dds_regresion_logistica_py.ipynb

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      "source": [
        "# Modelo de Regresión Logística\n",
        "\n",
        "**Diplomado en Data Science Versión 2024** <br>\n",
        "**Facultad de Matemáticas**<br>\n",
        "**Pontificia Universidad Católica de Chile**\n",
        "\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iemRRJogBl7V"
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      "source": [
        "Hoy nuestro interés estará centrado en la probabilidad de ocurrencia de determinandos eventos, dados algunos eventos externos y que ya han ocurrido. Denotemos:\n",
        "\n",
        "$$\n",
        "\\mathbb{P}(Y_i=1\\mid X=x_i)=\\pi_i\n",
        "$$\n",
        "\n",
        "como la probabilidad de ocurrencia del fenómeno binario (o Bernoulli) $Y_i$ (donde 1 significa que el evento ocurre) dados los eventos conocidos $x_i$. Entonces $Y_i$ se denomina **variable respuesta** y $x_i$ es un conjunto de **predictores, covariables o variables independientes**.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ABdbFL__Bl7V"
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      "source": [
        "Para ejempificar esto, consideremos una empresa de telecomunicaciones. Simulemos que nos interesa calcular la probabilidad de que el cliente N°5 finalize su contrato en la empresa, dado que lleva dos meses de antiguedad. Entonces, nuestro interés se centra en:\n",
        "\n",
        "$$\n",
        "\\mathbb{P}(\\text{FinalizaContrato}_5=1\\mid\\text{Antigüedad}=2)=\\pi_5\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "**¿Qué son las chances?**"
      ]
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zi72JLaJBl7W"
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      "source": [
        "Seguramente han escuchado una frase similar a \"las chances de que gane tal caballo es de 3 a 1\", es decir, de cuatro carreras, el caballo gana tres y pierde una. En otros términos:\n",
        "* La probabilidad de que gane el caballo la carrera es $\\pi={\\text{casos favorables} \\over \\text{casos posibles}} = 3/4$.\n",
        "* Las chances de que gane el caballo la carrera es de ${\\pi \\over 1 - \\pi}={0.75 \\over 1-0.75}=$ 3 a 1."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r0Ct-a62Bl7W"
      },
      "source": [
        "Basicamente las chances son una segunda forma de señalar la cantidad de evidencia hacia la ocurrencia de un evento y especialmente, son la base del modelo de regresión logística."
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "### La Regresión Logística"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_x3BxQxkBl7X"
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      "source": [
        "La **regresión logística** sirve para modelar la probabilidad de ocurrencia de un evento dado un conjunto de predictores en base a información del pasado. Se enmarca en el conjunto de **modelos lineales generalizados** o GLM por sus siglas en inglés.\n",
        "\n",
        "Por conveniencia matemática, la regresión logística modela el **logaritmo de las chances de que ocurra el evento** (tambien conocidas como **log-chances** o **logits**). Es decir, se puede denotar de la siguiente forma:"
      ]
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    {
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      "source": [
        "$$\n",
        "\\log{\\left(\\pi_i \\over 1 - \\pi_i\\right)} = \\beta_0 + \\beta_1 x_{i1} + \\dots + \\beta_n x_{in}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
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        "id": "y-KFtqI2Bl7X"
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      "source": [
        "O sea, buscar modelar los *logits* como una combinación lineal de los predictores. Entonces, el interés es obtener estimaciones de los parámetros $\\beta_0, \\beta_1, \\dots, \\beta_n$.\n",
        "\n",
        "Luego de estimar los parámetros de interés del modelo y con un poco de manipulación respecto al modelo mostrado, la probabilidad de ocurrencia del evento de interés esta dada por la siguiente fórmula:\n",
        "\n",
        "$$\n",
        "\\hat\\pi_i = {\\exp{(\\hat\\beta_0 + \\hat\\beta_1 x_{i1} + \\dots + \\hat\\beta_n x_{in})} \\over 1 + \\exp{(\\hat\\beta_0 + \\hat\\beta_1 x_{i1} + \\dots + \\hat\\beta_n x_{in})}}\n",
        "$$"
      ]
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      "source": [
        "En este caso, el acento circunflejo ^, hace referencia a que los valores corresponden a estimaciones de los parámetros de interés. Para obtener estas estimaciones, debemos tener un conjunto de datos que contenga observaciones para todas las variables independientes y la variable respuesta. El conjunto de datos debe ser representativo de la población o del fenómeno que se está estudiando."
      ]
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      "source": [
        "Para el ejemplo de modelar la probabilidad de fuga de un cliente dado que lleva dos meses en la empresa, consideremos la base de datos `EmpresaServicios.xlsx` que  contiene información de los clientes de esta empresa y que decidieron finalizar su contrato, o que a la fecha aún lo mantienen. Las variables de esta base de datos son las siguientes:\n",
        "\n",
        "* `Sexo`: Sexo del titular (Mujer, Hombre)\n",
        "* `TipoCliente`: Indica si el cliente es premium o regular\n",
        "* `MasUnPlan`: Si el titular posee más de un plan asociado.\n",
        "* `MultipleServicios`: Si cliente posee internet y telefonía o solo internet.\n",
        "* `Antiguedad`: Antigüedad del contrato (meses).\n",
        "* `Edad`: Edad en años del titular de la cuenta.\n",
        "* `Beneficios`: Si cliente accede a los beneficios de descuentos\n",
        "* `ParticipoEvento`: Si cliente participó de evento online de empresa.\n",
        "* `AsisteSucursal`: Si cliente asiste muchas, pocas o ninguna vez a sucursal.\n",
        "* `DeudaMembresia`: Si cliente presenta atraso por pagar su cuenta.\n",
        "* `PagaporServicio`: Monto de dinero que el cliente paga por su servicio\n",
        "* `Churn`: Si cliente finaliza o mantiene el contrato vigente (variable respuesta)."
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "Carguemos los datos y luego veamos algunos gráficos y tablas asociados a la variable respuesta."
      ]
    },
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              "    Sexo TipoCliente MasUnPlan    MultipleServicios  Antiguedad  Edad  \\\n",
              "0  Mujer     Regular        No        Solo Internet          67    31   \n",
              "1  Mujer     Regular        Si        Solo Internet          63    42   \n",
              "2  Mujer     Regular        No  Internet y Telefono          37    37   \n",
              "3  Mujer     Regular        No        Solo Internet          67    43   \n",
              "4  Mujer     Regular        No        Solo Internet          75    44   \n",
              "\n",
              "               Beneficios ParticipoEvento     AsisteSucursal DeudaMembresia  \\\n",
              "0  No Accede a Beneficios    No Participa  Una o ninguna vez      No Deudor   \n",
              "1     Accede a Beneficios    No Participa  Una o ninguna vez      No Deudor   \n",
              "2  No Accede a Beneficios    No Participa  Una o ninguna vez      No Deudor   \n",
              "3  No Accede a Beneficios    No Participa  Una o ninguna vez      No Deudor   \n",
              "4  No Accede a Beneficios    No Participa  Una o ninguna vez      No Deudor   \n",
              "\n",
              "   PagaporServicio              Churn  \n",
              "0         16.90000  Finaliza Contrato  \n",
              "1         14.30000  Mantiene Contrato  \n",
              "2         19.40000  Mantiene Contrato  \n",
              "3         19.70000  Finaliza Contrato  \n",
              "4         15.80000  Mantiene Contrato  "
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              "      <td>37</td>\n",
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              "      <td>No Participa</td>\n",
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              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-e7b75cc5-69fa-42fb-b891-d0b8c1ad3456 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "summary": "{\n  \"name\": \"display(data\",\n  \"rows\": 5,\n  \"fields\": [\n    {\n      \"column\": \"Sexo\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 1,\n        \"samples\": [\n          \"Mujer\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"TipoCliente\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 1,\n        \"samples\": [\n          \"Regular\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"MasUnPlan\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          \"Si\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"MultipleServicios\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          \"Internet y Telefono\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Antiguedad\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 14,\n        \"min\": 37,\n        \"max\": 75,\n        \"num_unique_values\": 4,\n        \"samples\": [\n          63\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Edad\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 5,\n        \"min\": 31,\n        \"max\": 44,\n        \"num_unique_values\": 5,\n        \"samples\": [\n          42\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Beneficios\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          \"Accede a Beneficios\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"ParticipoEvento\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 1,\n        \"samples\": [\n          \"No Participa\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"AsisteSucursal\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 1,\n        \"samples\": [\n          \"Una o ninguna vez\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"DeudaMembresia\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 1,\n        \"samples\": [\n          \"No Deudor\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"PagaporServicio\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2.320991167583366,\n        \"min\": 14.3,\n        \"max\": 19.7,\n        \"num_unique_values\": 5,\n        \"samples\": [\n          14.3\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Churn\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          \"Mantiene Contrato\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Librerías a utilizar\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "# Opciones para evitar notación científica\n",
        "np.set_printoptions(suppress=True)\n",
        "pd.set_option('display.float_format', lambda x: f\"{x:0.5f}\")\n",
        "\n",
        "# Configuración de los gráficos\n",
        "plt.style.use(\"ggplot\")\n",
        "%config InlineBackend.figure_format = \"retina\"\n",
        "\n",
        "# Cargamos datos\n",
        "data = pd.read_excel(\"EmpresaServicios.xlsx\")\n",
        "display(data.head())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4Bhe_c2JBl7Z",
        "outputId": "5b8fc239-225c-49e9-c2ca-4d41cfffba97",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "                   Cuenta  Porcentaje\n",
              "Churn                                \n",
              "Mantiene Contrato    1920     0.64000\n",
              "Finaliza Contrato    1080     0.36000"
            ],
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              "      <td>1920</td>\n",
              "      <td>0.64000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Finaliza Contrato</th>\n",
              "      <td>1080</td>\n",
              "      <td>0.36000</td>\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "      const buttonEl =\n",
              "        document.querySelector('#df-e677bc6c-c903-4dd4-af4f-f8a0af1e7a29 button.colab-df-convert');\n",
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              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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              "        const element = document.querySelector('#df-e677bc6c-c903-4dd4-af4f-f8a0af1e7a29');\n",
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              "                                                    [key], {});\n",
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              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
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              "    border-radius: 50%;\n",
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              "\n",
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              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
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              "      border-right-color: var(--fill-color);\n",
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              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
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              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
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              "        document.querySelector('#df-036fd9b6-a52d-4792-b3ae-246df25b427c button');\n",
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              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
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              "\n",
              "  <div id=\"id_f6a7a710-9ebd-4fcd-8adf-983caddf6c89\">\n",
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              "      .colab-df-generate {\n",
              "        background-color: #E8F0FE;\n",
              "        border: none;\n",
              "        border-radius: 50%;\n",
              "        cursor: pointer;\n",
              "        display: none;\n",
              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
              "        background-color: #E2EBFA;\n",
              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "        fill: #174EA6;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate {\n",
              "        background-color: #3B4455;\n",
              "        fill: #D2E3FC;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate:hover {\n",
              "        background-color: #434B5C;\n",
              "        box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "        filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "        fill: #FFFFFF;\n",
