03. Linear models/3.2 Logistic Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regresión logística"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La regresión logística es una variante de los modelos lineales en los que el valor que se predice se acota entre 0 y 1, representando la probabilidad de que ocurra un evento, por lo que se aplica a lo que se denomina *clasificación binaria*. La ecuación general de los modelos lineales se modifica así:\n",
    "\n",
    "## $\\log \\frac{p}{1 - p} = b_0 + b_1 x_1 + b_2 x_2 + \\cdots + b_n x_n$\n",
    "\n",
    "donde ahora $p$ representa la probabilidad de que ocurra el evento que se estudia (por ejemplo, que un paciente al que se le hace un análisis de sangre tenga un tumor maligno o no). Cuando se hace una predicción usando un modelo de regresión logística sobre nuevos datos, se obtiene un número entre 0 y 1 que se suele denominar *score*. Si supera cierto valor umbral (denominado también *punto de corte*) entonces se considera que se va a producir el evento. Por tanto, no solo hay que entrenar el modelo, además hay que elegir un valor umbral que sea óptimo. Para ello se utilizan las curvas ROC (Receiver Operating Characteristic)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comenzamos como siempre, cargando las librerías que vamos a necesitar y configurando el entorno:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "mjnuJ19dJV7v"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "import matplotlib.pyplot as plt\n",
    "# Graphics in SVG format are more sharp and legible\n",
    "%config InlineBackend.figure_format = 'svg' "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Subimos el archivo de datos a Colab y lo cargamos en memoria, especificando que PassengerId se tomará como índice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 228
    },
    "colab_type": "code",
    "id": "5_a_wDxGJV8E",
    "outputId": "4a0b4d26-87ec-417c-f627-7744e11faf68"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2020-02-10 20:05:20--  https://raw.githubusercontent.com/CenticMurcia/curso-ciencia-datos/master/data/titanic_train.csv\n",
      "Resolviendo raw.githubusercontent.com (raw.githubusercontent.com)... 151.101.192.133, 151.101.128.133, 151.101.64.133, ...\n",
      "Conectando con raw.githubusercontent.com (raw.githubusercontent.com)[151.101.192.133]:443... conectado.\n",
      "Petición HTTP enviada, esperando respuesta... 200 OK\n",
      "Longitud: 61194 (60K) [text/plain]\n",
      "Guardando como: “./../data/titanic_train.csv.9”\n",
      "\n",
      "titanic_train.csv.9 100%[===================>]  59,76K  --.-KB/s    en 0,09s   \n",
      "\n",
      "2020-02-10 20:05:21 (692 KB/s) - “./../data/titanic_train.csv.9” guardado [61194/61194]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "##### DOWNLOAD DATASET. ONLY IN COLAB !!!\n",
    "!wget -P ./../data/ https://raw.githubusercontent.com/CenticMurcia/curso-ciencia-datos/master/data/titanic_train.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "wAy8TnVPJV8S"
   },
   "outputs": [],
   "source": [
    "train_df = pd.read_csv(\"../data/titanic_train.csv\", \n",
    "                       index_col='PassengerId') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Echamos un vistazo a los datos y hacemos una breve descripción estadística, primero de las variables cuantitativas y luego de las cualitativas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 285
    },
    "colab_type": "code",
    "id": "Rs8qRGUxJV8b",
    "outputId": "7098fb55-2e93-4f2b-d4de-ef2845545e59"
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
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       "      <th>SibSp</th>\n",
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       "      <th>Ticket</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Cabin</th>\n",
       "      <th>Embarked</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PassengerId</th>\n",
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       "      <td>1</td>\n",
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       "      <td>A/5 21171</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>female</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>PC 17599</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>C85</td>\n",
       "      <td>C</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>female</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
       "      <td>female</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>113803</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>C123</td>\n",
       "      <td>S</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Allen, Mr. William Henry</td>\n",
       "      <td>male</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>373450</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
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       "  </tbody>\n",
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      ],
      "text/plain": [
       "             Survived  Pclass  \\\n",
