2+ee+45rrvuOs4777zm1FFmZiYLFy7kqquuoqioiD59+vh8/hNPPMG7777L8OHDKS4uZuPGjfTq1Ytx48YxbNgw5s2bx+WXX87111/P2LFjGT58OLNnz+bo0aMUFRUxZ84cRowYwZQpUzj//PMj/OmNMbFKVDXaZWi30aNHa8tFdjZt2sS5554bpRIlHjufxiQeESlV1dG+9iV0m4IxxiSCSM6dFLb0kYg8KyL7RGS9j313ioiKyGnOYxGR/xKRrSLymYgUhatcxhgTT5rmTnJXVqN8NXfS0jXusLxfONsUngMmt9woImcAlwM7vTZPAQqdn7nAU2EslzHGxI1Iz50UtqCgqu8DFT52PQ7cBXg3ZkwH/qAeHwE5ItIvXGUzxph4Eem5kyLa+0hEpgNuVf20xa48YJfXY5ezzRhjklqk506KWFAQkWzgXuDfO/g6c0VktYistgVgjDGJLtJzJ0XyTuFsoAD4VER2APlAmYicDriBM7yOzXe2nUJVF6rqaFUd3bt37zAXuf1cLhfTp0+nsLCQs88+m9tvv53a2tqTJrWLJV26dIl2EYwxPlwzKo/HZg4nLycLAfJysnhs5vCw9T6KWJdUVV0HNI/EcgLDaFU9ICLLgB+LyCLga8BhVd0dqbKFmqoyc+ZMbr31Vl555RUaGhqYO3cu9913H0OHhn7qjfr6etLSrHexMYkqknMnhbNL6gvA34FBIuISkZtbOXw5sA3YCvwP8MNwlaulpWvcjFuwkoL5rzNuwcqQdPNauXIlmZmZfOc73wE8E9Y9/vjjPPvss1RVVbFr1y4mTJhAYWEhDz30EOCZ5uKqq65ixIgRDBs2jBdffBGA0tJSxo8fT3FxMVdccQW7d3ti5YQJE7jjjjsYPXo0jzzyCGeeeWbzGg3Hjx/njDPOoK6uji+++ILJkydTXFzMRRddxObNmwHYvn1780jn+++/v8Of2RiTGMJ2eamq17Wxf4DX7wr8KFxl8Sdca6du2LDhlKmou3XrRv/+/amvr+eTTz5h/fr1ZGdnc/7553PVVVfx5Zdfkpuby+uvvw7A4cOHqaur4yc/+QmvvPIKvXv35sUXX+S+++7j2WefBTwzqzaN6C4rK+Ovf/0rl1xyCa+99hpXXHEF6enpzJ07l6effprCwkI+/vhjfvjDH7Jy5Upuv/12br31Vm644QaefPLJdn9WY0xiSeq5j6K1dupll11Gr169yMrKYubMmfztb39j+PDhvP3229x999188MEHdO/enc8//5z169dz2WWXMXLkSB5++GFcLlfz63ivtTBnzpzmu4tFixYxZ84cjh07xocffsi1117LyJEjueWWW5rvNFatWsV113ni9re//e2wfl5jTPxI6kR0uPr/DhkyhMWLF5+07ciRI+zcuZO0tDRE5KR9IsLAgQMpKytj+fLl3H///UyaNIkZM2YwdOhQ/v73v/t8H++puKdNm8a9995LRUUFpaWlTJw4kePHj5OTk+N3Ou6W5TDGmKS+UwhX/99JkyZRVVXVvAhOQ0MDd955JzfddBPZ2dm8/fbbVFRUUF1dzdKlSxk3bhzl5eVkZ2fzrW99i3nz5lFWVsagQYPYv39/c1Coq6tjw4YNPt+zS5cunH/++dx+++1MnTqV1NRUunXrRkFBAS+99BLgaQD/9FPPEJFx48axaNEiAP70pz916PMaYxJHUgeFcPX/FRFefvllXnrpJQoLCxk4cCCZmZk8+uijAIwZM4ZZs2Zx3nnnMWvWLEaPHs26desYM2YMI0eO5KGHHuL+++8nIyODxYsXc/fddzNixAhGjhzJhx9+6Pd958yZwx//+MeT0kp/+tOfeOaZZxgxYgRDhw7llVdeATxTbz/55JMMHz4ctzs8c6gYY+JP0k+dHcnZB+ORTZ1tTOKxqbNbEU9rpxpjTLgldfrIGGPMyRIyKMRzSiyW2Hk0JvkkXPooMzOTgwcP0qtXL+ty2QGqysGDB8nMzIx2UUwMsLa35JFwQSE/Px+Xy4XNoNpxmZmZ5OfnR7sYJsrCNfLfxKaECwrp6ekUFBREuxjGJIzWRv5bUEg8CdmmYIwJnUiv/GWiy4KCMaZVkV75y0SXBQVjTKsivfKXia6Ea1MwxoRWU7tBIvc+st5VX7GgYIxpUyKP/LfeVScL58prz4rIPhFZ77XtlyKyWUQ+E5GXRSTHa989IrJVRD4XkSvCVS5jjPEWrXVVYlU42xSeAya32PY2MExVzwP+CdwDICJDgG8CQ53n/FZEUjHGmDCz3lUnC1tQUNX3gYoW21aoar3z8COgaWTUdGCRqp5Q1e141moeE66yGWNME+tddbJo9j76LvCG83sesMtrn8vZdgoRmSsiq0VktY1aNsZ0lPWuOllUgoKI3AfUA0Ev+aWqC1V1tKqO7t27d+gLZ4xJKteMyuOxmcPJy8lCgLycLB6bOTwpG5khCr2PROQmYCowSb+ahtMNnOF1WL6zzRhjwi6Re1cFK6J3CiIyGbgLmKaqVV67lgHfFJFOIlIAFAKfRLJsxhhjwninICIvABOA00TEBTyAp7dRJ+BtZ1rrj1T1B6q6QUT+DGzEk1b6kao2+H5lY4wx4ZJwazQbY4xpXWtrNNvcR8YYY5pZUDDGGNPM5j4yxiQsm+gueBYUjDEJySa6ax9LHxljEpJNdNc+FhSMMQnJJrprHwsKxpiEZBPdtY8FBWNMQrKJ7trHGpqNMQkpGZYRDQcLCsaYhGUT3QXPgoIxJibYmILYYEHBGBN1NqYgdlhQMCaBxcvVd2tjCmKxvInMgoIxCSqerr5tTEHssC6pxiSoeBrRa2MKYkfYgoKIPCsi+0Rkvde2niLytohscf7t4WwXEfkvEdkqIp+JSFG4ymVMsoinq28bUxA7wnmn8BwwucW2+cA7qloIvOM8BpiCZwnOQmAu8FQYy2VMUoinq+9rRuXx2Mzh5OVkIUBeThaPzRwec2muZBC2NgVVfV9EBrTYPB3PEp0AzwPvAXc72/+gnmXgPhKRHBHpp6q7w1U+YxLdvCsGndSmALF99W1jCmJDpBua+3pV9HuAvs7vecAur+NczjYLCsa0k43oNe0Rtd5HqqoiEvQC0SIyF0+Kif79+4e8XMYkEn9X3/HSVdVEXqR7H+0VkX4Azr/7nO1u4Ayv4/KdbadQ1YWqOlpVR/fu3TushTUmETV1VXVXVqN81VV16Rqf/+VMkol0UFgG3Oj8fiPwitf2G5xeSBcAh609wZjwiKeuqibywpY+EpEX8DQqnyYiLuABYAHwZxG5GfgS+IZz+HLgSmArUAV8J1zlMibZxVNXVRN54ex9dJ2fXZN8HKvAj8JVFmPMV3JzsnD7CACx2FXVRJ6NaDYmyfgaKCZ42hbGLVhpbQsdsHSNm3ELVlIw//W4PZc295ExSca7q6q7shoBmroBxvL8SLEuEnNNqSqfbK+gpMzFZUNO57Ihfdt+UpAsKBiThJq6qo5bsPKUVFIszE4aj11mwznT666KKkrKXCwpc7OzoorOGamc269bh17THwsKxiSxWGx0jqfZXb0Fei4DDXjHTtSzfN1uSkpdfLy9AhH4+tm9uOPSQiYPO53sjPBU3xYUjElisdjoHK9rKwRyLtsKeI2NykfbDrK4zMUb6/ZQXddAwWmd+dnlA5lRlE9eBL4XCwrGJLFozI/U1pVyLN69BCKQc+kv4D22fBNf7D/GkjI37spqumamcc2oPGYX51HUvwciErHPYUHBmCQW6fmRAkkNxeLdSyACOZf+Atveoyd48t2tXFTYm7unDObyIX3JbNFDLFLEM0QgPo0ePVpXr14d7WIYYwLkq2EbPFNlr5o/ETg1cIDnijsRptL++mPvUH645pTt3TLTWPHT8Xy07WBzUOmelY4IVFbVnRRgQtEILyKlqjra1z67UzDGREwgqaFEmd3Vu/Lu3bUTw/O7c7y2weexR2rqmfyb9zleW09dg+dCvbK6rnl/0x3V6i8rKCl1h7UR3oKCMSZiAk0NxfvaCkvXuJlf8hk19Y0A7Dt6gnc27WNIv27MGJXHig17KD9cc9IYEe8g4Et1XQMvfLyLhhbZnVA3wtuIZmNMxCT6spv1DY2s3LyXe5asaw4I3g5X1/HgtKF8eM8k8nKyCDZ53zIgNAllI7zdKRhjIiZRUkMtfb7nKItLd7F0bTn7j57we5x35d2eijxVxGdgCGUjvAUFY0xExXtqqEnF8VqWrXWzuMzFevcR0lKEiYP7MKs4n4eWbfDZoOxdeftLpfmTlZ7KrOK8k9oUmraH8k7LgoIxJu5FalqMuoZG3t28j5IyFys376OuQRma240Hrh7CtBG59OrSCYDq2oY2xyz4GteQniJ0yUyjsqrOb++j0Wf2DOtntaBgjIlrkZgWY0P5YRaXunhlbTkVx2s5rUsnbhw7gFnF+T7nIAokTdbeVFq477RsnIIxJq4FMvahPfYfPcEra90sLnWxec9RMlJTuHRIH2YV5TN+YG/SUuO3n07MjVMQkZ8C38PTG2sdnpXW+gGLgF5AKfBtVa2NRvmMMfEjlNNinKhv4J1N+ygpdfHeP/fT0KiMOCOH/5w+lKtH5JKTndHR4sa8iAcFEckDbgOGqGq1iPwZ+Cae5TgfV9VFIvI0cDPwVKTLZ4yJLx2dFkNV+czlSQ8t+7Scw9V19O3Wie9dVMC1xfmc06drqIsc06LVppAGZIlIHZAN7AYmAtc7+58HHsSCgjGmDe2d1G/vkRpeXuOmpNTFln3H6JSWwuVDT2d2cT4XnnMaqSmRm4QulkQ8KKiqW0R+BewEqoEVeNJFlapa7xzmAny2pIjIXGAuQP/+/cNfYGNMTAumwbamroEVG/dSUurigy37aVQoPrMHj80czlXn9aNbZnqkix9zopE+6gFMBwqASuAlYHKgz1fVhcBC8DQ0h6OMxiSieFzNLFCt9chRVcp2VlJS5uLVT8s5WlNPbvdMfjjhHGYW5XFW7y4RLm1si0b66FJgu6ruBxCRJcA4IEdE0py7hXwg/la8NiZGxetqZh1RXlndnB7aduA4mekpXDmsH7OK8xl7Vi9SkjQ91JZoBIWdwAUiko0nfTQJWA28C8zG0wPpRuCVKJTNmIQUr6uZBau6toE3N+ympNTNqi8OoApjCnryg/FnM2X46XS19FCbotGm8LGILAbKgHpgDZ500OvAIhF52Nn2TKTLZkyiitfVzKDttJeq8sn2CkrKXCxft4djJ+o5o2cWt00sZFZRPv17ZUex9PEnKr2PVPUB4IEWm7cBY6JQHGMSXqRWMwt1u0Vraa/iM3tQUuZiSZmbnRVVdM5I5crh/ZhdnM/5A3paeqidbJoLkxQSuZE1EJFYizkc7Rb+0l53Lf6M2oZGRGDsWb2449JCJg87newMq9I6ys6gSXjJ2MjaUiSmrA5Hu4W/9FZtQyM/u3wgM4ryyQvibifZLw4CYUHBJLxkaGQNpLIL90RqoW632HHgOF06pXH0RP0p+3K7Z/LjiYVBvZ5dHATGgoJJePHcyBqIWKnsQtFucaSmjuWf7WZxqYvVXx5CBFIEGr1GJGWlp3LX5MFBly8ZLg5Cwe80fyKyXEQGRK4oxoSHv0op1I2s0dJaZRdJ7V1qs6FRef+f+7nthTWc//BfmL9kHYeqarl78mD+Pn8Sv/7GSPJyshA8M58+NnN4uyrxRL84CJXW7hR+D6wQkeeBX6hq66tKGxOjItHIGk2xUtkF226xdd8xSspcvFzmZs+RGrpnpXPt6HxmFeUz8owcRKT5dUNxJR+pHljxzm9QUNWXROQN4N+A1SLyv0Cj1/5fR6B8xnRYoq4L3CSWKru2KvDDVXUs+6ycklIXa3dVkpoijB/Ym3+bOoRLh/ShU1qq3+d2VCgvDhK5wbqtNoVa4DjQCeiKV1AwJp7E87rAbVVAsX4nVN/QyPtb9lNS6ubtjXupbWhk8Oldue/Kc5k+Kpc+XTPb9brBVsyhujiIlTaccPEbFERkMvBrYBlQpKpVESuVSTqJfOXVEYFUQOG6E+rod7J5zxFKSl0sXVvO/qMn6JGdzvVf68/s4nyG5nZrTg+1t2ztqZhDcXGQ6A3Wrd0p3Adcq6obIlUYk5wS/cqrIwKtgEJ9J9Te76TieC3L1rpZXOZivfsIaSnCxMF9mFWczyWD+pCRFpolLKNZMcdKG064tNamcFEkC2KSV6JfefkTyJV4tCqgtno0eZf7Xy8bSNfMNErKXKzcvI+6BmVobjceuHoI00bk0qtLp5CXL5oVs782HMWzXnS83+XaOAUTdYl+5eWLryvxn764ljteXEueV4CIViOyv3PfdMfgXe47X/oUgNO6dOLGsQOYVZzPuf26hbV80Wxc99WG0yQR7nJDcy9nTAck+jgCX3xdiTeNz2qqWJaucbe7739H+Tv3KeCzMuzZOYOP7pnI/VOHhD0gQPvHRITCNaPyeGzmcL/Ta0RjjEgoWVAwURfN/+DR0tZdkHf6rKkC6ujgrWD4+k5SxH/3w0PHa0lLjVx1Eq3z4v3+q+ZPxF9TeTzf5Vr6yERdrI4jCGePKH/pD29NFUs0utNOH5nLzoNV/Pf7X3C81nNn0DUznYZG5ZivuYhicExEJMTSGJFQsaBgYkIs/Af3Fu4eUa3lpZtEo2LZe6SmeQnLLfuO0SkthatH5DK7OJ8LzzmNVz8tj+kxEZEW62NE2iMqQUFEcoDfAcPwpFK/C3wOvAgMAHYA31DVQ9EonzEd7RHV1l2G992Ru7Ia4as2BYhsxVJT18CKjXspKXXxwZb9NCoU9c/h0RnDueq8fnTP+moJy1i9q/MWyTEv8XA+giWq2vZRoX5Tz3xKH6jq70QkA8gG7gUqVHWBiMwHeqjq3a29zujRo3X16tURKLFJNgXzX8fX/wwBti+4qtXntrzLAE8l31rOO9KD91SVsp2VlJS5ePXTco7W1JPbPZOZRfnMLMrjrN5dwvbe4dSec9/W6yVShd9EREpVdbSvfRG/UxCR7sDFwE0AqloL1IrIdGCCc9jzwHtAq0HBmHDpSK64PXcZkUqflVdWN6eHth04TmZ6ClcO68es4nzGntUr7pewDObct1XhJ+ugymikjwqA/cDvRWQEUArcDvRV1d3OMXuAvr6eLCJzgbkA/fv3D39pTVLqSK441sZdVNc28NaGPSwudbHqiwOowpiCnvxg/NlMGX46XTPT236ROBHouQ+kwk/WQZXRCAppQBHwE1X9WESeAOZ7H6CqKiI+81qquhBYCJ70UbgLa5JTR3LFsdAjRVX5x45DLC7dxfJ1ezh2op4zemZx28RCZhXl079XdsTKEkmBnvtAKvxYC+6REo2g4AJcqvqx83gxnqCwV0T6qepuEekH7ItC2Yxp1t6UTih6pLQ3l72rooolZW5KykB0ZMwAABfhSURBVFzsrKiic0YqU4b3Y1ZRPl8r6Bn36aG2BHruA6nwYyG4R0PEg4Kq7hGRXSIySFU/ByYBG52fG4EFzr+vRLpsxoRCR3ukBJvLPn6inuXrdlNS5uKjbRWIwNizenHHpYVMHnY62Rmx2/M81A25gZ771ir8pjJFu1dYtESr99FIPF1SM4BtwHfwjK7+M9Af+BJPl9SK1l7Heh+ZRDRuwUqfFVZeThar5k8EoLFR+WjbQRaXuXhj3R6q6xoY0CubWUX5zCjKI79H7KeHotlLy997zyrOo6TUfdL2psCQZ72PwkdV1wK+CjQp0mUxJta0ltrYceA4JWUulpS5cVdW07VTGteM8gwuK+rfo0NrFERasA25oewN5O+Owt+cVN4BOdHF7n2lMUnKX2ojPTWFCb96jxSBCwt7c/eUwVw+pC+ZLeYoipe+9cE25Ia6N5CvNqOfvrg2qDIlIgsKxgQp3JXuvCsGMb/kM2rqT55+Lic7ne+MK2DGqDxO7+57Cct46lsfbENuJHoDJWvjsjebJdWYIDRVuu7KapSTp7kOha37jvH53qN08rr675yRyh2XFvLxvZO4dcLZfgMCtL04TiwJdnbcSEyxnowz9rZkdwrGBCGYFckCvYM4XFXHss/KKSl1sXZXJakpwviBvZldnM+kc/vQKS21zddoEkt964OZ/ymQcxaJyecScS6jYEWl91GoWO+j6ApXGiWWc+L+5kQCTwUVaE+a+oZGPthygMWlLt7etJfa+kYG9e3K7OJ8po/KpU9X/3cDrQmk51IkhHoOIu/XjdW/jXgSc72PTPwLV+461nPi/nLOqSIBNYJ+vucoJWUuXl7jZv/RE/TITuf6Mf2ZXZzP0NxuHe49FCtTOYdriohYm2I9EVlQMO0Srv/0sT7fjL9K19+6COWV1VQcr2XZWjclZW7WuQ+TliJcMrgPs4vzuWRQHzLSQte0Fyvpj1hKY5ngWFAw7RKu//SxXpm01r/d1x1Ep/QUvvboX6hrUIbmduOBq4cwbUQuvbp0CmsZox1ArRdP/LKgYNolXP/p46Ey8Vfp+lpJLS0lha8V9GDT7iNsLD/C76q20yM7I+qVdrjFShrLBM+6pJqgLF3jbm7MbJn9DsV/+njsErj/6AkOHPO0DzTJTE/h+xcV8NC0oXyyvYJ9R0+EpQtrrLpmVB6PzRxOXk4Wgqehu6ONzCYy7E7BBKxlI7AS+nlhYiUn3pYT9Q2s3LSPkjIX736+n4ZGZUR+d26dcDZTz8ulR+cMwNMbKJbbSMIpFtJYJngWFEzAIjUvTCxWJkvXuPnFm5spP1xD54xUFKiqbaBvt058/6KzmFWUR2Hfrqc8L9bbSIxpyYKCCViyVnDPf7iD/3xtI/WNnhEKx2sbSBXhlovP4q7Jg0ltZY2CeGgjMcabtSmYgEVimoGWmtowCua/zrgFKyOWi6+pa+DVT8u56fef8MCyDc0BoUmDKq99trvVgADx2UZikpvdKZiARbpHSaQHsqkqZTsrKSlz8eqn5RytqSe3lXmGArlDipc2EmOaRC0oiEgqsBpwq+pUESkAFgG9gFLg26paG63ymVNFuoKL1EC28spqXl7jpqTUxbYDx8lMT2HKsH7MLs5n7Fm9uOgX73YoBRSLbSTG+BPNO4XbgU1AN+fxz4HHVXWRiDwN3Aw8Fa3CGd8iWcH5uxJ3V1YzbsHKDgWk6toG3tqwh8WlLlZ9cQBVGFPQkx9MOJsrh/ejS6ev/mtYn3uTTKISFEQkH7gKeAT4V/FM+DIRuN455HngQSwoJDV/jbTQvlSSqvKPHYdYXLqL5ev2cOxEPfk9srhtYiGzivLp38v3EpaWAjLJJFp3Cr8B7gKa+vD1AipVtd557AJ8