regresion_lineal.ipynb

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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mdpl8OMYZn7u"
      },
      "source": [
        "# 7. Regresión lineal"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZJ7gg0YqZn7z"
      },
      "source": [
        "Usaremos la función afín:\n",
        "\n",
        "$$\n",
        "\\hat{y} = \\mathbf{x}^{T}\\boldsymbol{\\beta} + v\n",
        "$$\n",
        "\n",
        "Esta función es llamada un **modelo de regresión**. En este caso las entradas de $\\mathbf{x}$ son llamadas *regresores* y a $\\hat{y}$ se le llama *predicción*. Hay que notar que la regresión es un modelo, nos estamos aproximando a estimar nuestra variable dependiente $y$, algunas veces llamada también *label*, *etiqueta* o *resultado esperado*. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0ii9aRkVZn70"
      },
      "source": [
        "Al vector $\\mathbf{\\beta}$ se le denomina el *vector de pesos* mientras que el escalar $v$ es llamado el offset o bias. En conjunto $v$ y $\\beta$ son los parámetros de la regresión. Recordamos que la notación $\\hat{y}$ es usando para enfatizar que es un estimado o prediccción del resultado esperado $y$. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dszq35wXZn70"
      },
      "source": [
        "## 7.1 Notación simplificada de un modelo de regresión. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6kRdfheEZn70"
      },
      "source": [
        "La concatenación de vectores nos puede ayudar a expresar de manera más sencilla la ecuación de regresión. Notemos que podemos definir el $(n+1)$-vector $\\boldsymbol{\\tilde{\\beta}}^{T} = [v\\; \\boldsymbol{\\beta}]$ y de igual forma el $(n+1)$-vector $\\mathbf{\\widetilde{x}}^{T} = [1 \\; \\boldsymbol{x}]$ de manera que:\n",
        "\n",
        "$$\n",
        "\\hat{y} = \\mathbf{x}^{T}\\boldsymbol{\\beta} + v = \\begin{bmatrix}1\\\\ \\mathbf{x}\\end{bmatrix}^{T} \\begin{bmatrix} v\\\\\\boldsymbol{\\beta}  \\end{bmatrix} = \\mathbf{\\widetilde{x}}^{T} \\boldsymbol{\\widetilde{\\beta}}\n",
        "$$\n",
        "\n",
        "Por simplicidad algunas veces solamente se escribe $\\hat{y}=\\mathbf{x}^{T}\\boldsymbol{\\beta}$ sobreentendiendo nuestra construcción. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hnz0RdcwZn71"
      },
      "source": [
        "## 7.2 Un ejemplo de regresión. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RGxMkAOSZn71"
      },
      "source": [
        "Vamos a considerar el siguiente ejemplo donde vamos a analizar una base de datos del *GOLDEN OAK RESEARCH GROUP*. Nuestra variable dependiente serán el ingreso promedio por casa y nuestros regresores serán simplemente la latitud y la longitud. \n",
        "\n",
        "Para poder cargar la base vamos a importar en conjunto a numpy también **pandas** la cual es una biblioteca de manejo y manipulación de bases de datos tomando como bases sus objetos *dataframe*. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gg2WF2gEZn72"
      },
      "source": [
        "import matplotlib.pyplot as plt # Para poder realizar visualizaciones\n",
        "import pandas as pd # Para poder acceder a pandas\n",
        "import numpy as np # Para poder tener vectores"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dYoge0HPZn72"
      },
      "source": [
        "df = pd.read_csv('income_db_GORG.csv')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IrJNPaRyZn73",
        "outputId": "78ccc96b-6f25-4f65-c312-bfdec6e47a29"
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      "source": [
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
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          "output_type": "execute_result",
          "data": {
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              "<div>\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>id</th>\n",
              "      <th>State_Code</th>\n",
              "      <th>State_Name</th>\n",
              "      <th>State_ab</th>\n",
              "      <th>County</th>\n",
              "      <th>City</th>\n",
              "      <th>Place</th>\n",
              "      <th>Type</th>\n",
              "      <th>Primary</th>\n",
              "      <th>Zip_Code</th>\n",
              "      <th>Area_Code</th>\n",