              "      }\n",
              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('tabla')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
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              "  </svg>\n",
              "    </button>\n",
              "    <script>\n",
              "      (() => {\n",
              "      const buttonEl =\n",
              "        document.querySelector('#id_f6a7a710-9ebd-4fcd-8adf-983caddf6c89 button.colab-df-generate');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('tabla');\n",
              "      }\n",
              "      })();\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "tabla",
              "summary": "{\n  \"name\": \"tabla\",\n  \"rows\": 2,\n  \"fields\": [\n    {\n      \"column\": \"Churn\",\n      \"properties\": {\n        \"dtype\": \"string\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          \"Finaliza Contrato\",\n          \"Mantiene Contrato\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Cuenta\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 593,\n        \"min\": 1080,\n        \"max\": 1920,\n        \"num_unique_values\": 2,\n        \"samples\": [\n          1080,\n          1920\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Porcentaje\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.19798989873223333,\n        \"min\": 0.36,\n        \"max\": 0.64,\n        \"num_unique_values\": 2,\n        \"samples\": [\n          0.36,\n          0.64\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {}
        }
      ],
      "source": [
        "conteos     = data[\"Churn\"].value_counts()\n",
        "porcentajes = data[\"Churn\"].value_counts(normalize=True)\n",
        "\n",
        "tabla = pd.concat([conteos, porcentajes], axis=1)\n",
        "tabla.columns = [\"Cuenta\", \"Porcentaje\"]\n",
        "display(tabla)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "%pip install estyp"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0-7gw2wO-OK5",
        "outputId": "0ee88867-5e65-4649-e1cd-428a6855c392"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting estyp\n",
            "  Downloading estyp-0.9.3-py3-none-any.whl (34 kB)\n",
            "Requirement already satisfied: numpy>=1.22.3 in /usr/local/lib/python3.10/dist-packages (from estyp) (1.25.2)\n",
            "Collecting scikit-learn>=1.3.0 (from estyp)\n",
            "  Downloading scikit_learn-1.5.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (13.4 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m13.4/13.4 MB\u001b[0m \u001b[31m35.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
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          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from estyp.testing import t_test\n",
        "\n",
        "t_test(data.query(\"Churn == 'Finaliza Contrato'\").Antiguedad, data.query(\"Churn == 'Mantiene Contrato'\").Antiguedad)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TS2n08ET-dqZ",
        "outputId": "e1512c3c-099b-46d5-ad9e-d8ba5063641a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "\n",
              "    \u001b[1m\u001b[4mWelch's Two Sample t-test\u001b[0m\n",
              "    T = -13.6985 | df = 2221.90 | p-value = <0.0001\n",
              "    alternative hypothesis: true difference in means is not equal to 0\n",
              "    95 percent confidence interval:\n",
              "     -7.464062 -5.594618\n",
              "    sample estimates:\n",
              "      [mean of x, mean of y]: [54.047222, 60.576563]\n",
              "    "
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "l_9RdBzTBl7Z",
        "outputId": "707a0543-5732-43e7-f554-76d135d41efe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 735
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Churn  Finaliza Contrato  Mantiene Contrato\n",
              "count         1080.00000         1920.00000\n",
              "mean            54.04722           60.57656\n",
              "std             12.56636           12.46901\n",
              "min             14.00000           18.00000\n",
              "25%             45.75000           52.00000\n",
              "50%             54.00000           61.00000\n",
              "75%             63.00000           69.00000\n",
              "max             97.00000           99.00000"
            ],
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              "      <th>Churn</th>\n",
              "      <th>Finaliza Contrato</th>\n",
              "      <th>Mantiene Contrato</th>\n",
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              "  </thead>\n",
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              "      <th>count</th>\n",
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              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
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              "      <th>std</th>\n",
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              "summary": "{\n  \"name\": \");\",\n  \"rows\": 8,\n  \"fields\": [\n    {\n      \"column\": \"Finaliza Contrato\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 365.64678302706164,\n        \"min\": 12.566361074139943,\n        \"max\": 1080.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          54.047222222222224,\n          54.0,\n          1080.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Mantiene Contrato\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 660.6113925756752,\n        \"min\": 12.469007860105494,\n        \"max\": 1920.0,\n        \"num_unique_values\": 8,\n        \"samples\": [\n          60.5765625,\n          61.0,\n          1920.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
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          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
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          },
          "metadata": {
            "image/png": {
              "width": 574,
              "height": 435
            }
          }
        }
      ],
      "source": [
        "antiguedad_segun_churn = data.groupby(\"Churn\")[\"Antiguedad\"].describe()\n",
        "display(antiguedad_segun_churn.T)\n",
        "sns.violinplot(\n",
        "    data  = data,\n",
        "    x     = \"Churn\",\n",
        "    y     = \"Antiguedad\",\n",
        "    order = [\"Mantiene Contrato\", \"Finaliza Contrato\"]\n",
        ");"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xY-IzJFrBl7Z"
      },
      "source": [
        "El modelo que buscamos realizar considera solo la antigüedad del cliente y es el siguiente:\n",
        "\n",
        "$$\n",
        "\\log{\\left(\\pi_i \\over 1 - \\pi_i\\right)} = \\beta_0 + \\beta_1 \\cdot \\text{Antigüedad}_i\n",
        "$$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ldbSAONTBl7Z"
      },
      "source": [
        "Para realizarlo en Python, utilizaremos el módulo `api` la librería `statsmodels` nuevamente."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zercxVmoBl7Z"
      },
      "outputs": [],
      "source": [
        "import statsmodels.api as sm"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Vqs9zHmBl7Z"
      },
      "source": [
        "Para realizar el modelo, utilizaremos la clase `Logit` del módulo `api` que cargamos previamente. Para utilizar esta clase, la variable respuesta debe estar codificada con los valores 0 y 1 (donde 1 significa que ocurrió el evento de interés)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lGfH4BCvBl7Z"
      },
      "outputs": [],
      "source": [
        "data[\"Churn_num\"] = np.where(data[\"Churn\"] == \"Finaliza Contrato\", 1, 0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "g3YFILOFBl7a",
        "outputId": "81ce4fd3-0fa6-428d-8e30-f2d6139fdc58"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Optimization terminated successfully.\n",
            "         Current function value: 0.623008\n",
            "         Iterations 5\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "        <td>Model:</td>              <td>Logit</td>           <td>Method:</td>          <td>MLE</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <td>Dependent Variable:</td>     <td>Churn_num</td>    <td>Pseudo R-squared:</td>    <td>0.047</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "         <td>Date:</td>        <td>2023-10-18 17:13</td>       <td>AIC:</td>         <td>3742.0456</td>\n",
              "</tr>\n",
              "<tr>\n",
              "   <td>No. Observations:</td>        <td>3000</td>             <td>BIC:</td>         <td>3754.0583</td>\n",
              "</tr>\n",
              "<tr>\n",
              "       <td>Df Model:</td>              <td>1</td>         <td>Log-Likelihood:</td>    <td>-1869.0</td> \n",
              "</tr>\n",
              "<tr>\n",
              "     <td>Df Residuals:</td>          <td>2998</td>           <td>LL-Null:</td>        <td>-1960.3</td> \n",
              "</tr>\n",
              "<tr>\n",
              "      <td>Converged:</td>           <td>1.0000</td>        <td>LLR p-value:</td>    <td>1.4046e-41</td>\n",
              "</tr>\n",
              "<tr>\n",
              "    <td>No. Iterations:</td>        <td>5.0000</td>           <td>Scale:</td>         <td>1.0000</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>Intercept</th>  <td>1.8106</td>   <td>0.1859</td>   <td>9.7388</td>  <td>0.0000</td> <td>1.4462</td>  <td>2.1749</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Antiguedad</th> <td>-0.0416</td>  <td>0.0032</td>  <td>-12.9414</td> <td>0.0000</td> <td>-0.0479</td> <td>-0.0353</td>\n",
              "</tr>\n",
              "</table><br/>\n"
            ],
            "text/latex": [
              "\\begin{table}\n",
              "\\caption{Results: Logit}\n",
              "\\label{}\n",
              "\\begin{center}\n",
              "\\begin{tabular}{llll}\n",
              "\\hline\n",
              "Model:              & Logit            & Method:           & MLE         \\\\\n",
              "Dependent Variable: & Churn\\_num       & Pseudo R-squared: & 0.047       \\\\\n",
              "Date:               & 2023-10-18 17:13 & AIC:              & 3742.0456   \\\\\n",
              "No. Observations:   & 3000             & BIC:              & 3754.0583   \\\\\n",
              "Df Model:           & 1                & Log-Likelihood:   & -1869.0     \\\\\n",
              "Df Residuals:       & 2998             & LL-Null:          & -1960.3     \\\\\n",
              "Converged:          & 1.0000           & LLR p-value:      & 1.4046e-41  \\\\\n",
              "No. Iterations:     & 5.0000           & Scale:            & 1.0000      \\\\\n",
              "\\hline\n",
              "\\end{tabular}\n",
              "\\end{center}\n",
              "\n",
              "\\begin{center}\n",
              "\\begin{tabular}{lrrrrrr}\n",
              "\\hline\n",
              "           &   Coef. & Std.Err. &        z & P$> |$z$|$ &  [0.025 &  0.975]  \\\\\n",
              "\\hline\n",
              "Intercept  &  1.8106 &   0.1859 &   9.7388 &      0.0000 &  1.4462 &  2.1749  \\\\\n",
              "Antiguedad & -0.0416 &   0.0032 & -12.9414 &      0.0000 & -0.0479 & -0.0353  \\\\\n",
              "\\hline\n",
              "\\end{tabular}\n",
              "\\end{center}\n",
              "\\end{table}\n",
              "\\bigskip\n"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary2.Summary'>\n",
              "\"\"\"\n",
              "                         Results: Logit\n",
              "=================================================================\n",
              "Model:              Logit            Method:           MLE       \n",
              "Dependent Variable: Churn_num        Pseudo R-squared: 0.047     \n",
              "Date:               2023-10-18 17:13 AIC:              3742.0456 \n",
              "No. Observations:   3000             BIC:              3754.0583 \n",
              "Df Model:           1                Log-Likelihood:   -1869.0   \n",
              "Df Residuals:       2998             LL-Null:          -1960.3   \n",
              "Converged:          1.0000           LLR p-value:      1.4046e-41\n",
              "No. Iterations:     5.0000           Scale:            1.0000    \n",
              "------------------------------------------------------------------\n",
              "              Coef.   Std.Err.     z      P>|z|    [0.025   0.975]\n",
              "------------------------------------------------------------------\n",
              "Intercept     1.8106    0.1859    9.7388  0.0000   1.4462   2.1749\n",
              "Antiguedad   -0.0416    0.0032  -12.9414  0.0000  -0.0479  -0.0353\n",
              "=================================================================\n",
              "\n",
              "\"\"\""
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "modelo_antig = sm.Logit.from_formula(\n",
        "    formula = \"Churn_num ~ Antiguedad\",\n",
        "    data    = data\n",
        ").fit()\n",
        "modelo_antig.summary2()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D4HI1QOjBl7a"
      },
      "source": [
        "Viendo los coeficientes de la parte inferior de la tabla, como resultado obtenemos que $\\hat\\beta_0=1.8106$ (`Intercept`) y $\\hat\\beta_1=-0.0416$ (`Antiguedad`). Reemplazando en la fórmula del modelo de regresión logística obtenemos:\n",
        "\n",
        "$$\n",
        "\\mathbf\\log{\\left(\\hat\\pi_i \\over 1 - \\hat\\pi_i\\right)} = \\hat\\beta_0 + \\hat\\beta_1 \\cdot \\text{Antigüedad}_i = 1.8106 - 0.0416 \\cdot \\text{Antigüedad}_i\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RM4pOcodBl7a"
      },
      "source": [
        "Y finalmente, la probabilidad estimada $\\pi_i$ estará dada por:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OKomHqqhBl7a"
      },
      "source": [
        "$$\n",
        "\\hat\\pi_i = {\\exp{(\\hat\\beta_0 + \\hat\\beta_1 \\cdot \\text{Antigüedad}_i)} \\over 1 + \\exp{(\\hat\\beta_0 + \\hat\\beta_1 \\cdot \\text{Antigüedad}_i)}}= {\\exp{(1.8106 - 0.0416 \\cdot \\text{Antigüedad}_i)} \\over 1 + \\exp{(1.8106 - 0.0416 \\cdot \\text{Antigüedad}_i)}}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6M0YcCpQBl7a"
      },
      "source": [
        "Veamos el gráfico que resulta de obtener las probabilidades estimadas para distintos valores de la antigüedad de los clientes."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9i7r8X6CBl7a",
