Multiple_linear_regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Multiple linear regression.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Shibu Mohapatra\n",
        "\n",
        "Artificial Intelligence"
      ],
      "metadata": {
        "id": "XYlXus3blUB2"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jDi2qbpjPiOt"
      },
      "source": [
        "**Multiple linear regression and diagnostic measures using neural Network procedure to predict data. Compare how neural network is better over ordinary least square estimates.**"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **A. Multiple linear regression and diagnostic measures using neural Network procedure to predict data**"
      ],
      "metadata": {
        "id": "AM-HyfO_w_R-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "import pandas as pd\n",
        "import tensorflow as tf\n",
        "import matplotlib.pyplot as plt\n",
        "from tensorflow.keras import Model\n",
        "from tensorflow.keras import Sequential\n",
        "from tensorflow.keras.optimizers import Adam\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from tensorflow.keras.layers import Dense, Dropout\n",
        "from sklearn.model_selection import train_test_split\n",
        "from tensorflow.keras.losses import MeanSquaredLogarithmicError\n",
        "\n",
        "#Dataset\n",
        "TRAIN_DATA_PATH = '/content/sample_data/california_housing_train.csv'\n",
        "TEST_DATA_PATH = '/content/sample_data/california_housing_test.csv'\n",
        "TARGET_NAME = 'median_house_value'"
      ],
      "metadata": {
        "id": "u-ujVwy1vR-h"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# x_train = features, y_train = target\n",
        "train_data = pd.read_csv(TRAIN_DATA_PATH)\n",
        "test_data = pd.read_csv(TEST_DATA_PATH)\n",
        "x_train, y_train = train_data.drop(TARGET_NAME, axis=1), train_data[TARGET_NAME]\n",
        "x_test, y_test = test_data.drop(TARGET_NAME, axis=1), test_data[TARGET_NAME]"
      ],
      "metadata": {
        "id": "f4uCgsPMvdML"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def scale_datasets(x_train, x_test):\n",
        "\n",
        "  # Standard Scale test and train data\n",
        "  # Z - Score normalization\n",
        "\n",
        "  standard_scaler = StandardScaler()\n",
        "  x_train_scaled = pd.DataFrame(standard_scaler.fit_transform(x_train),columns=x_train.columns)\n",
        "  x_test_scaled = pd.DataFrame(standard_scaler.transform(x_test),columns = x_test.columns)\n",
        "  return x_train_scaled, x_test_scaled\n",
        "x_train_scaled, x_test_scaled = scale_datasets(x_train, x_test)"
      ],
      "metadata": {
        "id": "423cNgc_vhQz"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "hidden_units1 = 160\n",
        "hidden_units2 = 480\n",
        "hidden_units3 = 256\n",
        "learning_rate = 0.01\n",
        "# Creating model using the Sequential in tensorflow\n",
        "def build_model_using_sequential():\n",
        "  model = Sequential([\n",
        "    Dense(hidden_units1, kernel_initializer='normal', activation='relu'),\n",
        "    Dropout(0.2),\n",
        "    Dense(hidden_units2, kernel_initializer='normal', activation='relu'),\n",
        "    Dropout(0.2),\n",
        "    Dense(hidden_units3, kernel_initializer='normal', activation='relu'),\n",
        "    Dense(1, kernel_initializer='normal', activation='linear')\n",
        "  ])\n",
        "  return model\n",
        "# build the model\n",
        "model = build_model_using_sequential()"
      ],
      "metadata": {
        "id": "fZgwRNEqwfwR"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# loss function\n",
        "msle = MeanSquaredLogarithmicError()\n",
        "model.compile(loss=msle, optimizer=Adam(learning_rate=learning_rate), metrics=[msle])\n",
        "\n",
        "# train the model\n",
        "history = model.fit(x_train_scaled.values, y_train.values, epochs=10, batch_size=64, validation_split=0.2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "K-mjbn0Wwjui",
        "outputId": "53ad7893-da50-4b46-a8b8-8754139808b4"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 1/10\n",
            "213/213 [==============================] - 3s 9ms/step - loss: 5.1650 - mean_squared_logarithmic_error: 5.1536 - val_loss: 0.6676 - val_mean_squared_logarithmic_error: 0.6633\n",
            "Epoch 2/10\n",
            "213/213 [==============================] - 2s 7ms/step - loss: 0.2706 - mean_squared_logarithmic_error: 0.2704 - val_loss: 0.3791 - val_mean_squared_logarithmic_error: 0.3843\n",
            "Epoch 3/10\n",
            "213/213 [==============================] - 2s 7ms/step - loss: 0.2046 - mean_squared_logarithmic_error: 0.2045 - val_loss: 0.2907 - val_mean_squared_logarithmic_error: 0.2988\n",
            "Epoch 4/10\n",
            "213/213 [==============================] - 2s 7ms/step - loss: 0.1626 - mean_squared_logarithmic_error: 0.1625 - val_loss: 0.2252 - val_mean_squared_logarithmic_error: 0.2336\n",
            "Epoch 5/10\n",
            "213/213 [==============================] - 2s 7ms/step - loss: 0.1343 - mean_squared_logarithmic_error: 0.1342 - val_loss: 0.1648 - val_mean_squared_logarithmic_error: 0.1724\n",
            "Epoch 6/10\n",
            "213/213 [==============================] - 2s 7ms/step - loss: 0.1153 - mean_squared_logarithmic_error: 0.1154 - val_loss: 0.1407 - val_mean_squared_logarithmic_error: 0.1487\n",
            "Epoch 7/10\n",
