6) Model_Evaluation_and_Refinement_(_Google_Colab_).ipynb

{
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    "kernelspec": {
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      "display_name": "Pyolite",
      "language": "python"
    },
    "colab": {
      "provenance": []
    },
    "widgets": {
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              "widget-interact"
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            "_model_module": "@jupyter-widgets/controls",
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              "IPY_MODEL_1e10b0b931714b39b95a9b914a23325e",
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            ],
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            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "IntSliderView",
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          "model_name": "FloatSliderModel",
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            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
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            "description": "test_data",
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            "_view_name": "OutputView",
            "layout": "IPY_MODEL_c3be4fcf18d04e1c912c351716abebbf",
            "msg_id": "",
            "outputs": [
              {
                "output_type": "display_data",
                "data": {
                  "text/plain": "<Figure size 864x720 with 1 Axes>",
                  "image/png": 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  "nbformat_minor": 0,
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "<center>\n",
        "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Module%205/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\">\n",
        "</center>\n",
        "\n",
        "# Model Evaluation and Refinement\n",
        "\n",
        "Estimated time needed: **30** minutes\n",
        "\n",
        "## Objectives\n",
        "\n",
        "After completing this lab you will be able to:\n",
        "\n",
        "*   Evaluate and refine prediction models\n"
      ],
      "metadata": {
        "id": "wcIKAzFgBuKD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<h2>Table of Contents</h2>\n",
        "<ul>\n",
        "    <li><a href=\"https://#ref1\">Model Evaluation </a></li>\n",
        "    <li><a href=\"https://#ref2\">Over-fitting, Under-fitting and Model Selection </a></li>\n",
        "    <li><a href=\"https://#ref3\">Ridge Regression </a></li>\n",
        "    <li><a href=\"https://#ref4\">Grid Search</a></li>\n",
        "</ul>\n"
      ],
      "metadata": {
        "id": "0a0B2MAhBuLU"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<h4>Setup</h4>\n"
      ],
      "metadata": {
        "tags": [],
        "id": "cP5H8fN3BuLx"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "you are running the lab in your  browser, so we will install the libraries using `piplite`\n"
      ],
      "metadata": {
        "id": "xRVgR0l5BuMt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "If you run the lab locally using Anaconda, you can load the correct library and versions by uncommenting the following:\n"
      ],
      "metadata": {
        "id": "1tFb_bSuBuNy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np"
      ],
      "metadata": {
        "trusted": true,
        "id": "ZeSIaVu1BuOc"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "This function will download the dataset into your browser\n"
      ],
      "metadata": {
        "id": "D3TRAs4QBuOf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This dataset was hosted on IBM Cloud object. Click <a href=\"https://cocl.us/DA101EN_object_storage?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\">HERE</a> for free storage.\n"
      ],
      "metadata": {
        "id": "fPe_isQRBuO-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "path = '/content/sample_data/automobileEDA.csv'\n",
        "df = pd.read_csv(path)"
      ],
      "metadata": {
        "trusted": true,
        "id": "MjWbgy59BuPE"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "you will need to download the dataset; if you are running locally, please comment out the following\n"
      ],
      "metadata": {
        "id": "POZeXvx8BuPG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "df = pd.read_csv(path)"
      ],
      "metadata": {
        "trusted": true,
        "id": "ZR5kZp4HBuPV"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df.to_csv('module_5_auto.csv')"
      ],
      "metadata": {
        "trusted": true,
        "id": "Aq4Xwh8VBuPW"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "First, let's only use numeric data:\n"
      ],
      "metadata": {
        "id": "dBafXKlFBuPY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "df=df._get_numeric_data()\n",
        "df.head()"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "id": "rreJ3gkhBuPn",
        "outputId": "1fee6960-dd32-4fae-e83f-acf9ca8ab010"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   symboling  normalized-losses  wheel-base    length     width  height  \\\n",
              "0          3                122        88.6  0.811148  0.890278    48.8   \n",
              "1          3                122        88.6  0.811148  0.890278    48.8   \n",