       "PassengerId                     \n",
       "1                   0       3   \n",
       "2                   1       1   \n",
       "3                   1       3   \n",
       "4                   1       1   \n",
       "5                   0       3   \n",
       "\n",
       "                                                          Name     Sex   Age  \\\n",
       "PassengerId                                                                    \n",
       "1                                      Braund, Mr. Owen Harris    male  22.0   \n",
       "2            Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0   \n",
       "3                                       Heikkinen, Miss. Laina  female  26.0   \n",
       "4                 Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0   \n",
       "5                                     Allen, Mr. William Henry    male  35.0   \n",
       "\n",
       "             SibSp  Parch            Ticket     Fare Cabin Embarked  \n",
       "PassengerId                                                          \n",
       "1                1      0         A/5 21171   7.2500   NaN        S  \n",
       "2                1      0          PC 17599  71.2833   C85        C  \n",
       "3                0      0  STON/O2. 3101282   7.9250   NaN        S  \n",
       "4                1      0            113803  53.1000  C123        S  \n",
       "5                0      0            373450   8.0500   NaN        S  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 891 entries, 1 to 891\n",
      "Data columns (total 11 columns):\n",
      "Survived    891 non-null int64\n",
      "Pclass      891 non-null int64\n",
      "Name        891 non-null object\n",
      "Sex         891 non-null object\n",
      "Age         714 non-null float64\n",
      "SibSp       891 non-null int64\n",
      "Parch       891 non-null int64\n",
      "Ticket      891 non-null object\n",
      "Fare        891 non-null float64\n",
      "Cabin       204 non-null object\n",
      "Embarked    889 non-null object\n",
      "dtypes: float64(2), int64(4), object(5)\n",
      "memory usage: 83.5+ KB\n"
     ]
    }
   ],
   "source": [
    "train_df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 449
    },
    "colab_type": "code",
    "id": "0lwK7UxSJV8l",
    "outputId": "c5ab5404-b997-42ee-fd37-a9f6892ab4cd"
   },
   "outputs": [
    {
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       "      <th>Fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>891.000000</td>\n",
       "      <td>891.000000</td>\n",
       "      <td>714.000000</td>\n",
       "      <td>891.000000</td>\n",
       "      <td>891.000000</td>\n",
       "      <td>891.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.383838</td>\n",
       "      <td>2.308642</td>\n",
       "      <td>29.699118</td>\n",
       "      <td>0.523008</td>\n",
       "      <td>0.381594</td>\n",
       "      <td>32.204208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.486592</td>\n",
       "      <td>0.836071</td>\n",
       "      <td>14.526497</td>\n",
       "      <td>1.102743</td>\n",
       "      <td>0.806057</td>\n",
       "      <td>49.693429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.420000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>20.125000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.910400</td>\n",
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       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>28.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>14.454200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>38.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>31.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>512.329200</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "         Survived      Pclass         Age       SibSp       Parch        Fare\n",
       "count  891.000000  891.000000  714.000000  891.000000  891.000000  891.000000\n",
       "mean     0.383838    2.308642   29.699118    0.523008    0.381594   32.204208\n",
       "std      0.486592    0.836071   14.526497    1.102743    0.806057   49.693429\n",
       "min      0.000000    1.000000    0.420000    0.000000    0.000000    0.000000\n",
       "25%      0.000000    2.000000   20.125000    0.000000    0.000000    7.910400\n",
       "50%      0.000000    3.000000   28.000000    0.000000    0.000000   14.454200\n",
       "75%      1.000000    3.000000   38.000000    1.000000    0.000000   31.000000\n",
       "max      1.000000    3.000000   80.000000    8.000000    6.000000  512.329200"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Name</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Ticket</th>\n",
       "      <th>Cabin</th>\n",
       "      <th>Embarked</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>891</td>\n",
       "      <td>891</td>\n",
       "      <td>891</td>\n",
       "      <td>204</td>\n",
       "      <td>889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>891</td>\n",
