LinearRegression_Scikit-learn_Statsmodels.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f99fa3b0",
   "metadata": {},
   "source": [
    "### Modelo de Regresión utilizando Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ec22248d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "sns.set_theme()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "034d5603",
   "metadata": {},
   "source": [
    "#### 1. Obtención, preparación y visualización de datos\n",
    "\n",
    "Al igual que en ejercicio anterior, nuestro marco de datos viene determinado por una hoja de cálculo. En lugar de utilizar el módulo CSV, vamos a utilizar pd.read_excel ya que el archivo viene con la extensión xlsx. Asignaremos la variable *data* al marco de datos global.\n",
    "\n",
    "Posteriormente comenzamos la **segregación de datos**, denominando $X$ la columna ['House Size (sq.ft.)'] e $Y$ a la columna ['House Price'], puesto que ***intentamos poner en relación el precio que tendrá la vivienda con respecto al tamaño de la misma***. Es decir, el precio de la casa será nuestra variable dependiente. Una vez más, podemos acceder a una visualización del marco de datos mediante .head(), .tail() o utilizando .info() si buscamos obtener información general.\n",
    "\n",
    "Finalmente, obtenemos una **visualización general de los datos mediante un scatterplot**. Esto nos permitirá observar gráficamente los datos. En la columna $Y$ aparecerá el precio de la vivienda y en el eje $X$ el tamaño. A diferencia de en el ejercicio anterior, introducimos etiquetas de referencia xlabel e ylabel para marcar los nombres.\n",
    "\n",
    "Por último, para poner en contexto los datos desde el punto 0, debemos introducir una función plt.axis() que nos permite **personalizar las dimensiones del eje**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c91b9500",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .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>House Price</th>\n",
       "      <th>House Size (sq.ft.)</th>\n",
       "      <th>State</th>\n",
       "      <th>Number of Rooms</th>\n",
       "      <th>Year of Construction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1116000</td>\n",
       "      <td>1940</td>\n",
       "      <td>IN</td>\n",
       "      <td>8</td>\n",
       "      <td>2002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>860000</td>\n",
       "      <td>1300</td>\n",
       "      <td>IN</td>\n",
       "      <td>5</td>\n",
       "      <td>1992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>818400</td>\n",
       "      <td>1420</td>\n",
       "      <td>IN</td>\n",
       "      <td>6</td>\n",
       "      <td>1987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1000000</td>\n",
       "      <td>1680</td>\n",
       "      <td>IN</td>\n",
       "      <td>7</td>\n",
       "      <td>2000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>640000</td>\n",
       "      <td>1270</td>\n",
       "      <td>IN</td>\n",
       "      <td>5</td>\n",
       "      <td>1995</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   House Price  House Size (sq.ft.) State  Number of Rooms  \\\n",
       "0      1116000                 1940    IN                8   \n",
       "1       860000                 1300    IN                5   \n",
       "2       818400                 1420    IN                6   \n",
       "3      1000000                 1680    IN                7   \n",
       "4       640000                 1270    IN                5   \n",
       "\n",
       "   Year of Construction  \n",
       "0                  2002  \n",
       "1                  1992  \n",
       "2                  1987  \n",
       "3                  2000  \n",
       "4                  1995  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_excel('Housing.xlsx')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fa810113",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1940\n",
       "1    1300\n",
       "2    1420\n",
       "3    1680\n",
       "4    1270\n",
       "Name: House Size (sq.ft.), dtype: int64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data['House Size (sq.ft.)']\n",
    "Y = data['House Price']\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b0cef1f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1116000\n",
       "1     860000\n",
       "2     818400\n",
       "3    1000000\n",
       "4     640000\n",
       "Name: House Price, dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d996fcc1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,Y)\n",
    "plt.xlabel('House size')\n",
    "plt.ylabel('House Price')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "45273f5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,Y) \n",
    "plt.axis([0, 2500, 0, 1500000]) \n",
    "plt.xlabel(\"House size\") \n",
    "plt.ylabel(\"House Price\") \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13a22b18",
   "metadata": {},
   "source": [
    "#### 2. Preparamos la muestra para la regresión\n",
    "\n",