              "2          1                122        94.5  0.822681  0.909722    52.4   \n",
              "3          2                164        99.8  0.848630  0.919444    54.3   \n",
              "4          2                164        99.4  0.848630  0.922222    54.3   \n",
              "\n",
              "   curb-weight  engine-size  bore  stroke  compression-ratio  horsepower  \\\n",
              "0         2548          130  3.47    2.68                9.0       111.0   \n",
              "1         2548          130  3.47    2.68                9.0       111.0   \n",
              "2         2823          152  2.68    3.47                9.0       154.0   \n",
              "3         2337          109  3.19    3.40               10.0       102.0   \n",
              "4         2824          136  3.19    3.40                8.0       115.0   \n",
              "\n",
              "   peak-rpm  city-mpg  highway-mpg    price  city-L/100km  diesel  gas  \n",
              "0    5000.0        21           27  13495.0     11.190476       0    1  \n",
              "1    5000.0        21           27  16500.0     11.190476       0    1  \n",
              "2    5000.0        19           26  16500.0     12.368421       0    1  \n",
              "3    5500.0        24           30  13950.0      9.791667       0    1  \n",
              "4    5500.0        18           22  17450.0     13.055556       0    1  "
            ],
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              "\n",
              "  <div id=\"df-9295e21b-1dbe-492b-8887-d035fdb05808\">\n",
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              "<style scoped>\n",
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>symboling</th>\n",
              "      <th>normalized-losses</th>\n",
              "      <th>wheel-base</th>\n",
              "      <th>length</th>\n",
              "      <th>width</th>\n",
              "      <th>height</th>\n",
              "      <th>curb-weight</th>\n",
              "      <th>engine-size</th>\n",
              "      <th>bore</th>\n",
              "      <th>stroke</th>\n",
              "      <th>compression-ratio</th>\n",
              "      <th>horsepower</th>\n",
              "      <th>peak-rpm</th>\n",
              "      <th>city-mpg</th>\n",
              "      <th>highway-mpg</th>\n",
              "      <th>price</th>\n",
              "      <th>city-L/100km</th>\n",
              "      <th>diesel</th>\n",
              "      <th>gas</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>3</td>\n",
              "      <td>122</td>\n",
              "      <td>88.6</td>\n",
              "      <td>0.811148</td>\n",
              "      <td>0.890278</td>\n",
              "      <td>48.8</td>\n",
              "      <td>2548</td>\n",
              "      <td>130</td>\n",
              "      <td>3.47</td>\n",
              "      <td>2.68</td>\n",
              "      <td>9.0</td>\n",
              "      <td>111.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>21</td>\n",
              "      <td>27</td>\n",
              "      <td>13495.0</td>\n",
              "      <td>11.190476</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>3</td>\n",
              "      <td>122</td>\n",
              "      <td>88.6</td>\n",
              "      <td>0.811148</td>\n",
              "      <td>0.890278</td>\n",
              "      <td>48.8</td>\n",
              "      <td>2548</td>\n",
              "      <td>130</td>\n",
              "      <td>3.47</td>\n",
              "      <td>2.68</td>\n",
              "      <td>9.0</td>\n",
              "      <td>111.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>21</td>\n",
              "      <td>27</td>\n",
              "      <td>16500.0</td>\n",
              "      <td>11.190476</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>122</td>\n",
              "      <td>94.5</td>\n",
              "      <td>0.822681</td>\n",
              "      <td>0.909722</td>\n",
              "      <td>52.4</td>\n",
              "      <td>2823</td>\n",
              "      <td>152</td>\n",
              "      <td>2.68</td>\n",
              "      <td>3.47</td>\n",
              "      <td>9.0</td>\n",
              "      <td>154.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>19</td>\n",
              "      <td>26</td>\n",
              "      <td>16500.0</td>\n",
              "      <td>12.368421</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>2</td>\n",
              "      <td>164</td>\n",
              "      <td>99.8</td>\n",
              "      <td>0.848630</td>\n",
              "      <td>0.919444</td>\n",
              "      <td>54.3</td>\n",
              "      <td>2337</td>\n",
              "      <td>109</td>\n",
              "      <td>3.19</td>\n",
              "      <td>3.40</td>\n",
              "      <td>10.0</td>\n",
              "      <td>102.0</td>\n",
              "      <td>5500.0</td>\n",
              "      <td>24</td>\n",
              "      <td>30</td>\n",
              "      <td>13950.0</td>\n",
              "      <td>9.791667</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2</td>\n",
              "      <td>164</td>\n",
              "      <td>99.4</td>\n",
              "      <td>0.848630</td>\n",
              "      <td>0.922222</td>\n",