        "outputId": "f1769cd0-156a-4d9f-c70d-2383b209375a"
      },
      "outputs": [
        {
          "data": {
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DRTw1UE6f0dK5LbMfdOiA7Cdvy+3zr/QFlZNZUBkAAAAAwhmhDhBCTO16iniiv5y+L0pNWmQ/6OB+2f9MlNvnYbkzvuJW6AAAAAAQpgh1gBBkzjxbEU8+l37mTuPm2Q86sFf2o7fk9n1E7uzvZFNTA9skAAAAAKBQEeoAIczUrqeIpwbIeXaU1Oj87AftS5R9b7zc5x6TO2+mrJsW2CYBAAAAAIWCUAcIA6bOOYroNig93Gl4XvaDdifIvj1W7sAnZX+fI+u6Ae0RAAAAAFCwuPtVLhITE/XNN99o8eLFSkxMVGRkpOLi4tSmTRtdeeWVii6Auwxt3bpV06dP159//qnExEQlJyerRIkSqlmzppo3b67LLrtMxYsXL4Bng3Bn6pyjiO7Py/61Qu6X70url/kP2rFF7usjpZpnybnhTqlJi/TbqAMAAAAAQoqx1lqvmwhWixYt0iuvvKKjR49mW69WrZri4+NVpUqVUz7GV199pQ8++EBpaTlfElOpUiX16tVLtWrVOuXj5EVaWpp27txZqMcoCI7jKC4uTpKUkJAglzNOsmWtlVb9Iffz96QNa3IeWOccOTfdLVO/SeCagx/mNcIR8xrhiHmNcMXcRjgKxnldpUoVRUREFNj+CHVysHHjRvXv319JSUmKiYnRjTfeqMaNGys5OVlz5szRjBkzJEnVq1fX8OHDFRMTk+9jzJ07Vy+99JIkKTIyUldeeaWaNGmiMmXKKCEhQdOnT9eqVaskSeXLl9fYsWNVokSJAnuOWRHqhCdrrfTHb3K/mCJt3ZDzwEbny7npnzK16gSuOWRgXiMcMa8RjpjXCFfMbYSjYJzXBR3qcPlVDiZPnqykpCRFRESoX79+qlevXkatcePGqlq1qqZMmaJt27Zp2rRp6tSpU76P8emnn2Z83rNnTzVr1izjcd26dXXRRRdp9OjRWrhwofbt26cff/xR11577ek9MRQ5xhipaUs5TZpLi+bK/fIDKWGr/8A/F8v9c7FMi4tkbrhTJq564JsFAAAAAOQZCyVnY+3atfrzzz8lSR06dPAJdE649tprVb16+i+9X3/9tVLzebvoo0ePasuWLZKk2rVr+wQ6md16660Zn69evTpfxwAyM44j0+IiOYPGydzfXaoUl+04+9svcgc8Lve912T37QlwlwAAAACAvCLUycavv/6a8XmHDh2yHeM4jtq1aydJOnLkiFasWJGvY2QOgU62Jk/mWkpKSr6OAWTHOBFy2nSQ8/x4mTsflcqW9x/kurKzv5fb92G5U9+RPXIo8I0CAAAAAE6KUCcbJ9axiY6O1llnnZXjuIYNG/ptk1dlypRRqVKlJOmk69hkrlWrVi1fxwBOxkRGymnfUc7QN2Ru/qdUoqT/oJRk2e8/kxv/kNxvp8omJwW+UQAAAABAtlhTJxtbt6avNxIXF3fSBYwyhywntsmPyy+/XF988YU2bNigxYsX6/zzz/cbc2LdHcdxdOmll+b7GHv25H75TLly5TKep+MEf86XucdQ6DfoFS8hXdNZtv3Vcr+bKveHr6Ss4c2xI7KfvSs782tF3HiXTNtLZZyCW9wLzGuEJ+Y1whHzGuGKuY1wVBTmNXe/yiI5OVl33XWXJKlZs2Z69tlnTzr+7rvvVlJSks4++2wNHTo0X8c6fvy4XnjhBS1btkxRUVEZd78qXbq0du3apenTp2vFihVyHEf33Xefrrzyynw/n86dO+c6ZsKECYqNjc33vhGe0vbs1oGP/q0j330huWnZjomqVUdl731CMS0vTF+IGQAAAAAQcJypk8Xx48czPs/LbcpjYmKUlJTks11excTEqE+fPpo1a5a++OILTZs2TdOmTfMZ06pVK91www06++yz871/4FRExFZShcfjVfrGO3Vwyus6Onu635iUTeuUOKibops0V9n7n1R0vUYedAoAAAAARRuhThbJyckZn0dG5v7ynBiTebv8WLdunebMmaNdu3ZlW1+2bJnKlSun6tWrq0SJEvne/4QJE3IdU65cOUlSWlqadu/ene9jBJrjOKpcubIkadeuXXJd1+OOwlREMemeJxXZ7mqlTZ0ku3Kp35CkZb9rV/d7ZFperIib/ylTuaoHjYYH5jXCEfMa4Yh5jXDF3EY4CsZ5XalSpZMu85JfhDpZFCtWLOPzvNym/MSYzNvl1fz58zVu3DilpKSoVq1auvXWW9WwYUPFxMRoz549mjt3rj799FNNnz5dK1euVP/+/TMCmLzK72VVwTDJ88N13ZDrOeTUPEum+/Myfy6W++lkaesGvyH215+VumieTPuOMtd2kSlVJvB9hhHmNcIR8xrhiHmNcMXcRjgK13kdnisFnYbMl1zl5ZKqE2PycqlWZvv379drr72mlJQUnXHGGRo8eLBatWqlUqVKKTIyUlWqVNFNN92k3r17yxijLVu26O23387fkwEKiDFGpnEzOf3HytzfXapQ0X9QWqrsjK/Sb4M+/XPZlJTANwoAAAAARQihThbFihVT6dKlJeV+56jDhw8rKSn9LkH5PSNm7ty5GdvedNNNOYZCTZo0UePGjSVJCxYs0OHDh/N1HKAgGceR06aDnCGvy3S6L/vboB89IvvJJLnPPSb311/EWuwAAAAAUDgIdbJRo0YNSVJCQoLS0rK/+48kbd++3W+bvMp8C/TatWufdOxZZ50lSbLWaseOHfk6DlAYTFQxOVfeJGfYWzJX3iRFRvkPStwp++YouSN6ya5bFfgmAQAAACDMEepko379+pKkpKQkrV+/PsdxK1as8NsmrzIvjHSy4ChrvSAXVAJOlylZSk6n++QMHi/T6pLsB61fLXdEL7mvj5TdnRDYBgEAAAAgjBHqZKNVq1YZn8+cOTPbMa7r6qeffpIklSxZUo0a5e+WzidW4JakVatOfhbDypUrJaWva1KpUqV8HQcIBFOxipx/9ZQT/4JUt0G2Y+zvc9IvyfpkkuzRIwHuEAAAAADCD6FONurWrasGDdJ/MZ05c6bWrFnjN2batGnatm2bJKljx45+tz+fNWuWOnfurM6dO+vjjz/2275Zs2YyxkiSPvvsM+3duzfbXn744QetW7dOknT22WdnrPcDBCNzVn05vUbIefRZqVKc/4DUVNnpn8vt94jcn76TdU9+lhoAAAAAIGfc0jwH9957r/r376/k5GQNGTJEN910kxo1aqTk5GTNnTtXP/zwgySpatWquu666/K9/+rVq6t9+/aaOXOm9u7dq169eunqq69WgwYNVLx4cSUmJmru3Ln65ZdfJEmO4+j2228v0OcIFAZjjNSsrZxzW8rO+kb2q/9IR7Ms8H3ogOyU8bIzv5bT5UGZBk29aRYAAAAAQhihTg5q166tbt26ady4cTp27Jg+/PBDvzFVq1ZVfHy8ihcvfkrHePDBB5WUlKS5c+fq4MGD+uijj7IdFx0drYcffjjfl3gBXjKRUTKX3yDb5lLZrz+W/fFrKS3Vd9C2TXLH9JeatpJz6/0yVap50ywAAAAAhCBCnZNo0aKFRo8erW+++UaLFi3S3r17FRkZqbi4OLVu3VpXXXWVoqOjT3n/UVFR6tatmy6//HLNmjVLf/31l/bu3avU1FQVL15c1apVU5MmTXT55Zfn+5bpQLAwJUvLdH5Atn1HuZ+8Iy2Z7z9o6UK5yxfJXHatzDWdZUqUCnifAAAAABBqjLXWet0EgkNaWpp27tzpdRu5chxHcXHp67UkJCTIdV2PO0J+2JVL5X48Udq6MfsBpcrI3HCnzCVXyDhF525vzGuEI+Y1whHzGuGKuY1wFIzzukqVKgV6V2sWSgYQUKZBUzn9x8rc/ZhUuqz/gMMHZd+fIHfI07Jr/gx8gwAAAAAQIgh1AASccSLkXHKVnCGvy1x5kxSRzZWgWzbIfSFe7lujZfcmBr5JAAAAAAhyhDoAPGNKlJTT6T45z78qndc62zF24Wy5/R+V+/XHsinJAe4QAAAAAIIXoQ4Az5nK1RTxeB85Tw+WqtX0H5CcJPvFFLnPPS67ZL5YCgwAAAAACHUABBHToKmc516Wue0hqURJ/wGJO+W+NkzuSwNld2wJfIMAAAAAEEQIdQAEFRMRIeeya9PX27nkKskY/0ErFssd9KTcTybJHj8a+CYBAAAAIAgQ6gAISqZ0WTl3Pyan3xipbgP/AWlpstM/l9v/MbkLfuKSLAAAAABFDqEOgKBmataR02uEzIM9pHKx/gP275X994tyX+wnu21z4BsEAAAAAI8Q6gAIesYYORe0kzN4vEzHTlJkNrdAX71M7vNPyv14ouwxLskCAAAAEP4IdQCEDBNTXM7N/5QzYJzU6Hz/Aa4r+39fpt8Cff5MLskCAAAAENYIdQCEHBNXXc5TA+U8Gi9VqOQ/4MA+2Ylj5Y7uwyVZAAAAAMIWoQ6AkGSMkWnWRs7z42Wu6Zz9JVlr/pQ7+Cm5UyfJHj8W+CYBAAAAoBAR6gAIaSY6Ws6Nd8kZ9KrUpIX/gLQ02e8/lzvgcdlF87gkCwAAAEDYINQBEBZM5Wpynugv5/G+Umxl/wF7E+VOGC533GDZ3QmBbxAAAAAAChihDoCwYYyROe8COYNek7m6sxSRzSVZy36TO6Cr3K8/lk1JCXyTAAAAAFBACHUAhB0THS3nprvkDHxFOudc/wEpybJfTJH7/JOyK5cGvD8AAAAAKAiEOgDClomrIefpwTIP9pDKlvcfkLBN7pj+cieOlT10IPANAgAAAMBpINQBENaMMXIuaJd+l6xLr5WM/9uenT9Tbv/H5P7yfyykDAAAACBkEOoAKBJMiZJybn9ITt/R0pln+w84ckh28ji5o/vI7tgS+AYBAAAAIJ8IdQAUKaZWXTnxo2TufFQqXtJ/wJo/5Q56Su6X78umJAe+QQAAAADII0IdAEWOcSLktO8o5/nXZFpe7D8gLVV22n/kDnyChZQBAAAABC1CHQBFlilXQc5Dz8h5aoBUsYr/gF07WEgZAAAAQNAi1AFQ5JnGzeUMfFWm4y1SRIRf3c6fKfe5x+TOm8lCygAAAACCBqEOAEgy0dFybr5HTr+xUp1z/AccPiT79li5Lw2Q3Z0Q+AYBAAAAIAtCHQDIxNQ4U06vETkvpLxiidyBXeV+/7lsWlrgGwQAAACA/yHUAYAsjOP8vZBy8wv9ByQny06dJHdYT9lN6wLfIAAAAACIUAcAcmTKVZDzSG85j/eVysX6D9i8Tu6wHnKnTpJNSgp8gwAAAACKNEIdAMiFOe+C9LN22l8tGeNbdF3Z7z+XO4jbnwMAAAAILEIdAMgDU7yEnDsfkdNrhFT1DP8BuxPSb3/+7quyRw8HvkEAAAAARQ6hDgDkg6nbQE7/l2Suv0OKjPSr25+nyx3QVXbJAg+6AwAAAFCUEOoAQD6ZqCg5190m57mXpboN/Afs3yv3taFy33xB9tCBwDcIAAAAoEgg1AGAU2SqniHnmeEydzwsRRf3q9tff5b73GNyF/wka60HHQIAAAAIZ4Q6AHAajOPI6XCNnEHjpEbn+w84fEj23y/KfXWI7N7EwDcIAAAAIGwR6gBAATCxleU8NVDmvm5SiVL+A/74Ve7ArnJnf89ZOwAAAAAKBKEOABQQY4yctpfKef41qXlb/wHHjsq+95rclwbI7tkd+AYBAAAAhBVCHQAoYKZseUU88qycR5+VypTzH7BiidwBXeX+9B1n7QAAAAA4ZYQ6AFBITLO2cp5/TabNpf7FpGOyU8bLHfucbOLOwDcHAAAAIOQR6gBAITIlS8u5v5ucJwdI5WL9B6xcKnfgk0qb+Y2s6wa+QQAAAAAhi1AHAALANGkuZ9CrMhf9w7+YdEzulPHa3fcxpSZsC3xzAAAAAEISoQ4ABIgpUVLOPU/IeWqgVL6iXz3pj9+U8PhtSvvxa87aAQAAAJArQh0ACDDTuJmcgeNkLr7Cr2aPH5P7/gTukAUAAAAgV4Q6AOABU6KknH92ldNtkFShkv+AlUvlDuwq95f/4w5ZAAAAALJFqAMAHjKNzpczcJycdlf5F48fk508Tu64wbL79wS8NwAAAADBjVAHADxmipdQxD+7qtKQVxVRsYr/gGW/yR3whNz5szhrBwAAAEAGQh0ACBIx57dW3Pj/yFx4uX/x6GHZiWPkThgue3B/wHsDAAAAEHwIdQAgiDglSyny/m5yuvaXypb3H7B4vtwBXWV/nxv45gAAAAAEFUIdAAhCpmlLOQPHybS6xL94+KDc10fInThW9ujhgPcGAAAAIDgQ6gBAkDKlysj5V085jzwrlSrjV7fzZ8od+KTsiiWBbw4AAACA5wh1ACDImeZt5Qx6VTq/tX9xX6Lcsc/J/fBN2aSkwDcHAAAAwDOEOgAQAkyZcnIejZd5oLtUvKRf3f44Te6QbrIb/vKgOwAAAABeINQBgBBhjJHTuoOcga9IDZr6D0jYJnfEM3K//EA2NTXg/QEAAAAILEIdAAgxpkIlOd0Gydz2kBRVzLfourLTPpI7opfsji3eNAgAAAAgIAh1ACAEGceRc9m1cvq/JJ15tv+ATWvlDu4u98dpstYGvD8AAAAAhY9QBwBCmKlaQ07vkTLX3yE5Wd7SU5JlP3xT7iuDZPfv9aZBAAAAAIWGUAcAQpyJjJRz3W1y4l+Q4mr4D1i+SO6gJ2QXzQ18cwAAAAAKDaEOAIQJc+bZcvqPlbnsOv/i4UNyJ4yQ+87LssePBr45AAAAAAWOUAcAwogpFi3ntn/J6T5IKlfBr27nzJD7fDfZtSs96A4AAABAQSLUAYAwZBqeL2fAK1Lztv7F3QlyR8XL/WIKtz4HAAAAQhihDgCEKVOqjJyHe8vc102KKe5btK7s1x+n3/o8YZsn/QEAAAA4PYQ6ABDGjDFy2l4q57mXpboN/AdsWit3cDe5P0/n1ucAAABAiCHUAYAiwFSKk/PMMJmb7pYiInyLyUmy774q9/WRskcOedMgAAAAgHwj1AGAIsI4EXKuvvV/tz6v7j9g0Vy5A5+UXbk08M0BAAAAyDdCHQAoYkytunL6vSTT7ir/4v49csc+J3fqJNnUlMA3BwAAACDPCHUAoAgy0dFy7npMzuN9pFKlfYvWyn7/udzhvWR3bPWmQQAAAAC5ItQBgCLMnNdazoBxUsPz/Iub18kd0k3u7O9YRBkAAAAIQoQ6AFDEmXIV5Dw1UKbzA1JkpG8xOVn2vfFyXx/BIsoAAABAkCHUAQDIOI6cf9wgJ360VPUM/wGL5skd9JTsmuWBbw4AAABAtgh1AAAZTM2z5PQdI9P+av/ivkS5o/vJ/fID2bS0gPcGAAAAwBehDgDAh4mOlnPnI3K69stmEWVXdtpHckf3kd2zy5sGAQAAAEgi1AEA5MA0bSXnuVek+k38i2tXpl+O9dsvgW8MAAAAgCRCHQDASZjysXKefl7mprslJ8s/GceOyH1jlNzJ42STjnvTIAAAAFCEEeoAAE7KOBFyrr5VTu+RUsUqfnX7y//JHdJddssGD7oDAAAAii5CHQBAnpiz6svp/5JMq3b+xYRtcof1lDvza1lrA98cAAAAUAQR6gAA8syUKCnz4NMy93WTomN8i6kpsh+8IXfCcNkjhz3pDwAAAChKCHUAAPlijJHT9lI5/V+SatX1H7B4vtznn5JduzLgvQEAAABFCaEOAOCUmCrV5Dw7UubyG/yLe3fLfSFe7jefyLpu4JsDAAAAigBCHQDAKTORUXK6PCCna3+pVGnfouvKfv6e3JcGyB7Y502DAAAAQBgj1AEAnDbTtKWc516R6jX2L65cKnfQk7J/Lg58YwAAAEAYI9QBABQIUz5WTo/BMtffIZks/7wcOiD3pQFyP5ssm5bmTYMAAABAmCHUAQAUGONEyLnuNjk9hkjlYv3q9ttP5Y7uK7s30YPuAAAAgPBCqAMAKHCmfmM5z70sndvSv7h2hdzBT8ku+y3wjQEAAABhhFAHAFAoTOkycrr2k+nygBQR6Vs8fEjuK8/LnTpJNjXVmwYBAACAEEeoAwAoNMYYOZffIKf3SCm2sl/dfv+53NF9ZPfs9qA7AAAAILQR6gAACp2pfbac516SmrXxL65bJff5p2SXLAh4XwAAAEAoI9QBAASEKVFKziPPytz+kBSZ5XKso4flvjZU7n8myqameNMgAAAAEGIIdQAAAWOMkXPptXKeHSVVivOr2x++lDsqXnbPLg+6AwAAAEILoQ4AIOBMrbpy+o2VaXGRf3HDGrnPd5Nd+mvgGwMAAABCCKEOAMATpkRJmYeekbnzUSkyyrd49LDcVwfLnfoOd8cCAAAAckCoAwDwjDFGTvuOcuJfkCpX9avb7z+T+2I/2X17POgOAAAACG6EOgAAz5maZ6VfjtX8Qv/i2hXpd8f6c3HgGwMAAACCGKEOACAomOIlZB7ulX53rIgsd8c6fFDuywPlfjFF1k3zpkEAAAAgyBDqAACCRsbdsXqPlGIr+xatlf36Y7ljnpM9sM+bBgEAAIAgQqgDAAg6pvbZcvq/JDVt5V9cvUzu4G6ya5YHvC8AAAAgmBDqAACCkilZSs7jfWVuvU9ysvxzdWCf3Bf7yf3uU1lrvWkQAAAA8BihDgAgaBlj5Fxxk5xnhkvlK/oWXVf208lyXxsqe/SwNw0CAAAAHiLUAQAEPVO3QfrlWA3P9y8uXSh3cHfZzesC3hcAAADgJUIdAEBIMKXLyHnqOZnr75CM8S0m7pQ7vJfcn6dzORYAAACKDEIdAEDIME6EnOtuk9NtoFSqjG8xNUX23VdlJ70sm5TkSX8AAABAIBHqAABCjml4vpz+Y6U65/jV7Lwf5Q7vKZuwzYPOAAAAgMAh1AEAhCRToZKcnkNlLr/ev7htk9yhT8sumhv4xgAAAIAAIdQBAIQsExklp8uDch7pLcUU9y0ePyZ3wgi5UyfJpqV50yAAAABQiAh1AAAhzzS/UE7fMVL1Wn41+/3ncsf0lz2wz4POAAAAgMJDqAMACAsmrrqc+NEybTr4F9csT7/t+doVgW8MAAAAKCSEOgCAsGGio2Xu6yZz56NSZKRv8cBeuaP7yv3hS257DgAAgLBAqAMACCvGGDntO8rpNUKqUNG3mJYm+5+Jsm++IHv8qDcNAgAAAAWEUAcAEJZM7Xpy+r0kNTzPr2Z/+0Xu0J6yO7YEvC8AAACgoBDqAADClildRs5TA2Su6exfTNiaHuz8PifwjQEAAAAFgFAHABDWjBMh58a75DzRXypR0reYdEzu6yO57TkAAABCEqEOAKBIMOe2lNNvrHRGbb+a/f5zuWOfkz24P/CNAQAAAKeIUAcAUGSYSnFynh0l0/Yy/+LqZXKHPC27fnXgGwMAAABOAaEOAKBIMcWiZe59Mv225xFZbnu+L1HuC/Fyf/qO254DAAAg6BHqAACKnIzbnj8zTCoX61tMTZWdMl528iuyyUneNAgAAADkAaEOAKDIMnXOkdN/jFS/iV/Nzpkhd+Szsok7PegMAAAAyB2hDgCgSDNlysvp/rzMFTf6FzevS19nZ8XigPcFAAAA5IZQBwBQ5JmICDm33i/zUC8pOsa3eOSQ3JcGyf3uU9bZAQAAQFAh1AEA4H+clhfJiR8tVanuW7Cu7KeTZd8YJXv8mDfNAQAAAFkQ6gAAkImpXlNO3xel8y7wq9nf58gd/ozszu0edAYAAAD4ItQBACALU7yEnEfjZW64UzLGt7h9s9yhPWSX/upNcwAAAMD/EOoAAJAN4zhyru0i54nnpBIlfYvHjsh9dbDcrz6SdV1vGgQAAECRR6gDAMBJmCbN0y/Hql7Lr2b/+4Hc8cNkjx7xoDMAAAAUdYQ6AADkwlSuJif+BZmWF/sXly6UO6yn7I4tgW8MAAAARRqhDgAAeWCiY2T+1VPm1vskk+Wfz53b0oOdxfO9aQ4AAABFEqEOAAB5ZIyRc8VNcroPkkqV8S0ePyZ3/DC5X77POjsAAAAICEIdAADyyTRoKqffWKlmHb+anfYfua8NZZ0dAAAAFDpCHQAAToGJrSSn9wiZ1h38i3/8Knd4T9kdWwPfGAAAAIoMQh0AAE6RKRYtc383mS4PSk6Wf1ITtskd1kN2CevsAAAAoHBEet1AsEtMTNQ333yjxYsXKzExUZGRkYqLi1ObNm105ZVXKjo6usCO9ccff+jnn3/WqlWrtH//fjmOo3LlyqlmzZpq0qSJLrnkEsXExBTY8QAAp88YI3P59bI1zpT7xijp8MG/i8ePyX1tmMx1t8lce5tM1uAHAAAAOA2EOiexaNEivfLKKzp69GjG15KSkrRu3TqtW7dOP/74o+Lj41WlSpXTOs7hw4c1fvx4/fbbb361Y8eOaceOHVqwYIHq1aunM88887SOBQAoHOacc+X0GyN3/DBp83qfmv3qI9nN6+Xc312mREmPOgQAAEC4IdTJwcaNGzV27FglJSUpJiZGN954oxo3bqzk5GTNmTNHM2bM0Pbt2zVixAgNHz78lM+gOXr0qIYMGaL169N/AWjWrJnatm2ruLg4ua6rxMRErV27VgsWLCjIpwcAKAQmtrKc3iNl33tNdv4s3+LShXKHPyPn8b4ycdU96Q8AAADhhVAnB5MnT1ZSUpIiIiLUr18/1atXL6PWuHFjVa1aVVOmTNG2bds0bdo0derU6ZSO8/bbb2v9+vWKiIjQE088obZt2/qNueiii3TPPffI5Ra5ABD0TLFo6f7uUs06slMnSZnfuxO2yh3WU86/esg0aeFdkwAAAAgLXNyfjbVr1+rPP/+UJHXo0MEn0Dnh2muvVfXq6X9p/frrr5Wamprv46xatUqzZ8+WJN18883ZBjonGGMUERGR72MAAALPGCPnHzfI6TZIKlXat3jsiNxxg+V+O1XWWm8aBAAAQFgg1MnGr7/+mvF5hw7Z3KpWkuM4ateunSTpyJEjWrFiRb6P891330mSYmJidN11151CpwCAYGYaNJXTd4xU40zfgrWyn70r+9Zo2aTjnvQGAACA0Eeok41Vq1ZJkqKjo3XWWWflOK5hw4Z+2+RVampqRnh03nnnZazJk5aWpt27dysxMfGUzv4BAAQXU7GKnGdHybS4yK9mf/1Z7ojesok7PegMAAAAoY41dbKxdetWSVJcXNxJL3mqVq2a3zZ5tXHjRqWkpEiS6tWrp/379+uDDz7QvHnzlJSUJEmKiopS48aNdfPNN6t+/fr5fRqSpD179uQ6ply5chnP0wmB2+1m7jEU+gXygnkd5oqXkH2kt9xv68j97F0p82VXWzfIHdpDEY8+K+ecc73rsRAwrxGOmNcIV8xthKOiMK8JdbJITk7WoUOHJEmxsbEnHVuqVClFR0crKSkpT+FJZplDoJSUFPXo0SPjuJm/vnjxYi1ZskT//Oc/dc011+TrGJL06KOP5jpmwoQJio2NVUREhOLi4vJ9DC9VrlzZ6xaAAse8DmP3P6FjTc7Xnhf6yR45/PfXDx9U2ov9Vfpf3VXqui4yxnjXYyFhXiMcMa8RrpjbCEfhOq8JdbI4fvzvtQ3ycpvymJgYJSUl+WyXF4cP//3D/NSpU5WSkqJmzZqpc+fOOuOMM3T06FEtWLBA77//vo4dO6Z3331X1apV0/nnn5+v4wAAgkvxlhepytjJSny+h1K3bvy74KZp/xujlbJ+jco//qxMVDHPegQAAEBoINTJIjk5OePzyMjcX54TYzJvlxcnLrGS0s/Iad68uZ555pmMU8LKli2rK664QjVr1tSAAQNkrdWUKVN03nnn5esvuBMmTMh1TLly5ST9vZ5PsHMcJyNl3bVrF7d6R1hgXhcxEdHSs6Nk3hotu3ShT+nI//1XR9evUcTjfWXKlveowYLBvEY4Yl4jXDG3EY6CcV5XqlSpQO9sTaiTRbFif/9lNC8LFZ8Yk3m7vIiKivJ5fPfdd2d7jd8555yjCy64QPPnz9eWLVu0ZcsW1axZM8/Hye0SsqyCYZLnh+u6IdczkBvmdRERHSPzWB/pvx/Ifv2xT8muW6XU57vJebyPzJlne9RgwWJeIxwxrxGumNsIR+E6r8NzpaDTkPmSq7xcUnViTF4u1cqsePHiGZ9XrlzZZ9HlrJo2bZrx+dq1a/N1HABA8DKOI+fGu+Q88qxULNq3uH+P3FHxcufP8qQ3AAAABD9CnSyKFSum0qVLS8r9zlGHDx/OuIwqv2fEZB6f27aZ6wcPHszXcQAAwc80bysnfpQUm2UBv5Rk2Ylj5E6dJOumedMcAAAAghahTjZq1KghSUpISFBaWs4/RG/fvt1vm7w644wzMj7P7RSwzPVwvQ0bABR1pkZtOX3HSPWb+NXs95/LHTdY9ujhbLYEAABAUUVCkI369etLSl/MeP369TmOW7Fihd82eVWpUiVVrFhRUnp4dDI7d+7M+LxChQr5Og4AIHSY0mXkdBsk0+Ea/+LyRXKHPSO7Y2vgGwMAAEBQItTJRqtWrTI+nzlzZrZjXNfVTz/9JEkqWbKkGjVqlO/jXHDBBZKkAwcOaPXq1TmOW7jw7zujNGjQIN/HAQCEDhMZKeeOh2XuflyKyHI/g53b5A7vKbvsN2+aAwAAQFAh1MlG3bp1M8KTmTNnas2aNX5jpk2bpm3btkmSOnbs6Hf781mzZqlz587q3LmzPv74Y7/tJemaa67JuAvWpEmTsl2Yefbs2frzzz8lSc2aNcv32j0AgNDkXHKlnB5DpNJlfQvHjsodN1ju95/JWutNcwAAAAgKhDo5uPfee1WsWDGlpaVpyJAh+vzzz7VmzRotX75cb775pqZMmSJJqlq1qq677rpTOkbFihXVpUsXSdL69evVp08fzZo1S+vXr9fy5cs1ceJEjR8/XlL63bLuueeegnlyAICQYM5umL7OTs06vgVrZae+I/v2WNmUZG+aAwAAgOcicx9SNNWuXVvdunXTuHHjdOzYMX344Yd+Y6pWrar4+Hif25Pn1/XXX6/Dhw/ryy+/1NatWzNCnMzKli2rZ555RlWrVj3l4wAAQpOJrSSn1wjZya/I/vqzT83OnyW7c7ucx+JlynEmJwAAQFFDqHMSLVq00OjRo/XNN99o0aJF2rt3ryIjIxUXF6fWrVvrqquuUnR09Gkf54477lCLFi00ffp0rVy5Uvv371dUVJSqVq2qFi1aqGPHjipRokQBPCMAQCgy0dHSv3pKNc6U/WKKlPmyqw1r5A7tIeexvjK1z/auSQAAAAScsVyQj/9JS0vzudNWsHIcR3FxcZLS7xyW2y3hgVDAvEZe2SUL5P57jJR0zLcQGSVzzxNyWrf3pK/sMK8RjpjXCFfMbYSjYJzXVapUUURERIHtjzV1AAAIIea8C+TEvyBVivMtpKbIThwj99PJsm6aN80BAAAgoAh1AAAIMaZ6TTl9Rkv1m/jV7Hefyn1tmOyxox50BgAAgEAi1AEAIASZUmXkdBsk0+Ea/+Ifv8od/ozsrh2BbwwAAAABQ6gDAECIMpGRcu54WObux6Ss12bv2CJ3WE/ZVX940xwAAAAKHaEOAAAhzrnkKjlPD5ZKlfEtHDkk96UBcmd9401jAAAAKFSEOgAAhAFTr7Gcvi9K1Wv5FtLSZN9/Xe77r8umpnrTHAAAAAoFoQ4AAGHCVKwi59mR0nkX+NXsrG/kvjRA9vBBDzoDAABAYSDUAQAgjJiYEnIejZe5+lb/4upl6evs7NgS+MYAAABQ4Ah1AAAIM8Zx5Nx0t8yDPaSoYr7F3Qnpd8Za9ps3zQEAAKDAEOoAABCmnAvayXlmuFS2gm/h2FG54wbL/f5zWWu9aQ4AAACnjVAHAIAwZmqfnb6Acq26vgVrZadOkp38imxKijfNAQAA4LQQ6gAAEOZM+Vg5vYbLtLzYr2bnzJA7pp/swf2BbwwAAACnhVAHAIAiwBSLlvlXT5kb7/Ivrl2ZvoDy1g2BbwwAAACnjFAHAIAiwhgj55rOch6Nl6JjfIt7dskd0Vt2yXxvmgMAAEC+EeoAAFDEmGZt5PQeKVWo6FtIOi53/HC5305lAWUAAIAQQKgDAEARZM6onb6Acp1zfAvWyn72ruzbL8mmJHvTHAAAAPKEUAcAgCLKlCkvp8dQmTYd/Gp2/ky5o/vKHtjnQWcAAADIC0IdAACKMBMVJXNfN5lb7pGM8S2uXy13WA/Zzeu9aQ4AAAAnRagDAEARZ4yRc9Utch7vK0UX9y3uTZQ7srfsYhZQBgAACDaEOgAAQJJkmraS8+xIKbaybyE5Se74YSygDAAAEGQIdQAAQAZT48z0BZTrNvSrsYAyAABAcCHUAQAAPkzpsnKeHizT9jK/mp0/U+6L/WQPsoAyAACA1wh1AACAHxMVJXPvkzKd7vVfQHndKrlDe8pu3eBJbwAAAEhHqAMAALJljJFz5c05LKC8W+6I3rJLFnjTHAAAAAh1AADAyeW4gHLS8fQFlL/7lAWUAQAAPECoAwAAcmVqnCmnz2ipzjm+BWtlP50s+84rsikp3jQHAABQRBHqAACAPDFlysnpMVSmTQe/mp07Q+7Y/rKHDnjQGQAAQNFEqAMAAPLMREXJ3NdN5uZ7/BdQ/muF3GE9Zbdt9qY5AACAIoZQBwAA5IsxRk7HW+Q8Gi8Vi/YtJu6UO7KX7LLfvWkOAACgCCHUAQAAp8Sc31pO75FS+Yq+hWNH5Y4brLT/+5IFlAEAAAoRoQ4AADhlpuZZcvq+KNWu51uwrtyP3tK+14bLpqZ60xwAAECYI9QBAACnxZQtL6fnUJmWF/vVjnz7mXY/94Ts4UMedAYAABDeCHUAAMBpM8WiZf7VU+b6O/xqSUt/VeqwHrIJ2zzoDAAAIHwR6gAAgAJhjJFz3W0yD/WSoor5Fndulzv8GdmVS71pDgAAIAwR6gAAgALltLxIzjPDpbIVfAtHD8t9eaDc2d950xgAAECYIdQBAAAFztQ+W5H9xiiqTn3fQlqa7Hvj5f7n37JumjfNAQAAhAlCHQAAUChMhYqqPOrfKt6mg1/N/vBfua8OlT121IPOAAAAwgOhDgAAKDROTHHF9hkp5+pb/YvLfpM7srds4s7ANwYAABAGCHUAAEChMo6jiFvukbnvKSki0re4bZPcYT1l1670pjkAAIAQRqgDAAACwml7mZweQ6RSZXwLhw7IfbGv3PkzvWkMAAAgRBHqAACAgDFnN5TTZ7RU9QzfQmqq7MSxcj+fIuu63jQHAAAQYgh1AABAQJlKcXKeHSU1buZXs998LPfNUbJJSR50BgAAEFoIdQAAQMCZEiXldO0vc9l1/sXf58p9IV52/97ANwYAABBCCHUAAIAnTESEnNv+JXPnI5KT5UeSTWvTF1DevM6b5gAAAEIAoQ4AAPCU0/5qOU8NkIqX9C3sS5Q78lnZxfO9aQwAACDIEeoAAADPmYbny4kfJVWK8y0kJ8mdMFzud5/KWutNcwAAAEGKUAcAAAQFU/UMOfGjpbMb+haslf10suzkV2RTU7xpDgAAIAgR6gAAgKBhSpeR032wTJtL/Wp2zgy5Y5+TPXzQg84AAACCD6EOAAAIKiYqSua+p2Ruvse/uObP9AWUd2wNfGMAAABBhlAHAAAEHWOMnI63yHk0XioW7VvcnSB3xDOyK5d60xwAAECQINQBAABByzRrI6fXCKlcBd/C0SNyXxog96fvvGkMAAAgCBDqAACAoGZq1ZHT50WpZh3fguvKThkv9z//lnXTvGkOAADAQwENdWbMmKGtW7kGHgAA5I8pHyun13CpWRu/mv3hv3JfHSp7/KgHnQEAAHgnoKHOm2++qR49emjy5MmBPCwAAAgDJjpGzsO9ZTp28i8u+03uiN6ye3YFvjEAAACPeHL5VVoap0gDAID8M44j5+Z/ytz3lBQR6Vvctknu0B6y61Z50xwAAECAeRLqrFy5Ul999ZX++OMP7d+/P8/bpaSkaMyYMVqwYEHhNQcAAIKe0/YyOU8PlkqV9i0cOiB3dF+5C2d70xgAAEAAReY+JO9SU1M1depU3XbbbScdt3nzZk2ZMiXjcZkyZVSzZk3VqlUr46NGjRqKjPRvb8GCBdqyZYsuuOCCgmwdAACEGFOvkZz40XLHDZYSMq3Zl5oi+9ZouQnbZK67TcYY75oEAAAoRAUW6qxfv16vvfaatm7dmmuok9XBgwe1fPlyLV++PONrjuOoWrVqqlmzpmrWrKny5ctr2bJlkqTExMSCahsAAIQwU7mqnPhRct8YJa1Y4lOzX30o7dwm3fukTFQxbxoEAAAoRKcd6qSmpurjjz/WV199Jdd1dc455+S6Tb169VS9enVt3LhRW7ZsUWpqqt8Y13W1detWbd26VXPnzj3dNgEAQJgyJUrJeeI52f+8JTvrW5+aXThbNnGnnMf7yJQp71GHAAAAheO0Qp21a9dqwoQJGbcpv+GGG/J0lk7t2rV1//33S/o7vNm4caM2btyoTZs2aePGjTp8+HCO29epU+d02gYAAGHGREZKdzwixZ0h+59/S9b9u7h+tdyhPeU80V+mxpme9QgAAFDQTivU6d+/v1zXVenSpdW1a1edd955+d6H4zgZl1hdcsklGV/fs2dPRsizdetW7d69W8nJyapSpYpuv/3202kbAACEIWOMzGXXylauKvfNUdLxY38X9+6WO6K3nIefkWnSwrsmAQAACtBphTqum/5XsOuvv/6UAp2TiY2NVWxsrJo3b16g+wUAAOHNNGku59lR6Qso79n1dyHpmNxxQ2S6PCBz6bUsoAwAAELead3SvHr16pKk999/X2+88YZSUlIKpCkAAIDTYarXktNntFQny1p/1pX96C3Z9yfIZrOmHwAAQCg5rVBn1KhRuv766+U4jn788Uf16dNHO3bsKKjeAAAATpkpU05OjyEyrdr51exP38kd97zs0ZzX8AMAAAh2pxXqREZG6s4779TgwYNVvXp1bd68Wc8++2xB9QYAAHBaTFQxmQeflrnhDv/iiiVyh/eS3cUfpAAAQGg6rVDnhLp162actZOcnJzr+Hnz5mnMmDGaOnWqfv31V+3atSvXbQAAAE6FMUbOtbfJPPSMFFXMt5iwVe7wnrJrlnvTHAAAwGk4rYWSfXb0v7N2WrdunevYgwcPasGCBVqwYEHG12JiYjLuglWrVq2M/xYvXrygWgQAAEWY0/Ji2djKcl8bKh3c/3fh8CG5Y56TuftxORde5ll/AAAA+VVgoc4JderUOaXtjh8/rjVr1mjNmjU+X69YsaJPyFOrVi1VrVqVO1YAAIB8M2fVl9PnRbmvDpa2bvy7kJYq+87LcndulbnxbhmnQE5mBgAAKFQFHurkRcuWLdWsWTNt3rxZmzZt0ubNm3X4cPYLFSYmJioxMVG///57xteKFSum9957L1DtAgCAMGJiK8npPULuWy9Kf/zqU7Pffiq7c7uc+7vLRMd41CEAAEDeeBLqVKhQQZdeeqnP1/bu3ZsR8pwIerZv3660tDS/7fOybg8AAEBOTEwJOY/3kf3kHdkfvvQtLponN3GXnK79ZMrHetMgAABAHgQ01Jk4caLWrFmjiIgIv1qFChVUoUIFnXfeeRlfS01N1bZt2zJCnhP/3b9/f+CaBgAAYck4ETJdHpBbtbrsB29Imf+QtHmd3GE95HTtL1Pr1C4tBwAAKGwBDXVKlSqlZs2a5Xl8ZGRkxjo6mR06dKigWwMAAEWUc8lVspWqyn19hHT0yN+F/XvljnpWzgPdZZq19a5BAACAHITkKoClS5f2ugUAABBGTIOmcuJfkCpX9S0kJ8mdMELut1NlrfWmOQAAgByEZKgDAABQ0ExcjfRgp15jv5r97F3ZSS/LpqR40BkAAED2CHUAAAD+x5QqI6f7IJkLL/er2Xk/yh3bX/bQQQ86AwAA8EeoAwAAkImJjJK55wmZTvdKxvgW/1ohd3hP2R1bPOkNAAAgM0IdAACALIwxcq68Wc5j8VKxaN/i7gS5w3vJrljsTXMAAAD/Q6gDAACQA3Neazm9R0jlK/oWjh2R+/IgubO+8aYxAAAAEeoAAACclKlZR06f0dKZZ/sWXFf2/dflfvimbFqaN80BAIAijVAHAAAgF6ZcBTk9h8k0v9CvZn+cJvfVwbJHj3jQGQAAKMoIdQAAAPLAREfLPPSMzLVd/IvLF8kd0Ut2d0LgGwMAAEUWoQ4AAEAeGceRc8OdMg88LUVG+hZ3bJE7rKfsXyu8aQ4AABQ5hDoAAAD55LRuL6fHUKl0Wd/C4YNyx/STO/dHbxoDAABFCqEOAADAKTB1G6QvoFy9lm8hNVV20ktyP3tX1nW9aQ4AABQJhDoAAACnyFSsIqf3SKlJC7+a/Xaq3NdHyCYd96AzAABQFBDqAAAAnAZTvIScrn1lLr/ev7h4vtxRz8ruTQx8YwAAIOwR6gAAAJwm40TI6fKgzN2PSRERvsXN69MXUN74lzfNAQCAsEWoAwAAUECcS66S89RAqURJ38KBvXJHxcv+9osnfQEAgPBEqAMAAFCATIOmcuJfkCpX8y2kJMt9Y5TcaR/JWutNcwAAIKwQ6gAAABQwE1dDTp8XpPpN/Gr2yw9k//2ibHKSB50BAIBwQqgDAABQCEzJ0nK6DZK5+Aq/ml04W+7ovrIH9nnQGQAACBeEOgAAAIXEREbK3P24TJcHJJPlx64Na+QO6yG7ZYM3zQEAgJBHqAMAAFCIjDFyLr9BzhP9pJjivsW9iXJH9pZdssCb5gAAQEgj1AEAAAgA06SFnGdfkGIr+xaSjssdP0zud5+ygDIAAMgXQh0AAIAAMdVryun7olS3oW/BWtlPJ8tOelk2JcWb5gAAQMgh1AEAAAggU7qsnKcHy7S51K9m5/0od0w/2UMHPOgMAACEGkIdAACAADNRUTL3PSVz8z2SMb7FtSvlDu0hu22TN80BAICQQagDAADgAWOMnI63yHksXoqO8S3u2SV3eC/Zpb960xwAAAgJhDoAAAAeMue1ltN7pFShom8h6Zjc14bInf45CygDAIBsEeoAAAB4zJxRW06fF6Wz6vsWrJX9ZJLs5FdkU1lAGQAA+CLUAQAACAKmbHk5PYfKXNDOr2bnzJA7pr/soYMedAYAAIIVoQ4AAECQMFHFZB54WubGu/yLf62QO6yH7LbNgW8MAAAEJUIdAACAIGKMkXNNZzmPxkvFon2LiTvljnhG9g8WUAYAAIQ6AAAAQck0ayOn9wipfJYFlI8fk/vqELnfs4AyAABFHaEOAABAkDI168jpM1qqXc+3YK3s1P8toJzCAsoAABRVhDoAAABBzJSrIOeZYSdZQLmf7MH9gW8MAAB4jlAHAAAgyGUsoHzT3f7FtSvlDuspu3VD4BsDAACeItQBAAAIAcYYOVffKuexPlJ0jG9xzy65I3rLLpnvTXMAAMAThDoAAAAhxJzfWk7vkVKFLAsoJx2XO3643G+nsoAyAABFBKEOAABAiDFn1JbT90Wpzjm+BWtlP3tX9u2xsinJ3jQHAAAChlAHAAAgBJky5eX0GCrTpoNfzc6fJfeFPrL793rQGQAACBRCHQAAgBBloqJk7usm0+leyRjf4oY1cof2kN201pPeAABA4SPUAQAACGHGGDlX3izn8X5SdHHf4v49ckc9K/fXn71pDgAAFCpCHQAAgDBgmraUE/+CVCnOt5CcLPvmC3K/fF/Wdb1pDgAAFApCHQAAgDBhqteUEz9aqtfYr2an/UfuGyNlk4570BkAACgMhDoAAABhxJQuI6f7IJlLrvIvLpond0Rv2T27At8YAAAocIQ6AAAAYcZERsnc9ajMHQ9LTpYf97ZuSF9Aee0Kb5oDAAAFhlAHAAAgDBlj5HS4Rk63QVKJUr7FQwfkju4n95f/86Y5AABQIAh1AAAAwphp0FROn9FSXA3fQlqq7ORxcj96SzYtzZvmAADAaSHUAQAACHOmSrX0O2M1buZXszO+kvvyQNkjhzzoDAAAnA5CHQAAgCLAlCgp54n+Mlfc5F9cuVTusJ6yO7YEvjEAAHDKCHUAAACKCONEyLn1Ppn7ukmRkb7FXTvkDn9GdtlvnvQGAADyj1AHAACgiHHaXiqn5zCpbHnfwrGjcscNlvv9Z7LWetMcAADIM0IdAACAIsjUOUdOnxelWnV9C9bKTn1H9u2xsinJ3jQHAADyhFAHAACgiDIVKsrpNVym1SV+NTt/ltxR8bL79njQGQAAyAtCHQAAgCLMFIuWebCHzM3/lIzxLW78S+7QHrLrVnnTHAAAOKnI3IcUbYmJifrmm2+0ePFiJSYmKjIyUnFxcWrTpo2uvPJKRUdHF/gx9+3bp+7du+vo0aOSpIYNG2rgwIEFfhwAAABJMsbIdOwkW62m3LdelJKO/V08sFfu6D4ydz0u58LLvGsSAAD4IdQ5iUWLFumVV17JCFckKSkpSevWrdO6dev0448/Kj4+XlWqVCnQ47799ts+xwQAAAgE07SVnPgX5L42RNqd8HchNVX2nZflblkvc+v9MhER3jUJAAAycPlVDjZu3KixY8fq6NGjiomJ0W233aYhQ4boueee02WXpf+Vavv27RoxYoSOHz9eYMf97bfftGDBApUtW7bA9gkAAJBXpnpNOX1flBo09avZGV/JfXmg7JFDHnQGAACyItTJweTJk5WUlKSIiAj169dPN998s+rVq6fGjRvr4Ycf1l133SVJ2rZtm6ZNm1Ygxzx+/LgmTpwoSbr77rsLZJ8AAAD5ZUqWlvPUQJnLr/cvrlyavs7Ots2BbwwAAPgg1MnG2rVr9eeff0qSOnTooHr16vmNufbaa1W9enVJ0tdff63U1NTTPu4HH3ygPXv2qFGjRrrkEv+7UAAAAASKiYiQ0+VBmXuflCKzXLG/O0Hu8Gdkl8z3pjkAACCJUCdbv/76a8bnHTp0yHaM4zhq166dJOnIkSNasWLFaR1z7dq1+v777xUZGal//etfp7UvAACAguJceLmcnsOksuV9C0nH5L42TO60j2Rd15vmAAAo4gh1srFqVfptO6Ojo3XWWWflOK5hw4Z+25yKtLQ0vfHGG7LW6oYbblC1atVOeV8AAAAFzdQ5R07fMdKZZ/vV7JcfyH1jpOzxY9lsCQAAChN3v8rG1q1bJUlxcXGKOMndHTKHLye2ORVfffWVNm3apCpVquimm2465f1kZ8+ePbmOKVeuXMbzdJzgz/ky9xgK/QJ5wbxGOGJeh5nYSnJ6j1Da5Fdl58/0rS2aJ3fndkU+0V+mUpw3/QUI8xrhirmNcFQU5jWhThbJyck6dCj9jg6xsbEnHVuqVClFR0crKSkpT+FJdnbu3KmpU6dKkh588EEVK1bslPaTk0cffTTXMRMmTFBsbKwiIiIUFxdaP4hVrlzZ6xaAAse8RjhiXocP22+UDn3+vg5MekXKfNnVtk1yhzyt2GeHK+b8C7xrMICY1whXzG2Eo3Cd1+EZVZ2GzLcnj4mJyXX8iTGnelvzN998U8nJyWrbtq2aNvW/dSgAAEAwMcaozM13qdKgV2RKlvapuYcPavdzT+jQ5+/LWutRhwAAFB2cqZNFcnJyxueRWe/0kI0TYzJvl1c//fSTli1bpuLFi+uee+7J9/Z5MWHChFzHlCtXTlL62j67d+8ulD4KkuM4GSnrrl275LI4I8IA8xrhiHkd5qqdqYi+Lyr11SHS9ky3N3dd7f/3WB34c4ki/tlVpli0dz0WAuY1whVzG+EoGOd1pUqVTrrMS34R6mSR+fKnvNym/MSY/F42dfDgQb377ruSpNtvv13ly5fPZYtTk9slZFkFwyTPD9d1Q65nIDfMa4Qj5nWYqhQnJ36U3IkvSVlub27nzVTq9i1yHusjU6GiN/0VMuY1whVzG+EoXOc1l19lkfmSq7xcUnViTF4u1crs3Xff1aFDh1SnTh1dccUV+WsSAAAgSJiYEnIefVbmutv9i5vWyh36tOxfKwLfGAAARQBn6mRRrFgxlS5dWocOHcp18ePDhw8rKSlJUv7OiNm7d69mz54tSWrUqJHmzZt30vEHDhzQnDlzJKUv7nT22f63EwUAAPCKcRyZ62+XPaO23IljpaRMtzc/uF/ui31lbntIpt1VMsZ41ygAAGGGUCcbNWrU0MqVK5WQkKC0tLQcr3fbvn27zzZ5lfmyrv/+97+5jt+2bZtefvllSVK7du0IdQAAQFAy57eWE/+C3PFDpV07/i6kpcm+P0HavE66/WGZqCjvmgQAIIxw+VU26tevL0lKSkrS+vXrcxy3YsXfpxKf2AYAAKAoM9VryunzotTofL+a/Xm63NF9ZPef/GxoAACQN5ypk41WrVrpiy++kCTNnDkz2zNjXNfVTz/9JEkqWbKkGjVqlOf9V65cWR9//HGu4zp37ixJatiwoQYOHJjn/QMAAHjJlCwl58nnZD+fIvvdp77F9avlDnlaziPPytRt4E2DAACECc7UyUbdunXVoEH6DxkzZ87UmjVr/MZMmzZN27ZtkyR17NjR7/bns2bNUufOndW5c+c8BTgAAADhxDgRcm65R+ahXlLW25of2Cd3dF+5P33nTXMAAIQJQp0c3HvvvSpWrJjS0tI0ZMgQff7551qzZo2WL1+uN998U1OmTJEkVa1aVdddd53H3QIAAAQnp+VFcuJHSRWr+BbSUmWnjJf77quyKSneNAcAQIjj8qsc1K5dW926ddO4ceN07Ngxffjhh35jqlatqvj4eBUvXtyDDgEAAEKDqVFbTr8xct98QVqxxKdmf54uu32znEd6y5TL+91EAQAAZ+qcVIsWLTR69Ghdc801qlq1qqKjo1WyZEnVqVNHd955p0aNGqW4uDiv2wQAAAh6pmRpOU8OkLnyJv/iulVyhzwtu3aFfw0AAOTIWGut100gOKSlpWnnzp1et5Erx3EywrSEhAS5rutxR8DpY14jHDGvkRN34WzZya9Iycm+hYhImS4PyrTvKGOMJ73lhnmNcMXcRjgKxnldpUoVRUREFNj+OFMHAAAAAeW0ukTOsy9IsZV9C2mpsh+8LvvOK7IpydlvDAAAMhDqAAAAIODMGenr7KjheX41O3eG3JHPyu7ZHfjGAAAIIYQ6AAAA8IQpVUbOUwNkOt7iX9y0Vu6Q7rKr/gh8YwAAhAhCHQAAAHjGOBFybr5HziO9pegY3+Lhg3LHPid3+hdiGUgAAPwR6gAAAMBzpvmFcuJHS5Wr+RZcV/aTt2X//aJs0nFvmgMAIEgR6gAAACAomOo15fQdLZ3b0q9mF86WO/wZ2V3bPegMAIDgRKgDAACAoGFKlJLzeF+Z6273L27bJHdID9mlvwa+MQAAghChDgAAAIKKcRw5198up2t/qXgJ3+KxI3JfHSz3yw9kXdebBgEACBKEOgAAAAhKpmlLOX1elKrV9KvZaR/JHTdY9sghDzoDACA4EOoAAAAgaJm46nLiX5BpebF/cfnvcoc8Lbt5feAbAwAgCBDqAAAAIKiZmOIy/+op0/kBycny42viTrkjesmdN9Ob5gAA8BChDgAAAIKeMUbOP26Q8/QQqXRZ32JKsuzbY+V+8IZsaoo3DQIA4AFCHQAAAIQMU7+xnP4vSWfV96vZmV/LHd1Xdt+ewDcGAIAHCHUAAAAQUkz5WDnPDJNpf7V/cd0quYO7ya76I+B9AQAQaIQ6AAAACDkmMkrOnY/I3NdNiirmWzx0QO6Y5+R++6mstZ70BwBAIBDqAAAAIGQ5bS+V8+xIqWIV34J1ZT+bLHf8cNmjR7xpDgCAQkaoAwAAgJBmataR02+s1KSFf3HJfLlDe8hu3RjwvgAAKGyEOgAAAAh5pmQpOV37ydxwp2SMb3HXdrnDe8qdz23PAQDhhVAHAAAAYcE4jpxru8h5aqBUqrRvMTlZduJYue+/LpvCbc8BAOGBUAcAAABhxTQ6P/1yrDPP9qvZWd/IfSFeds9uDzoDAKBgEeoAAAAg7JjYynJ6jZC55Cr/4oY16bc9X/574BsDAKAAEeoAAAAgLJmoKDl3PyZz31P+tz0/ckjuK8/L/fIDWTfNmwYBADhNhDoAAAAIa07by+TEvyBVivMtWCs77SO5Lw+SPXTAm+YAADgNhDoAAAAIe+aM2unr7JzX2r+4Yonc57vJrl0Z+MYAADgNhDoAAAAoEkyJknIei5e59T7JyfJj8P49ckf3kfvDl7LWetMgAAD5RKgDAACAIsMYI+eKm+T0GCqVreBbTEuT/c9EuW+MlD121JsGAQDIB0IdAAAAFDmmXiM5/cdK9Zv4F3+fK3doD9mtGwLfGAAA+UCoAwAAgCLJlC0vp/vzMlff6l/cuU3usGfk/vJ/XI4FAAhahDoAAAAoskxEhJyb7pbTtb9UoqRvMSVZdvI42UkvyyYd96ZBAABOglAHAAAARZ5p2jL97li16vrV7Lwf5Q7rKbtjiwedAQCQM0IdAAAAQJKpFCen90iZDtf4F7dvlju0h9z5MwPfGAAAOSDUAQAAAP7HREXJueNhmYd6STHFfYtJx5X21ovaO26obHKSNw0CAJAJoQ4AAACQhdPyovTLsWrU9qsd+e5z7exxn+zO7R50BgDA3wh1AAAAgGyYKtXkxI+SufgKv1rK+jVKff4pub/+4kFnAACkI9QBAAAAcmCKRcv5Z1eZB7pLxaJ9i8ePyb45Su77E2RTkr1pEABQpBHqAAAAALlwWneQ0/dFqVpNv5qd9a3c4c9wORYAIOAIdQAAAIA8MNVqKrLfGJW4LJu7Y23ZIHdwd7kLfgp8YwCAIotQBwAAAMgjEx2j2KcHqUK3Af6XYyUdk/33i3LffZW7YwEAAoJQBwAAAMinkv+4TpH9x0pVz/Cr2Z+nyx3WU3bHVg86AwAUJYQ6AAAAwCkw1WrK6TtG5sLL/YvbNskd+rTc+TMD3xgAoMgg1AEAAABOkYmOlnPvkzL3d5eiY3yLScdlJ46VO+ll2aTj3jQIAAhrhDoAAADAaXLadJDTd4xUvZZfzc6dIXfI07JbN3jQGQAgnBHqAAAAAAXAVK0hp89omYuv8C8mbJU7tKfcWd/IWhv45gAAYYlQBwAAACggpli0nH92lXmwhxRT3LeYmiL7/utyXx8pe/SwNw0CAMIKoQ4AAABQwJwL2snpP1aqVde/uGiu3Oe7ya5bFfjGAABhhVAHAAAAKASmcjU5vUfKXH6Df3HPLrmjnpX77aeyrhv45gAAYYFQBwAAACgkJipKTpcH5HTtL5Uq7Vt0XdnPJst9eZDsgX3eNAgACGmEOgAAAEAhM01byun/slSvkX9xxWK5g56UXf574BsDAIQ0Qh0AAAAgAEyFinJ6DJG57jbJGN/ioQNyXx4k9+OJsikp3jQIAAg5hDoAAABAgBgnQs71d8jpMUQqV8Gvbv/vS7kjeskmbPOgOwBAqCHUAQAAAALM1G8i57lXpHNb+hc3r5M7pLvcOTNkrQ18cwCAkEGoAwAAAHjAlC4jp2s/mdsfkiKjfItJx2XfeVn2rdGyR4940yAAIOgR6gAAAAAeMcbIufRaOX1HS1XP8KvbX3+W+/xTsutWedAdACDYEeoAAAAAHjM1asvpO0bmkiv9i3t2yR31rNxp/5F10wLfHAAgaBHqAAAAAEHAREfLuftxOY88K5Uo6Vt0Xdkv35c7uq/snt3eNAgACDqEOgAAAEAQMc3bpi+iXLehf/GvFXIHPSn3158D3xgAIOgQ6gAAAABBxsRWktNzqMx1t0smy4/sx47IvvmC3LfHyh4/6k2DAICgQKgDAAAABCETESHn+tvl9BomxVb2q9t5M+U+341FlAGgCCPUAQAAAIKYqdtQznMvy1zQzr+4O+F/iyh/xCLKAFAEEeoAAAAAQc6UKCnnwR4yDzwtFS/hW3Rd2S8/kPtCX9k9u7xpEADgCUIdAAAAIEQ4rdvL6f+SVOcc/+La/y2iPG+mrLUB7w0AEHiEOgAAAEAIMZXi5DwzPIdFlI/Kvj1W9s0XZI8c8qZBAEDAEOoAAAAAIebvRZSHSxWr+NXtb7/IHfik7IolgW8OABAwhDoAAABAiDJ1G6QvotzmUv/i/j1yxz4n9z8TZVOSA98cAKDQEeoAAAAAIcwULyHn/m5yHuktlSjlV7c/fCl3aA/ZLRs86A4AUJgIdQAAAIAwYJpfKGfgOKnhef7FbZvkDush9/vPZV030K0BAAoJoQ4AAAAQJkz5WDlPDZTp8qAUGeVbTE2VnTpJ7pj+3PocAMIEoQ4AAAAQRozjyLn8ejn9xko1avsPWL0s/dbnc2dw63MACHGEOgAAAEAYMtVryukzWubKmyVjfIvHjspOelnu+OGyB/d70h8A4PQR6gAAAABhykRFyel0r5weQ6QKlfwHLJkvd+ATsksWBL45AMBpI9QBAAAAwpyp30TOgFdk2l7mXzx0QO5rQ+W+84rssaOBbw4AcMoIdQAAAIAiwJQoKee+p+Q8Gi+VKuNXt3N+kDvoSdk1yz3oDgBwKgh1AAAAgCLENGsjZ9A4qWkr/+KeXXJH95X7yduyyUmBbw4AkC+EOgAAAEARY8qUl/N4X5l7n9T/t3ff4VGV+fvH7zNp1AQIJRRpAUKT3lG6goCKiuiqq7irroq76q4NEVHBBcuKvXcRVxZRpChIh9AJPYTQawKEAOl1zu+P+eV8J8wkmUAyyYT367q4riHznHOeST4p556nqFLl/E+apszFv8g++UmZh2LLpoMAAI8Q6gAAAABXIMMwZOs7RLZJ70qt2rk2iD8u+7RnZP95hsycbO93EABQJEIdAAAA4Apm1K4n279elXH7/ZJ/QP4n7XaZC2fJ/uq/ZB49WDYdBAAUiFAHAAAAuMIZNpts198i28TpUpMWrg2OH5b93/+Sff5/ZebkeL+DAAC3CHUAAAAASJKMBo1le+51GTffLfn55X8yN1fm3JmyT3tG5smjZdNBAEA+hDoAAAAALIa/v2wj75Dt+f9IjZq6NjiyX/bJT8r++08y7ble7x8A4P8Q6gAAAABwYTRuLtvz/5Ex/HbJuOi2ISdb5k/fyD7tWZlxx8qmgwAAQh0AAAAA7hkBAbLd8mfZxr8uhTVybXAoVvZXnpD9t59k5jJqBwC8jVAHAAAAQKGMZq1kmzhdxnU3S4aR/8mcbJlzvmGtHQAoA4Q6AAAAAIpkBAbJNuavsj0zVarbwLXB4X2yT35C9t9mM2oHALyEUAcAAACAx4wWbWV78Z0CRu3kyJzzrexTn5Z5glE7AFDaCHUAAAAAFIsRlDdqZ5pUr6FrgyP7ZZ/yhOwLZsnMyfF+BwHgCkGoAwAAAOCSGC3ayPbi2zKuv8XNDlk5Mn+ZIfu//yXz6IGy6SAAVHCEOgAAAAAumREYJNvt98v27DQpzM2onWOHZH/1X7LP+VZmdpb3OwgAFRihDgAAAIDLZoS3lm3i2zKG3uo6asdul/nbbNlfeULm/j1l00EAqIAIdQAAAACUCCMwSLbRY2Ub/7rUoLFrg/jjsr/+nOz//UxmRrr3OwgAFQyhDgAAAIASZTRrJdvE6TJuvFPy88v/pGnKXDpP9pf+LjN6W5n0DwAqCkIdAAAAACXO8A+Q7aa7ZHthutSkhWuDs6dln/6i7F+/KzM1xfsdBIAKgFAHAAAAQKkxGjWVbfwbMkaPlQICXZ43I5fI/uKjMjevkWma3u8gAPgwQh0AAAAApcrw85Nt6K2yvfiO1LKta4Ok87J/8rrsH7wqMzHB+x0EAB9FqAMAAADAK4ywhrI99W8Zdz8sBVV2bbB9o+yTxsm+fKFMu937HQQAH0OoAwAAAMBrDJtNtgHDZXvlfenqbq4NMtJlzvxY9tefk3nyqPc7CAA+hFAHAAAAgNcZterI9veJMh56Wqoe4trgQIzsrzwh+68zZWZne7+DAOADCHUAAAAAlAnDMGTrfq1skz+U0Xewa4PcHJnz/iv75Cdk7ov2fgcBoJwj1AEAAABQpoyq1WUb+7hs/5ws1QlzbRB3TPbXn5P92/dlpiZ7v4MAUE4R6gAAAAAoF4w2HWWb9J6MYbdJNtdbFXP1YtknPir7+hVsfw4AItQBAAAAUI4YQUGy3XafbBP+IzVp4dog+YLML96S/e1JMk/Heb+DAFCOEOoAAAAAKHeMxuGyjX9Dxh0PuN/+PHqb7C/9XfYFs2TmsJAygCsToQ4AAACAcsnw85NtyE2O7c879XRtkJ0l85cZsr/CQsoArkyEOgAAAADKNaNWHfmNmyDbo89LNWu7NshbSPnrd2UmJ3m/gwBQRgh1AAAAAPgEo3Mv2V55X8bgGyXDzULKkUtkn/iI7KsXy7Tby6CHAOBdhDoAAAAAfIZRqYpsdz4o2/NvSI3DXRukJsv89n3ZX39O5vFD3u8gAHgRoQ4AAAAAn2M0bSnb82/KuOOv7hdSPhAj++QnZZ/1hcyMNO93EAC8gFAHAAAAgE9yLKR8s2yTP5TRta9rA7td5h9zZZ84TuaWSJmm6f1OAkApItQBAAAA4NOMmqGyPfysbI+/JNUJc21w/qzsH78m+7svyzx90uv9A4DSQqgDAAAAoEIw2neR7eX3Zdx4p+Tv79pgV5Tskx6T/ZcZMjMzvd9BAChhhDoAAAAAKgwjIFC2m+6S7aX3pbadXBvk5MhcMEv2SeNkRq1jShYAn0aoAwAAAKDCMeo1kO2Jl2U89IwUUsu1wdnTsn80VfZ3XpJ5iilZAHwToQ4AAACACskwDNm6X+NYSPm6myWbm9uf3Vtlf+kx2X/+TmZmhvc7CQCXgVAHAAAAQIVmVK4i25i/yvbiu1LE1a4NcnJkLvyf7C8+KnPLWqZkAfAZhDoAAAAArghGw8ay/WuKjAefkmq4mZKVmCD7x9Nkn/6izJNHvd9BACgmQh0AAAAAVwzDMGTr0c8xJev6WyQ/P9dGe7bL/vI/ZP/xc5lpKd7vJAB4iFAHAAAAwBXHqFRFttvvl+3Fd9xPybLbZS75VfYXHpF99WKZdrv3OwkARSDUAQAAAHDFMhr8/ylZDz0t1azt2iD5gsxv35f930/JPBDj/Q4CQCEIdQAAAABc0Ry7ZF3rmJI1YozkH+Da6Mh+2ac9I/uX02WeT/R+JwHADUIdAAAAAJBkBFWSbdQ9sr3ygdSpl9s25rrljilZv/0kMzvLyz0EgPwIdQAAAADAiVEnTH7jnpftiZelsEauDTLTZc75RvYXx8mMYgt0AGWHUAcAAAAA3DDadZZt0rsyxvxVqlzFtUHCKdk/mib7mxNkHj3g/Q4CuOIR6gAAAABAAQx/f9muu1m2KR/J6DtEMgzXRrG7