              "      <th>ALand</th>\n",
              "      <th>AWater</th>\n",
              "      <th>Lat</th>\n",
              "      <th>Lon</th>\n",
              "      <th>Mean</th>\n",
              "      <th>Median</th>\n",
              "      <th>Stdev</th>\n",
              "      <th>sum_w</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1011000</td>\n",
              "      <td>1</td>\n",
              "      <td>Alabama</td>\n",
              "      <td>AL</td>\n",
              "      <td>Mobile County</td>\n",
              "      <td>Chickasaw</td>\n",
              "      <td>Chickasaw city</td>\n",
              "      <td>City</td>\n",
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              "      <td>-88.079697</td>\n",
              "      <td>38773</td>\n",
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              "      <td>1638.260513</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1011010</td>\n",
              "      <td>1</td>\n",
              "      <td>Alabama</td>\n",
              "      <td>AL</td>\n",
              "      <td>Barbour County</td>\n",
              "      <td>Louisville</td>\n",
              "      <td>Clio city</td>\n",
              "      <td>City</td>\n",
              "      <td>place</td>\n",
              "      <td>36048</td>\n",
              "      <td>334</td>\n",
              "      <td>26070325</td>\n",
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              "      <td>31.708516</td>\n",
              "      <td>-85.611039</td>\n",
              "      <td>37725</td>\n",
              "      <td>19528</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1011020</td>\n",
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              "      <td>Alabama</td>\n",
              "      <td>AL</td>\n",
              "      <td>Shelby County</td>\n",
              "      <td>Columbiana</td>\n",
              "      <td>Columbiana city</td>\n",
              "      <td>City</td>\n",
              "      <td>place</td>\n",
              "      <td>35051</td>\n",
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              "      <td>33.191452</td>\n",
              "      <td>-86.615618</td>\n",
              "      <td>54606</td>\n",
              "      <td>31930</td>\n",
              "      <td>57348</td>\n",
              "      <td>926.031000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1011030</td>\n",
              "      <td>1</td>\n",
              "      <td>Alabama</td>\n",
              "      <td>AL</td>\n",
              "      <td>Mobile County</td>\n",
              "      <td>Satsuma</td>\n",
              "      <td>Creola city</td>\n",
              "      <td>City</td>\n",
              "      <td>place</td>\n",
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              "      <td>1011040</td>\n",
              "      <td>1</td>\n",
              "      <td>Alabama</td>\n",
              "      <td>AL</td>\n",
              "      <td>Mobile County</td>\n",
              "      <td>Dauphin Island</td>\n",
              "      <td>Dauphin Island</td>\n",
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              "      <td>67225</td>\n",
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              "        id  State_Code State_Name State_ab          County            City  \\\n",
              "0  1011000           1    Alabama       AL   Mobile County       Chickasaw   \n",
              "1  1011010           1    Alabama       AL  Barbour County      Louisville   \n",
              "2  1011020           1    Alabama       AL   Shelby County      Columbiana   \n",
              "3  1011030           1    Alabama       AL   Mobile County         Satsuma   \n",
              "4  1011040           1    Alabama       AL   Mobile County  Dauphin Island   \n",
              "\n",
              "             Place  Type Primary  Zip_Code Area_Code     ALand     AWater  \\\n",
              "0   Chickasaw city  City   place     36611       251  10894952     909156   \n",
              "1        Clio city  City   place     36048       334  26070325      23254   \n",
              "2  Columbiana city  City   place     35051       205  44835274     261034   \n",