              "      <td>54.3</td>\n",
              "      <td>2824</td>\n",
              "      <td>136</td>\n",
              "      <td>3.19</td>\n",
              "      <td>3.40</td>\n",
              "      <td>8.0</td>\n",
              "      <td>115.0</td>\n",
              "      <td>5500.0</td>\n",
              "      <td>18</td>\n",
              "      <td>22</td>\n",
              "      <td>17450.0</td>\n",
              "      <td>13.055556</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-9295e21b-1dbe-492b-8887-d035fdb05808')\"\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",
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              "  </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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              "\n",
              "    .colab-df-convert:hover {\n",
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              "      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",
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              "\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-9295e21b-1dbe-492b-8887-d035fdb05808 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-9295e21b-1dbe-492b-8887-d035fdb05808');\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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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Libraries for plotting:\n"
      ],
      "metadata": {
        "id": "pLtO4U9yBuP4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "%%capture\n",
        " !python -m pip install ipywidgets"
      ],
      "metadata": {
        "trusted": true,
        "id": "t8yYcWvMBuP6"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from ipywidgets import interact, interactive, fixed, interact_manual"
      ],
      "metadata": {
        "trusted": true,
        "id": "M37PWc97BuQf"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "<h2>Functions for Plotting</h2>\n"
      ],
      "metadata": {
        "id": "-ObIXApXBuQg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def DistributionPlot(RedFunction, BlueFunction, RedName, BlueName, Title):\n",
        "    width = 12\n",
        "    height = 10\n",
        "    plt.figure(figsize=(width, height))\n",
        "\n",
        "    ax1 = sns.distplot(RedFunction, hist=False, color=\"r\", label=RedName)\n",
        "    ax2 = sns.distplot(BlueFunction, hist=False, color=\"b\", label=BlueName, ax=ax1)\n",
        "\n",
        "    plt.title(Title)\n",
        "    plt.xlabel('Price (in dollars)')\n",
        "    plt.ylabel('Proportion of Cars')\n",
        "\n",
        "    plt.show()\n",
        "    plt.close()"
      ],
      "metadata": {
        "trusted": true,
        "id": "HuI3joxmBuQs"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def PollyPlot(xtrain, xtest, y_train, y_test, lr,poly_transform):\n",
        "    width = 12\n",
        "    height = 10\n",
        "    plt.figure(figsize=(width, height))\n",
        "    \n",
        "    \n",
        "     #training data\n",
        "    \n",
        "     #testing data\n",
        "    \n",
        "     # lr:  linear regression object \n",
        "    \n",
        "     #poly_transform:  polynomial transformation object \n",
        " \n",
        "    xmax=max([xtrain.values.max(), xtest.values.max()])\n",
        "\n",
        "    xmin=min([xtrain.values.min(), xtest.values.min()])\n",
        "\n",
        "    x=np.arange(xmin, xmax, 0.1)\n",
        "\n",
        "\n",
        "    plt.plot(xtrain, y_train, 'ro', label='Training Data')\n",
        "    plt.plot(xtest, y_test, 'go', label='Test Data')\n",
        "    plt.plot(x, lr.predict(poly_transform.fit_transform(x.reshape(-1, 1))), label='Predicted Function')\n",
        "    plt.ylim([-10000, 60000])\n",
        "    plt.ylabel('Price')\n",
        "    plt.legend()"
      ],
      "metadata": {
        "trusted": true,
        "id": "_KtbVjxkBuQz"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "<h2 id=\"ref1\">Part 1: Training and Testing</h2>\n",
        "\n",
        "<p>An important step in testing your model is to split your data into training and testing data. We will place the target data <b>price</b> in a separate dataframe <b>y_data</b>:</p>\n"
      ],
      "metadata": {
        "id": "QqRYdPeaBuRP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y_data = df['price']"
      ],
      "metadata": {
        "trusted": true,
        "id": "SCjKDNSSBuRf"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Drop price data in dataframe **x_data**:\n"
      ],
      "metadata": {
        "id": "spxQVwcPBuRg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_data=df.drop('price',axis=1)"
      ],
      "metadata": {
        "trusted": true,
        "id": "X6-44W1ABuRh"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, we randomly split our data into training and testing data using the function <b>train_test_split</b>.\n"
      ],
      "metadata": {
        "id": "uiJTlhIpBuSB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "\n",
        "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.10, random_state=1)\n",
        "\n",
        "\n",
        "print(\"number of test samples :\", x_test.shape[0])\n",
        "print(\"number of training samples:\",x_train.shape[0])\n"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Wdkt3FvfBuSC",
        "outputId": "54bdc0fc-fbe6-472c-f152-5b7decc9b58d"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "number of test samples : 21\n",
            "number of training samples: 180\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The <b>test_size</b> parameter sets the proportion of data that is split into the testing set. In the above, the testing set is 10% of the total dataset.\n"
      ],
      "metadata": {
        "id": "LiPFo0CKBuSD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
        "<h1> Question  #1):</h1>\n",
        "\n",
        "<b>Use the function \"train_test_split\" to split up the dataset such that 40% of the data samples will be utilized for testing. Set the parameter \"random_state\" equal to zero. The output of the function should be the following:  \"x_train1\" , \"x_test1\", \"y_train1\" and  \"y_test1\".</b>\n",
        "\n",
        "</div>\n"
      ],
      "metadata": {
        "id": "X2LyOPniBuSE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0) \n",
        "print(\"number of test samples :\", x_test1.shape[0])\n",
        "print(\"number of training samples:\",x_train1.shape[0])"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YGy6vp15BuSy",
        "outputId": "75f8ead6-5d0d-41d1-b556-2f0a5b933c23"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "number of test samples : 81\n",
            "number of training samples: 120\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's import <b>LinearRegression</b> from the module <b>linear_model</b>.\n"
      ],
      "metadata": {
        "id": "arI17zFwBuSz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import LinearRegression"
      ],
      "metadata": {
        "trusted": true,
        "id": "jS-GXqCqBuS0"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We create a Linear Regression object:\n"
      ],
      "metadata": {
        "id": "dJq_gy3kBuTt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lre=LinearRegression()"
      ],
      "metadata": {
        "trusted": true,
        "id": "_fVMpogVBuTz"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We fit the model using the feature \"horsepower\":\n"
      ],
      "metadata": {
        "id": "scdQtnf6BuT0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lre.fit(x_train[['horsepower']], y_train)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hf1t7wQKBuT1",
        "outputId": "b0429f0a-2c99-484c-ced5-35c126796d59"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's calculate the R^2 on the test data:\n"
      ],
      "metadata": {
        "id": "TX1HYw4kBuUi"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lre.score(x_test[['horsepower']], y_test)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Dt6L6SRuBuUv",
        "outputId": "b5dd91ac-4502-47a6-a845-5d15719aa6db"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.36358755750788263"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can see the R^2 is much smaller using the test data compared to the training data.\n"
      ],
      "metadata": {
        "id": "M-HzGkViBuUw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lre.score(x_train[['horsepower']], y_train)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ml6BD_ojBuVL",
        "outputId": "2efb57ea-35fb-4f6e-d9de-d382bd8b1069"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.6619724197515104"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
        "<h1> Question  #2): </h1>\n",
        "<b> \n",
        "Find the R^2  on the test data using 40% of the dataset for testing.\n",
        "</b>\n",
        "</div>\n"
      ],
      "metadata": {
        "id": "eJLiaNVpBuVb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0)\n",
        "lre.fit(x_train1[['horsepower']],y_train1)\n",
        "lre.score(x_test1[['horsepower']],y_test1)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ibwbmM0XBuVc",
        "outputId": "514692ea-2e21-4cd5-b4aa-e819ef190d3f"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7139364665406973"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Sometimes you do not have sufficient testing data; as a result, you may want to perform cross-validation. Let's go over several methods that you can use for cross-validation.\n"
      ],
      "metadata": {
        "id": "wJpFR_NJBuV6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<h2>Cross-Validation Score</h2>\n"
      ],
      "metadata": {
        "id": "winCfGK8BuV7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's import <b>model_selection</b> from the module <b>cross_val_score</b>.\n"
      ],
      "metadata": {
        "id": "MhyWHetPBuWP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import cross_val_score"
      ],
      "metadata": {
        "trusted": true,
        "id": "MWsqvhrABuWj"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We input the object, the feature (\"horsepower\"), and the target data (y_data). The parameter 'cv' determines the number of folds. In this case, it is 4.\n"
      ],
      "metadata": {
        "id": "hENMNZUtBuWt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Rcross = cross_val_score(lre, x_data[['horsepower']], y_data, cv=4)"
      ],
      "metadata": {
        "trusted": true,
        "id": "iqGOEQOXBuW6"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The default scoring is R^2. Each element in the array has the average R^2 value for the fold:\n"
