2_Regresion_Linear_Algebra.ipynb

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  "metadata": {
    "colab": {
      "name": "2_Regresion_Linear_Algebra.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyN3eSZglFnFeFy6yuzAQsFw",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/XavierCarrera/Tutorial-Machine-Learning-Regresion-Lineal/blob/main/2_Regresion_Linear_Algebra.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lpS9IhRJsmEM"
      },
      "source": [
        "# Introducción\n",
        "\n",
        "En esta ocasión, usaremos algebra lineal para entender que tanto se separa nuestros data points. Esta es una métrica muy importante para saber que tan bien se desempeña un modelo de regresión lineal.\n",
        "\n",
        "En este caso utilizaremos la librería **Scikit-Learn** (que sirvce para mahcine learning) con los siguientes modulos:\n",
        "\n",
        "* **linear_model**: con el cual entrenamos un modelo de machine learning de regresión lineal.\n",
        "* **train_test_split**: que nos sirve separar datos de entrenamiento y pruebas.\n",
        "* **metrics**: donde podemos encontrar formas de medir el desempeño de nuestro modelo."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_R4yrqxvqz3K"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd \n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import mean_squared_error, r2_score\n",
        "\n",
        "\n",
        "%matplotlib inline\n",
        "plt.rcParams['figure.figsize'] = (20, 10)\n",
        "plt.style.use('ggplot')\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XdQcu1kudrOS"
      },
      "source": [
        "Seguimos usando el mismo dataset de pingüinos del notebook anterior."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 419
        },
        "id": "G38GEea2r_N6",
        "outputId": "4c436a7c-e15a-434e-c71c-a2439faa58ba"
      },
      "source": [
        "df = sns.load_dataset(\"penguins\")\n",
        "df"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>species</th>\n",
              "      <th>island</th>\n",
              "      <th>bill_length_mm</th>\n",
              "      <th>bill_depth_mm</th>\n",
              "      <th>flipper_length_mm</th>\n",
              "      <th>body_mass_g</th>\n",
              "      <th>sex</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Adelie</td>\n",
              "      <td>Torgersen</td>\n",
              "      <td>39.1</td>\n",
              "      <td>18.7</td>\n",
              "      <td>181.0</td>\n",
              "      <td>3750.0</td>\n",
              "      <td>Male</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Adelie</td>\n",
              "      <td>Torgersen</td>\n",
              "      <td>39.5</td>\n",
              "      <td>17.4</td>\n",
              "      <td>186.0</td>\n",
              "      <td>3800.0</td>\n",
              "      <td>Female</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Adelie</td>\n",
              "      <td>Torgersen</td>\n",
              "      <td>40.3</td>\n",
              "      <td>18.0</td>\n",
              "      <td>195.0</td>\n",
              "      <td>3250.0</td>\n",
              "      <td>Female</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Adelie</td>\n",
              "      <td>Torgersen</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Adelie</td>\n",
              "      <td>Torgersen</td>\n",
              "      <td>36.7</td>\n",
              "      <td>19.3</td>\n",
              "      <td>193.0</td>\n",
              "      <td>3450.0</td>\n",
              "      <td>Female</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>339</th>\n",
              "      <td>Gentoo</td>\n",
              "      <td>Biscoe</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>340</th>\n",
              "      <td>Gentoo</td>\n",
              "      <td>Biscoe</td>\n",
              "      <td>46.8</td>\n",
              "      <td>14.3</td>\n",
              "      <td>215.0</td>\n",
              "      <td>4850.0</td>\n",
              "      <td>Female</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>341</th>\n",
              "      <td>Gentoo</td>\n",
              "      <td>Biscoe</td>\n",
              "      <td>50.4</td>\n",
              "      <td>15.7</td>\n",
              "      <td>222.0</td>\n",
              "      <td>5750.0</td>\n",
              "      <td>Male</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>342</th>\n",
              "      <td>Gentoo</td>\n",
              "      <td>Biscoe</td>\n",
              "      <td>45.2</td>\n",
              "      <td>14.8</td>\n",
              "      <td>212.0</td>\n",
              "      <td>5200.0</td>\n",
              "      <td>Female</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>343</th>\n",
              "      <td>Gentoo</td>\n",
              "      <td>Biscoe</td>\n",
              "      <td>49.9</td>\n",
              "      <td>16.1</td>\n",
              "      <td>213.0</td>\n",
              "      <td>5400.0</td>\n",
              "      <td>Male</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>344 rows × 7 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "    species     island  bill_length_mm  ...  flipper_length_mm  body_mass_g     sex\n",
              "0    Adelie  Torgersen            39.1  ...              181.0       3750.0    Male\n",
              "1    Adelie  Torgersen            39.5  ...              186.0       3800.0  Female\n",
              "2    Adelie  Torgersen            40.3  ...              195.0       3250.0  Female\n",
              "3    Adelie  Torgersen             NaN  ...                NaN          NaN     NaN\n",
              "4    Adelie  Torgersen            36.7  ...              193.0       3450.0  Female\n",