            "213/213 [==============================] - 2s 7ms/step - loss: 0.1083 - mean_squared_logarithmic_error: 0.1083 - val_loss: 0.1296 - val_mean_squared_logarithmic_error: 0.1370\n",
            "Epoch 8/10\n",
            "213/213 [==============================] - 2s 7ms/step - loss: 0.1038 - mean_squared_logarithmic_error: 0.1038 - val_loss: 0.1234 - val_mean_squared_logarithmic_error: 0.1302\n",
            "Epoch 9/10\n",
            "213/213 [==============================] - 2s 7ms/step - loss: 0.1001 - mean_squared_logarithmic_error: 0.1002 - val_loss: 0.1177 - val_mean_squared_logarithmic_error: 0.1232\n",
            "Epoch 10/10\n",
            "213/213 [==============================] - 2s 7ms/step - loss: 0.0995 - mean_squared_logarithmic_error: 0.0995 - val_loss: 0.1157 - val_mean_squared_logarithmic_error: 0.1212\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_history(history, key):\n",
        "  plt.plot(history.history[key])\n",
        "  plt.plot(history.history['val_'+key])\n",
        "  plt.xlabel(\"Epochs\")\n",
        "  plt.ylabel(key)\n",
        "  plt.legend([key, 'val_'+key])\n",
        "  plt.show()\n",
        "# Plot the history\n",
        "plot_history(history, 'mean_squared_logarithmic_error')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "-5yyEYSVwn4D",
        "outputId": "b01d94b4-74d3-479e-d266-2604d5ae028f"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_test['prediction'] = model.predict(x_test_scaled)\n",
        "x_test.head(5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "5dov4NNTwqip",
        "outputId": "8ca1b066-9cb8-44a0-c283-997cf7a0c78e"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-19cf09eb-b3dd-404d-83c4-3e0844ee6d91\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>longitude</th>\n",
              "      <th>latitude</th>\n",
              "      <th>housing_median_age</th>\n",
              "      <th>total_rooms</th>\n",
              "      <th>total_bedrooms</th>\n",
              "      <th>population</th>\n",
              "      <th>households</th>\n",
              "      <th>median_income</th>\n",
              "      <th>prediction</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-122.05</td>\n",
              "      <td>37.37</td>\n",
              "      <td>27.0</td>\n",
              "      <td>3885.0</td>\n",
              "      <td>661.0</td>\n",
              "      <td>1537.0</td>\n",
              "      <td>606.0</td>\n",
              "      <td>6.6085</td>\n",
              "      <td>343966.093750</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-118.30</td>\n",
              "      <td>34.26</td>\n",
              "      <td>43.0</td>\n",
              "      <td>1510.0</td>\n",
              "      <td>310.0</td>\n",
              "      <td>809.0</td>\n",
              "      <td>277.0</td>\n",
              "      <td>3.5990</td>\n",
              "      <td>188352.859375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-117.81</td>\n",
              "      <td>33.78</td>\n",
              "      <td>27.0</td>\n",
              "      <td>3589.0</td>\n",
              "      <td>507.0</td>\n",
              "      <td>1484.0</td>\n",
              "      <td>495.0</td>\n",
              "      <td>5.7934</td>\n",
              "      <td>261868.187500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-118.36</td>\n",
              "      <td>33.82</td>\n",
              "      <td>28.0</td>\n",
              "      <td>67.0</td>\n",
              "      <td>15.0</td>\n",
              "      <td>49.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>6.1359</td>\n",
              "      <td>326603.593750</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-119.67</td>\n",
              "      <td>36.33</td>\n",
              "      <td>19.0</td>\n",
              "      <td>1241.0</td>\n",
              "      <td>244.0</td>\n",
              "      <td>850.0</td>\n",
              "      <td>237.0</td>\n",
              "      <td>2.9375</td>\n",
              "      <td>92568.203125</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-19cf09eb-b3dd-404d-83c4-3e0844ee6d91')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\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",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
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              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert: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-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert: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",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-19cf09eb-b3dd-404d-83c4-3e0844ee6d91 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-19cf09eb-b3dd-404d-83c4-3e0844ee6d91');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\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",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   longitude  latitude  ...  median_income     prediction\n",
              "0    -122.05     37.37  ...         6.6085  343966.093750\n",
              "1    -118.30     34.26  ...         3.5990  188352.859375\n",
              "2    -117.81     33.78  ...         5.7934  261868.187500\n",
              "3    -118.36     33.82  ...         6.1359  326603.593750\n",
              "4    -119.67     36.33  ...         2.9375   92568.203125\n",
              "\n",
              "[5 rows x 9 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **B. Comparing how neural network is better over ordinary least square estimates.**"
      ],
      "metadata": {