/o8TkbnAXID+/fuHuZgmmnxdoXsLNJW0q6KKJWVuSspc7KyoonNGKlcO78es4nzGDOhJShuNxWApIJM8Ih4URGQqsE9VS0VkQrDPV9WFwELwTJ0d4uKZGOJ9he7vjsFfiun4iXqWr9tNSZmLj7ZVIAJjz+rF7ZMKmTL8dLIz4rOPhU0dbcItGv8zxgHTRORKIBNPm8ITQI6IpDl3C/lAYs8DYALSdIXub50A78bexkblo+0HWVzq4o11e6iua2BAr2zuvGwgM4ryyO/hOz0UL2J9WnGTGCIeFFT1HuAeAOdO4Weq+i8i8hIwG08PpBuBVyJdNhO7Wmvs3XHgOEvKXJSUuXFXVtO1UxrXjMplVlE+xWf26PAaBa2J5JV7rE8rbhJDLN1D3w0sEpGHgTXAM1EujwlSsBVkMMe3bOw9vXsmFxf25o8ffckdL64lReDCwt7cPWUwlw/pS2Z64EtYtrdij/SVe7KOKDeRFdWgoKrvAe85v28DxkSzPKb9gq0g21OhXj0il56dMygpc/Hm+j28uHoXZ/fuzN2TBzNjVB6nd89k6Ro3k/7PX4MKTO2t2CN95W5TZphIiKU7BRPHgq0ggzl+675jniUsy9zsOVJD96x0rh2dz+ziMxiR3705PdSeCr4jFXukr9xtvISJBAsKScg7XdI9Kx0RqKyq83tlHUh6JdAKsum12upNdLiqjmWflVNS6mLtrkpSU4TxA3vz71cPYdK5feiUdmp6qD0VfEcq9khfudt4CRMJFhSSTMur6crquuZ9vq6sA736DqSCbPlavvTsnMGP/lTG2xv3UtvQyKC+XbnvynOZPiqXPl39z0ME7avgO1KxR+PK3cZLmHCzWVKTjK+raW9NV9atHd/yGAhsNtC23hvg4PFaPvziANd/rT+v/eRC3rzjIr5/8VltBgRo3yyuHZnF1FYXM4nI7hSSTCBpEe9jAr36DiS10dZ7D8vrxo8vKWTi4D5kpAV/vdKeK/eOpmTsyt0kGgsKSaa1+YS8j2nreF9X321VkP26Z1J+uOaU7d2z0ll553h6denUarna0t4K3ip2Y75iQSHJtDWfUMsr61DkzTeUH6ak1M2RmvpT9mWlp/LQtKEdDghNrII3pmMsKCSZllfTbfU+au/V94FjJ1i6xk1JmZtNu4+QnipcNqQveTlZvP7ZbnYfrgl77xmbJygy7DwnFlGN3znlRo8eratXr452MYzjRH0DKzfto6TMxbuf76ehURmR353ZxflcPSKXnOyMiJXFV0+nrPTUNhuCrYILTnvPs4kuESlV1dG+9tmdgukQVeUz12FKylws+7Scyqo6+nTtxPcuKmB2UT6Ffbu2/SId5Ksib8+YBZtwLng2H1PisaBg2mXvkZrmJSy37DtGp7QULh96OrOK8rjwnNNIS41Mb2d/Fbm/NpPWekBZBRc8m48p8VhQMAGrqWvg7Y17WVzq4oMt+2lUKD6zB4/OGM5V5/Wje1Z6xMvkryJPFaHBR2q0tTELVsEFz+ZjSjwWFEyrVJWynZWUlLl49dNyjtbU0697JrdOOJtZRfmc1btLVMvnr8JuUCUrPTWoXlNWwQXP5mNKPBYUjE+7D1d7lrAsdbHtwHEy01OYMqwfs4ryGXt2L1IDWMIyEvxV5HlebQuBNhpbBRc8m48p8VjvI9OsuraBtzbsYXGpi1VfHEAVxhT0ZHZxPlcO70eXTrF3DRHq3i/W+8gkA+t9ZPxSVf6x4xAlpS5eX7ebYyfqye+RxW0TC5lVlE//XrG9hGWor1TDPfjNgo6JdREPCiJyBvAHoC+gwEJVfUJEegIvAgOAHcA3VPVQpMsXj4KdChtgV0UVS8rcLFnj4suDVXTOSOXK4f2YVZzPmAE9SelgeiiSlV+8jGK2Lq8mHkQ8fSQi/YB+qlomIl2BUuAa4CagQlUXiMh8oIeq3t3aayV6+iiQirWt6ai9UynHT9SzfN1uSspcfLStAoCvn92L2cX5TB52Ois27A1JRW4Dmnwbt2Cl3/aPVfMnRqFEp7I7meQQU+kjVd0N7HZ+Pyoim4A8YDowwTnseTzLdLYaFBJZoFeVgUyF/fBrG3l/y37eWLeH6roGBvTK5s7LBjKjKI/8HtlBvV8grL+/b7He5dXuZAxEuU1BRAYAo4CPgb5OwADYgye95Os5c4G5AP379w9/IaMk0Io1kArlwPFa3t6wl2tG5TKrKJ/iM3s0L2EZ7PsFItYrv2gJdZfXUF/VWzA3EMWgICJdgBLgDlU94l1JqaqKiM+8lqouBBaCJ30UibJGQ6AVayBTYffITufv90wiM/3UJSyDfb9AWH9/30LZ5TUcV/UWzFuXLKm1qKy8JiLpeALCn1R1ibN5r9Pe0NTusC8aZYuGpWvcjFuwkoL5rzNuwUqWrnEHvIrYnZcNJKOVKSWy0lN54OqhvLl+zynv0drrtrW9NR1ZzSyRhXKltkBXxAtGKP8GEk1TEHZXVqN8FYRb/j9KBNHofSTAM8AmVf21165lwI3AAuffVyJdtmjwd8U3qziPklK336vKrfuOUVLm4uUyN7UNjYiAKnTplEpainC4ur75agZo86oylFexNqDJv1D1lArHVb0N3vMvmVJr0UgfjQO+DawTkbXOtnvxBIM/i8jNwJfAN6JQtojz98f27ub9PDZz+EkV648uOZtjJ+q55slVrN1VSWqKcHHhafzb1CFMOreP3/TQuAUr2/yDjrf+/skuHCk6C+b+JVNqLRq9j/4G+OsEPymSZYkFrf2xXTMqj6nn9eODLQdYXObiwVc3UlvfyKC+XbnvynOZPio3oAXtg1lnOV4qgGTJ7/oTrqv6ePobiKRkaiezEc1R5u+PrXfXTjy6fBMvr3Gz/+gJemSnc/2Y/swuzmdobrdTeg/50lRx+muNj9QfdKgrcOs6aVf1kZZMqTWb+ygMgqkEfQ30amofSEsRLhnch1lF+Uwc3IeMtJSTntfaewQzqC2cwjGQLR4GgZnEk0h3pzE1eC3RBXsVe9V5/VjvPswfP/6SmrpGAPK6Z/HdCwuYPjLX54L2gbxHa4Pa8iL4Bx2OBrpkyu+a2JEsqbWodElNZIF2FdxQfpj/eHUjFzz6Dr/723a6dErjexcWMO/yQSjwn69tZNr/W+Wzy1sg7+GvghRg1fyJEfvjDkcFbl0njQkfu1MIMX+VnbuymgsefYcLzurJ53uPsWn3ETJSU5h0ric9NH5Qb17/bHdAdxmBVLSx0jAWjnIkU37XmEizO4UQa62y23OkhqVryzl+op7/mD6Uj++dxFPfKubSIX1JT00J+C4jkCvljg4g8zWgrj3CMZAtlIPAjDEnszuFEJt3xSDml3xGTX2j32MaGpVumelM/b9/O6nRKtBUSyBXyh3pnRLK3j3h6iWTLPldYyLNeh+F0L4jNby8xs3vV+1gz5GaVo/1tX5wZnoKh6rqTjnWV6+acPaEsN49xiQ2630URjV1Dby9cS8lZS7e/+d+GhWK+udw26RC/u87W9jtJzj4ShN1SksJeLH5cF4pJ0PvnkTqXmhMKFlQCNLSNW5+8eZmyg/XkJ2RSqMqNXWN5HbP5IcTzmFmUR5n9e4CQHZGaqtjBVo6XF3H43NGRr2yipVG6nCxwW/G+GdBIQBNV5UtK8qq2gZSRbh1/NnMu2LQKUtYeufT25reGjyVbmt3AJG6uk303j3JNLmZMcGy3kdt+PM/djFv8ad+K/UGVZZ9Wu53TeNrRuWxav5Ev5M9NWmr0o3k1L2J3rsnGdJjxrSX3Sn4oKr8Y8chSkpd/Hn1Lr9zBzUJpDJpbTGcQEYYR/rqNpF79yR6esyYjrCg4GVXRRVLytwsWePiy4NVCLQZECCwysRfSibQK3C7ug2dRE+PGdMRSR8UXvxkJ4+9uZlKH11BAwkIgieVM/KhFYhAZVWdz3x/R/vr29Vt6NgMo8b4F3PjFERkMvAEkAr8TlUX+Du2PeMUvHsPpacKdQ3Bf/6mO4jW7iRCPQtpOGYbNcYkp9bGKcRUQ7OIpAJPAlOAIcB1IjIkVK/fVLGWH/aMHWhPQMjLyeLxOSPJy8lq9U6io+vltpTojb/GmNgQa+mjMcBWVd0GICKLgOnAxlC8eGvTSQfCe0TvT19c28bRoc/3J3LjrzEmNsTUnQKQB+zyeuxytjUTkbkislpEVu/fvz+oF+9IJd2yITKQXL7l+40x8SbWgkKbVHWhqo5W1dG9e/cO6rnBVtJNYwt8pWp8zf7pzXqzGGPiUaylj9zAGV6P851tIeGrK2J6itAlM43Kqjq6Z6W32oPIW8seLME81xhjYlWsBYV/AIUiUoAnGHwTuD5ULx7qroiW4zfGJJqYCgqqWi8iPwbewtMl9VlV3RDK97CK3Bhj/IupoACgqsuB5dEuhzHGJKO4a2g2xhgTPhYUjDHGNLOgYIwxppkFBWOMMc1irqHZGJN4bE3s+GFBwRgTVrYmdnyx9JExJqxaWzXQxB4LCsaYsLJVA+OLBQVjTFj5m4jSZhGOTRYUjDFh5WtGYZtFOHZZQ7MxJqxsTez4YkHBGBN2NhFl/LD0kTHGmGYWFIwxxjSzoGCMMaaZBQVjjDHNLCgYY4xpJqoa7TK0m4jsB75s59NPAw6EsDjxIhk/dzJ+ZkjOz52MnxmC/9xnqmpvXzviOih0hIisVtXR0S5HpCXj507GzwzJ+bmT8TNDaD+3pY+MMcY0s6BgjDGmWTIHhYXRLkCUJOPnTsbPDMn5uZPxM0MIP3fStikYY4w5VTLfKRhjjGnBgoIxxphmSRkURGSyiHwuIltFZH60yxMOInKGiLwrIhtFZIOI3O5s7ykib4vIFuffHtEuaziISKqIrBGR15zHBSLysfOdvygiGdEuYyiJSI6ILBaRzSKySUTGJsN3LSI/df6+14vICyKSmYjftYg8KyL7RGS91zaf3694/Jfz+T8TkaJg3ivpgoKIpAJPAlOAIcB1IjIkuqUKi3rgTlUdAlwA/Mj5nPOBd1S1EHjHeZyIbgc2eT3+OfC4qp4DHAJujkqpwucJ4E1VHQyMwPPZE/q7FpE84DZgtKoOA1KBb5KY3/VzwOQW2/x9v1OAQudnLvBUMG+UdEEBGANsVdVtqloLLAKmR7lMIaequ1W1zPn9KJ5KIg/PZ33eOex54JrolDB8RCQfuAr4nfNYgInAYueQhPrcItIduBh4BkBVa1W1kiT4rvGsCZMlImlANrCbBPyuVfV9oKLFZn/f73TgD+rxEZAjIv0Cfa9kDAp5wC6vxy5nW8ISkQHAKOBjoK+q7nZ27QH6RqlY4fQb4C6g0XncC6hU1XrncaJ95wXAfuD3TsrsdyLSmQT/rlXVDfwK2IknGBwGSkns79qbv++3Q3VcMgaFpCIiXYAS4A5VPeK9Tz39kROqT7KITAX2qWpptMsSQWlAEfCUqo4CjtMiVZSg33UPPFfFBUAu0JlTUyxJIZTfbzIGBTdwhtfjfGdbwhGRdDwB4U+qusTZvLfpVtL5d1+0yhcm44BpIrIDT2pwIp58e46TYoDE+85dgEtVP3YeL8YTJBL9u74U2K6q+1W1DliC5/tP5O/am7/vt0N1XDIGhX8AhU4PhQw8DVPLolymkHPy6M8Am1T11167lgE3Or/fCLwS6bKFk6reo6r5qjoAz3e7UlX/BXgXmO0cllCfW1X3ALtEZJCzaRKwkQT/rvGkjS4QkWzn773pcyfsd92Cv+93GXCD0wvpAuCwV5qpTUk5ollErsSTd04FnlXVR6JcpJATkQuBD4B1fJVbvxdPu8Kfgf54ph3/hqq2bMBKCCIyAfiZqk4VkbPw3Dn0BNYA31LVE9EsXyiJyEg8DesZwDbgO3gu+hL6uxaRh4A5eHrbrQG+hyd/nlDftYi8AEzAM0X2XuABYCk+vl8nQP4/PKm0KuA7qro64PdKxqBgjDHGt2RMHxljjPHDgoIxxphmFhSMMcY0s6BgjDGmmQUFY4wxzSwoGBMizsy020Wkp/O4h/N4QHRLZkzgLCgYEyKqugvPjJQLnE0LgIWquiNqhTImSDZOwZgQcqYWKQWeBb4PjHSmYDAmLqS1fYgxJlCqWici84A3gcstIJh4Y+kjY0JvCp6pnIdFuyDGBMuCgjEh5MxBdBme1e5+GsziJsbEAgsKxoSIMxHZU3jWrtgJ/BLPIjDGxA0LCsaEzveBnar6tvP4t8C5IjI+imUyJijW+8gYY0wzu1MwxhjTzIKCMcaYZhYUjDHGNLOgYIwxppkFBWOMMc0sKBhjjGlmQcEYY0yz/x+Jrz2O+OQBpgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Artificially create dataset with changing variance around a line\n",
    "y2 = xs*(1 + .5*np.random.randn(100))\n",
    "\n",
    "# Perform linear regression\n",
    "slr2 = regression.linear_model.OLS(y2, sm.add_constant(xs)).fit()\n",
    "fit2 = slr2.params[0] + slr2.params[1]*xs\n",
    "\n",
    "# Plot data and regression line\n",
    "plt.scatter(xs, y2)\n",
    "plt.plot(xs, fit2)\n",
    "plt.title('Heteroskedastic errors')\n",
    "plt.legend(['Predicted', 'Observed'])\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "\n",
    "# Print summary of regression results\n",
    "slr2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing for Heteroskedasticity\n",
    "\n",
    "You can test for heteroskedasticity using a few tests, we'll use the Breush Pagan test from the statsmodels library. We'll also test for normality, which in this case also picks up the weirdness in the second case. HOWEVER, it is possible to have normally distributed residuals which are also heteroskedastic, so both tests must be performed to be sure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value for residuals1 being normal 0.9326051529224062\n",
      "p-value for residuals2 being normal 5.218479112026894e-05\n",
      "p-value for residuals1 being heteroskedastic 0.739893980428236\n",
      "p-value for residuals2 being heteroskedastic 0.0007308587273541759\n"
     ]
    }
   ],
   "source": [
    "residuals1 = y1-fit1\n",
    "residuals2 = y2-fit2\n",
    "\n",
    "xs_with_constant = sm.add_constant(xs)\n",
    "\n",
    "_, jb_pvalue1, _, _ = statsmodels.stats.stattools.jarque_bera(residuals1)\n",
    "_, jb_pvalue2, _, _ = statsmodels.stats.stattools.jarque_bera(residuals2)\n",
    "print(\"p-value for residuals1 being normal\", jb_pvalue1)\n",
    "print(\"p-value for residuals2 being normal\", jb_pvalue2)\n",
    "\n",
    "_, pvalue1, _, _ = stats.diagnostic.het_breuschpagan(residuals1, xs_with_constant)\n",
    "_, pvalue2, _, _ = stats.diagnostic.het_breuschpagan(residuals2, xs_with_constant)\n",
    "print(\"p-value for residuals1 being heteroskedastic\", pvalue1)\n",
    "print(\"p-value for residuals2 being heteroskedastic\", pvalue2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correcting for Heteroskedasticity\n",
    "\n",
    "How does heteroskedasticity affect our analysis? The problematic situation, known as conditional heteroskedasticity, is when the error variance is correlated with the independent variables as it is above. This makes the F-test for regression significance and t-tests for the significances of individual coefficients unreliable. Most often this results in overestimation of the significance of the fit.\n",
    "\n",
