Regressão linear com o pacote Statsmodels.

statsmodels.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regressão Linear com Statsmodels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Statsmodels](http://statsmodels.sourceforge.net/) é um pacote em Python que permite a \n",
    "seus usuários explorar dados, estimar modelos estatśticos e executar testes estatísticos. \n",
    "Uma extensa lista de estatśtica descriptiva, testes estatśticos, funções para plotagem e \n",
    "resultados estatísticos estão disponíveis para diferentes tipos de dados e estimadores. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Mantém o exemplo reprodutível\n",
    "np.random.seed(12)\n",
    "\n",
    "n = 20 # Tamnaho da amostra\n",
    "\n",
    "# Aleatoriamente, seleciona os valores de 'x' a partir de uma\n",
    "# lista \n",
    "x = np.random.choice(np.linspace(0, 10), size=n, replace=False)\n",
    "\n",
    "# Definimos uma reta\n",
    "reta = lambda y : 1 + 2*x\n",
    "# Definimos o valor de y e adicionamos um erro gaussiano\n",
    "\n",
    "y = reta(x)\n",
    "y += np.random.normal(scale=10, size=n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f5757c46fd0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2ct+7FNEf1JbMLA6cDXzqsOIC9nPgDtJzcorNGOB9M/tVZsjtYTMrC7uobHH3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\nIhKIAkNERAJRYIiISCD/H5mxbilqgJlFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f575a03a588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(x, reta(x), 'b-', label='Reta verdadeira')\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$')\n",
    "\n",
    "plt.legend(loc='lower right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para calcular uma regressão linear do tipo $y=a+b.x$, fazemos o seguinte:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Adicionamos uma constante aos valores de 'x'.\n",
    "# Estes correspondem a constante de interceptação no\n",
    "# eixo 'y'\n",
    "x2 = sm.add_constant(x)\n",
    "\n",
    "# Criamos o modelo linear e ajustamos\n",
    "ols = sm.OLS(y, x2)\n",
    "ml = ols.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O método `summary`  nos dá um sumário sobre o ajuste."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "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>   0.105</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.055</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   2.116</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 20 Jun 2016</td> <th>  Prob (F-statistic):</th>  <td> 0.163</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:17:41</td>     <th>  Log-Likelihood:    </th> <td> -75.306</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    20</td>      <th>  AIC:               </th> <td>   154.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    18</td>      <th>  BIC:               </th> <td>   156.6</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>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    3.2334</td> <td>    5.782</td> <td>    0.559</td> <td> 0.583</td> <td>   -8.915    15.381</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    1.3560</td> <td>    0.932</td> <td>    1.455</td> <td> 0.163</td> <td>   -0.602     3.314</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.111</td> <th>  Durbin-Watson:     </th> <td>   2.963</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.574</td> <th>  Jarque-Bera (JB):  </th> <td>   0.960</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.478</td> <th>  Prob(JB):          </th> <td>   0.619</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.512</td> <th>  Cond. No.          </th> <td>    14.9</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.105\n",
       "Model:                            OLS   Adj. R-squared:                  0.055\n",
       "Method:                 Least Squares   F-statistic:                     2.116\n",
       "Date:                Mon, 20 Jun 2016   Prob (F-statistic):              0.163\n",
       "Time:                        16:17:41   Log-Likelihood:                -75.306\n",
       "No. Observations:                  20   AIC:                             154.6\n",
       "Df Residuals:                      18   BIC:                             156.6\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "const          3.2334      5.782      0.559      0.583        -8.915    15.381\n",
       "x1             1.3560      0.932      1.455      0.163        -0.602     3.314\n",
       "==============================================================================\n",
       "Omnibus:                        1.111   Durbin-Watson:                   2.963\n",
       "Prob(Omnibus):                  0.574   Jarque-Bera (JB):                0.960\n",
       "Skew:                           0.478   Prob(JB):                        0.619\n",
       "Kurtosis:                       2.512   Cond. No.                         14.9\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ml.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f5757729c18>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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Eyty92syOB5a6++g456nonSXOOQf+9rfDtXCOZxvjqODco1dw1+UVhzbyibckd58+bYeT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\nECUMERFJyP8HMB6GSnmzk+gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f575785a6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(x, reta(x), 'b-', lw=2, label='Reta verdadeira')\n",
    "\n",
    "ordem = np.argsort(x)\n",
    "plt.plot(x[ordem], ml.fittedvalues[ordem], 'r-', \n",
    "         lw=2, zorder=5, label='Ajuste')\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$')\n",
    "\n",
    "plt.legend(loc='lower right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Statsmodels calcula diversos resultados estatísticos, como vimos na tabela acima. \n",
    "Porém, para obter alguns resultados, é preciso outras ferramentas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.outliers_influence import summary_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nós iremos obter o intervalo de confiança de 95% do nosso ajuste. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "st, ml_stats, ss2 = summary_table(ml)\n",
    "\n",
    "inter_conf_inf = ml_stats[:, 4]\n",
    "inter_conf_sup = ml_stats[:, 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f57576c9be0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Nb7yukYjUkWhMeg8E1ltrswGMMXOBUcCaY95Laq6oyE2Ye/llFywKCtz5nBwF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\nhl7J/AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f57576f1668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(x, reta(x), 'b-', lw=2, label='Reta verdadeira')\n",
    "\n",
    "\n",
    "plt.plot(x[ordem], ml.fittedvalues[ordem], 'r-', lw=2, label='Ajuste')\n",
    "plt.plot(x[ordem], inter_conf_inf[ordem], 'r--', lw=2)\n",
    "plt.plot(x[ordem], inter_conf_sup[ordem], 'r--', lw=2)\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$')\n",
    "\n",
    "plt.legend(loc='lower right')"
   ]
  }
 ],
 "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}