ZJ/yT9m/fV9m0jnvdxLAFYtQBwAAAACKYATXlG3sP2Sb8B+pRVvXBqYpc/Vi2Sc8zHo7ALyGUAcAAAAAPGQ0aSHbM1NlPPSMFFrXtUGG03o7WyJZbwdAqSLUAQAAAIBicGyBfo1sr3wgY9Q9UlAl10YJp2T/+DXZX39O5sG93u8kgCsCoQ4AAAAAXAIjMEi2EWMc6+30Gey+0f49sk99WvZP35CZcMq7HQRQ4fmXdQfKu4SEBC1cuFBbt25VQkKC/P39FRYWpt69e2vo0KEKCgq65HOnpaVp69at2rlzpw4dOqRTp04pMzNTVapU0VVXXaUuXbpo8ODBqlq1agm+IgAAAAAlyagRKuP+x2UOHC77j59L+/e4tDE3rZa5db2MwTfKGH67jCr8jQ/g8hkmkzwLFBUVpXfffVdpaWlun2/QoIHGjx+vevXqFfvcW7du1Ztvvqns7OxC24WEhOjxxx9X+/bti32N4srNzdWpU+X/3QObzaawsDBJUnx8vOx2exn3CLh81DUqIuoaFRF1jaKYpiltiZT9p2+kgkbmVAuWcdOfZFw7VIZ/+XifndpGRVQe67pevXry8/MrsfOVj58g5dDhw4c1ffp0ZWZmqlKlSho1apTat2+vrKwsRUZGaunSpTp58qSmTZumqVOnqlIlN/NoC5GcnKzs7GwZhqEOHTqoU6dOatKkiapWraqzZ89qzZo1Wrt2rS5cuKDXXntNkydPVtOmTUvnxQIAAAAoEYZhSN2uka1jT5nL58ucP0tKT83fKCVJ5sxPZC6bL9ttY6WOPRzHAUAxEeoU4JtvvlFmZqb8/Pz0wgsvqFWrVtZz7du3V/369TVjxgydOHFC8+fP1+jRo4t1fn9/fw0ZMkS33nqrateune+5Zs2aqVu3boqIiNBXX32lzMxMffvtt3rxxRdL5LUBAAAAKF1GQICM62+R2WewzPk/ylyxUMrNzd8o/oTsH7wqtWwr2+j7ZTSPKJvOAvBZLJTsxv79+7V7925J0sCBA/MFOnlGjhyphg0bSpIWLFignJycYl2jT58+euihh1wCHWc33HCDwsPDJUm7d+9WcnJysa4BAAAAoGwZ1YJlu/NB2V56X+rUy32jfdGyT31auR9Pk3nqpFf7B8C3Eeq4sWnTJuvxwIED3bax2Wzq37+/JCk1NVXR0dGl0pe2bdtKcszNPX36dKlcAwAAAEDpMsIaym/c87I99W+pSQv3jbaslX3SONlnfiwz6bxX+wfANxHquBETEyNJCgoKUvPmzQtslxe4OB9T0pwXUmaeLQAAAODbjIj2sj3/poy//lMKrevaIDdX5vKFsj//N9nn/1dmZob3OwnAZ7CmjhvHjx+XJIWFhRW6KnWDBg1cjilpe/Y4tkP08/OzVu0ujrNnzxbZpkaNGtbrtNnKf87n3Edf6C/gCeoaFRF1jYqIukaJsNmkPoNkdr9W9mXzZZ//o5SWkr9NZrrMuTNlrvhNtpvuku2a60p1pyxqGxXRlVDXhDoXycrKstauCQ0NLbRttWrVFBQUpMzMTI/Ck+KKiorSkSNHJEkdO3ZUlSpVin2ORx55pMg2H330kUJDQy85OCpLdeu6eXcD8HHUNSoi6hoVEXWNEnHfI7Lfdo+S/ve1kuf+IGVn5X/+wjnZv/tAtqW/KvjPj6jyNUNklPLNKbWNiqii1nXFjKouQ0bG/w1v9GSb8rw2zseVhJSUFH3xxReSHIniHXfcUaLnBwAAAFA+2KpVV437/676n85RlcEjJTfLLuScPKazrz2vU0/8Welb1sk0zTLoKYDyhpE6F8nK+r9k3N+D4Y15bZyPu1x2u13vvvuuzpw5I0m69dZb1axZs0s610cffVRkmxo1akiScnNzrWuWZzabzUpZT58+LbvdXsY9Ai4fdY2KiLpGRURdo9Td9bD8rx2q3Nlfy9y1xeXp7AN7lfDi32VEXC3bbffJFt66RC5LbaMiKo91XadOnUKXeSkuQp2LBAYGWo892aY8r43zcZfr888/17Zt2yRJXbp00ejRoy/5XEVNIbtYeSjy4rDb7T7XZ6Ao1DUqIuoaFRF1jVLTsIlsj0+SuWe77D9/Jx2KdWli7t2p3H8/pdxOvWS75R4ZDRqX2OWpbVREFbWuCXUu4jzlypMpVXltPJmq5YmZM2dqyZIlkqTWrVvrn//8Z4Vd0AkAAABAwYw2HWVr3UHauk72n2dI8W42Z9m2XvbtG2X0GiDjxjtl1PGtNTIBXB5CnYsEBgaqevXqSk5OLnLx45SUFGVmZkoq/ogYd3755Rf98ssvkqRmzZrpueeeK9ERQAAAAAB8i2EYUpc+snXsKXPdMpm//iCdS8jfyLQ7ntu4Ssa118kYMUZGjcu/PwFQ/jEExI1GjRpJkuLj45Wbm1tgu5MnT7occ6kWLVqkmTNnSpIaNmyoCRMmXNJuVwAAAAAqHsPPT7ZrrpPt1Y9l3P4XqVp110a5OTJX/Cb783+TfdYXMpMveL+jALyKUMeNiIgISVJmZqYOHjxYYLvo6GiXYy7FqlWr9OWXX0qS6tWrp4kTJyo4OPiSzwcAAACgYjICAmW7fpRsr34qY+QdUpCbZSCys2T+MVf28Q/K/vMMmWkp3u8oAK8g1HGjR48e1uPly5e7bWO327Vy5UpJUtWqVdWuXbtLutaGDRv04YcfyjRNhYaGauLEiapVq9YlnQsAAADAlcGoUlW2m++W7d+fyhhys+Qf4NooM0PmwlmOcGfBLJkZ6d7vKIBSRajjRosWLdSmTRtJjlAnNtZ1tfn58+frxIkTkqQbbrjBZfvzFStWaMyYMRozZoxmzZrl9jrbt2/XO++8I7vdrpCQEE2cONHabg0AAAAAimIE15Dtjr/K9uonMvoNk9xtlZyWKvOXGY5wZ9EcmZlFbwgDwDewUHIBxo4dq4kTJyorK0tTpkzRLbfconbt2ikrK0tr1661dqiqX7++brzxxmKfPzY2Vm+++aZycnLk5+en++67Tzk5OTp69GiBx4SGhqpq1aqX/JoAAAAAVExGrdoy/vyozGG3ypz3g8z1KyXzou2bU5Jkzv5a5qKfZQy7VUb/4TKCgsqmwwBKBKFOAZo1a6YnnnhC7733ntLT0/XDDz+4tKlfv77Gjx+vypUrF/v827Zts3bOys3N1bvvvlvkMY8++qgGDBhQ7GsBAAAAuDIYdcJk/OVJmTeMljl3pswtka6Nki/I/N9XjnDnhtscI3wqFf+eBkDZI9QpRLdu3fTmm29q4cKFioqKUmJiovz9/RUWFqZevXpp2LBhCiLZBgAAAFDOGPWvkvHwszKPHpR97vfSjk2ujZLOy/zxC5m//ywNHy1zzH0yArm/AXyJYZqmWdadQPmQm5urU6dOlXU3imSz2RQWFibJse283W4v4gig/KOuURFR16iIqGv4KvNQrOy//iDt2lJgG7/QOqp++1ildOot04/3/+H7yuPP7Hr16snP3dpXl4jvVAAAAACo4IxmreT3+CSZB2Jkn/eDtHurS5vcs2d0/uM3pJBajjV3rh3KmjtAOcfuVwAAAABwhTDCW8vviZdle/Y1qW0n940uJMr88XPZn39Q9kU/s1sWUI4R6gAAAADAFcZo0UZ+T74i2zPTpNYd3DdKOi9z9leyP/eA7L/NlpmR5t1OAigSoQ4AAAAAXKGMlm3l968p8ntmmoI69nDfKCVJ5pxvZX/uQdnn/ygzLdW7nQRQIEIdAAAAALjC2SLaq+6/P1TdNz6X0b6L+0apyTLnfu8YufPzDJnJSd7tJAAXhDoAAAAAAElSUNtO8n/yFdmef1Pq0N19o/RUmQtnyf7cX2X/8XOZ5856t5MALOx+BQAAAADIx2jWSn5/nyjzyAHZ5/8obVvv2igrU+aSX2UuXyijzyDHjll1G3i/s8AVjFAHAAAAAOCW0SRcfuOel3n8kCPciVonmWb+Rrk5MlcvlrlmiYzu18q44TYZjZqWSX+BKw2hDgAAAACgUEajZvJ7+DmZccdk/jZb5oaVkt2ev5Fpl7lxpcyNK6WOPWS7YbSM8NZl02HgCkGoAwAAAADwiFH/Khl/eVLmTXfJXPSzzDV/SDnZrg23b5R9+0apZVvZht0mXd1NhmF4v8NABUeoAwAAAAAoFqN2PRl3PyxzxBiZS+bKXPG7lJnu2nBftOz7oqWGTWQMvdUxPcuf21CgpLD7FQAAAADgkhg1ask2+n7ZXvtcxo1/kqpUc9/wxBGZX06XfcLfZF/yq8zMDO92FKigCHUAAAAAAJfFqFpdtpv+5Ah3bv+LVCPUfcPEMzJ//Fz2Z/8q+9yZMpMveLejQAXDuDcAAAAAQIkwKlWRcf0omYNGyNywUubvc6T4464NU5Nlzv+vzEVzHNuhD7lZRlhD73cY8HGEOgAAAACAEmX4B8joO0Rm70HSjo2y/z5HOhDj2jA7S+bK32WuWiR17Cnb0FFSeBsWVQY8RKgDAAAAACgVhs0mdeolW8eejkWTf/9J2rnZtaFpStvWy75tvdSslWxDb5E695Jh8/N+pwEfQqgDAAAAAChVhmFIrdrJr1U7mSeOyFw0R+bG1VJujmvjQ7Gyf/yaVCdMxpCbZPQZLKNSZe93GvABLJQMAAAAAPAao2ET2f7ypGxTP5Mx7DapclX3Dc/Ey/zhU9mf/Yvss7+SefaMdzsK+ABG6gAAAAAAvM6oGSrjtvtkjrhd5po/ZP7xq5ToJrhJS5W56GeZf8yV0aWPY/ROeGvvdxgohwh1AAAAAABlxqhURcaQm2UOHCkzaq3MRT9LR/a7NrTbZW5eI3PzGqlZK0e406WPDH9ua3HlovoBAAAAAGXO8POT0f1amd2ukWJ3y/7HL9KOTY5FlC92KFbmZ2/KrFlbxsARMvpdL6Nqda/3GShrhDoAAAAAgHLDMAwpor38ItrLPHVS5tJ5MtculTIzXBufS5A55xuZ83+Q0XOAjEEjZDRq5v1OA2WEUAcAAAAAUC4Z9RrIuOtvMkfdLXP1HzKXzXe/7k5WlszVi2WuXiy1ai/b4JFSx54y/NgSHRUboQ4AAAAAoFwzqlSTMfQWmUNukrauk33Jr9KBGPeNY3fJHrtLqlVbxoDhMq65Xkb1YK/2F/AWQh0AAAAAgE8w/PykbtfIr9s1Mg/Fylzyq8wtkVJurmvjxASZc76VOe+/Mnr0c0zNahzu/U4DpYhQBwAAAADgc4xmrWQ8+JTM2++XuXKRzFW/S0nnXRtmZ8mMXCIzconUPELGwOEyuvaVERDo9T4DJY1QBwAAAADgs4waoTJuvkvm8Ntlblkjc9kC6VCs+8YH98o8uFfmj1/IuOY6Gf2GyqgT5t0OAyWIUAcAAAAA4POMgAAZvQZKvQY6pmYtmy9z0xopN8e1cUqSzN9/krlojtS+q2wDh0vtOsuwsbAyfAuhDgAAAACgQjGatZLx13/KHH2/zFX/f2rW+UTXhqYp7dws+87NUu16MvoNk9F3sIzgGl7vM3ApCHUAAAAAABWSEVJTxo13yrxhtLRjo+wrfpP2bHffOOGUzDnfyJz7vYzOvWT0Gyq17iDDMLzbaaAYCHUAAAAAABWa4e8vdekjvy59ZMYdl7nyN5lrl0rpaa6Nc3Nkbl4jc/MaqW4Dx7o7fQazLTrKJUIdAAAAAMAVw6jfSMadD8q85c8yN6yUuXyhdPyQ+8anT8qc/ZXMX76T0aWPjH7DpFbtGL2DcoNQBwAAAABwxTGCKsnoN1TmtddLB2Jkrvpd5uZIKTvLtXFOjsyNq2RuXCWFNXTsnNV7oIzgmt7vOOCEUAcAAAAAcMUyDENq0UZGizYy73hA5rrlMlctkuKOuT8g/oTM2V/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            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 462,
              "width": 570
            }
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def pi(antiguedad):\n",
        "    exp = np.exp(1.8106 - 0.0416 * antiguedad)\n",
        "    return exp / (1 + exp)\n",
        "\n",
        "antiguedades = np.arange(0, 100)\n",
        "probs_churn  = pi(antiguedades)\n",
        "\n",
        "sns.lineplot(x=antiguedades, y=probs_churn, ax=ax)\n",
        "plt.title(r\"$\\hat\\pi$ según antigüedad del cliente\")\n",
        "plt.xlabel(\"Antigüedad del cliente (meses)\")\n",
        "plt.ylabel(r\"$\\hat\\pi$\")\n",
        "plt.ylim(0, 1);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ULg3khcRBl7a"
      },
      "source": [
        "El cálculo de que el cliente se fugue, dado que lleva dos meses en la empresa está dado por:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Sjsidf_GBl7a",
        "outputId": "14a40692-193f-4917-f3b3-e27d34a4b131"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Probabilidad de fuga: 0.849\n"
          ]
        }
      ],
      "source": [
        "prob_fuga = pi(2)\n",
        "print(f\"Probabilidad de fuga: {prob_fuga:0.3f}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0mFyAjcCBl7a"
      },
      "source": [
        "Es decir, $\\mathbb{P}(\\text{FinalizaContrato}_5=1\\mid\\text{Antigüedad}=2)=0.849$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-tSEKw8pBl7a"
      },
      "source": [
        "Ahora, supongamos que es de interés crear una regla de decisión para decidir cuando el cliente se fugará. En este contexto, usted decide que cuando la probabilidad de fuga exceda 0.5, el cliente potencialmente se fugará. Necesitaremos saber que valores de antigüedad satisfacen la siguiente inecuación:\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y0DX6xvYBl7a"
      },
      "source": [
        "$$\n",
        "\\hat\\pi_i = {\\exp{(1.8106 - 0.0416 \\cdot \\text{Antigüedad}_i)} \\over 1 + \\exp{(1.8106 - 0.0416 \\cdot \\text{Antigüedad}_i)}} > 0.5 \\\\\n",
        " \\longleftrightarrow \\text{Antigüedad}_i < 43.524\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9TXyaRheBl7a"
      },
      "source": [
        "Despejando la variable $\\text{Antigüedad}_i$ con álgebra, resulta que cuando la antigüedad de un cliente es menor a 43.524 ([fuente](https://www.wolframalpha.com/input?i=exp%281.8106+-+0.0416+*+x%29+%2F+%281+%2B+exp%281.8106+-+0.0416+*+x%29%29+%3E+0.5+solve+for+x&lang=es)), la probabilidad de fuga según el modelo estimado es mayor a 0.5."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VLqig1NWBl7b"
      },
      "source": [
        "**Variables Indicadoras o Dummies**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z0W9U2FMBl7b"
      },
      "source": [
        "A continuación, realicemos un modelo de regresión logística con una mayor cantidad de predictores:\n",
        "\n",
        "$$\n",
        "\\log{\\left(\\pi_i \\over 1 - \\pi_i\\right)} = \\beta_0 + \\beta_1 \\cdot \\mathbb{I}_{\\{\\text{DeudaMembresia}_i=\\text{Deudor}\\}} + \\beta_2 \\cdot \\mathbb{I}_{\\{\\text{MasUnPlan}_i=\\text{Si}\\}} + \\beta_3 \\cdot \\text{Antigüedad}_i\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4Wz38JtXBl7b"
      },
      "source": [
        "Para implementar este modelo, en la formula debemos fijar una categoría como referencia en las variables cualitativas con la sintaxis <br> `\"C(variable, Treatment('categoria de referencia'))\"`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9sck7dZTBl7b",
        "outputId": "515a2359-432c-44da-c61b-a20dfc503746"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Optimization terminated successfully.\n",
            "         Current function value: 0.607783\n",
            "         Iterations 5\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "        <td>Model:</td>              <td>Logit</td>           <td>Method:</td>          <td>MLE</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <td>Dependent Variable:</td>     <td>Churn_num</td>    <td>Pseudo R-squared:</td>    <td>0.070</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "         <td>Date:</td>        <td>2023-10-18 17:15</td>       <td>AIC:</td>         <td>3654.7002</td>\n",
              "</tr>\n",
              "<tr>\n",
              "   <td>No. Observations:</td>        <td>3000</td>             <td>BIC:</td>         <td>3678.7257</td>\n",
              "</tr>\n",
              "<tr>\n",
              "       <td>Df Model:</td>              <td>3</td>         <td>Log-Likelihood:</td>    <td>-1823.4</td> \n",
              "</tr>\n",
              "<tr>\n",
              "     <td>Df Residuals:</td>          <td>2996</td>           <td>LL-Null:</td>        <td>-1960.3</td> \n",
              "</tr>\n",
              "<tr>\n",
              "      <td>Converged:</td>           <td>1.0000</td>        <td>LLR p-value:</td>    <td>4.6279e-59</td>\n",
              "</tr>\n",
              "<tr>\n",
              "    <td>No. Iterations:</td>        <td>5.0000</td>           <td>Scale:</td>         <td>1.0000</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>Intercept</th>                                           <td>2.0005</td>   <td>0.1912</td>   <td>10.4608</td> <td>0.0000</td> <td>1.6256</td>  <td>2.3753</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor]</th> <td>0.5682</td>   <td>0.1676</td>   <td>3.3904</td>  <td>0.0007</td> <td>0.2397</td>  <td>0.8966</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>C(MasUnPlan, Treatment('No'))[T.Si]</th>                 <td>-1.0341</td>  <td>0.1237</td>   <td>-8.3620</td> <td>0.0000</td> <td>-1.2765</td> <td>-0.7917</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Antiguedad</th>                                          <td>-0.0429</td>  <td>0.0033</td>  <td>-13.1024</td> <td>0.0000</td> <td>-0.0494</td> <td>-0.0365</td>\n",
              "</tr>\n",
              "</table><br/>\n"
            ],
            "text/latex": [
              "\\begin{table}\n",
              "\\caption{Results: Logit}\n",
              "\\label{}\n",
              "\\begin{center}\n",
              "\\begin{tabular}{llll}\n",
              "\\hline\n",
              "Model:              & Logit            & Method:           & MLE         \\\\\n",
              "Dependent Variable: & Churn\\_num       & Pseudo R-squared: & 0.070       \\\\\n",
              "Date:               & 2023-10-18 17:15 & AIC:              & 3654.7002   \\\\\n",
              "No. Observations:   & 3000             & BIC:              & 3678.7257   \\\\\n",
              "Df Model:           & 3                & Log-Likelihood:   & -1823.4     \\\\\n",
              "Df Residuals:       & 2996             & LL-Null:          & -1960.3     \\\\\n",
              "Converged:          & 1.0000           & LLR p-value:      & 4.6279e-59  \\\\\n",
              "No. Iterations:     & 5.0000           & Scale:            & 1.0000      \\\\\n",
              "\\hline\n",
              "\\end{tabular}\n",
              "\\end{center}\n",
              "\n",
              "\\begin{center}\n",
              "\\begin{tabular}{lrrrrrr}\n",
              "\\hline\n",
              "                                                    &   Coef. & Std.Err. &        z & P$> |$z$|$ &  [0.025 &  0.975]  \\\\\n",
              "\\hline\n",
              "Intercept                                           &  2.0005 &   0.1912 &  10.4608 &      0.0000 &  1.6256 &  2.3753  \\\\\n",
              "C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor] &  0.5682 &   0.1676 &   3.3904 &      0.0007 &  0.2397 &  0.8966  \\\\\n",
              "C(MasUnPlan, Treatment('No'))[T.Si]                 & -1.0341 &   0.1237 &  -8.3620 &      0.0000 & -1.2765 & -0.7917  \\\\\n",
              "Antiguedad                                          & -0.0429 &   0.0033 & -13.1024 &      0.0000 & -0.0494 & -0.0365  \\\\\n",
              "\\hline\n",
              "\\end{tabular}\n",
              "\\end{center}\n",
              "\\end{table}\n",
              "\\bigskip\n"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary2.Summary'>\n",
              "\"\"\"\n",
              "                                           Results: Logit\n",
              "====================================================================================================\n",
              "Model:                           Logit                       Method:                      MLE       \n",
              "Dependent Variable:              Churn_num                   Pseudo R-squared:            0.070     \n",
              "Date:                            2023-10-18 17:15            AIC:                         3654.7002 \n",