       "      <td>2</td>\n",
       "      <td>681</td>\n",
       "      <td>147</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>Meek, Mrs. Thomas (Annie Louise Rowley)</td>\n",
       "      <td>male</td>\n",
       "      <td>1601</td>\n",
       "      <td>G6</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>1</td>\n",
       "      <td>577</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>644</td>\n",
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      ],
      "text/plain": [
       "                                           Name   Sex Ticket Cabin Embarked\n",
       "count                                       891   891    891   204      889\n",
       "unique                                      891     2    681   147        3\n",
       "top     Meek, Mrs. Thomas (Annie Louise Rowley)  male   1601    G6        S\n",
       "freq                                          1   577      7     4      644"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df.describe(include=['object', 'bool'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que hay un total de 891 pasajeros, pero solo tenemos la edad de 714. Y solo conocemos el camarote (Cabin) de 204 y el puerto de embarque (Embarked) de 889. También vemos que hay algunas variables que no parecen contener ninguna información: el nombre del pasajero (Name), el número de ticket (Ticket) y el número de camarote (Cabin). Por tanto haremos varias cosas para limpiar el dataset:\n",
    "\n",
    "- Eliminar las variables (columnas) Name, Ticket, y Cabin\n",
    "- Eliminar los casos (filas) en los que no estén especificados la edad y/o el puerto de embarque"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 961
    },
    "colab_type": "code",
    "id": "g5wXRw6WUEg-",
    "outputId": "fa9eff70-ead8-4ea6-d536-098a7966914a"
   },
   "outputs": [],
   "source": [
    "train_df = train_df.drop(['Name', 'Ticket', 'Cabin'], axis=1).dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "e3TN2XuvJV9F",
    "outputId": "f8270d2b-68f7-4383-fbf0-bdb58f5a8dad"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 712 entries, 1 to 891\n",
      "Data columns (total 8 columns):\n",
      "Survived    712 non-null int64\n",
      "Pclass      712 non-null int64\n",
      "Sex         712 non-null object\n",
      "Age         712 non-null float64\n",
      "SibSp       712 non-null int64\n",
      "Parch       712 non-null int64\n",
      "Fare        712 non-null float64\n",
      "Embarked    712 non-null object\n",
      "dtypes: float64(2), int64(4), object(2)\n",
      "memory usage: 50.1+ KB\n"
     ]
    }
   ],
   "source": [
    "train_df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nos hemos quedado con un dataset cuadrado de 712 filas y 8 columnas, sin columnas que carezcan de información ni casos con valores perdidos. Ahora recodificaremos con la técnica one-hot la variable Embarked. Más adelante, cuando expliquemos los resultados del modelo, veremos el por qué."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# One-hot-encoding para Embarked\n",
    "one_hot = pd.get_dummies(train_df['Embarked'])\n",
    "train_df = train_df.drop('Embarked', axis = 1)\n",
    "train_df = train_df.join(one_hot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para la variable Sexo vamos a definir que los hombres serán 1 y las mujeres 0. De nuevo, la utilidad de esto la veremos más adelante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "male      453\n",
       "female    259\n",
       "Name: Sex, dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df.Sex.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import preprocessing \n",
    "\n",
    "label_encoder = preprocessing.LabelEncoder() \n",
    "train_df['Sex']= label_encoder.fit_transform(train_df['Sex']) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora hemos eliminado la columnna Embarked, sustituyéndola por tres columnas: C (Cherbourg), Q (Queenstown) y S (Southampton). Para el sexo, tenemos ahora que male=1 y female=0. Con el one-hot-encoding nunca habrá un caso en el que C sea 1 y Q o S sean también 1, ni ninguna otra combinación. Solo una de las tres puede ser 1. Esta transformación nos permite incluir variables cualitativas en los modelos lineales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Fare</th>\n",
       "      <th>C</th>\n",
       "      <th>Q</th>\n",
       "      <th>S</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.404494</td>\n",
       "      <td>2.240169</td>\n",
       "      <td>0.636236</td>\n",
       "      <td>29.642093</td>\n",
       "      <td>0.514045</td>\n",
       "      <td>0.432584</td>\n",
       "      <td>34.567251</td>\n",
       "      <td>0.182584</td>\n",
       "      <td>0.039326</td>\n",
       "      <td>0.778090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.491139</td>\n",
       "      <td>0.836854</td>\n",
       "      <td>0.481420</td>\n",
       "      <td>14.492933</td>\n",
       "      <td>0.930692</td>\n",
       "      <td>0.854181</td>\n",