      ],
      "metadata": {
        "id": "6f6baYuxBuXI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Rcross"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qPnhlWAaBuXM",
        "outputId": "ed33a4f1-a541-479a-ddcf-a650bdf5ef92"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.7746232 , 0.51716687, 0.74785353, 0.04839605])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can calculate the average and standard deviation of our estimate:\n"
      ],
      "metadata": {
        "id": "xQVETaqvBuXQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"The mean of the folds are\", Rcross.mean(), \"and the standard deviation is\" , Rcross.std())"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IfI0sugcBuXV",
        "outputId": "bcee3ac0-f81c-48e0-d877-f53499e51e71"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The mean of the folds are 0.522009915042119 and the standard deviation is 0.291183944475603\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can use negative squared error as a score by setting the parameter  'scoring' metric to 'neg_mean_squared_error'.\n"
      ],
      "metadata": {
        "id": "l9KWlJTcBuXX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "-1 * cross_val_score(lre,x_data[['horsepower']], y_data,cv=4,scoring='neg_mean_squared_error')"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "U9xgv37JBuXZ",
        "outputId": "140279b8-afdc-4ae5-e043-65b18de6b585"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([20254142.84026702, 43745493.2650517 , 12539630.34014931,\n",
              "       17561927.72247591])"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
        "<h1> Question  #3): </h1>\n",
        "<b> \n",
        "Calculate the average R^2 using two folds, then find the average R^2 for the second fold utilizing the \"horsepower\" feature: \n",
        "</b>\n",
        "</div>\n"
      ],
      "metadata": {
        "id": "jByqYwjYBuXg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Rc=cross_val_score(lre,x_data[['horsepower']], y_data,cv=2)\n",
        "Rc.mean()"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bkOUKnAJBuXh",
        "outputId": "4f54cfa2-d073-46db-ea52-19b9b60bd7d5"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5166761697127429"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "You can also use the function 'cross_val_predict' to predict the output. The function splits up the data into the specified number of folds, with one fold for testing and the other folds are used for training. First, import the function:\n"
      ],
      "metadata": {
        "id": "XNkHnU-pBuXn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import cross_val_predict"
      ],
      "metadata": {
        "trusted": true,
        "id": "gGvIi42WBuXv"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We input the object, the feature <b>\"horsepower\"</b>, and the target data <b>y_data</b>. The parameter 'cv' determines the number of folds. In this case, it is 4. We can produce an output:\n"
      ],
      "metadata": {
        "id": "WeuX5u46BuXw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "yhat = cross_val_predict(lre,x_data[['horsepower']], y_data,cv=4)\n",
        "yhat[0:5]"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1HiaRk1vBuXx",
        "outputId": "f18e03e9-c447-448e-fb2e-122530dc6934"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([14141.63807508, 14141.63807508, 20814.29423473, 12745.03562306,\n",
              "       14762.35027598])"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "<h2 id=\"ref2\">Part 2: Overfitting, Underfitting and Model Selection</h2>\n",
        "\n",
        "<p>It turns out that the test data, sometimes referred to as the \"out of sample data\", is a much better measure of how well your model performs in the real world.  One reason for this is overfitting.\n",
        "\n",
        "Let's go over some examples. It turns out these differences are more apparent in Multiple Linear Regression and Polynomial Regression so we will explore overfitting in that context.</p>\n"
      ],
      "metadata": {
        "id": "OPz30PdZBuXz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's create Multiple Linear Regression objects and train the model using <b>'horsepower'</b>, <b>'curb-weight'</b>, <b>'engine-size'</b> and <b>'highway-mpg'</b> as features.\n"
      ],
      "metadata": {
        "id": "0U6WPaD8BuX_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "lr = LinearRegression()\n",
        "lr.fit(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_train)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MpM-K0lTBuYA",
        "outputId": "1e74e4e0-ae60-40e4-e963-57cf9de0fbc8"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Prediction using training data:\n"
      ],
      "metadata": {
        "id": "p4XobFlABuYQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "yhat_train = lr.predict(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
        "yhat_train[0:5]"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "q9rqxgZUBuYb",
        "outputId": "fa8f46c8-2482-42be-daa9-a845272792ee"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 7426.6731551 , 28323.75090803, 14213.38819709,  4052.34146983,\n",
              "       34500.19124244])"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Prediction using test data:\n"
