Regresión Logísitca - Teoría, Supuestos y Aplicación..ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"color:darkblue\">Regresión Logísitca</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introducción.\n",
    "La regresión lógistica es muy parecida a los modelos de regresión lineales: predice el valor esperado $E(Y)$ de una variable dependiente $Y$ dado el valor de una o de distintas variables independientes $X_1, X_2, ... X_n$\n",
    "El modelo logistico es para estimar la relación entre una variable dependiente cualitativa dicotómica, dadas una o varias variables independientes cualitativas o cuantitativas. \n",
    "\n",
    "\n",
    "### Función.\n",
    "La regresión logíca calcula la probabilidad $P$ de que ocurra $Y$ a partir de las variables predictorias $X_n$\n",
    "> <h2> $ P(Y) = \\frac{1}{1+ e^{-{\\beta_0 +\\beta_1 X_1 + \\beta_2 X_2 + ... + \\beta_n X_n}}} $ </h2>\n",
    "\n",
    "\n",
    "### Supuestos\n",
    "- Linealidad: Existe una relación binaria entre cada variable predictoria y el logaritmo de la variable respuesta.\n",
    "- Independencia de los errores: Los residuos no siguen un patron claro, estan aleatoriamente distribuidos.\n",
    "- Multicolinealidad: Las variables predictoras no deben estar altamente correlacionadas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#librerias\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejemplo\n",
    "\n",
    "Se desea medir el efecto de la enseñanza personalizada para los estudiantes, si Y = 1 significa que su calificación final fue A y si Y = 0 significa que fue diferente de A. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#datos \n",
    "data = pd.read_excel(\"Datasets/gpa.xlsx\",)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>GPA</th>\n",
       "      <th>TUCE</th>\n",
       "      <th>PSI</th>\n",
       "      <th>calificación</th>\n",
       "      <th>letra</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.66</td>\n",
       "      <td>20</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.89</td>\n",
       "      <td>22</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.28</td>\n",
       "      <td>24</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.92</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.00</td>\n",
       "      <td>21</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    GPA  TUCE  PSI  calificación letra\n",
       "0  2.66    20    0             0     C\n",
       "1  2.89    22    0             0     B\n",
       "2  3.28    24    0             0     B\n",
       "3  2.92    12    0             0     B\n",
       "4  4.00    21    0             1     A"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notas:\n",
    " \n",
    " - Y=1 si la calificación final fue A\n",
    " - Y=0 si la calificación final fue B o C\n",
    " - TUCE  calificación en un examen presentado al comienzo del curso para evaluar los conocimientos previos de macroeconomía\n",
    " - PSI  1 con el nuevo método de enseñanza\n",
    " - 0 en otro caso\n",
    " - GPA  promedio de puntos de calificación inicial\n",
    "\n",
    "Fuente: L. Spector y M. Mazzero, “Probit Analysis and Economic Education”, Journal of Economic Education, vol. 11, 1980, pp. 37-44."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 32 entries, 0 to 31\n",
      "Data columns (total 5 columns):\n",
      "GPA             32 non-null float64\n",
      "TUCE            32 non-null int64\n",
      "PSI             32 non-null int64\n",
      "calificación    32 non-null int64\n",
      "letra           32 non-null object\n",
      "dtypes: float64(1), int64(3), object(1)\n",
      "memory usage: 1.3+ KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x255c3abf780>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 784.25x720 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(data, hue=\"calificación\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#variables del modelo logistico\n",
    "Y = data[\"calificación\"]\n",
    "X = data[[\"GPA\", \"TUCE\", \"PSI\"]]\n",
    "X = sm.add_constant(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.402801\n",
      "         Iterations 7\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>   <td>calificación</td>   <th>  No. Observations:  </th>  <td>    32</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>    28</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     3</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 26 Jul 2020</td> <th>  Pseudo R-squ.:     </th>  <td>0.3740</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>21:24:12</td>     <th>  Log-Likelihood:    </th> <td> -12.890</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -20.592</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>0.001502</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>  -13.0213</td> <td>    4.931</td> <td>   -2.641</td> <td> 0.008</td> <td>  -22.687</td> <td>   -3.356</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>GPA</th>   <td>    2.8261</td> <td>    1.263</td> <td>    2.238</td> <td> 0.025</td> <td>    0.351</td> <td>    5.301</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TUCE</th>  <td>    0.0952</td> <td>    0.142</td> <td>    0.672</td> <td> 0.501</td> <td>   -0.182</td> <td>    0.373</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PSI</th>   <td>    2.3787</td> <td>    1.065</td> <td>    2.234</td> <td> 0.025</td> <td>    0.292</td> <td>    4.465</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:           calificación   No. Observations:                   32\n",