    "Una vez visualizados los datos, pasamos a preparar el modelo de regresión utilizando Scikit-learn. El primer paso que tenemos que realizar es el de **separar nuestra muestra** en el grupo de entrenamiento (train) y de testeo (test). Para ello utilizaremos el módulo *train_test_split*, donde indicaremos los datos a introducir (X,Y), el tamaño de la muestra que queremos incluir (test_size = 0.2) = 20% de la muestra, *dejando el otro 80% para train* y por último random_state = 0 que nos permite reproducir el mismo modelo.\n",
    "\n",
    "Finalmente tenemos que ***convertir los datos segmentados en el formato y dimensión adecuada que nos requerirá Scikit-Learn*** para poder implementar la regresión. Para ello utilizamos la función reshape() de numpy para los array.\n",
    "\n",
    "Por último, si queremos comprobar los parámetros de la segmentación, podemos hacerlo pasando la función len(X_train), para ver la cantidad, type(X_train) para ver el formato o X_train.shape para ver la dimensión del array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dd24dbaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "194352df",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X,Y, test_size = 0.2, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f0ccb4e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train= np.array(X_train).reshape(-1,1) \n",
    "y_train= np.array(y_train).reshape(-1,1) \n",
    "X_test= np.array(X_test).reshape(-1,1) \n",
    "y_test= np.array(y_test).reshape(-1,1) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18fc5def",
   "metadata": {},
   "source": [
    "#### 3. Implementación de la Regresión \n",
    "\n",
    "Una vez tenemos los datos preparados, estamos listos para implementar el modelo de regresión de Scikit-Learn. En primer lugar, importaremos la *class* necesaria e ***inicializaremos el objeto LinearRegression()*** al que asignaremos el nombre linregression para poder utilizar los *métodos* de la misma.\n",
    "\n",
    "Posteriormente, pasaremos los datos sobre los que queremos hacer la regresión mediante el método .fit() aplicado al objeto inicializado que llamamos linregression. El paso siguiente será la obtención de métricas y comprobaciones de precisión."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "70c752b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression \n",
    "linregression = LinearRegression()\n",
    "linregression.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddf11ea8",
   "metadata": {},
   "source": [
    "#### 4. Obtención y comparación de resultados\n",
    "\n",
    "Una vez establecemos la regresión, podemos podemos obtener la precisión sobre la predicción de datos para nuestra variable independiente (Precio de la vivienda). Para ello podemos utilizar la función .predict() sobre el marco de datos utilizado para el \"entrenamiento\" del algoritmo *X_test*. ***Esto nos permitirá comprobar posteriormente si los datos obtenidos están en concordancia con los datos de la muestra y con qué precisión.***\n",
    "\n",
    "Además, es relativamente sencillo obtener el *intercept* y el *slope* mediante las funciones .intercept_ y .coef_ del objeto LinearRegression() de scikit-learn. ***De este modo podemos obtener la ecuación para nuestra recta de regresión***.\n",
    "\n",
    "$ Y = \\alpha + \\beta · x$, donde $\\alpha =$ intercept y $\\beta =$ slope.\n",
    "\n",
    "Por útlimo, podemos obtener más métricas sobre el modelo en caso de que lo precisemos para un mayor detalle como $R^2$ mediante linregression.score(), etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "da072d8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[634973.36884605],\n",
       "       [772590.58762453],\n",
       "       [752930.98494189],\n",
       "       [890548.20372037]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = linregression.predict(X_test)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d9a6ed52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([261440.9178759])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linregression.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "07e1467c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[393.19205365]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linregression.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5eaef346",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt \n",
    "plt.scatter(X_train, y_train) \n",
    "plt.plot(X_train, linregression.predict(X_train), 'r') \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fceea49",
   "metadata": {},
   "source": [
    "# Comentario\n",
    "\n",
    "\n",
    "Una vez implementado nuestro modelo, es interesante comprobar, como comentamos anteriormente, la precisión de los datos obtenidos para $Y predict$ por el algoritmo en nuestra muestra conocida en comparación con los datos reales de $Y test$. Dependiendo del estudio, bastará con ver los np.array, generar un dataframe mayor para obtener métricas o visualizar de forma gráfica como en el ejmplo mostrado. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c88ec2d2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Muestra real = [[ 650000]\n",
      " [ 860000]\n",
      " [ 680000]\n",
      " [1100000]]\n",
      "Predicción = [[634973.37]\n",
      " [772590.59]\n",
      " [752930.98]\n",
      " [890548.2 ]]\n"
     ]
    }
   ],
   "source": [
    "print(f'Muestra real = {y_test}')\n",