       "      <td>52.938648</td>\n",
       "      <td>0.386597</td>\n",
       "      <td>0.194506</td>\n",
       "      <td>0.415823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.420000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8.050000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>28.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>15.645850</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>38.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>33.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>512.329200</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Survived      Pclass         Sex         Age       SibSp       Parch  \\\n",
       "count  712.000000  712.000000  712.000000  712.000000  712.000000  712.000000   \n",
       "mean     0.404494    2.240169    0.636236   29.642093    0.514045    0.432584   \n",
       "std      0.491139    0.836854    0.481420   14.492933    0.930692    0.854181   \n",
       "min      0.000000    1.000000    0.000000    0.420000    0.000000    0.000000   \n",
       "25%      0.000000    1.000000    0.000000   20.000000    0.000000    0.000000   \n",
       "50%      0.000000    2.000000    1.000000   28.000000    0.000000    0.000000   \n",
       "75%      1.000000    3.000000    1.000000   38.000000    1.000000    1.000000   \n",
       "max      1.000000    3.000000    1.000000   80.000000    5.000000    6.000000   \n",
       "\n",
       "             Fare           C           Q           S  \n",
       "count  712.000000  712.000000  712.000000  712.000000  \n",
       "mean    34.567251    0.182584    0.039326    0.778090  \n",
       "std     52.938648    0.386597    0.194506    0.415823  \n",
       "min      0.000000    0.000000    0.000000    0.000000  \n",
       "25%      8.050000    0.000000    0.000000    1.000000  \n",
       "50%     15.645850    0.000000    0.000000    1.000000  \n",
       "75%     33.000000    0.000000    0.000000    1.000000  \n",
       "max    512.329200    1.000000    1.000000    1.000000  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definimos ahora las variables de entrenamiento (X) y la variable a predecir (Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "HqGsD6bmNNgu"
   },
   "outputs": [],
   "source": [
    "y = train_df['Survived']\n",
    "x = train_df.drop(['Survived'], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 173
    },
    "colab_type": "code",
    "id": "I1yeir7_OBtH",
    "outputId": "e1926bde-aea4-41d8-fd99-01a6e9d0ff3d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    712.000000\n",
       "mean       0.404494\n",
       "std        0.491139\n",
       "min        0.000000\n",
       "25%        0.000000\n",
       "50%        0.000000\n",
       "75%        1.000000\n",
       "max        1.000000\n",
       "Name: Survived, dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "id": "zDmno037OLnk",
    "outputId": "e3703668-7599-4674-bcde-33ac7c51c7b0"
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Fare</th>\n",
       "      <th>C</th>\n",
       "      <th>Q</th>\n",
       "      <th>S</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
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       "      <td>712.000000</td>\n",
       "      <td>712.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.240169</td>\n",
       "      <td>0.636236</td>\n",
       "      <td>29.642093</td>\n",
       "      <td>0.514045</td>\n",
       "      <td>0.432584</td>\n",
       "      <td>34.567251</td>\n",
       "      <td>0.182584</td>\n",
       "      <td>0.039326</td>\n",
       "      <td>0.778090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.836854</td>\n",
       "      <td>0.481420</td>\n",
       "      <td>14.492933</td>\n",
       "      <td>0.930692</td>\n",
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       "      <td>52.938648</td>\n",
       "      <td>0.386597</td>\n",
       "      <td>0.194506</td>\n",
       "      <td>0.415823</td>\n",
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       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.420000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8.050000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>28.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>15.645850</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>38.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>33.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>512.329200</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Pclass         Sex         Age       SibSp       Parch        Fare  \\\n",
       "count  712.000000  712.000000  712.000000  712.000000  712.000000  712.000000   \n",
       "mean     2.240169    0.636236   29.642093    0.514045    0.432584   34.567251   \n",
       "std      0.836854    0.481420   14.492933    0.930692    0.854181   52.938648   \n",
       "min      1.000000    0.000000    0.420000    0.000000    0.000000    0.000000   \n",
       "25%      1.000000    0.000000   20.000000    0.000000    0.000000    8.050000   \n",