              "No. Observations:                3000                        BIC:                         3678.7257 \n",
              "Df Model:                        3                           Log-Likelihood:              -1823.4   \n",
              "Df Residuals:                    2996                        LL-Null:                     -1960.3   \n",
              "Converged:                       1.0000                      LLR p-value:                 4.6279e-59\n",
              "No. Iterations:                  5.0000                      Scale:                       1.0000    \n",
              "----------------------------------------------------------------------------------------------------\n",
              "                                                     Coef.  Std.Err.    z     P>|z|   [0.025  0.975]\n",
              "----------------------------------------------------------------------------------------------------\n",
              "Intercept                                            2.0005   0.1912  10.4608 0.0000  1.6256  2.3753\n",
              "C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor]  0.5682   0.1676   3.3904 0.0007  0.2397  0.8966\n",
              "C(MasUnPlan, Treatment('No'))[T.Si]                 -1.0341   0.1237  -8.3620 0.0000 -1.2765 -0.7917\n",
              "Antiguedad                                          -0.0429   0.0033 -13.1024 0.0000 -0.0494 -0.0365\n",
              "====================================================================================================\n",
              "\n",
              "\"\"\""
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "modelo = sm.Logit.from_formula(\n",
        "    formula = \"\"\"\n",
        "        Churn_num ~\n",
        "            C(DeudaMembresia, Treatment('No Deudor')) +\n",
        "            C(MasUnPlan, Treatment('No')) +\n",
        "            Antiguedad\n",
        "    \"\"\",\n",
        "    data = data\n",
        ").fit()\n",
        "modelo.summary2()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n7u9Y4DdBl7b"
      },
      "source": [
        "El modelo estimado es el siguiente:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LGijtk9sBl7b"
      },
      "source": [
        "$$\n",
        "\\begin{align*}\n",
        "\\log{\\left(\\hat\\pi_i \\over 1 - \\hat\\pi_i\\right)} &= 2 + 0.567 \\cdot \\mathbb{I}_{\\{\\text{DeudaMembresia}_i=\\text{Deudor}\\}} -1.034 \\cdot \\mathbb{I}_{\\{\\text{MasUnPlan}_i=\\text{Si}\\}} -0.043 \\cdot \\text{Antigüedad}_i\n",
        "\\end{align*}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pVjvtbtyBl7e"
      },
      "source": [
        "Supongamos que necesitamos obtener la probabilidad de fuga del siguiente cliente:\n",
        "\n",
        "* `DeudaMembresia`: $\\color{violet}{\\text{Deudor}}$.\n",
        "* `MasUnPlan`: $\\color{red}{\\text{No}}$\n",
        "* `Antiguedad`: $\\color{orange}{\\text{5 meses}}$\n",
        "\n",
        "$$\n",
        "\\hat\\pi_i =\n",
        "{\n",
        "    \\exp{(2 + 0.567 \\cdot \\color{violet}{1} -1.034 \\cdot \\color{red}{0} -0.043 \\cdot \\color{orange}{5})}\n",
        "    \\over\n",
        "    1 + \\exp{(2 + 0.567 \\cdot \\color{violet}{1} -1.034 \\cdot \\color{red}{0} -0.043 \\cdot \\color{orange}{5})}\n",
        "} = 0.9132\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pWPHkG9WBl7f"
      },
      "source": [
        "**Razón de Chances** (***Odds Ratio***)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pt-tXQj1Bl7f"
      },
      "source": [
        "Retomando el ejemplo de que un caballo \"A\" gane la carrera es 3 a 1, también suponga que hay otros caballos:\n",
        "* Caballo A (el que vimos anteriormente): tienen chances de ganar la carrera de 3 a 1.\n",
        "* Caballo B: tienen chances de ganar la carrera de 2 a 1.\n",
        "* Caballo C: tienen chances de ganar la carrera de 4 a 1.\n",
        "\n",
        "Interesa saber cuántas chanches más tienen de ganar el caballo A, respecto a los otros caballos.\n",
        "\n",
        "Para responder a esta necesidad, se utilizan las razones de chances, que están dadas por la siguiente fórmula:\n",
        "\n",
        "$$\n",
        "\\text{Odds Ratio} = {\\text{Chances del Evento 1} \\over \\text{Chances del Evento 2}}\n",
        "$$\n",
        "\n",
        "* Entonces, el Odds Ratio entre el caballo A y el B es de $3/2=1.5$, o sea, el caballo A tiene 50% más de chances de ganar la carrera que el caballo B.  \n",
        "* Por otro lado, el Odds Ratio entre el caballo A y el C es de $3/ 4=0.75$, o sea, el caballo A tiene un 25% menos de chances de ganar la carrera que el caballo C."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZvjwXOx6Bl7f"
      },
      "source": [
        "En el caso de la fuga de los clientes, supongamos que nos interesa calcular cuantas chances hay de que un cliente se fuge cuando es un mes más antiguo. Definamos a este cliente en ambos meses:\n",
        "* Cliente~1~: Es el cliente con una antigüedad de $x$ meses.\n",
        "* Cliente~2~: Es el mismo cliente pero tiene una antigüedad de $x+1$ meses.\n",
        "\n",
        "Calculemos las chances considerando que el modelo entrega las **log-chances** de que el cliente se fugue.\n",
        "\n",
        "$$\n",
        "{\\color{green}{\\text{Chances del Cliente}_1} \\over \\color{blue}{\\text{Chances del Cliente}_2}} =  {\\color{green}{\\exp\\left\\{\\beta_0 + \\beta_1 \\cdot \\mathbb{I}_{\\{\\text{DeudaMembresia}_i=\\text{Deudor}\\}} + \\beta_2 \\cdot \\mathbb{I}_{\\{\\text{MasUnPlan}_i=\\text{Si}\\}} + \\beta_3 \\cdot (x+1) \\right\\}} \\over \\color{blue}{\\exp\\left\\{\\beta_0 + \\beta_1 \\cdot \\mathbb{I}_{\\{\\text{DeudaMembresia}_i=\\text{Deudor}\\}} + \\beta_2 \\cdot \\mathbb{I}_{\\{\\text{MasUnPlan}_i=\\text{Si}\\}} + \\beta_3 \\cdot x \\right\\}} }\n",
        "$$\n",
        "\n",
        "Utilizando propiedades de las potencias, obtenemos el siguiente resultado:\n",
        "\n",
        "$$\n",
        "\\text{Odds Ratio} = {\\text{Chances del Cliente}_1 \\over \\text{Chances del Cliente}_2} = \\exp\\{\\beta_3\\}\n",
        "$$\n",
        "\n",
        "O sea, independiente de la cantidad de meses de antigüedad, el Odds Ratio cuando el cliente es un mes más antiguo es $\\exp\\{\\beta_3\\}$. Este resultado también aplica para el resto de los predictores, cuando se desea calcular el Odds Ratio para evaluar el cambio en una unidad. O sea también se cumple que:\n",
        "\n",
        "* Odds ratio de \"Cliente Deudor\" respecto a \"Ciente No Deudor\" es igual a $\\exp\\{\\beta_1\\}$.\n",
        "* Odds ratio de \"Cliente con más de un plan\" respecto a \"Ciente con un Plan\" es igual a $\\exp\\{\\beta_2\\}$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x6gt_h90Bl7f"
      },
      "source": [
        "Obtengamos estimaciones de los Odds Ratios mediante el modelo estimado:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "m9YGHwepBl7f",
        "outputId": "ce9bf1e3-be72-400c-cf11-e01d929abbb9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Razones de chances:\n",
            "C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor]   1.76502\n",
            "C(MasUnPlan, Treatment('No'))[T.Si]                   0.35554\n",
            "Antiguedad                                            0.95796\n",
            "dtype: float64\n"
          ]
        }
      ],
      "source": [
        "odds_ratio = np.exp(modelo.params[1:]) # Se utiliza [1:] para excluir intercepto\n",
        "print(\"Razones de chances:\")\n",
        "print(odds_ratio)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YXciB2jtBl7f"
      },
      "source": [
        "Esto quiere decir que:\n",
        "\n",
        "* Un \"Cliente Deudor\" tiene un 76.5% (1.76502-1) más de chances de fugarse que un \"Cliente No Deudor\".\n",
        "* Un cliente con \"Más de un plan\" tiene un 64.4% (1 - 0.35554) menos de chances de fugarse que un cliente con \"Un Plan\".\n",
        "* Un cliente tiene 4.2% (1 - 0.95796) menos de chances de fugarse, por cada mes de antigüedad que lleva en la empresa."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jog4D8hFBl7f"
      },
      "source": [
        "Además, se pueden clasificar los Odds Ratio de la siguiente forma:\n",
        "* $\\text{Odds Ratio}>1$: El predictor es un **Factor de Riesgo**.\n",
        "* $\\text{Odds Ratio}<1$: El predictor es un **Factor Protector**.\n",
        "* $\\text{Odds Ratio}=1$: **No hay efecto** por parte del predictor.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YBelZC73Bl7f"
      },
      "source": [
        "Se pueden obtener intervalos de confianza al 95% para los Odds Ratio mediante el método `conf_int()` del modelo ajustado."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PiT8GkQOBl7f",
        "outputId": "f3a22d47-413b-4b72-d0e7-d37dbe8d5497"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "- Intervalo de confianza al 95% para los Odds Ratio:\n"
          ]
        },
        {
          "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>[2.5%</th>\n",
              "      <th>97.5%]</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor]</th>\n",
              "      <td>1.27088</td>\n",
              "      <td>2.45128</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C(MasUnPlan, Treatment('No'))[T.Si]</th>\n",
              "      <td>0.27901</td>\n",
              "      <td>0.45306</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Antiguedad</th>\n",
              "      <td>0.95182</td>\n",
              "      <td>0.96413</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                                                     [2.5%  97.5%]\n",
              "C(DeudaMembresia, Treatment('No Deudor'))[T.Deu... 1.27088 2.45128\n",
              "C(MasUnPlan, Treatment('No'))[T.Si]                0.27901 0.45306\n",
              "Antiguedad                                         0.95182 0.96413"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "ic95_odds_ratio = np.exp(modelo.conf_int().iloc[1:, :])\n",
        "ic95_odds_ratio.columns = [\"[2.5%\", \"97.5%]\"]\n",
        "\n",
        "print(\"- Intervalo de confianza al 95% para los Odds Ratio:\")\n",
        "display(ic95_odds_ratio)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nq6zDofdBl7g"
      },
      "source": [
        "Como ninguno de los intervalos de confianza al 95% contiene al valor 1, hay evidencia estadística respecto a que todos los predictores son Factores de Riesgo o Factores Protectores:\n",
        "\n",
        "* `DeudaMembresia=\"Deudor\"`: Factor de Riesgo.\n",
        "* `MasUnPlan=\"Si\"`: Factor Protector.\n",
        "* `Antiguedad`: Factor Protector."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zXMX_PvOBl7g"
      },
      "source": [
        "**Inferencia sobre los parámetros**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AoDtS-NLBl7g"
      },
      "source": [
        "La tabla que se obtiene con el método `summary2()` entrega los valores-p asociados a la siguiente familia de hipótesis.\n",
        "\n",
        "$$\n",
        "H_0:\\beta_i = 0 \\\\\n",
        "H_1:\\beta_i \\not= 0\n",
        "$$\n",
        "\n",
        "Para todos los coeficientes $\\beta_i$ del modelo. Se rechaza $H_0$ si el valor-p es menor a un nivel de significancia $\\alpha$ (usualmente 0.05).\n",
        "\n",
        "Trabajemos con $\\alpha=0.05$ ¿Qué hacemos cuando tenemos muchos parámetros con un valor-p asociado mayor a 0.05?\n",
        "\n",
        "Realicemos un modelo con aún más predictores:\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "G89vD1lIBl7g",
        "outputId": "aa90c348-2e06-4e23-96b5-f96a2e1d67de"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Optimization terminated successfully.\n",
            "         Current function value: 0.597177\n",
            "         Iterations 6\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "        <td>Model:</td>              <td>Logit</td>           <td>Method:</td>          <td>MLE</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <td>Dependent Variable:</td>     <td>Churn_num</td>    <td>Pseudo R-squared:</td>    <td>0.086</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "         <td>Date:</td>        <td>2023-10-18 17:15</td>       <td>AIC:</td>         <td>3599.0619</td>\n",
              "</tr>\n",
              "<tr>\n",
              "   <td>No. Observations:</td>        <td>3000</td>             <td>BIC:</td>         <td>3647.1128</td>\n",
              "</tr>\n",
              "<tr>\n",
              "       <td>Df Model:</td>              <td>7</td>         <td>Log-Likelihood:</td>    <td>-1791.5</td> \n",
              "</tr>\n",
              "<tr>\n",
              "     <td>Df Residuals:</td>          <td>2992</td>           <td>LL-Null:</td>        <td>-1960.3</td> \n",
              "</tr>\n",
              "<tr>\n",
              "      <td>Converged:</td>           <td>1.0000</td>        <td>LLR p-value:</td>    <td>5.9849e-69</td>\n",
              "</tr>\n",
              "<tr>\n",
              "    <td>No. Iterations:</td>        <td>6.0000</td>           <td>Scale:</td>         <td>1.0000</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>Intercept</th>                                           <td>2.4434</td>   <td>0.3568</td>   <td>6.8486</td>  <td>0.0000</td> <td>1.7441</td>  <td>3.1426</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor]</th> <td>0.5879</td>   <td>0.1697</td>   <td>3.4637</td>  <td>0.0005</td> <td>0.2552</td>  <td>0.9206</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>C(TipoCliente, Treatment('Regular'))[T.Premium]</th>     <td>-1.0836</td>  <td>0.1495</td>   <td>-7.2486</td> <td>0.0000</td> <td>-1.3766</td> <td>-0.7906</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>C(MasUnPlan, Treatment('No'))[T.Si]</th>                 <td>-1.0562</td>  <td>0.1248</td>   <td>-8.4626</td> <td>0.0000</td> <td>-1.3009</td> <td>-0.8116</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>C(Sexo, Treatment('Hombre'))[T.Mujer]</th>               <td>0.0994</td>   <td>0.0812</td>   <td>1.2230</td>  <td>0.2213</td> <td>-0.0599</td> <td>0.2586</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Edad</th>                                                <td>-0.0069</td>  <td>0.0065</td>   <td>-1.0567</td> <td>0.2906</td> <td>-0.0198</td> <td>0.0059</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>PagaporServicio</th>                                     <td>-0.0004</td>  <td>0.0017</td>   <td>-0.2106</td> <td>0.8332</td> <td>-0.0036</td> <td>0.0029</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Antiguedad</th>                                          <td>-0.0443</td>  <td>0.0033</td>  <td>-13.2994</td> <td>0.0000</td> <td>-0.0508</td> <td>-0.0377</td>\n",