    "The Breusch-Pagan test and the White test can be used to detect conditional heteroskedasticity. If we suspect that this effect is present, we can alter our model to try and correct for it. One method is generalized least squares, which requires a manual alteration of the original equation. Another is computing robust standard errors, which corrects the fit statistics to account for the heteroskedasticity. `statsmodels` can compute robust standard errors; note the difference in the statistics below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.598\n",
      "Model:                            OLS   Adj. R-squared:                  0.594\n",
      "Method:                 Least Squares   F-statistic:                     145.9\n",
      "Date:                Mon, 08 Jun 2020   Prob (F-statistic):           4.12e-21\n",
      "Time:                        23:07:33   Log-Likelihood:                -451.39\n",
      "No. Observations:                 100   AIC:                             906.8\n",
      "Df Residuals:                      98   BIC:                             912.0\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          1.5371      4.429      0.347      0.729      -7.252      10.326\n",
      "x1             0.9334      0.077     12.077      0.000       0.780       1.087\n",
      "==============================================================================\n",
      "Omnibus:                        9.008   Durbin-Watson:                   1.964\n",
      "Prob(Omnibus):                  0.011   Jarque-Bera (JB):               19.721\n",
      "Skew:                          -0.114   Prob(JB):                     5.22e-05\n",
      "Kurtosis:                       5.164   Cond. No.                         114.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.598\n",
      "Model:                            OLS   Adj. R-squared:                  0.594\n",
      "Method:                 Least Squares   F-statistic:                     159.0\n",
      "Date:                Mon, 08 Jun 2020   Prob (F-statistic):           3.08e-22\n",
      "Time:                        23:07:33   Log-Likelihood:                -451.39\n",
      "No. Observations:                 100   AIC:                             906.8\n",
      "Df Residuals:                      98   BIC:                             912.0\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HC1                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          1.5371      2.576      0.597      0.552      -3.575       6.649\n",
      "x1             0.9334      0.074     12.610      0.000       0.787       1.080\n",
      "==============================================================================\n",
      "Omnibus:                        9.008   Durbin-Watson:                   1.964\n",
      "Prob(Omnibus):                  0.011   Jarque-Bera (JB):               19.721\n",
      "Skew:                          -0.114   Prob(JB):                     5.22e-05\n",
      "Kurtosis:                       5.164   Cond. No.                         114.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors are heteroscedasticity robust (HC1)\n"
     ]
    }
   ],
   "source": [
    "print(slr2.summary())\n",
    "print(slr2.get_robustcov_results().summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Serial correlation of errors\n",
    "\n",
    "A common and serious problem is when errors are correlated across observations (known serial correlation or autocorrelation). This can occur, for instance, when some of the data points are related, or when we use time-series data with periodic fluctuations. If one of the independent variables depends on previous values of the dependent variable - such as when it is equal to the value of the dependent variable in the previous period - or if incorrect model specification leads to autocorrelation, then the coefficient estimates will be inconsistent and therefore invalid. Otherwise, the parameter estimates will be valid, but the fit statistics will be off. For instance, if the correlation is positive, we will have inflated F- and t-statistics, leading us to overestimate the significance of the model.\n",
    "\n",