        "id": "0CbTLwVi0Xbg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# load numpy and pandas for data manipulation\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import statsmodels.api as sm\n",
        "# load the longley dataset into a pandas data frame - first column (year) used as row labels\n",
        "df = pd.read_csv('https://vincentarelbundock.github.io/Rdatasets/csv/datasets/longley.csv', index_col=0) \n",
        "df.head(3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "id": "mBaIyxRKzjbV",
        "outputId": "e994eddf-da79-4562-e813-3a8eaa4593f2"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-4cccf7f4-789e-44bb-b7fb-ad8641eb1a67\">\n",
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              "<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>GNP.deflator</th>\n",
              "      <th>GNP</th>\n",
              "      <th>Unemployed</th>\n",
              "      <th>Armed.Forces</th>\n",
              "      <th>Population</th>\n",
              "      <th>Year</th>\n",
              "      <th>Employed</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1947</th>\n",
              "      <td>83.0</td>\n",
              "      <td>234.289</td>\n",
              "      <td>235.6</td>\n",
              "      <td>159.0</td>\n",
              "      <td>107.608</td>\n",
              "      <td>1947</td>\n",
              "      <td>60.323</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1948</th>\n",
              "      <td>88.5</td>\n",
              "      <td>259.426</td>\n",
              "      <td>232.5</td>\n",
              "      <td>145.6</td>\n",
              "      <td>108.632</td>\n",
              "      <td>1948</td>\n",
              "      <td>61.122</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1949</th>\n",
              "      <td>88.2</td>\n",
              "      <td>258.054</td>\n",
              "      <td>368.2</td>\n",
              "      <td>161.6</td>\n",
              "      <td>109.773</td>\n",
              "      <td>1949</td>\n",
              "      <td>60.171</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
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              "        const buttonEl =\n",
              "          document.querySelector('#df-4cccf7f4-789e-44bb-b7fb-ad8641eb1a67 button.colab-df-convert');\n",
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              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-4cccf7f4-789e-44bb-b7fb-ad8641eb1a67');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\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",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "      GNP.deflator      GNP  Unemployed  ...  Population  Year  Employed\n",
              "1947          83.0  234.289       235.6  ...     107.608  1947    60.323\n",
              "1948          88.5  259.426       232.5  ...     108.632  1948    61.122\n",
              "1949          88.2  258.054       368.2  ...     109.773  1949    60.171\n",
              "\n",
              "[3 rows x 7 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y = df.Employed  # response\n",
        "X = df.GNP  # predictor\n",
        "X = sm.add_constant(X)  # Adds a constant term to the predictor\n",
        "X.head(3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        },
        "id": "_d-ryFaazogQ",
        "outputId": "a963f3f3-3e79-4a5b-ec0b-0eccf55a373f"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-303e69e2-0fe6-414e-aae8-d094edad74ce\">\n",
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              "      <div>\n",
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              "    .dataframe tbody tr th:only-of-type {\n",
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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>const</th>\n",
              "      <th>GNP</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1947</th>\n",
              "      <td>1.0</td>\n",
              "      <td>234.289</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1948</th>\n",
              "      <td>1.0</td>\n",
              "      <td>259.426</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1949</th>\n",
              "      <td>1.0</td>\n",
              "      <td>258.054</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-303e69e2-0fe6-414e-aae8-d094edad74ce')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\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",
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              "      \n",
              "  <style>\n",
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              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
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              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "\n",
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              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-303e69e2-0fe6-414e-aae8-d094edad74ce button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-303e69e2-0fe6-414e-aae8-d094edad74ce');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\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",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
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              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "      const      GNP\n",
              "1947    1.0  234.289\n",
              "1948    1.0  259.426\n",
              "1949    1.0  258.054"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "est=sm.OLS(y, X)\n",