              "..      ...        ...             ...  ...                ...          ...     ...\n",
              "339  Gentoo     Biscoe             NaN  ...                NaN          NaN     NaN\n",
              "340  Gentoo     Biscoe            46.8  ...              215.0       4850.0  Female\n",
              "341  Gentoo     Biscoe            50.4  ...              222.0       5750.0    Male\n",
              "342  Gentoo     Biscoe            45.2  ...              212.0       5200.0  Female\n",
              "343  Gentoo     Biscoe            49.9  ...              213.0       5400.0    Male\n",
              "\n",
              "[344 rows x 7 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6Kke9L_8eKgM"
      },
      "source": [
        "El dataset viene con datos nulos, que no nos sirven para entrenar un modelo de machine learning. Por ende, los contaremos y luego los eliminaremos. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "217LQBfZtsHg",
        "outputId": "6fc1da77-d96d-4de5-edf2-0eb3068d4e3d"
      },
      "source": [
        "df.isnull().sum()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "species               0\n",
              "island                0\n",
              "bill_length_mm        2\n",
              "bill_depth_mm         2\n",
              "flipper_length_mm     2\n",
              "body_mass_g           2\n",
              "sex                  11\n",
              "dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pli5XaQEt1Ny"
      },
      "source": [
        "df.dropna(inplace=True)"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G_7z0jjeea-0"
      },
      "source": [
        "Para este ejercicio, crearemos un gráfico de correlación linear como el que hicimos anteriormente. En este caso suponemos que existe una relación entre la masa corporal de los pingüinos y el tamaño de sus alas."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 625
        },
        "id": "K6jWtgpTsE3q",
        "outputId": "7af6876b-1659-43eb-f318-211aa5f8571c"
      },
      "source": [
        "sns.regplot(x=df[\"body_mass_g\"], y=df[\"flipper_length_mm\"])"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fb3edc86da0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 1440x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u83QqoA5sqF8"
      },
      "source": [
        "# Entrenamiento del Modelo\n",
        "\n",
        "A partir de la correlación linear anterior, entrenaremos un modelo simple de regresión linear. \n",
        "\n",
        "Lo primero es crear dos vectores. En este caso usamos la masa corporal como nuestro vector X (predictor) y el tamaño de las alas como el vector y (valor por predecirse).\n",
        "\n",
        "La función *train_test_split* es fundamental en machine learning, ya que nos divide nuestro data sets en datos de entrenamiento y prueba. Los datos de prueba nos servirán para medir el desempeño de nuestro modelo.\n",
        "\n",
        "Las funciones *values* y *reshape* nos permiten crear un arreglo artificial en 2D que nos permitirá entrenar nuestro modelo.\n",
        "\n",
        "Para entrenar al modelo, solo tenemos que invocar a *Linear Regression* y luego entrenar al modelo con la función *fit*."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "geqh7kcjzAVN"
      },
      "source": [
        "X = df[\"body_mass_g\"].values.reshape(-1,1)\n",
        "y = df[\"flipper_length_mm\"]\n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.20, random_state = 42)"
      ],
      "execution_count": 48,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KMrZah8Tzcd8",
        "outputId": "80b66d50-14fd-456c-df70-54ac3d94fc4a"
      },
      "source": [
        "reg = LinearRegression()\n",
        "reg.fit(X_train, y_train)"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jCdwCPWd0TtP"
      },
      "source": [
        "# Suma de Errores Cuadráticos\n",
        "\n",
        "En este modelo tenemos ya un modelo entrenado y listo para ser medido.\n",
        "\n",
        "*Scikit Learn* no tiene un modulo para calcular la summa de errores cuadráticos por lo que lo haremos manualemente.\n",
        "\n",
        "Lo que tenemos es una vector llamado *y_test* (datos reales) que utiliza a *X_test* para generar una predicción. Lo que hacemos con una sola línea de código es sumar todos los vectores al cuadrado."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZhEYwh6h0R6o",
        "outputId": "2dd8ee9b-0bbb-4b27-f6b6-6b3f9815d5c2"
      },
      "source": [
        "sec = np.sum((y_test - reg.predict(X_test))**2)\n",
        "sec"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2913.7808139174745"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "znhuZj_P1MDh"
      },
      "source": [
        "# Otras Métricas de Desempeño\n",
        "\n",
        "En este caso usamos dos métricas adicionales que vienen preconstruidas en *Scikit Learn*. \n",
        "\n",
        "Por un lado tenemos al promedio de los errores cuadráticos (mean_squared_error). Como su nombre lo indica, hace un promedio de los errores cuadráticos en vez de sumarlos.\n",
        "\n",
        "Una métrica que se usa popularmente en regresión linear son los mínimos cuadrados ordinarios (r²). Este genera un rango de 0 a 1 para medir la varianza capturada por el modelo. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XfEhnt6QNRJt",
        "outputId": "3816b7a2-ea87-49f1-8988-72ef08868c9e"
      },
      "source": [
        "y_test_predict = reg.predict(X_test)\n",
        "\n",
        "rmse = mean_squared_error(y_test, y_test_predict)\n",
        "r2 = r2_score(y_test, y_test_predict)\n",
        "\n",
        "print(rmse)\n",
        "print(r2)"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "43.48926587936529\n",
            "0.7903633255525706\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}