       "50%      2.000000    1.000000   28.000000    0.000000    0.000000   15.645850   \n",
       "75%      3.000000    1.000000   38.000000    1.000000    1.000000   33.000000   \n",
       "max      3.000000    1.000000   80.000000    5.000000    6.000000  512.329200   \n",
       "\n",
       "                C           Q           S  \n",
       "count  712.000000  712.000000  712.000000  \n",
       "mean     0.182584    0.039326    0.778090  \n",
       "std      0.386597    0.194506    0.415823  \n",
       "min      0.000000    0.000000    0.000000  \n",
       "25%      0.000000    0.000000    1.000000  \n",
       "50%      0.000000    0.000000    1.000000  \n",
       "75%      0.000000    0.000000    1.000000  \n",
       "max      1.000000    1.000000    1.000000  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dividimos el dataset en subconjuntos de entrenamiento (80%) y de validación (20%), estratificando según la supervivencia del pasajero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "oiYdupsDLEnu"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7luTGp_uMER1"
   },
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, stratify = y, random_state=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "id": "PVGBbJzMOVoG",
    "outputId": "862d7d11-466b-49fd-8dc1-5ab025ff1af4"
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Fare</th>\n",
       "      <th>C</th>\n",
       "      <th>Q</th>\n",
       "      <th>S</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.00000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
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       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.223199</td>\n",
       "      <td>0.625659</td>\n",
       "      <td>29.54877</td>\n",
       "      <td>0.497364</td>\n",
       "      <td>0.472759</td>\n",
       "      <td>34.105594</td>\n",
       "      <td>0.179262</td>\n",
       "      <td>0.036907</td>\n",
       "      <td>0.783831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.837768</td>\n",
       "      <td>0.484378</td>\n",
       "      <td>14.35011</td>\n",
       "      <td>0.929037</td>\n",
       "      <td>0.907546</td>\n",
       "      <td>48.595484</td>\n",
       "      <td>0.383909</td>\n",
       "      <td>0.188699</td>\n",
       "      <td>0.411993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.42000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>20.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8.050000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>28.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>15.850000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>39.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>34.375000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>74.00000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>512.329200</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
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       "           Pclass         Sex        Age       SibSp       Parch        Fare  \\\n",
       "count  569.000000  569.000000  569.00000  569.000000  569.000000  569.000000   \n",
       "mean     2.223199    0.625659   29.54877    0.497364    0.472759   34.105594   \n",
       "std      0.837768    0.484378   14.35011    0.929037    0.907546   48.595484   \n",
       "min      1.000000    0.000000    0.42000    0.000000    0.000000    0.000000   \n",
       "25%      1.000000    0.000000   20.00000    0.000000    0.000000    8.050000   \n",
       "50%      2.000000    1.000000   28.00000    0.000000    0.000000   15.850000   \n",
       "75%      3.000000    1.000000   39.00000    1.000000    1.000000   34.375000   \n",
       "max      3.000000    1.000000   74.00000    5.000000    6.000000  512.329200   \n",
       "\n",
       "                C           Q           S  \n",
       "count  569.000000  569.000000  569.000000  \n",
       "mean     0.179262    0.036907    0.783831  \n",
       "std      0.383909    0.188699    0.411993  \n",
       "min      0.000000    0.000000    0.000000  \n",
       "25%      0.000000    0.000000    1.000000  \n",
       "50%      0.000000    0.000000    1.000000  \n",
       "75%      0.000000    0.000000    1.000000  \n",
       "max      1.000000    1.000000    1.000000  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "id": "mXKPT9gBOYTj",
    "outputId": "3762298d-94a1-4eea-f420-0d7f9afe803a"
   },
   "outputs": [
    {
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       "      <th>Pclass</th>\n",
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       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
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       "      <td>143.000000</td>\n",
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       "      <td>143.000000</td>\n",
       "      <td>143.000000</td>\n",
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       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.307692</td>\n",