      ],
      "metadata": {
        "id": "x7kfbeicBuYf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "yhat_test = lr.predict(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
        "yhat_test[0:5]"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "msh2-dVxBuYi",
        "outputId": "0ce81d24-0747-41dd-9789-5a8466167684"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([11349.35089149,  5884.11059106, 11208.6928275 ,  6641.07786278,\n",
              "       15565.79920282])"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's perform some model evaluation using our training and testing data separately. First, we import the seaborn and matplotlib library for plotting.\n"
      ],
      "metadata": {
        "id": "1PPjE1e4BuYt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "import seaborn as sns"
      ],
      "metadata": {
        "trusted": true,
        "id": "fO7f51xpBuYt"
      },
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's examine the distribution of the predicted values of the training data.\n"
      ],
      "metadata": {
        "id": "Z71Z5Ib8BuYy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Title = 'Distribution  Plot of  Predicted Value Using Training Data vs Training Data Distribution'\n",
        "DistributionPlot(y_train, yhat_train, \"Actual Values (Train)\", \"Predicted Values (Train)\", Title)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 714
        },
        "id": "A1kEeNCABuYy",
        "outputId": "38710710-d9f3-460f-89e2-5149dbbb27a2"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.8/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
            "  warnings.warn(msg, FutureWarning)\n",
            "/usr/local/lib/python3.8/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
            "  warnings.warn(msg, FutureWarning)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Figure 1: Plot of predicted values using the training data compared to the actual values of the training data.\n"
      ],
      "metadata": {
        "id": "ErfJz-_pBuY6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "So far, the model seems to be doing well in learning from the training dataset. But what happens when the model encounters new data from the testing dataset? When the model generates new values from the test data, we see the distribution of the predicted values is much different from the actual target values.\n"
      ],
      "metadata": {
        "id": "IzgS4G3OBuY7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n",
        "DistributionPlot(y_test,yhat_test,\"Actual Values (Test)\",\"Predicted Values (Test)\",Title)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 714
        },
        "id": "mvecDRgyBuZF",
        "outputId": "bbfbdf4d-d0a7-46e1-be1f-2985d20446b3"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.8/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
            "  warnings.warn(msg, FutureWarning)\n",
            "/usr/local/lib/python3.8/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
            "  warnings.warn(msg, FutureWarning)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Figure 2: Plot of predicted value using the test data compared to the actual values of the test data.\n"
      ],
      "metadata": {
        "id": "w7u_BtfgBuZH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<p>Comparing Figure 1 and Figure 2, it is evident that the distribution of the test data in Figure 1 is much better at fitting the data. This difference in Figure 2 is apparent in the range of 5000 to 15,000. This is where the shape of the distribution is extremely different. Let's see if polynomial regression also exhibits a drop in the prediction accuracy when analysing the test dataset.</p>\n"
      ],
      "metadata": {
        "id": "MoKq5EmsBuZS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.preprocessing import PolynomialFeatures"
      ],
      "metadata": {
        "trusted": true,
        "id": "pcSAE5w6BuZS"
      },
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "<h4>Overfitting</h4>\n",
        "<p>Overfitting occurs when the model fits the noise, but not the underlying process. Therefore, when testing your model using the test set, your model does not perform as well since it is modelling noise, not the underlying process that generated the relationship. Let's create a degree 5 polynomial model.</p>\n"
      ],
      "metadata": {
        "id": "r7gqhfC5BuZY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's use 55 percent of the data for training and the rest for testing:\n"
      ],
      "metadata": {
        "id": "VMIxVXxgBuZY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.45, random_state=0)"
      ],
      "metadata": {
        "trusted": true,
        "id": "XSOX0tO6BuZZ"
      },
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We will perform a degree 5 polynomial transformation on the feature <b>'horsepower'</b>.\n"
      ],
      "metadata": {
        "id": "4uZpjPwuBuZa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pr = PolynomialFeatures(degree=5)\n",
        "x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
        "x_test_pr = pr.fit_transform(x_test[['horsepower']])\n",
        "pr"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "L2kGhDSuBuZm",