        "est = est.fit()\n",
        "est.summary()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        },
        "id": "cpCPdEuXzrZt",
        "outputId": "084f1a9c-e748-43ef-fc16-31283132df06"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/scipy/stats/stats.py:1535: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=16\n",
            "  \"anyway, n=%i\" % int(n))\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>        <td>Employed</td>     <th>  R-squared:         </th> <td>   0.967</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.965</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   415.1</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Tue, 18 Jan 2022</td> <th>  Prob (F-statistic):</th> <td>8.36e-12</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>13:39:36</td>     <th>  Log-Likelihood:    </th> <td> -14.904</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>    16</td>      <th>  AIC:               </th> <td>   33.81</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>    14</td>      <th>  BIC:               </th> <td>   35.35</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th> <td>   51.8436</td> <td>    0.681</td> <td>   76.087</td> <td> 0.000</td> <td>   50.382</td> <td>   53.305</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>GNP</th>   <td>    0.0348</td> <td>    0.002</td> <td>   20.374</td> <td> 0.000</td> <td>    0.031</td> <td>    0.038</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td> 1.925</td> <th>  Durbin-Watson:     </th> <td>   1.619</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.382</td> <th>  Jarque-Bera (JB):  </th> <td>   1.215</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td> 0.664</td> <th>  Prob(JB):          </th> <td>   0.545</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 2.759</td> <th>  Cond. No.          </th> <td>1.66e+03</td>\n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.66e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:               Employed   R-squared:                       0.967\n",
              "Model:                            OLS   Adj. R-squared:                  0.965\n",
              "Method:                 Least Squares   F-statistic:                     415.1\n",
              "Date:                Tue, 18 Jan 2022   Prob (F-statistic):           8.36e-12\n",
              "Time:                        13:39:36   Log-Likelihood:                -14.904\n",
              "No. Observations:                  16   AIC:                             33.81\n",
              "Df Residuals:                      14   BIC:                             35.35\n",
              "Df Model:                           1                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const         51.8436      0.681     76.087      0.000      50.382      53.305\n",
              "GNP            0.0348      0.002     20.374      0.000       0.031       0.038\n",
              "==============================================================================\n",
              "Omnibus:                        1.925   Durbin-Watson:                   1.619\n",
              "Prob(Omnibus):                  0.382   Jarque-Bera (JB):                1.215\n",
              "Skew:                           0.664   Prob(JB):                        0.545\n",
              "Kurtosis:                       2.759   Cond. No.                     1.66e+03\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "[2] The condition number is large, 1.66e+03. This might indicate that there are\n",
              "strong multicollinearity or other numerical problems.\n",
              "\"\"\""
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "est.params"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZgspA1a4zwln",
        "outputId": "eb13bbeb-0502-43a8-e9f5-9bf210764d13"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "const    51.843590\n",
              "GNP       0.034752\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Make sure that graphics appear inline in the iPython notebook \n",
        "%pylab inline \n",
        "\n",
        "# We pick 100 hundred points equally spaced from the min to the max \n",
        "X_prime = np.linspace(X.GNP.min(), X.GNP.max(), 100)[:, np.newaxis] \n",
        "X_prime = sm.add_constant(X_prime) \n",
        "\n",
        "# add constant as we did before \n",
        "# Now we calculate the predicted values \n",
        "y_hat = est.predict(X_prime) \n",
        "plt.scatter(X.GNP, y, alpha=0.3) \n",
        "\n",
        "# Plot the raw data \n",
        "plt.xlabel(\"Gross National Product\") \n",
        "plt.ylabel(\"Total Employment\") \n",
        "plt.plot(X_prime[:, 1], y_hat, 'r', alpha=0.9) \n",
        "\n",
        "# Add the regression line, colored in red Populating the interactive namespace from numpy and matplotlib"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        },
        "id": "YGhP_1Eqz0Qj",
        "outputId": "0a5a8ce2-5693-4e65-e20c-7ff70669340f"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Populating the interactive namespace from numpy and matplotlib\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f8dc892ced0>]"
            ]
          },
          "metadata": {},
          "execution_count": 27
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# import formula api as alias smf \n",
        "import statsmodels.formula.api as smf \n",
        "\n",
        "# formula: response ~ predictors \n",
        "est = smf.ols(formula='Employed ~ GNP', data=df).fit() \n",