    "If the errors are homoskedastic, we can test for autocorrelation using the Durbin-Watson test, which is conveniently reported in the regression summary in `statsmodels`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>        <td>Adj Close</td>    <th>  R-squared:         </th> <td>   0.670</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.669</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   507.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 08 Jun 2020</td> <th>  Prob (F-statistic):</th> <td>3.93e-62</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>23:08:46</td>     <th>  Log-Likelihood:    </th> <td> -583.54</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   252</td>      <th>  AIC:               </th> <td>   1171.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   250</td>      <th>  BIC:               </th> <td>   1178.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   27.7045</td> <td>    0.309</td> <td>   89.609</td> <td> 0.000</td> <td>   27.096</td> <td>   28.313</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.0480</td> <td>    0.002</td> <td>   22.532</td> <td> 0.000</td> <td>    0.044</td> <td>    0.052</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>30.510</td> <th>  Durbin-Watson:     </th> <td>   0.085</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  44.725</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.750</td> <th>  Prob(JB):          </th> <td>1.94e-10</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.418</td> <th>  Cond. No.          </th> <td>    289.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:              Adj Close   R-squared:                       0.670\n",
       "Model:                            OLS   Adj. R-squared:                  0.669\n",
       "Method:                 Least Squares   F-statistic:                     507.7\n",
       "Date:                Mon, 08 Jun 2020   Prob (F-statistic):           3.93e-62\n",
       "Time:                        23:08:46   Log-Likelihood:                -583.54\n",
       "No. Observations:                 252   AIC:                             1171.\n",
       "Df Residuals:                     250   BIC:                             1178.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         27.7045      0.309     89.609      0.000      27.096      28.313\n",
       "x1             0.0480      0.002     22.532      0.000       0.044       0.052\n",
       "==============================================================================\n",
       "Omnibus:                       30.510   Durbin-Watson:                   0.085\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               44.725\n",
       "Skew:                          -0.750   Prob(JB):                     1.94e-10\n",
       "Kurtosis:                       4.418   Cond. No.                         289.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 9,
     "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": [
    "# Load pricing data for an asset\n",
    "start_date = '2014-01-01'\n",
    "end_date = '2015-01-01'\n",
    "y = pdr.get_data_yahoo('DAL', start=start_date, end=end_date, interval = \"1d\")['Adj Close']\n",
    "x = np.arange(len(y))\n",
    "\n",
    "# Regress pricing data against time\n",
    "model = regression.linear_model.OLS(y, sm.add_constant(x)).fit()\n",
    "\n",
    "# Construct the fit line\n",
    "prediction = model.params[0] + model.params[1]*x\n",
    "\n",
    "# Plot pricing data and regression line\n",
    "plt.plot(x,y)\n",
    "plt.plot(x, prediction, color='r')\n",
    "plt.legend(['DAL Price', 'Regression Line'])\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Price')\n",
    "\n",
    "# Print summary of regression results\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing for Autocorrelation\n",
    "\n",
    "We can test for autocorrelation in both our prices and residuals. We'll use the built-in method to do this, which is based on the Ljun-Box test. This test computes the probability that the n-th lagged datapoint is predictive of the current. If no max lag is given, then the function computes a max lag and returns the p-values for all lags up to that one. We can see here that for the 5 most recent datapoints, a significant correlation exists with the current. Therefore we conclude that both the data is autocorrelated.\n",
    "\n",
    "We also test for normality for fun."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prices autocorrelation p-values [8.84140625e-052 5.65401714e-096 9.54932296e-136 8.25054196e-172\n",
      " 3.49532356e-204 1.31949805e-232 1.14534498e-257 9.32137555e-280\n",
      " 1.87470094e-299 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000]\n",
      "Residuals autocorrelation p-values [8.84140625e-052 5.65401714e-096 9.54932296e-136 8.25054196e-172\n",
      " 3.49532356e-204 1.31949805e-232 1.14534498e-257 9.32137555e-280\n",
      " 1.87470094e-299 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
      " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000]\n",
      "Jarque-Bera p-value that residuals are normally distributed 1.9415332079496208e-10\n"
     ]
    }
   ],
   "source": [
    "_, prices_qstats, prices_qstat_pvalues = statsmodels.tsa.stattools.acf(y, qstat=True)\n",