       "      <td>0.678322</td>\n",
       "      <td>30.013427</td>\n",
       "      <td>0.580420</td>\n",
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       "      <td>0.195804</td>\n",
       "      <td>0.048951</td>\n",
       "      <td>0.755245</td>\n",
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       "      <th>std</th>\n",
       "      <td>0.832701</td>\n",
       "      <td>0.468762</td>\n",
       "      <td>15.093983</td>\n",
       "      <td>0.937577</td>\n",
       "      <td>0.571406</td>\n",
       "      <td>67.689748</td>\n",
       "      <td>0.398213</td>\n",
       "      <td>0.216524</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
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       "      <th>25%</th>\n",
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       "      <td>0.000000</td>\n",
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       "      <td>1.000000</td>\n",
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       "           Pclass         Sex         Age       SibSp       Parch        Fare  \\\n",
       "count  143.000000  143.000000  143.000000  143.000000  143.000000  143.000000   \n",
       "mean     2.307692    0.678322   30.013427    0.580420    0.272727   36.404195   \n",
       "std      0.832701    0.468762   15.093983    0.937577    0.571406   67.689748   \n",
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       "std      0.398213    0.216524    0.431453  \n",
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       "75%      0.000000    0.000000    1.000000  \n",
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     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
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    "x_test.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 173
    },
    "colab_type": "code",
    "id": "0xJSL4bzOaUL",
    "outputId": "d3113861-fdb3-45be-c732-3032419cd058"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    569.000000\n",
       "mean       0.404218\n",
       "std        0.491172\n",
       "min        0.000000\n",
       "25%        0.000000\n",
       "50%        0.000000\n",
       "75%        1.000000\n",
       "max        1.000000\n",
       "Name: Survived, dtype: float64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 173
    },
    "colab_type": "code",
    "id": "kY1uWk6-OcLw",
    "outputId": "3562463f-3197-424c-dc82-b07ad579e9cc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    143.000000\n",
       "mean       0.405594\n",
       "std        0.492733\n",
       "min        0.000000\n",
       "25%        0.000000\n",
       "50%        0.000000\n",
       "75%        1.000000\n",
       "max        1.000000\n",
       "Name: Survived, dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ya podemos crear el modelo de regresión logística:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "monuuQhHL7B_"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=2000,\n",
       "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                   random_state=1, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "# check classification scores of logistic regression\n",
    "logreg = LogisticRegression(max_iter=2000, random_state=1)\n",
    "logreg.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora para cada pasajero tenemos tanto la predicción como una probabilidad de que sobreviva. Podemos representar la matriz de confusión y cómo se relacionan estas probabilidades con el verdadero valor de Survived, tanto para el entrenamiento como para la validación:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import accuracy_score, balanced_accuracy_score, plot_confusion_matrix\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 80.4920913884007\n",
      "Balanced accuracy:  79.08490445042965\n"
     ]
    },
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   "source": [
    "# Para el entrenamiento\n",
    "y_pred = logreg.predict(x_train)\n",
    "y_pred_proba = logreg.predict_proba(x_train)[:, 1]\n",
    "\n",
    "print(\"Accuracy:\", accuracy_score(y_train, y_pred)*100)\n",
    "print(\"Balanced accuracy: \", balanced_accuracy_score(y_train, y_pred)*100)\n",
    "\n",
    "_, axes = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "plot_confusion_matrix(logreg, x_train, y_train,\n",
    "                      cmap=plt.cm.Blues, normalize=\"pred\",\n",
    "                      ax=axes[0]);\n",
    "\n",
    "g = sns.boxplot(x = y_train, y = y_pred_proba, ax=axes[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que la precisión ponderada del modelo (balanced accuracy) es razonablemente buena (79.1%), aunque no demasiado: como la proporción de fallecidos es del 59.6% (424 / 712) si decimos sin analizar ningún dato que el pasajero se ahoga tenemos una probabilidad basal del 59.6% de acertar. Vemos en el gráfico de cajas que la distribución de *scores* es muy parecida entre los que se ahogan y los que no. Cuando los modelos son muy buenos las cajas están muy separadas. No es el caso aquí."