    "print(f'Predicción = {np.round(y_pred,2)}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8d113f88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x179d479d880>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y_test, label='Muestra',marker='o', color = 'b')\n",
    "plt.plot(y_pred, label='Predicción', marker='o', linestyle='--', color='r')\n",
    "plt.xticks(list(range(len(y_pred))))\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b760cc22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6980267531453604"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linregression.score(X_train, y_train) # R^2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96eea3f9",
   "metadata": {},
   "source": [
    "### Enfoque utilizando StatsModels\n",
    "\n",
    "Por último, comentar que podemos implementar el módulo statsmodels para implementar el modelo de regresión obteniendo las siguientes métricas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d294b703",
   "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>   0.678</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.660</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   37.95</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 08 Apr 2022</td> <th>  Prob (F-statistic):</th> <td>8.13e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:19:12</td>     <th>  Log-Likelihood:    </th> <td> -260.43</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    20</td>      <th>  AIC:               </th> <td>   524.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    18</td>      <th>  BIC:               </th> <td>   526.8</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>Intercept</th> <td> 2.608e+05</td> <td> 9.76e+04</td> <td>    2.673</td> <td> 0.016</td> <td> 5.58e+04</td> <td> 4.66e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>X</th>         <td>  401.9163</td> <td>   65.243</td> <td>    6.160</td> <td> 0.000</td> <td>  264.846</td> <td>  538.987</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.238</td> <th>  Durbin-Watson:     </th> <td>   1.810</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.538</td> <th>  Jarque-Bera (JB):  </th> <td>   0.715</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.459</td> <th>  Prob(JB):          </th> <td>   0.699</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.884</td> <th>  Cond. No.          </th> <td>5.66e+03</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 5.66e+03. 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:                      Y   R-squared:                       0.678\n",
       "Model:                            OLS   Adj. R-squared:                  0.660\n",
       "Method:                 Least Squares   F-statistic:                     37.95\n",
       "Date:                Fri, 08 Apr 2022   Prob (F-statistic):           8.13e-06\n",
       "Time:                        15:19:12   Log-Likelihood:                -260.43\n",
       "No. Observations:                  20   AIC:                             524.9\n",
       "Df Residuals:                      18   BIC:                             526.8\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept   2.608e+05   9.76e+04      2.673      0.016    5.58e+04    4.66e+05\n",
       "X            401.9163     65.243      6.160      0.000     264.846     538.987\n",
       "==============================================================================\n",
       "Omnibus:                        1.238   Durbin-Watson:                   1.810\n",
       "Prob(Omnibus):                  0.538   Jarque-Bera (JB):                0.715\n",
       "Skew:                          -0.459   Prob(JB):                        0.699\n",
       "Kurtosis:                       2.884   Cond. No.                     5.66e+03\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 5.66e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.formula.api as smf\n",
    "\n",
    "formula = \"Y ~ X\"\n",
    "\n",
    "modelo = smf.ols(formula, data = data).fit()\n",
    "modelo.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "3be291d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    260806.236056\n",
       "X               401.916286\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "modelo.params"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf949519",
   "metadata": {},
   "source": [
    "### Resultado de los dos modelos\n",
    "\n",
    "El modelo de **Scikit-Learn** arroja un resultado de $Y = 261440.92 + 393.19x$ con un $R^2 = 0.698$ \n",
    "\n",
    "El modelo de **Statsmodels** arroja un resultado de $Y= 260806.23 + 401.92x$ con un $R^2 = 0.678$\n",
    "\n",
    "\n",
    "Pese a que los modelos explican claramente que existe una relación lineal entre el tamaño y el precio de la vivienda para la muestra seleccionada, ***sería interesante introducir alguna variable más o incrementar la muestra de tal forma que nos ayude a definir con mayor precisión esta relación.*** \n",
    "\n",
    "Pasariamos por tanto de un modelo de regresión simple a un modelo de regresión múltiple, en el cual intentaríamos buscar un incremento de métricas tales como $R^2$ o la reducción de $SE(\\alpha)$ y $SE(\\beta)$ mediante el aumento de la muestra. "
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