       "Model:                          Logit   Df Residuals:                       28\n",
       "Method:                           MLE   Df Model:                            3\n",
       "Date:                Sun, 26 Jul 2020   Pseudo R-squ.:                  0.3740\n",
       "Time:                        21:24:12   Log-Likelihood:                -12.890\n",
       "converged:                       True   LL-Null:                       -20.592\n",
       "                                        LLR p-value:                  0.001502\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        -13.0213      4.931     -2.641      0.008     -22.687      -3.356\n",
       "GPA            2.8261      1.263      2.238      0.025       0.351       5.301\n",
       "TUCE           0.0952      0.142      0.672      0.501      -0.182       0.373\n",
       "PSI            2.3787      1.065      2.234      0.025       0.292       4.465\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# modelo\n",
    "model = sm.Logit(Y, X).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Interpretación:</b>\n",
    ">  La llamada \"Pseudo $R^2$ es lo que se conoce como $R^2 \\space McFadden$ que es:\n",
    "> $R^2 = \\frac{Predicciones}{Observaciones}$ En este caso como $R^2=0.374$ significa que este modelo se ajusta al 37.4% de los datos.\n",
    ">\n",
    "> Coeficientes: \n",
    "- Ya que el GPA = 2.826, significa que si los demás coeficientes permanecen constante, por cada aumento en 1 del GPA, aumenta en promedio el logit en 2.826.\n",
    "- Se puede representar de forma analoga todos los demás coeficientes. Todos poseen una relación positiva con el logit.\n",
    "- el p-valor asociado a casi todos los coeficientes es menor al 5%, lo cual indica que son significativos a nivel estadístico. La única excepción es el coeficiente de TUCE, cuyo p-valor es de 0.501 = 50.1% por lo que podría omitirse este coeficiente.\n",
    ">\n",
    "> Todas las variables regresoras tienen un impacto en la calificación, dado que el p-valor asociado al modelo en su conjunto es de LLR p = 0.001502 por lo que es muy significativo a nivel estadístico.\n",
    ">\n",
    "> nota: la hipotesis nula $H_0$ asociada al p-valor de los coeficientes, mide la probabilidad e que que un coeficiente sea igual a cero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.410205\n",
      "         Iterations 7\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>   <td>calificación</td>   <th>  No. Observations:  </th>  <td>    32</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>    29</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     2</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 26 Jul 2020</td> <th>  Pseudo R-squ.:     </th>  <td>0.3625</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>21:24:20</td>     <th>  Log-Likelihood:    </th> <td> -13.127</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -20.592</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>0.0005727</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>  -11.6016</td> <td>    4.213</td> <td>   -2.754</td> <td> 0.006</td> <td>  -19.859</td> <td>   -3.344</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>GPA</th>   <td>    3.0634</td> <td>    1.223</td> <td>    2.505</td> <td> 0.012</td> <td>    0.667</td> <td>    5.460</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PSI</th>   <td>    2.3378</td> <td>    1.041</td> <td>    2.246</td> <td> 0.025</td> <td>    0.298</td> <td>    4.378</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:           calificación   No. Observations:                   32\n",
       "Model:                          Logit   Df Residuals:                       29\n",
       "Method:                           MLE   Df Model:                            2\n",
       "Date:                Sun, 26 Jul 2020   Pseudo R-squ.:                  0.3625\n",
       "Time:                        21:24:20   Log-Likelihood:                -13.127\n",
       "converged:                       True   LL-Null:                       -20.592\n",
       "                                        LLR p-value:                 0.0005727\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        -11.6016      4.213     -2.754      0.006     -19.859      -3.344\n",
       "GPA            3.0634      1.223      2.505      0.012       0.667       5.460\n",
