{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Régression Linéaire\n",
    "\n",
    "Solution exacte - OLS\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_regression\n",
    "# http://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_regression.html#sklearn.datasets.make_regression\n",
    "from time import time\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Régression - 10 échantillons - 2 variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.50468651, -1.0363914 ],\n",
       "       [ 1.1360658 , -1.5329035 ],\n",
       "       [ 1.0361652 ,  0.9173159 ],\n",
       "       [-0.07087342, -1.30225772],\n",
       "       [-0.53991563,  0.58699332],\n",
       "       [ 0.49611293,  1.26571269],\n",
       "       [ 0.64199009,  1.78886413],\n",
       "       [-0.22783139, -0.36292215],\n",
       "       [ 1.05649997, -0.87559053],\n",
       "       [ 0.89530471,  0.50068718]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, y = make_regression(n_samples=10, n_features=2)\n",
    "\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "?make_regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l'erreur résiduelle moyenne est -0.0000 \n"
     ]
    }
   ],
   "source": [
    "\n",
    "# example simple 10 echantillons , 2 predicteurs\n",
    "X, y = make_regression(n_samples=10, n_features=2)\n",
    "\n",
    "# OLS, moindre carrés\n",
    "beta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "\n",
    "# prediction\n",
    "yhat = X[:, 0]* beta[0] + X[:,1] * beta[1]\n",
    "\n",
    "# erreur residuelle\n",
    "e = y - yhat\n",
    "\n",
    "print(\"l'erreur résiduelle moyenne est {:.4f} \".format(np.mean(y-yhat)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Régression 100k échantillons, 1000 variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calcul fait en 2.89s\n",
      "l'erreur résiduelle moyenne est -0.0000 \n"
     ]
    }
   ],
   "source": [
    "# maintenant le meme exemple avcec un autre ordre de grandeur\n",
    "N = 100000\n",
    "M = 1000\n",
    "X, y = make_regression(n_samples=N, n_features=M)\n",
    "t = time()\n",
    "beta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "print(\"Calcul fait en {:.2f}s\".format( (time() -t) ))\n",
    "\n",
    "# prediction\n",
    "yhat = [0 for i in range(N)]\n",
    "for k in range(M):\n",
    "    yhat += X[:, k]* beta[k]\n",
    "\n",
    "# erreur residuelle\n",
    "e = y - yhat\n",
    "\n",
    "print(\"l'erreur résiduelle moyenne est {:.4f} \".format(np.mean(y-yhat)))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. On rajoute du bruit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calcul fait en 0.00s\n",
      "l'erreur résiduelle moyenne est 0.7927 \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Résidus')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Z7nvDXIg+8UTpxBrVFOeTxyLNo6cnsWjxEty66WBj+cw29FLN1fP3sV7vum4D3nTZyvoZ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/YVzVHkbZT9a/kpdrhko335QeaLmJ4+xQieo0MNePT4VLGRlTTFvk3iOVuWWQag3I5C8hxUUSa2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\nbEpMKpfXa6hdlWQdns8DOOl10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Yniz0ioMle0hFMgrjUtjTzLKrYMVecXkz9uGotS8LF9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\nCQNfFnVzikdaDbh018pa8xwgHgOhuAJOtKHdidAU8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hQXzpHienlHO2nz7CKS+pWhuHDu\noOo1w5FiFaLzq0/YRzQx77KqJnQViiPiSxHxYET8KSJ+GRF71FWYeqU9fcIvoDo4fUKl8JMuadh0\nO1L81cw8KDMPAe4CvlBDTeqh9qDNWjNxLZw+IUmd8ytUTeoqFGfmmnGL2+L5WgNn7PvHScW1mOGE\nJBXCaRCaDvvvPgeAd+yxfcOVqERdX6c4Iq4EzgFeBt7bdUXqqd3mtK6Fuv02sxuuZDg4UqxS+EnX\ndDh2/1359ecXs+dO2zZdigo0YSiOiHuA3Tby0NLMvCMzlwJLI+Iy4FPAFZt4niXAEoCRkZHOK1at\nLlz8NhbM3YYPHrR706UMBecUS1J3DMRqyoShODOPm+Rz/Qj4GZsIxZl5LXAtwOjoqMfq+8QWM2dw\n2qHzmi5jaHhIWaXwoy5p2HR79Yl9xy2eAjzSXTmSpEHgD0BJw6bbOcVXRcR+wFrgSeDC7kuSJEmS\nequrUJyZp9dViCRJktQULyAlSZKk4nV9STZJE7vt40fx+ptrmy5DkiRtgqFY6oHD99yx6RIkSdJm\nOH1CkiRJxTMUS5IkqXiGYkmSJBXPUCxJkqTieaKdVIOvn3kw/3j+labLkCRJHTIUSzU4/fD5TZcg\nSZK64PQJSZIkFc9QLEmSpOIZiiVJ0+7sRSNNlyBJm2UoliRNuy+fdiBPXHVS02VI0iYZiiVJklQ8\nQ7EkSZKKZyiWJElS8QzFkiRJKp6hWJIkScUzFEuSJKl4hmJJkiQVz1AsSZKk4hmKJUmSVDxDsSRJ\nkopnKJYkSVLxDMWSJEkqnqFYkiRJxTMUS5IkqXizmi5AkjQ4brngSJaveLHpMiSpdoZiSdKkHbFw\nLkcsnNt0GZJUO6dPSJIkqXiGYkmSJBXPUCxJkqTiGYolSZJUPEOxJEmSimcoliRJUvEMxZIkSSpe\nLaE4Ii6OiIyInet4PkmSJKmXug7FEbEAeB+wovtyJEmSpN6rY6T4auASIGt4LkmSJKnnugrFEXEK\n8HRm/rmmeiRJkqSemzXRBhFxD7DbRh5aClwOHD+ZF4qIJcASgJGRkSmUKEmSJE2vyOxs1kNEHAjc\nC7xarZoPPAMckZnPbe7fjo6O5rJlyzp6XUmSJGmyIuKBzBydcLtOQ/FGXvAJYDQz/zWJbV8Anqzl\nhadmZ2DC+jTwbOcy2M5lsJ3LYDuXoal23jMz3zrRRhNOn5gOkylsOkTEssn8UtBgs53LYDuXwXYu\ng+1chn5v59pCcWbuVddzSZIkSb3kHe0kSZJUvNJC8bVNF6CesJ3LYDuXwXYug+1chr5u59pOtJMk\nSZIGVWkjxZIkSdIGignFEXFCRPw9Ih6LiEubrkedi4gFEXFfRDwcEX+NiIuq9XMj4u6IeLT6c8dq\nfUTEt6u2fzAiDmv2HWiyImJmRCyPiLuq5YURcX/Vxj+JiNnV+i2r5ceqx/dqsm5NXkTsEBG3RsQj\nVZ8+0r48fCLis9X39UMRcXNEbGV/HnwRcUNErIqIh8atm3L/jYhzq+0fjYhzm3gvUEgojoiZwHeB\nE4EDgA9HxAHNVqUuvAl8LjP3BxYBn6za81Lg3szcl9aNZdo/fk4E9q3+WwJc0/uS1aGLgIfHLX8F\nuLpq4xeB86v15wMvZuY+wNXVdhoM3wJ+nplvBw6m1d725SESEfOAT9O6l8E7gZnAWdifh8H3gBPW\nWzel/hsRc4ErgHcBRwBXtIN0rxURimn9T34sMx/PzNeBHwOnNlyTOpSZz2bmH6u/v0JrJzqPVpve\nVG12E3Ba9fdTge9ny++AHSJi9x6XrSmKiPnAScB11XIAxwC3Vpus38bttr8VOLbaXn0sIuYA7wGu\nB8jM1zPzJezLw2gWsHVEzAK2AZ7F/jzwMvM3wOr1Vk+1/74fuDszV2fmi8DdbBi0e6KUUDwPeGrc\n8spqnQZcdVjtUOB+YNfMfBZawRnYpdrM9h9M3wQuAdZWyzsBL2Xmm9Xy+HYca+Pq8Zer7dXf9gZe\nAG6spslcFxHbYl8eKpn5NPA1YAWtMPwy8AD252E11f7bN/26lFC8sV+YXnZjwEXEdsBtwGcyc83m\nNt3IOtu/j0XEycCqzHxg/OqNbJqTeEz9axZwGHBNZh4K/Jt1h1o3xnYeQNWh8FOBhcAewLa0DqWv\nz/483DbVrn3T3qWE4pXAgnHL84FnGqpFNYiILWgF4h9m5u3V6ufbh1KrP1dV623/wfNu4JSIeILW\ndKdjaI0c71AdfoX/b8exNq4e354ND+mp/6wEVmbm/dXyrbRCsn15uBwH/DMzX8jMN4DbgaOwPw+r\nqfbfvunXpYTiPwD7Vme6zqY1wf/OhmtSh6q5ZdcDD2fmN8Y9dCfQPmv1XOCOcevPqc58XQS83D60\no/6UmZdl5vzq9vFnAb/KzI8A9wFnVJut38bttj+j2t6RpT6Xmc8BT0XEftWqY4G/YV8eNiuARRGx\nTfX93W5n+/Nwmmr//QVwfETsWB1VOL5a13PF3LwjIj5Aa6RpJnBDZl7ZcEnqUEQcDfwW+Avr5pte\nTmte8S3ACK0v4TMzc3X1JfwdWhP3XwXOy8xlPS9cHYmIxcDFmXlyROxNa+R4LrAcODszX4uIrYAf\n0Jpfvho4KzMfb6pmTV5EHELrZMrZwOPAebQGbOzLQyQivgh8iNbVg5YDH6M1b9T+PMAi4mZgMbAz\n8Dytq0j8lCn234j4KK39OMCVmXljL99HWzGhWJIkSdqUUqZPSJIkSZtkKJYkSVLxDMWSJEkqnqFY\nkiRJxTMUS5IkqXiGYkmSJBXPUCxJkqTiGYolSZJUvP8BEXI7PEgpFIsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1029b87f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# maintenant avec du bruit gaussien de variance 10\n",
    "N = 1000\n",
    "M = 10\n",
    "\n",
    "X, y = make_regression(n_samples=N, n_features=M, noise =1)\n",
    "t = time()\n",
    "beta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "print(\"Calcul fait en {:.2f}s\".format( (time() -t) ))\n",
    "\n",
    "# prediction\n",
    "yhat = [0 for i in range(N)]\n",
    "for k in range(M):\n",
    "    yhat += X[:, k]* beta[k]\n",
    "\n",
    "# erreur residuelle\n",
    "e = y - yhat\n",
    "\n",
    "print(\"l'erreur résiduelle moyenne est {:.4f} \".format(np.mean(np.abs(e))))\n",