    "_, prices_qstats, prices_qstat_pvalues = statsmodels.tsa.stattools.acf(y-prediction, qstat=True)\n",
    "\n",
    "print('Prices autocorrelation p-values', prices_qstat_pvalues)\n",
    "print('Residuals autocorrelation p-values', prices_qstat_pvalues)\n",
    "\n",
    "_, jb_pvalue, _, _ = statsmodels.stats.stattools.jarque_bera(y-prediction)\n",
    "\n",
    "print('Jarque-Bera p-value that residuals are normally distributed', jb_pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Newey-West\n",
    "\n",
    "Newey-West is a method of computing variance which accounts for autocorrelation. A naive variance computation will actually produce inaccurate standard errors with the presence of autocorrelation.\n",
    "\n",
    "We can attempt to change the regression equation to eliminate serial correlation. A simpler fix is adjusting the standard errors using an appropriate method and using the adjusted values to check for significance. Below we use the Newey-West method from `statsmodels` to compute adjusted standard errors for the coefficients. They are higher than those originally reported by the regression, which is what we expected for positively correlated errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Old standard errors: 0.30917188282698177 0.002131349947945898\n",
      "Adjusted standard errors: 0.4556001392289641 0.00461489650846474\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "\n",
    "# Find the covariance matrix of the coefficients\n",
    "cov_mat = stats.sandwich_covariance.cov_hac(model)\n",
    "\n",
    "# Print the standard errors of each coefficient from the original model and from the adjustment\n",
    "print('Old standard errors:', model.bse[0], model.bse[1])\n",
    "print('Adjusted standard errors:', sqrt(cov_mat[0,0]), sqrt(cov_mat[1,1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " # Multicollinearity\n",
    "\n",
    "When using multiple independent variables, it is important to check for multicollinearity; that is, an approximate linear relation between the independent variables, such as\n",
    "$$ X_2 \\approx 5 X_1 - X_3 + 4.5 $$\n",
    "\n",
    "With multicollinearity, it is difficult to identify the independent effect of each variable, since we can change around the coefficients according to the linear relation without changing the model. As with truly unnecessary variables, this will usually not hurt the accuracy of the model, but will cloud our analysis. In particular, the estimated coefficients will have large standard errors. The coefficients will also no longer represent the partial effect of each variable, since with multicollinearity we cannot change one variable while holding the others constant.\n",
    "\n",
    "High correlation between independent variables is indicative of multicollinearity. However, it is not enough, since we would want to detect correlation between one of the variables and a linear combination of the other variables. If we have high R-squared but low t-statistics on the coefficients (the fit is good but the coefficients are not estimated precisely) we may suspect multicollinearity. To resolve the problem, we can drop one of the independent variables involved in the linear relation.\n",
    "\n",
    "For instance, using two stock indices as our independent variables is likely to lead to multicollinearity. Below we can see that removing one of them improves the t-statistics without hurting R-squared.\n",
    "\n",
    "Another important thing to determine here is which variable may be the casual one. If we hypothesize that the market influences both MDY and HPQ, then the market is the variable that we should use in our predictive model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "R-squared: 0.9088309948246416\n",
      "t-statistics of coefficients:\n",
      " const   -12.616281\n",
      "x1       25.273402\n",
      "x2       -5.351658\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Price')"
      ]
     },
     "execution_count": 14,
     "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": [
    "# Load pricing data for asset and two market indices\n",
    "start_date = '2014-01-01'\n",
    "end_date = '2015-01-01'\n",
    "b1 = pdr.get_data_yahoo('SPY', start=start_date, end=end_date, interval = \"1d\")['Adj Close']\n",
    "b2 = pdr.get_data_yahoo('MDY', start=start_date, end=end_date, interval = \"1d\")['Adj Close']\n",
    "a = pdr.get_data_yahoo('HPQ', start=start_date, end=end_date, interval = \"1d\")['Adj Close']\n",
    "\n",
    "# Run multiple linear regression\n",