        "est.summary()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        },
        "id": "JjfNDxjHz4R6",
        "outputId": "5dd6d594-f9aa-43ec-9d47-8742124ec9bd"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/scipy/stats/stats.py:1535: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=16\n",
            "  \"anyway, n=%i\" % int(n))\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>        <td>Employed</td>     <th>  R-squared:         </th> <td>   0.967</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.965</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   415.1</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Tue, 18 Jan 2022</td> <th>  Prob (F-statistic):</th> <td>8.36e-12</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>13:39:36</td>     <th>  Log-Likelihood:    </th> <td> -14.904</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>    16</td>      <th>  AIC:               </th> <td>   33.81</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>    14</td>      <th>  BIC:               </th> <td>   35.35</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Intercept</th> <td>   51.8436</td> <td>    0.681</td> <td>   76.087</td> <td> 0.000</td> <td>   50.382</td> <td>   53.305</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>GNP</th>       <td>    0.0348</td> <td>    0.002</td> <td>   20.374</td> <td> 0.000</td> <td>    0.031</td> <td>    0.038</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td> 1.925</td> <th>  Durbin-Watson:     </th> <td>   1.619</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.382</td> <th>  Jarque-Bera (JB):  </th> <td>   1.215</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td> 0.664</td> <th>  Prob(JB):          </th> <td>   0.545</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 2.759</td> <th>  Cond. No.          </th> <td>1.66e+03</td>\n",
              "</tr>\n",
              "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 1.66e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:               Employed   R-squared:                       0.967\n",
              "Model:                            OLS   Adj. R-squared:                  0.965\n",
              "Method:                 Least Squares   F-statistic:                     415.1\n",
              "Date:                Tue, 18 Jan 2022   Prob (F-statistic):           8.36e-12\n",
              "Time:                        13:39:36   Log-Likelihood:                -14.904\n",
              "No. Observations:                  16   AIC:                             33.81\n",
              "Df Residuals:                      14   BIC:                             35.35\n",
              "Df Model:                           1                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "Intercept     51.8436      0.681     76.087      0.000      50.382      53.305\n",
              "GNP            0.0348      0.002     20.374      0.000       0.031       0.038\n",
              "==============================================================================\n",
              "Omnibus:                        1.925   Durbin-Watson:                   1.619\n",
              "Prob(Omnibus):                  0.382   Jarque-Bera (JB):                1.215\n",
              "Skew:                           0.664   Prob(JB):                        0.545\n",
              "Kurtosis:                       2.759   Cond. No.                     1.66e+03\n",
              "==============================================================================\n",
              "\n",
              "Warnings:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "[2] The condition number is large, 1.66e+03. This might indicate that there are\n",
              "strong multicollinearity or other numerical problems.\n",
              "\"\"\""
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Fit the no-intercept model \n",
        "est_no_int = smf.ols(formula='Employed ~ GNP - 1', data=df).fit() \n",
        "\n",
        "# We pick 100 hundred points equally spaced from the min to the max \n",
        "X_prime_1 = pd.DataFrame({'GNP': np.linspace(X.GNP.min(), X.GNP.max(), 100)}) \n",
        "X_prime_1 = sm.add_constant(X_prime_1) \n",
        "\n",
        "# add constant as we did before \n",
        "y_hat_int = est.predict(X_prime_1) \n",
        "y_hat_no_int = est_no_int.predict(X_prime_1) \n",
        "fig = plt.figure(figsize=(8,4)) \n",
        "splt = plt.subplot(121) \n",
        "splt.scatter(X.GNP, y, alpha=0.3) # Plot the raw data plt.ylim(30, 100) \n",
        "\n",
        "# Set the y-axis to be the same \n",
        "plt.xlabel(\"Gross National Product\") \n",
        "plt.ylabel(\"Total Employment\") \n",
        "plt.title(\"With intercept\") \n",
        "splt.plot(X_prime[:, 1], y_hat_int, 'r', alpha=0.9) # Add the regression line, colored in red \n",
        "splt = plt.subplot(122) \n",
        "splt.scatter(X.GNP, y, alpha=0.3) \n",
        "\n",
        "# Plot the raw data \n",
        "plt.xlabel(\"Gross National Product\") \n",
        "plt.title(\"Without intercept\") \n",
        "splt.plot(X_prime[:, 1], y_hat_no_int, 'r', alpha=0.9) # Add the regression line, colored in red"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "k1cRO0ht0Mxp",
        "outputId": "9b6c217f-085a-4364-b149-11f749dafb51"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f8dc8894850>]"
            ]
          },
          "metadata": {},
          "execution_count": 29
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}