              "</tr>\n",
              "</table><br/>\n"
            ],
            "text/latex": [
              "\\begin{table}\n",
              "\\caption{Results: Logit}\n",
              "\\label{}\n",
              "\\begin{center}\n",
              "\\begin{tabular}{llll}\n",
              "\\hline\n",
              "Model:              & Logit            & Method:           & MLE         \\\\\n",
              "Dependent Variable: & Churn\\_num       & Pseudo R-squared: & 0.086       \\\\\n",
              "Date:               & 2023-10-18 17:15 & AIC:              & 3599.0619   \\\\\n",
              "No. Observations:   & 3000             & BIC:              & 3647.1128   \\\\\n",
              "Df Model:           & 7                & Log-Likelihood:   & -1791.5     \\\\\n",
              "Df Residuals:       & 2992             & LL-Null:          & -1960.3     \\\\\n",
              "Converged:          & 1.0000           & LLR p-value:      & 5.9849e-69  \\\\\n",
              "No. Iterations:     & 6.0000           & Scale:            & 1.0000      \\\\\n",
              "\\hline\n",
              "\\end{tabular}\n",
              "\\end{center}\n",
              "\n",
              "\\begin{center}\n",
              "\\begin{tabular}{lrrrrrr}\n",
              "\\hline\n",
              "                                                    &   Coef. & Std.Err. &        z & P$> |$z$|$ &  [0.025 &  0.975]  \\\\\n",
              "\\hline\n",
              "Intercept                                           &  2.4434 &   0.3568 &   6.8486 &      0.0000 &  1.7441 &  3.1426  \\\\\n",
              "C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor] &  0.5879 &   0.1697 &   3.4637 &      0.0005 &  0.2552 &  0.9206  \\\\\n",
              "C(TipoCliente, Treatment('Regular'))[T.Premium]     & -1.0836 &   0.1495 &  -7.2486 &      0.0000 & -1.3766 & -0.7906  \\\\\n",
              "C(MasUnPlan, Treatment('No'))[T.Si]                 & -1.0562 &   0.1248 &  -8.4626 &      0.0000 & -1.3009 & -0.8116  \\\\\n",
              "C(Sexo, Treatment('Hombre'))[T.Mujer]               &  0.0994 &   0.0812 &   1.2230 &      0.2213 & -0.0599 &  0.2586  \\\\\n",
              "Edad                                                & -0.0069 &   0.0065 &  -1.0567 &      0.2906 & -0.0198 &  0.0059  \\\\\n",
              "PagaporServicio                                     & -0.0004 &   0.0017 &  -0.2106 &      0.8332 & -0.0036 &  0.0029  \\\\\n",
              "Antiguedad                                          & -0.0443 &   0.0033 & -13.2994 &      0.0000 & -0.0508 & -0.0377  \\\\\n",
              "\\hline\n",
              "\\end{tabular}\n",
              "\\end{center}\n",
              "\\end{table}\n",
              "\\bigskip\n"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary2.Summary'>\n",
              "\"\"\"\n",
              "                                           Results: Logit\n",
              "====================================================================================================\n",
              "Model:                           Logit                       Method:                      MLE       \n",
              "Dependent Variable:              Churn_num                   Pseudo R-squared:            0.086     \n",
              "Date:                            2023-10-18 17:15            AIC:                         3599.0619 \n",
              "No. Observations:                3000                        BIC:                         3647.1128 \n",
              "Df Model:                        7                           Log-Likelihood:              -1791.5   \n",
              "Df Residuals:                    2992                        LL-Null:                     -1960.3   \n",
              "Converged:                       1.0000                      LLR p-value:                 5.9849e-69\n",
              "No. Iterations:                  6.0000                      Scale:                       1.0000    \n",
              "----------------------------------------------------------------------------------------------------\n",
              "                                                     Coef.  Std.Err.    z     P>|z|   [0.025  0.975]\n",
              "----------------------------------------------------------------------------------------------------\n",
              "Intercept                                            2.4434   0.3568   6.8486 0.0000  1.7441  3.1426\n",
              "C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor]  0.5879   0.1697   3.4637 0.0005  0.2552  0.9206\n",
              "C(TipoCliente, Treatment('Regular'))[T.Premium]     -1.0836   0.1495  -7.2486 0.0000 -1.3766 -0.7906\n",
              "C(MasUnPlan, Treatment('No'))[T.Si]                 -1.0562   0.1248  -8.4626 0.0000 -1.3009 -0.8116\n",
              "C(Sexo, Treatment('Hombre'))[T.Mujer]                0.0994   0.0812   1.2230 0.2213 -0.0599  0.2586\n",
              "Edad                                                -0.0069   0.0065  -1.0567 0.2906 -0.0198  0.0059\n",
              "PagaporServicio                                     -0.0004   0.0017  -0.2106 0.8332 -0.0036  0.0029\n",
              "Antiguedad                                          -0.0443   0.0033 -13.2994 0.0000 -0.0508 -0.0377\n",
              "====================================================================================================\n",
              "\n",
              "\"\"\""
            ]
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "modelo = sm.Logit.from_formula(\n",
        "    formula = \"\"\"\n",
        "        Churn_num ~\n",
        "            C(DeudaMembresia, Treatment('No Deudor')) +\n",
        "            C(TipoCliente, Treatment('Regular')) +\n",
        "            C(MasUnPlan, Treatment('No')) +\n",
        "            C(Sexo, Treatment('Hombre')) +\n",
        "            Edad +\n",
        "            PagaporServicio +\n",
        "            Antiguedad\n",
        "    \"\"\",\n",
        "    data = data\n",
        ").fit()\n",
        "modelo.summary2()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YnUmMuEHBl7g"
      },
      "source": [
        "En este caso, y al igual que con el modelo de regresión lineal, debemos realizar una eliminación de variables de forma **secuencial**. No hacerlo de esta forma puede llevar a eliminar variables que son significativas sin la presencia de otras variables.\n",
        "\n",
        "Una diferencia, es que no usamos la tabla ANOVA, sino que realizamos el Test F de Modelos Anidados.\n",
        "\n",
        "Utilizamos la misma clase `Stepwise()` del módulo `linear_model` de la librería ESTYP. También contamos con la opción de realizar la selección con los criterios AIC y BIC en caso de que se desee.\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "% pip install estyp"
      ],
      "metadata": {
        "id": "aT5Yuh1QCSsz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UFIA5yLoBl7g",
        "outputId": "a818e8c5-d8bf-4a7d-ea1a-6a8f38f60de1"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "- Term dropped: \"PagaporServicio\" | p-value: 0.8474\n",
            "- Term dropped: \"Edad\" | p-value: 0.3369\n",
            "- Term dropped: \"C(Sexo, Treatment('Hombre'))\" | p-value: 0.2711\n",
            "\u001b[92m\u001b[4m\u001b[1mBackward selection completed\u001b[0m\n",
            "- Dropped terms: 3\n",
            "- Obtained formula: \"Churn_num ~ C(DeudaMembresia, Treatment('No Deudor')) + C(TipoCliente, Treatment('Regular')) + C(MasUnPlan, Treatment('No')) + Antiguedad\"\n"
          ]
        }
      ],
      "source": [
        "from estyp.linear_model import Stepwise\n",
        "\n",
        "searcher = Stepwise(\n",
        "    formula = \"\"\"\n",
        "        Churn_num ~\n",
        "            C(DeudaMembresia, Treatment('No Deudor')) +\n",
        "            C(TipoCliente, Treatment('Regular')) +\n",
        "            C(MasUnPlan, Treatment('No')) +\n",
        "            C(Sexo, Treatment('Hombre')) +\n",
        "            Edad +\n",
        "            PagaporServicio +\n",
        "            Antiguedad\n",
        "    \"\"\",\n",
        "    data      = data,\n",
        "    model     = sm.Logit,\n",
        "    direction = \"backward\",\n",
        "    criterion = \"f-test\"\n",
        ")\n",
        "searcher.fit()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nZlt3KHWBl7g",
        "outputId": "94a4e720-e694-44c8-ddf6-24ad84219330"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Optimization terminated successfully.\n",
            "         Current function value: 0.597610\n",
            "         Iterations 6\n"
          ]
        },
        {
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "        <td>Model:</td>              <td>Logit</td>           <td>Method:</td>          <td>MLE</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <td>Dependent Variable:</td>     <td>Churn_num</td>    <td>Pseudo R-squared:</td>    <td>0.085</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "         <td>Date:</td>        <td>2023-10-18 17:19</td>       <td>AIC:</td>         <td>3595.6608</td>\n",
              "</tr>\n",
              "<tr>\n",
              "   <td>No. Observations:</td>        <td>3000</td>             <td>BIC:</td>         <td>3625.6927</td>\n",
              "</tr>\n",
              "<tr>\n",
              "       <td>Df Model:</td>              <td>4</td>         <td>Log-Likelihood:</td>    <td>-1792.8</td> \n",
              "</tr>\n",
              "<tr>\n",
              "     <td>Df Residuals:</td>          <td>2995</td>           <td>LL-Null:</td>        <td>-1960.3</td> \n",
              "</tr>\n",
              "<tr>\n",
              "      <td>Converged:</td>           <td>1.0000</td>        <td>LLR p-value:</td>    <td>3.2735e-71</td>\n",
              "</tr>\n",
              "<tr>\n",
              "    <td>No. Iterations:</td>        <td>6.0000</td>           <td>Scale:</td>         <td>1.0000</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>Intercept</th>                                           <td>2.1775</td>   <td>0.1955</td>   <td>11.1396</td> <td>0.0000</td> <td>1.7944</td>  <td>2.5606</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor]</th> <td>0.5896</td>   <td>0.1695</td>   <td>3.4787</td>  <td>0.0005</td> <td>0.2574</td>  <td>0.9218</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>C(TipoCliente, Treatment('Regular'))[T.Premium]</th>     <td>-1.0836</td>  <td>0.1493</td>   <td>-7.2578</td> <td>0.0000</td> <td>-1.3762</td> <td>-0.7910</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>C(MasUnPlan, Treatment('No'))[T.Si]</th>                 <td>-1.0562</td>  <td>0.1247</td>   <td>-8.4679</td> <td>0.0000</td> <td>-1.3006</td> <td>-0.8117</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Antiguedad</th>                                          <td>-0.0442</td>  <td>0.0033</td>  <td>-13.2802</td> <td>0.0000</td> <td>-0.0507</td> <td>-0.0377</td>\n",
              "</tr>\n",
              "</table><br/>\n"
            ],
            "text/latex": [
              "\\begin{table}\n",
              "\\caption{Results: Logit}\n",
              "\\label{}\n",
              "\\begin{center}\n",
              "\\begin{tabular}{llll}\n",
              "\\hline\n",
              "Model:              & Logit            & Method:           & MLE         \\\\\n",
              "Dependent Variable: & Churn\\_num       & Pseudo R-squared: & 0.085       \\\\\n",
              "Date:               & 2023-10-18 17:19 & AIC:              & 3595.6608   \\\\\n",
              "No. Observations:   & 3000             & BIC:              & 3625.6927   \\\\\n",
              "Df Model:           & 4                & Log-Likelihood:   & -1792.8     \\\\\n",
              "Df Residuals:       & 2995             & LL-Null:          & -1960.3     \\\\\n",
              "Converged:          & 1.0000           & LLR p-value:      & 3.2735e-71  \\\\\n",
              "No. Iterations:     & 6.0000           & Scale:            & 1.0000      \\\\\n",
              "\\hline\n",
              "\\end{tabular}\n",
              "\\end{center}\n",
              "\n",
              "\\begin{center}\n",
              "\\begin{tabular}{lrrrrrr}\n",
              "\\hline\n",
              "                                                    &   Coef. & Std.Err. &        z & P$> |$z$|$ &  [0.025 &  0.975]  \\\\\n",
              "\\hline\n",
              "Intercept                                           &  2.1775 &   0.1955 &  11.1396 &      0.0000 &  1.7944 &  2.5606  \\\\\n",
              "C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor] &  0.5896 &   0.1695 &   3.4787 &      0.0005 &  0.2574 &  0.9218  \\\\\n",
              "C(TipoCliente, Treatment('Regular'))[T.Premium]     & -1.0836 &   0.1493 &  -7.2578 &      0.0000 & -1.3762 & -0.7910  \\\\\n",
              "C(MasUnPlan, Treatment('No'))[T.Si]                 & -1.0562 &   0.1247 &  -8.4679 &      0.0000 & -1.3006 & -0.8117  \\\\\n",
              "Antiguedad                                          & -0.0442 &   0.0033 & -13.2802 &      0.0000 & -0.0507 & -0.0377  \\\\\n",
              "\\hline\n",
              "\\end{tabular}\n",
              "\\end{center}\n",
              "\\end{table}\n",
              "\\bigskip\n"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary2.Summary'>\n",
              "\"\"\"\n",
              "                                           Results: Logit\n",
              "====================================================================================================\n",
              "Model:                           Logit                       Method:                      MLE       \n",
              "Dependent Variable:              Churn_num                   Pseudo R-squared:            0.085     \n",
              "Date:                            2023-10-18 17:19            AIC:                         3595.6608 \n",
              "No. Observations:                3000                        BIC:                         3625.6927 \n",
              "Df Model:                        4                           Log-Likelihood:              -1792.8   \n",
              "Df Residuals:                    2995                        LL-Null:                     -1960.3   \n",