              "3      Creola city  City   place     36572       251  36878729    2374530   \n",
              "4   Dauphin Island  Town   place     36528       251  16204185  413605152   \n",
              "\n",
              "         Lat        Lon   Mean  Median  Stdev        sum_w  \n",
              "0  30.771450 -88.079697  38773   30506  33101  1638.260513  \n",
              "1  31.708516 -85.611039  37725   19528  43789   258.017685  \n",
              "2  33.191452 -86.615618  54606   31930  57348   926.031000  \n",
              "3  30.874343 -88.009442  63919   52814  47707   378.114619  \n",
              "4  30.250913 -88.171268  77948   67225  54270   282.320328  "
            ]
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        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nfhi8GmBZn74"
      },
      "source": [
        "¿Qué data contiene la base de datos?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3PlFOPLaZn74"
      },
      "source": [
        "¿Qué tamaño tiene?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LypWu3gAZn74",
        "outputId": "6897450b-fc09-4a72-904a-ce98e94b6825"
      },
      "source": [
        "len(df)*len(df.columns)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "617994"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9pvJIkp4Zn74",
        "outputId": "f19caf71-72ad-4d5d-8364-ab2ea87285d8"
      },
      "source": [
        "len(df)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "32526"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1WLspsuHZn75"
      },
      "source": [
        "Ahora bien, como comenté nuestros regresores en términos de columnas son:\n",
        "* Lat\n",
        "* Lon\n",
        "\n",
        "Mientras que nuestra variable dependiente es:\n",
        "* Mean "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3GExtc1dZn75"
      },
      "source": [
        "Ahora, calcular el vector predicciones $\\hat{y}$ ya que cada valor de Lat y Lon tendrá asociado un valor de Mean y es justo el que queremos aproximar con $\\hat{y}$. Ahora, como no forma parte de este curso ya tenemos unos parámetros dados:\n",
        "\n",
        "$$\n",
        "v = 30980.48, \\qquad \\boldsymbol{\\beta} = \\begin{bmatrix}744.83 \\\\ -83.45\\end{bmatrix}\n",
        "$$\n",
        "\n",
        "Con lo cual ya podemos realizar las predicciones $\\hat{y}_{i} = \\mathbf{x}^{T}_{i} \\boldsymbol{\\beta} + v$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "diiqDOAoZn75"
      },
      "source": [
        "def pred(x):\n",
        "    beta = np.array([744.83,-83.45])\n",
        "    v = 30980.48\n",
        "    return x@beta + v"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gcRvR3v3Zn75",
        "outputId": "49c89353-0a9c-496f-b51c-356427e9a17f"
      },
      "source": [
        "type(df['Lat'].values)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6RRUbYiSZn76"
      },
      "source": [
        "X = df[['Lat','Lon']].values"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yQAGr3UBZn76"
      },
      "source": [
        "Y_hat = pred(X)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AOhoUNu2Zn76"
      },
      "source": [
        "Y = df['Mean'].values"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0FTP4BjxZn76",
        "outputId": "45b1a58d-b5a5-4e5d-f128-df1e5a3c35a7"
      },
      "source": [
        "fig, ax = plt.subplots(1,1,figsize=(7,7),dpi=120)\n",
        "\n",
        "ax.scatter(Y_hat,Y,marker ='o',color='red')\n",
        "ax.plot(Y,Y,ls='--')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 840x840 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-PnDqVAbZn77"
      },
      "source": [
        "¿Cómo calculamos el error?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K0oXi0MQZn77"
      },
      "source": [
        "## 7.3 Ejercicio. \n",
        "\n",
        "Considera que ya no solamente usamos Lat y Lon como regresores sino también comenzamos a usar Zip_Code como regresor, ajustar ese modelo nos deja con los siguientes parámetros:\n",
        "$$\n",
        "v = 4152.02, \\qquad \\boldsymbol{\\beta} = \\begin{bmatrix}6.55490348e+02 \\\\ 5.75918372e+02 \\\\ -2.94216316e-01\\end{bmatrix}\n",
        "$$\n",
        "\n",
        "¿Mejora la preducción al introducir un nuevo regresor?"
      ]
    }
  ]
}