    "\n",
    "fig, ax = plt.subplots(1,1, figsize=(12,6))\n",
    "plt.plot(e)\n",
    "plt.title('Résidus')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calcul fait en 0.00s\n",
      "l'erreur résiduelle moyenne est 2883.4586 \n"
     ]
    }
   ],
   "source": [
    "N = 100\n",
    "M = 200\n",
    "\n",
    "X, y = make_regression(n_samples=N, n_features=M)\n",
    "t = time()\n",
    "beta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "print(\"Calcul fait en {:.2f}s\".format( (time() -t) ))\n",
    "\n",
    "# prediction\n",
    "yhat = [0 for i in range(N)]\n",
    "for k in range(M):\n",
    "    yhat += X[:, k]* beta[k]\n",
    "\n",
    "# erreur residuelle\n",
    "e = y - yhat\n",
    "\n",
    "print(\"l'erreur résiduelle moyenne est {:.4f} \".format(np.mean(np.abs(e))))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>model year</th>\n",
       "      <th>origin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>15.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165.0</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>16.0</td>\n",
       "      <td>8</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>17.0</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0   mpg  cylinders  displacement  horsepower  weight  \\\n",
       "0           1  18.0          8         307.0       130.0    3504   \n",
       "1           2  15.0          8         350.0       165.0    3693   \n",
       "2           3  18.0          8         318.0       150.0    3436   \n",
       "3           4  16.0          8         304.0       150.0    3433   \n",
       "4           5  17.0          8         302.0       140.0    3449   \n",
       "\n",
       "   acceleration  model year  origin  \n",
       "0          12.0          70       1  \n",
       "1          11.5          70       1  \n",
       "2          11.0          70       1  \n",
       "3          12.0          70       1  \n",
       "4          10.5          70       1  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "df = pd.read_csv('../data/autos_mpg.csv')\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>mpg</td>       <th>  R-squared:         </th> <td>   0.717</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.713</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   165.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 26 Sep 2018</td> <th>  Prob (F-statistic):</th> <td>4.84e-104</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:45:29</td>     <th>  Log-Likelihood:    </th> <td> -1131.1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   398</td>      <th>  AIC:               </th> <td>   2276.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   391</td>      <th>  BIC:               </th> <td>   2304.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     6</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>Intercept</th>    <td>   42.7111</td> <td>    2.693</td> <td>   15.861</td> <td> 0.000</td> <td>   37.417</td> <td>   48.005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cylinders</th>    <td>   -0.5256</td> <td>    0.404</td> <td>   -1.302</td> <td> 0.194</td> <td>   -1.320</td> <td>    0.268</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>displacement</th> <td>    0.0106</td> <td>    0.009</td> <td>    1.133</td> <td> 0.258</td> <td>   -0.008</td> <td>    0.029</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>horsepower</th>   <td>   -0.0529</td> <td>    0.016</td> <td>   -3.277</td> <td> 0.001</td> <td>   -0.085</td> <td>   -0.021</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight</th>       <td>   -0.0051</td> <td>    0.001</td> <td>   -6.441</td> <td> 0.000</td> <td>   -0.007</td> <td>   -0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>acceleration</th> <td>    0.0043</td> <td>    0.120</td> <td>    0.036</td> <td> 0.972</td> <td>   -0.232</td> <td>    0.241</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>origin</th>       <td>    1.4269</td> <td>    0.345</td> <td>    4.136</td> <td> 0.000</td> <td>    0.749</td> <td>    2.105</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>32.659</td> <th>  Durbin-Watson:     </th> <td>   0.886</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  43.338</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.624</td> <th>  Prob(JB):          </th> <td>3.88e-10</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.028</td> <th>  Cond. No.          </th> <td>3.99e+04</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.99e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                    mpg   R-squared:                       0.717\n",
       "Model:                            OLS   Adj. R-squared:                  0.713\n",
       "Method:                 Least Squares   F-statistic:                     165.5\n",
       "Date:                Wed, 26 Sep 2018   Prob (F-statistic):          4.84e-104\n",
       "Time:                        11:45:29   Log-Likelihood:                -1131.1\n",
       "No. Observations:                 398   AIC:                             2276.\n",
       "Df Residuals:                     391   BIC:                             2304.\n",
       "Df Model:                           6                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "================================================================================\n",
       "                   coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------\n",
       "Intercept       42.7111      2.693     15.861      0.000      37.417      48.005\n",
       "cylinders       -0.5256      0.404     -1.302      0.194      -1.320       0.268\n",
       "displacement     0.0106      0.009      1.133      0.258      -0.008       0.029\n",
       "horsepower      -0.0529      0.016     -3.277      0.001      -0.085      -0.021\n",
       "weight          -0.0051      0.001     -6.441      0.000      -0.007      -0.004\n",
       "acceleration     0.0043      0.120      0.036      0.972      -0.232       0.241\n",
       "origin           1.4269      0.345      4.136      0.000       0.749       2.105\n",
       "==============================================================================\n",
       "Omnibus:                       32.659   Durbin-Watson:                   0.886\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               43.338\n",
       "Skew:                           0.624   Prob(JB):                     3.88e-10\n",
       "Kurtosis:                       4.028   Cond. No.                     3.99e+04\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 3.99e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = smf.ols(formula='mpg ~ cylinders + displacement + horsepower + weight + acceleration + origin ', data=df).fit()\n",
    "lm.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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