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apliquemos ahora el modelo al conjunto de validación:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 79.72027972027972\n",
      "Balanced accuracy:  77.46450304259636\n"
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   "source": [
    "# Para la validación\n",
    "y_pred = logreg.predict(x_test)\n",
    "y_pred_proba = logreg.predict_proba(x_test)[:, 1]\n",
    "\n",
    "print(\"Accuracy:\", accuracy_score(y_test, y_pred)*100)\n",
    "print(\"Balanced accuracy: \", balanced_accuracy_score(y_test, y_pred)*100)\n",
    "\n",
    "_, axes = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "plot_confusion_matrix(logreg, x_test, y_test,\n",
    "                      cmap=plt.cm.Blues, normalize=\"pred\",\n",
    "                      ax=axes[0]);\n",
    "\n",
    "g = sns.boxplot(x = y_test, y = y_pred_proba, ax=axes[1])"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los resultados son parecidos a los del conjunto de entrenamiento. Tenemos una balanced accuracy algo menor, del 77.5%, y la distribución de scores entre grupos es también muy parecida y no demasiado buena. Ojo, aún no hemos estudiado el punto de corte óptimo para separar los dos grupos, lo que haremos usando la curva ROC:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 507
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    "colab_type": "code",
    "id": "gurkOjipOmlI",
    "outputId": "775a124c-6ff2-48f7-c26d-df15da1d0f4d"
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   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train/Test split results:\n",
      "LogisticRegression accuracy is 0.797\n",
      "LogisticRegression log_loss is 0.447\n",
      "LogisticRegression auc is 0.861\n"
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     "text": [
      "Using a threshold of 0.083 guarantees a sensitivity of 0.966 and a specificity of 0.235, i.e. a false positive rate of 76.47%.\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve, accuracy_score, log_loss, auc\n",
    "\n",
    "[fpr, tpr, thr] = roc_curve(y_test, y_pred_proba)\n",
    "print('Train/Test split results:')\n",
    "print(logreg.__class__.__name__+\" accuracy is %2.3f\" % accuracy_score(y_test, y_pred))\n",
    "print(logreg.__class__.__name__+\" log_loss is %2.3f\" % log_loss(y_test, y_pred_proba))\n",
    "print(logreg.__class__.__name__+\" auc is %2.3f\" % auc(fpr, tpr))\n",
    "\n",
    "idx = np.min(np.where(tpr > 0.95)) # index of the first threshold for which the sensibility > 0.95\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(fpr, tpr, color='coral', label='ROC curve (area = %0.3f)' % auc(fpr, tpr))\n",
    "plt.plot([0, 1], [0, 1], 'k--')\n",
    "plt.plot([0,fpr[idx]], [tpr[idx],tpr[idx]], 'k--', color='blue')\n",
    "plt.plot([fpr[idx],fpr[idx]], [0,tpr[idx]], 'k--', color='blue')\n",
    "plt.xlim([0.0, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel('False Positive Rate (1 - specificity)', fontsize=14)\n",
    "plt.ylabel('True Positive Rate (recall)', fontsize=14)\n",
    "plt.title('Receiver operating characteristic (ROC) curve')\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()\n",
    "\n",
    "print(\"Using a threshold of %.3f \" % thr[idx] + \"guarantees a sensitivity of %.3f \" % tpr[idx] +  \n",
    "      \"and a specificity of %.3f\" % (1-fpr[idx]) + \n",