       "PSI            2.3378      1.041      2.246      0.025       0.298       4.378\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#modelo sin variable TUCE\n",
    "Y = data[\"calificación\"]\n",
    "X = data[[\"GPA\", \"PSI\"]]\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "model2 = sm.Logit(Y, X).fit()\n",
    "model2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Ahora el modelo en su conjunto es más significativo $R^2 = 0.3625$ y $LLR_{p-value} = 0.0005$, asi como también son más significativos los coeficientes de forma individual. \n",
    "\n",
    "###### Multicolinealidad\n",
    "Para verificar este supuesto se utilizará el VIF (Variance Inflation Factor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.stats.outliers_influence import variance_inflation_factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "vif = pd.DataFrame()\n",
    "#X.shape[1] = 3, ya que existen 3 variables\n",
    "# la funcion \"variance_inflation_factor\" toma como parametros los datos y el numero de variables\n",
    "\n",
    "vif[\"VIF Factor\"] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]\n",
    "vif[\"Variables\"] = X.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>VIF Factor</th>\n",
       "      <th>Variables</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>47.424321</td>\n",
       "      <td>const</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.001577</td>\n",
       "      <td>GPA</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.001577</td>\n",
       "      <td>PSI</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   VIF Factor Variables\n",
       "0   47.424321     const\n",
       "1    1.001577       GPA\n",
       "2    1.001577       PSI"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = pd.concat([Y, X], axis=1)\n",
    "\n",
    "plt.figure(figsize=(10,8))\n",
    "sns.heatmap(Z.corr(), cmap=\"Blues\", annot=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Aunque el VIF de la constante es superior a 10 (que es cuando un VIF indica multicolinealidad) es una variable artificial que no guarda correlación con las otras variables explicatorias, por lo que no hay evidencia de multicolinealidad."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Independencia de los errores\n",
    "\n",
    "Para evualuar la independencia de los errores, se utilizará el estadístico Durbin-Watson. Este toma valores entre 0 y 4, donde 2 inidica que no existe relacion entre los errores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.2609\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.stats.stattools import durbin_watson\n",
    "dw = durbin_watson(model2.resid_generalized)\n",
    "print(round(dw,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Como el Durbin-Watson resulto cercano a 2, se acepta que los errores no esta relacionados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Modelo con Sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.feature_selection import RFE\n",
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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>GPA</th>\n",
       "      <th>TUCE</th>\n",
       "      <th>PSI</th>\n",
       "      <th>calificación</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>GPA</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.386986</td>\n",
       "      <td>0.039683</td>\n",
       "      <td>0.497147</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TUCE</th>\n",
       "      <td>0.386986</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.112780</td>\n",
       "      <td>0.303055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PSI</th>\n",
       "      <td>0.039683</td>\n",
       "      <td>0.112780</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.422760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>calificación</th>\n",
       "      <td>0.497147</td>\n",
       "      <td>0.303055</td>\n",
       "      <td>0.422760</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   GPA      TUCE       PSI  calificación\n",
       "GPA           1.000000  0.386986  0.039683      0.497147\n",
       "TUCE          0.386986  1.000000  0.112780      0.303055\n",
       "PSI           0.039683  0.112780  1.000000      0.422760\n",
       "calificación  0.497147  0.303055  0.422760      1.000000"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Variables\n",
    "Y = data[\"calificación\"]\n",
    "X = data[[\"GPA\", \"TUCE\",\"PSI\"]]\n",
    "X = sm.add_constant(X)\n",
    "\n",
    "#Selección de variables\n",
    "lr = LogisticRegression()\n",
    "\n",
    "n=1\n",
    "\n",
    "rfe = RFE(lr, n)\n",
    "rfe = rfe.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False,  True])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfe.support_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 4, 1])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfe.ranking_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('const', False, 2), ('GPA', False, 3), ('TUCE', False, 4), ('PSI', True, 1)]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = zip(X.columns, rfe.support_, rfe.ranking_)\n",