        "outputId": "9fb72b50-028c-4058-8ed2-830f4e58126a"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PolynomialFeatures(degree=5)"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, let's create a Linear Regression model \"poly\" and train it.\n"
      ],
      "metadata": {
        "id": "OLuMpnCvBuZn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "poly = LinearRegression()\n",
        "poly.fit(x_train_pr, y_train)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iGVG9Z_vBuZo",
        "outputId": "b5798d28-a7d4-4ce5-97b9-6ba05663349c"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can see the output of our model using the method \"predict.\" We assign the values to \"yhat\".\n"
      ],
      "metadata": {
        "id": "EMs3wErpBuZq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "yhat = poly.predict(x_test_pr)\n",
        "yhat[0:5]"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b85-JzS-BuZ7",
        "outputId": "553e8f0b-c031-4878-e13f-2c7133891192"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 6728.65561887,  7307.98782321, 12213.78770965, 18893.24804015,\n",
              "       19995.95195136])"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's take the first five predicted values and compare it to the actual targets.\n"
      ],
      "metadata": {
        "id": "qc0yuFDkBuZ_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Predicted values:\", yhat[0:4])\n",
        "print(\"True values:\", y_test[0:4].values)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tLDRbQ9LBuaD",
        "outputId": "829d22c0-89e6-4075-e6b0-54c914d982f7"
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Predicted values: [ 6728.65561887  7307.98782321 12213.78770965 18893.24804015]\n",
            "True values: [ 6295. 10698. 13860. 13499.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We will use the function \"PollyPlot\" that we defined at the beginning of the lab to display the training data, testing data, and the predicted function.\n"
      ],
      "metadata": {
        "id": "fZ79YW7OBuaM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train, y_test, poly,pr)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 595
        },
        "id": "lC2s2rkWBuaN",
        "outputId": "3a39a90a-ee0c-4231-c4bc-bc8cdcbfc023"
      },
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Figure 3: A polynomial regression model where red dots represent training data, green dots represent test data, and the blue line represents the model prediction.\n"
      ],
      "metadata": {
        "id": "3G3Yd3yyBuaO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We see that the estimated function appears to track the data but around 200 horsepower, the function begins to diverge from the data points.\n"
      ],
      "metadata": {
        "id": "opIjFd2mBuaP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "R^2 of the training data:\n"
      ],
      "metadata": {
        "id": "6V04Rv9tBuad"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "poly.score(x_train_pr, y_train)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xwxv8a9oBuax",
        "outputId": "a64ac034-420a-49c1-d78e-f009fcf6bd52"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.556771690212023"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "R^2 of the test data:\n"
      ],
      "metadata": {
        "id": "uDhSzPNTBua2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "poly.score(x_test_pr, y_test)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2IrAT5CFBua2",
        "outputId": "70b0b461-6027-4b12-c56b-862308b2d46c"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-29.87134030204415"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We see the R^2 for the training data is 0.5567 while the R^2 on the test data was -29.87.  The lower the R^2, the worse the model. A negative R^2 is a sign of overfitting.\n"
      ],
      "metadata": {
        "id": "6jnlh_VCBua3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's see how the R^2 changes on the test data for different order polynomials and then plot the results:\n"
      ],
      "metadata": {
        "id": "eWeawoy4BubC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Rsqu_test = []\n",
        "\n",
        "order = [1, 2, 3, 4]\n",
        "for n in order:\n",
        "    pr = PolynomialFeatures(degree=n)\n",
        "    \n",
        "    x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
        "    \n",
        "    x_test_pr = pr.fit_transform(x_test[['horsepower']])    \n",
        "    \n",
        "    lr.fit(x_train_pr, y_train)\n",
        "    \n",
        "    Rsqu_test.append(lr.score(x_test_pr, y_test))\n",
        "\n",
        "plt.plot(order, Rsqu_test)\n",
        "plt.xlabel('order')\n",
        "plt.ylabel('R^2')\n",
        "plt.title('R^2 Using Test Data')\n",
        "plt.text(3, 0.75, 'Maximum R^2 ')    "
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "id": "vDSD5btNBubF",
        "outputId": "98ee320b-0fdf-4b43-e688-9cf5c82f7b4f"
      },
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(3, 0.75, 'Maximum R^2 ')"
            ]
          },
          "metadata": {},
          "execution_count": 43
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We see the R^2 gradually increases until an order three polynomial is used. Then, the R^2 dramatically decreases at an order four polynomial.\n"
      ],
      "metadata": {