    "      \", i.e. a false positive rate of %.2f%%.\" % (np.array(fpr[idx])*100))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El principal parámetro de calidad de una curva ROC es el área bajo la curva (AUC, Area Under Curve), que en este caso es 0.861. Su valor oscila entre 0.5 (modelo no informativo) y 1 (modelo perfecto), por lo que nuestro modelo es razonablemente bueno, aunque nada del otro mundo. En la gráfica se nos indica que el punto de corte óptimo es 0.083, una cifra bastante baja: todos los pasajeros que tengan una probabilidad mayor se clasifican como supervivientes, el resto como ahogados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Existen muchas maneras de definir la calidad de un modelo, habiendo multitud de índices cada uno con sus ventajas e inconvenientes. Para saber más sobre ellos se puede consultar por ejemplo este link:\n",
    "https://blog.exsilio.com/all/accuracy-precision-recall-f1-score-interpretation-of-performance-measures/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ya hemos visto que el AUC es razonablemente alto, y la sensibilidad también lo es (0.966), pero resulta curioso que la especificidad sea tan baja (0.235). Probablemente indica que el modelo tiende a predecir que el pasajero va a ahogarse, y luego va afinando la predicción."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aunque el modelo no es muy bueno, tenemos ahora la ventaja de que podemos determinar cómo afecta cada variable a al predicción. Para ello se usa el concepto de \"odds ratio\" (OR), que es cuánto crece o decrece la probabilidad de salvarse cuando el valor de la variable cambia en 1 unidad:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>Variable</th>\n",
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       "      <th>6</th>\n",
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       "      <td>-0.575215</td>\n",
       "      <td>0.562584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>S</td>\n",
       "      <td>0.126947</td>\n",
       "      <td>1.135357</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Variable  Coeficiente        OR\n",
       "0   Pclass    -1.103159  0.331821\n",
       "1      Sex    -2.540529  0.078825\n",
       "2      Age    -0.049134  0.952054\n",
       "3    SibSp    -0.410865  0.663076\n",
       "4    Parch    -0.044901  0.956092\n",
       "5     Fare    -0.000241  0.999759\n",
       "6        C     0.439433  1.551828\n",
       "7        Q    -0.575215  0.562584\n",
       "8        S     0.126947  1.135357"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "odds = [math.exp(x) for x in logreg.coef_[0]]\n",
    "\n",
    "coef = dict(zip(x_train.columns, zip(logreg.coef_[0], odds)))\n",
    "\n",
    "\n",
    "data = {'Variable':x_train.columns, \n",
    "        'Coeficiente':logreg.coef_[0],\n",
    "        'OR': odds} \n",
    "\n",
    "data = pd.DataFrame(data)\n",
    "data\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos a interpretar estos resultados. El OR para Pclass es 0.43, lo que quiere decir que cuando la clase aumenta en 1 unidad, la probabilidad de salvarse se multiplica por 0.33. O sea, si los de primera clase (pclass=1) tienen cierta probabilidad de salvarse P1, los de segunda clase tienen una probabilidad P2 = 0.33·P1 de salvarse (un tercio) que los de primera clase, y los de tercera clase P3 = 0.33·P2 = 0.33·0.33·P1, aproximadamente un 10% de la probabilidad de los de primera clase. Vemos que para sexo, la probabilidad de salvarse para los hombres es menos de una décima parte que para las mujeres (0.08). Vemos también que la edad prácticamente no influye, ya que el OR está muy próximo a 1 (misma probabilidad sea cual sea la edad). Resulta también curioso que los que embarcaron en Cherbourg tienen más probabilidad de salvarse que los de Southampton y los de Queenstown (1.55 / 1.13 / 0.56)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La conclusión que sacamos de la regresión logística es que aunque el modelo no es muy potente (accuracy de alrededor de 80%), sí que podemos sacar muchas conclusiones de él y manipularlo a nuestro gusto muy fácilmente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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