    "z = list(z)\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Las variables más importantes para predecir la calificación son: PSI, GPA y la constante. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data[[\"GPA\",\"PSI\"]]\n",
    "X = sm.add_constant(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8125"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sk_logit = LogisticRegression().fit(X, Y)\n",
    "\n",
    "#R cuadrada\n",
    "sk_logit.score(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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>Variables</th>\n",
       "      <th>Coef</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>const</td>\n",
       "      <td>[-0.8873227060465951]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>GPA</td>\n",
       "      <td>[0.2520660384223032]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>PSI</td>\n",
       "      <td>[0.9872760191869184]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Variables                   Coef\n",
       "0     const  [-0.8873227060465951]\n",
       "1       GPA   [0.2520660384223032]\n",
       "2       PSI   [0.9872760191869184]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Coeficientes:\n",
    "coeficientes = list( zip( X.columns, np.transpose(sk_logit.coef_) ) )\n",
    "coeficientes = pd.DataFrame(coeficientes, columns=[\"Variables\", \"Coef\"])\n",
    "coeficientes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>   <td>calificación</td>   <th>  No. Observations:  </th>  <td>    32</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>Logit</td>      <th>  Df Residuals:      </th>  <td>    29</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     2</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 26 Jul 2020</td> <th>  Pseudo R-squ.:     </th>  <td>0.3625</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>21:37:13</td>     <th>  Log-Likelihood:    </th> <td> -13.127</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -20.592</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th> <td>0.0005727</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>  -11.6016</td> <td>    4.213</td> <td>   -2.754</td> <td> 0.006</td> <td>  -19.859</td> <td>   -3.344</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>GPA</th>   <td>    3.0634</td> <td>    1.223</td> <td>    2.505</td> <td> 0.012</td> <td>    0.667</td> <td>    5.460</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>PSI</th>   <td>    2.3378</td> <td>    1.041</td> <td>    2.246</td> <td> 0.025</td> <td>    0.298</td> <td>    4.378</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:           calificación   No. Observations:                   32\n",
       "Model:                          Logit   Df Residuals:                       29\n",
       "Method:                           MLE   Df Model:                            2\n",
       "Date:                Sun, 26 Jul 2020   Pseudo R-squ.:                  0.3625\n",
       "Time:                        21:37:13   Log-Likelihood:                -13.127\n",
       "converged:                       True   LL-Null:                       -20.592\n",
       "                                        LLR p-value:                 0.0005727\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const        -11.6016      4.213     -2.754      0.006     -19.859      -3.344\n",
       "GPA            3.0634      1.223      2.505      0.012       0.667       5.460\n",
       "PSI            2.3378      1.041      2.246      0.025       0.298       4.378\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#imprimir el resumen del modelo con statsmodels para comparación\n",
    "model2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Conclusiones:\n",
    "El model de regresión logística es uno de los más comunes y utilizados. Es importante siempre profundizar en las matemáticas detras del modelo, como los supuestos, el método de newton-raphson que se utiliza en el modelo logit y la máxima verosimilitud.\n",
    "\n",
    "En el ejemplo realizado, solamente se pudo calcular el 36% de las calificaciones dado que la relación entre las variables era muy leve.\n",
    "\n",
    "### Fuentes:\n",
    "- Ferre Jaén M. E. (2019) FEIR 45: Regresión logística. Apuntes del curso FEIR3, curso 2014/15 actualizados. Extraído el 30 de junio de 2020 de: http://gauss.inf.um.es/feir/45/\n",
    "- Gujarati & Porter (2010) El modelo logit (cap. 15 Modelos de regresión de respuesta cualitativa) . Econometría (5ta Edición). McGraw-Hill Education. Ciduad de México.\n",
    "- Tavares E. (2017) Variance Inflation Factor (VIF) Explained. Extraído el 30 de junio de 2020 de: https://etav.github.io/python/vif_factor_python.html"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}