              "Converged:                       1.0000                      LLR p-value:                 3.2735e-71\n",
              "No. Iterations:                  6.0000                      Scale:                       1.0000    \n",
              "----------------------------------------------------------------------------------------------------\n",
              "                                                     Coef.  Std.Err.    z     P>|z|   [0.025  0.975]\n",
              "----------------------------------------------------------------------------------------------------\n",
              "Intercept                                            2.1775   0.1955  11.1396 0.0000  1.7944  2.5606\n",
              "C(DeudaMembresia, Treatment('No Deudor'))[T.Deudor]  0.5896   0.1695   3.4787 0.0005  0.2574  0.9218\n",
              "C(TipoCliente, Treatment('Regular'))[T.Premium]     -1.0836   0.1493  -7.2578 0.0000 -1.3762 -0.7910\n",
              "C(MasUnPlan, Treatment('No'))[T.Si]                 -1.0562   0.1247  -8.4679 0.0000 -1.3006 -0.8117\n",
              "Antiguedad                                          -0.0442   0.0033 -13.2802 0.0000 -0.0507 -0.0377\n",
              "====================================================================================================\n",
              "\n",
              "\"\"\""
            ]
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "modelo_seleccionado = sm.Logit.from_formula(searcher.optimal_formula_, data=data).fit()\n",
        "modelo_seleccionado.summary2()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H-RWNxxgBl7g"
      },
      "source": [
        "* Finalmente, todos los predictores del modelo tienen un valor-p menor a 0.05.\n",
        "\n",
        "El modelo resultante es del tipo:\n",
        "\n",
        "$$\n",
        "\\log{\\left(\\pi_i \\over 1 - \\pi_i\\right)} = \\beta_0 + \\beta_1 \\cdot \\mathbb{I}_{\\{\\text{DeudaMembresia}_i=\\text{Deudor}\\}} + \\beta_2 \\cdot \\mathbb{I}_{\\{\\text{TipoCliente}_i=\\text{Premium}\\}} + \\beta_4 \\cdot \\mathbb{I}_{\\{\\text{MasUnPlan}_i=\\text{Si}\\}} + \\beta_4 \\cdot \\text{Antigüedad}_i\n",
        "$$\n",
        "\n",
        "\n",
        "Ahora, estudiemos mediante el método `predict()`, la probabilidad de fuga de los siguientes clientes:\n",
        "\n",
        "\n",
        "|   **Predictor**  | **Cliente A** | **Cliente B** |\n",
        "|:----------------:|:-------------:|:-------------:|\n",
        "| `DeudaMembresia` |     Deudor    |   No Deudor   |\n",
        "|   `TipoCliente`  |    Regular    |    Premium    |\n",
        "|    `MasUnPlan`   |       Si      |       Si      |\n",
        "|   `Antiguedad`   |       10      |       25      |\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WEaEW3aYBl7g",
        "outputId": "f8ec4be6-213d-42c1-eae2-297f125dddc4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "- Clientes de interés:\n"
          ]
        },
        {
          "data": {
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              "\n",
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              "    }\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>DeudaMembresia</th>\n",
              "      <th>TipoCliente</th>\n",
              "      <th>MasUnPlan</th>\n",
              "      <th>Antiguedad</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Deudor</td>\n",
              "      <td>Regular</td>\n",
              "      <td>Si</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>No Deudor</td>\n",
              "      <td>Premium</td>\n",
              "      <td>Si</td>\n",
              "      <td>25</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "  DeudaMembresia TipoCliente MasUnPlan  Antiguedad\n",
              "0         Deudor     Regular        Si          10\n",
              "1      No Deudor     Premium        Si          25"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "- Probabilidades de fuga según modelo:\n",
            "0   0.78059\n",
            "1   0.25602\n",
            "dtype: float64\n"
          ]
        }
      ],
      "source": [
        "clientes = pd.DataFrame([\n",
        "    {\"DeudaMembresia\": \"Deudor\", \"TipoCliente\": \"Regular\", \"MasUnPlan\": \"Si\", \"Antiguedad\": 10},\n",
        "    {\"DeudaMembresia\": \"No Deudor\", \"TipoCliente\": \"Premium\", \"MasUnPlan\": \"Si\", \"Antiguedad\": 25}\n",
        "])\n",
        "\n",
        "pi_clientes = modelo_seleccionado.predict(clientes)\n",
        "\n",
        "print(\"- Clientes de interés:\")\n",
        "display(clientes)\n",
        "print(\"- Probabilidades de fuga según modelo:\")\n",
        "print(pi_clientes)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fcx6PeNRBl7h"
      },
      "source": [
        "### Métricas de Desempeño\n",
        "\n",
        "* Al ser un modelo de clasiﬁcación, se puede utilizar la matriz de confusión para evaluar el desempeño del modelo.\n",
        "* Para realizar una evaluación correcta del modelo se debe utilizar una base de datos distinta a la utilizada para ajustar el modelo. Sin embargo, para efectos de este curso, utilizaremos la misma base de datos para evaluar el modelo (nunca deben hacerlo).\n",
        "* La matriz de confusión es una tabla que muestra la cantidad de predicciones correctas e incorrectas realizadas por el modelo. A partir de ella se pueden calcular distintas métricas de desempeño.\n",
        "* En las filas de la matriz se encuentran los valores reales de la variable respuesta y en las columnas las predicciones realizadas por el modelo.\n",
        "* Con la función `pd.crosstab()` se puede realizar esta matriz.\n",
        "\n",
        "La matriz de confusión tiene la siguiente forma\n",
        "\n",
        "|   **Matriz de Confusión**  | **Predicción 0** | **Predicción 1** |\n",
        "|:--------------------------:|:----------------:|:----------------:|\n",
        "| **Valor Real 0** |     Verdadero Negativo    |   Falso Positivo   |\n",
        "| **Valor Real 1** |    Falso Negativo    |    Verdadero Positivo    |"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MsvPflVpBl7h",
        "outputId": "999a0416-f88e-4b1e-c196-dcdc13f2b3e2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array(['Finaliza Contrato', 'Mantiene Contrato'], dtype=object)"
            ]
          },
          "execution_count": 30,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data[\"Churn\"].unique()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2k7No3GMBl7h",
        "outputId": "510ac9f4-17bf-40aa-d90b-6e3f963b1201"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\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>col_0</th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Churn_num</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1682</td>\n",
              "      <td>238</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>725</td>\n",
              "      <td>355</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "col_0         0    1\n",
              "Churn_num           \n",
              "0          1682  238\n",
              "1           725  355"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "probabilidades_predichas = modelo.predict(data)\n",
        "etiquetas_predichas = np.where(probabilidades_predichas >= 0.5, 1, 0)\n",
        "\n",
        "matriz_confusion = pd.crosstab(data[\"Churn_num\"], etiquetas_predichas)\n",
        "matriz_confusion"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EiGg4OdiBl7h"
      },
      "source": [
        "Solo esta vez utilizaremos `scikit-learn` para calcular las métricas de desmpeño. En especial, utilizaremos la función `classification_report()` del módulo `metrics`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "v0-q9XlxBl7h",
        "outputId": "898700f2-c472-48f6-dd6b-49a2878c1098"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "              precision    recall  f1-score   support\n",
            "\n",
            "           0       0.70      0.88      0.78      1920\n",
            "           1       0.60      0.33      0.42      1080\n",
            "\n",
            "    accuracy                           0.68      3000\n",
            "   macro avg       0.65      0.60      0.60      3000\n",
            "weighted avg       0.66      0.68      0.65      3000\n",
            "\n"
          ]
        }
      ],
      "source": [
        "from sklearn.metrics import classification_report\n",
        "\n",
        "print(classification_report(data[\"Churn_num\"], etiquetas_predichas))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ONfzTdP-Bl7h"
      },
      "source": [
        "De acuerdo a lo que estamos viendo:\n",
        "\n",
        "* **precision 0**: es la proporción de predicciones correctas de que un cliente no se fuga, respecto a todas las predicciones de que un cliente no se fuga.\n",
        "* **precision 1**: es la proporción de predicciones correctas de que un cliente se fuga, respecto a todas las predicciones de que un cliente se fuga.\n",
        "* **recall 0**: es una tasa de detección de que un cliente no se fuga, respecto a todos los clientes que no se fugaron.\n",
        "* **recall 1**: es una tasa de detección de que un cliente se fuga, respecto a todos los clientes que se fugaron.\n",
        "* **f1-score**: es una media armónica entre precision y recall. Es útil para casos donde el dataset es desbalanceado (hay más clientes que no se fugan que clientes que se fugan).\n",
        "* **support**: es la cantidad de observaciones que hay en cada categoría.\n",
        "* **accuracy**: es la proporción de predicciones correctas, respecto a todas las predicciones realizadas por el modelo.\n",
        "* **macro avg**: es un promedio de las métricas de desempeño de cada categoría.\n",
        "* **weighted avg**: es un promedio de las métricas de desempeño de cada categoría, ponderado por la cantidad de observaciones en cada categoría.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v7ErkWSNBl7h"
      },
      "source": [
        "## Ejercicios de práctica"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SbINWfyCBl7h"
      },
      "source": [
        "La base de datos `titanic.tsv` contiene información sobre los pasajeros que abordaron el barco Titanic en su último y fatal viaje. La descripción de las variables de la base de datos es la siguiente:\n",
        "\n",
        "* `idPasajero`: Código de identificación del pasajero.\n",
        "* `sobrevive`: Indica si el pasajero sobrevive al accidente (Si o No).\n",
        "* `clasePasaje`: Indica la clase del pasaje del pasajero (1ra clase, 2da clase o 3ra clase).\n",
        "* `nombre`: Nombre del pasajero (primero el apellido, trato y después el nombre).\n",
        "* `sexo`: Sexo del pasajero (Masculino o Femenino).\n",
        "* `nroHermanos`: Cantidad de hermanos con los que viaja el pasajero (valor entero no negativo).\n",
        "* `nroPadresHijos`: Cantidad de padres o hijos con los que viaja el pasajero (valor entero no negativo).\n",
        "* `idPasaje`: Código de identificación del pasaje.\n",
        "* `embarque`: Nombre del puerto donde el pasajero realiza el embarque (Southampton, Cherbourg o Queenstown).\n",
        "* `precioPasaje`: Valor del pasaje en florines (moneda usada en la época en Reino Unido) (valor decimal positivo).\n",
        "\n",
        "Interesa calcular la probabilidad de que un pasajero con determinadas características fallezca."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aB8OgspbBl7i"
      },
      "source": [
        "**1.** Cargue la base de datos y realice un análisis inicial. Indique el porcentaje de pasajeros que fallecieron en el accidente."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "eZ92uNgXBl7i"
      },
      "outputs": [],
      "source": [
        "# Responda aquí:\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J160DBfABl7i"
      },
      "source": [
        "**2.** Realice un modelo que entregue la probabilidad de que un pasajero fallezca (`sobrevive=\"No\"`), utilice como predictores las variables\t`clasePasaje` (categoria \"3ra clase\" como referencia),\t`sexo` (categoria \"Masculino\" como referencia),\t`edad`,\t`nroHermanos`,\t`nroPadresHijos`,\t`embarque` (categoría \"Queenstown\" como referencia) y `precioPasaje`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0KBOaP_wBl7i"
      },
      "outputs": [],
      "source": [
        "# Responda aquí:\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0SoikNlrBl7i"
      },
      "source": [
        "**3.** Realice selección secuencial (uno a uno) de predictores mediante valor-p."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hd5TM0TNBl7i"
      },
      "outputs": [],
      "source": [
        "# Responda aquí:\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0v3kUIASBl7i"
      },
      "source": [
        "**4.** Indique cuáles predictores son factores de riesgo o protección según corresponda."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yBJcXPDuBl7i"
      },
      "outputs": [],
      "source": [
        "# Responda aquí:\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8QTL_8AKBl7i"
      },
      "source": [
        "**5.** Interprete las razones de chances del modelo en términos del contexto."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PQ-fRT_wBl7i"
      },
      "outputs": [],
      "source": [
        "# Responda aquí:\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TyI9lkHbBl7i"
      },
      "source": [
        "**6.** Indique la probabilidad de que fallezcam los siguientes pasajeros en base al modelo.\n",
        "\n",
        "* Pasajero A:\n",
        "  * `clasePasaje`: 2da clase.\n",
        "  * `sexo`: Masculino.\n",
        "  * `edad`: 30.\n",
        "  * `nroHermanos`: 1.\n",
        "* Pasajero B:\n",
        "  * `clasePasaje`: 3ra clase.\n",
        "  * `sexo`: Femenino.\n",
        "  * `edad`: 60.\n",
        "  * `nroHermanos`: 0."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-EAdwHeUBl7i"
      },
      "outputs": [],
      "source": [
        "# Responda aquí:\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bXFVSCBZBl7j"
      },
      "source": [
        "**7.** ¿Cuántas chances más tiene de fallecer el pasajero A respecto al pasajero B?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "g3CJEeoRBl7j"
      },
      "outputs": [],
      "source": [
        "# Responda aquí:\n"
      ]
    }
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