    "mlr = regression.linear_model.OLS(a, sm.add_constant(np.column_stack((b1,b2)))).fit()\n",
    "\n",
    "# Construct fit curve using dependent variables and estimated coefficients\n",
    "mlr_prediction = mlr.params[0] + mlr.params[1]*b1 + mlr.params[2]*b2\n",
    "\n",
    "# Print regression statistics \n",
    "print('R-squared:', mlr.rsquared_adj)\n",
    "print('t-statistics of coefficients:\\n', mlr.tvalues)\n",
    "\n",
    "# Plot asset and model\n",
    "a.plot()\n",
    "mlr_prediction.plot()\n",
    "plt.legend(['Asset', 'Model']);\n",
    "plt.ylabel('Price')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/numpy/core/fromnumeric.py:2389: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R-squared: 0.8987512606667984\n",
      "t-statistics of coefficients:\n",
      " const       -24.939298\n",
      "Adj Close    47.212744\n",
      "dtype: float64\n"
     ]
    },
    {
     "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": [
    "# Perform linear regression\n",
    "slr = regression.linear_model.OLS(a, sm.add_constant(b1)).fit()\n",
    "slr_prediction = slr.params[0] + slr.params[1]*b1\n",
    "\n",
    "# Print fit statistics\n",
    "print('R-squared:', slr.rsquared_adj)\n",
    "print('t-statistics of coefficients:\\n', slr.tvalues)\n",
    "\n",
    "# Plot asset and model\n",
    "a.plot()\n",
    "slr_prediction.plot()\n",
    "plt.ylabel('Price')\n",
    "plt.legend(['Asset', 'Model']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Anscombe's quartet\n",
    "\n",
    "Anscombe constructed 4 datasets which not only have the same mean and variance in each variable, but also the same correlation coefficient, regression line, and R-squared regression value. Below, we test this result as well as plotting the datasets. A quick glance at the graphs shows that only the first dataset satisfies the regression model assumptions. Consequently, the high R-squared values of the other three are not meaningful, which agrees with our intuition that the other three are not modeled well by the lines of best fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cofficients: [3.00009091 0.50009091] [3.00090909 0.5       ] [3.00245455 0.49972727] [3.00172727 0.49990909]\n",
      "Pearson r: 0.81642051634484 0.8162365060002427 0.8162867394895982 0.8165214368885029\n",
      "R-squared: 0.6665424595087751 0.6662420337274844 0.6663240410665592 0.6667072568984653\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import pearsonr\n",
    "\n",
    "# Construct Anscombe's arrays\n",
    "x1 = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n",
    "y1 = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68]\n",
    "x2 = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n",
    "y2 = [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74]\n",
    "x3 = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n",
    "y3 = [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73]\n",
    "x4 = [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8]\n",
    "y4 = [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89]\n",
    "\n",
    "# Perform linear regressions on the datasets\n",
    "slr1 = regression.linear_model.OLS(y1, sm.add_constant(x1)).fit()\n",
    "slr2 = regression.linear_model.OLS(y2, sm.add_constant(x2)).fit()\n",
    "slr3 = regression.linear_model.OLS(y3, sm.add_constant(x3)).fit()\n",
    "slr4 = regression.linear_model.OLS(y4, sm.add_constant(x4)).fit()\n",
    "\n",
    "# Print regression coefficients, Pearson r, and R-squared for the 4 datasets\n",
    "print('Cofficients:', slr1.params, slr2.params, slr3.params, slr4.params)\n",
    "print('Pearson r:', pearsonr(x1, y1)[0], pearsonr(x2, y2)[0], pearsonr(x3, y3)[0], pearsonr(x4, y4)[0])\n",
    "print('R-squared:', slr1.rsquared, slr2.rsquared, slr3.rsquared, slr4.rsquared)\n",
    "\n",
    "# Plot the 4 datasets with their regression lines\n",
    "f, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2,2)\n",
    "xs = np.arange(20)\n",
    "ax1.plot(slr1.params[0] + slr1.params[1]*xs, 'r')\n",
    "ax1.scatter(x1, y1)\n",
    "ax1.set_xlabel('x1')\n",
    "ax1.set_ylabel('y1')\n",
    "ax2.plot(slr2.params[0] + slr2.params[1]*xs, 'r')\n",
    "ax2.scatter(x2, y2)\n",
    "ax2.set_xlabel('x2')\n",
    "ax2.set_ylabel('y2')\n",
    "ax3.plot(slr3.params[0] + slr3.params[1]*xs, 'r')\n",
    "ax3.scatter(x3, y3)\n",
    "ax3.set_xlabel('x3')\n",
    "ax3.set_ylabel('y3')\n",
    "ax4.plot(slr4.params[0] + slr4.params[1]*xs, 'r')\n",
    "ax4.scatter(x4,y4)\n",
    "ax4.set_xlabel('x4')\n",
    "ax4.set_ylabel('y4');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}