        "id": "mBmjqYluBubJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following function will be used in the next section. Please run the cell below.\n"
      ],
      "metadata": {
        "id": "aQsJOskoBubJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def f(order, test_data):\n",
        "    x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=test_data, random_state=0)\n",
        "    pr = PolynomialFeatures(degree=order)\n",
        "    x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
        "    x_test_pr = pr.fit_transform(x_test[['horsepower']])\n",
        "    poly = LinearRegression()\n",
        "    poly.fit(x_train_pr,y_train)\n",
        "    PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train,y_test, poly, pr)"
      ],
      "metadata": {
        "trusted": true,
        "id": "adMxs0gLBubX"
      },
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following interface allows you to experiment with different polynomial orders and different amounts of data.\n"
      ],
      "metadata": {
        "id": "_l4ltgN7BubX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "interact(f, order=(0, 6, 1), test_data=(0.05, 0.95, 0.05))"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 677,
          "referenced_widgets": [
            "f0e8b8ac416b48c78e65c44e4ccac34f",
            "7de09c154c2740109167c6687a64237e",
            "1e10b0b931714b39b95a9b914a23325e",
            "7787db9a20ec47b8a39ccdc5adf618cb",
            "dd7885001d61434a911492729233685f",
            "d92c19d6ca744e1f8771b0c683a38b4a",
            "44aa0be2ecc94b428849717a8cb50d6c",
            "c2d79eff37444b8c8f338fa42d666eb8",
            "a3f58e3d889e43c5848db6290116a356",
            "c3be4fcf18d04e1c912c351716abebbf"
          ]
        },
        "id": "Kb4kOFjKBubc",
        "outputId": "0503da4f-e7fc-4c84-b1fa-e4fb1b8da006"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "interactive(children=(IntSlider(value=3, description='order', max=6), FloatSlider(value=0.45, description='tes…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "f0e8b8ac416b48c78e65c44e4ccac34f"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<function __main__.f(order, test_data)>"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
        "<h1> Question  #4a):</h1>\n",
        "\n",
        "<b>We can perform polynomial transformations with more than one feature. Create a \"PolynomialFeatures\" object \"pr1\" of degree two.</b>\n",
        "\n",
        "</div>\n"
      ],
      "metadata": {
        "id": "0mMNtAPABubf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pr1=PolynomialFeatures(degree=2)\n"
      ],
      "metadata": {
        "trusted": true,
        "id": "LDcKeJNYBubv"
      },
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
        "<h1> Question  #4b): </h1>\n",
        "\n",
        "<b> \n",
        " Transform the training and testing samples for the features 'horsepower', 'curb-weight', 'engine-size' and 'highway-mpg'. Hint: use the method \"fit_transform\".</b>\n",
        "</div>\n"
      ],
      "metadata": {
        "id": "2HIF7G0LBubw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_train_pr1=pr1.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
        "\n",
        "x_test_pr1=pr1.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])"
      ],
      "metadata": {
        "trusted": true,
        "id": "d5MgjQSpBubx"
      },
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "<!-- The answer is below:\n",
        "\n",
        "x_train_pr1=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
        "x_test_pr1=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
        "\n",
        "-->\n"
      ],
      "metadata": {
        "id": "PkZWVybPBuby"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
        "<h1> Question  #4c): </h1>\n",
        "<b> \n",
        "How many dimensions does the new feature have? Hint: use the attribute \"shape\".\n",
        "</b>\n",
        "</div>\n"
      ],
      "metadata": {
        "id": "XZCd9dtZBucC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_train_pr1.shape \n",
        "\n",
        " # There are now 15 features"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BnP3Hu3DBucD",
        "outputId": "75ffc87d-3e4d-46e9-9c76-2a609c7dc93c"
      },
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(110, 15)"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
        "<h1> Question  #4d): </h1>\n",
        "\n",
        "<b> \n",
        "Create a linear regression model \"poly1\". Train the object using the method \"fit\" using the polynomial features.</b>\n",
        "</div>\n"
      ],
      "metadata": {
        "id": "M56CXVsSBucS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "poly1=LinearRegression().fit(x_train_pr1,y_train)"
      ],
      "metadata": {
        "trusted": true,
        "id": "0k9WZ7F1BucT"
      },
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        " <div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
        "<h1> Question  #4e): </h1>\n",
        "<b>Use the method  \"predict\" to predict an output on the polynomial features, then use the function \"DistributionPlot\" to display the distribution of the predicted test output vs. the actual test data.</b>\n",
        "</div>\n"
      ],
      "metadata": {
        "id": "bDit1mVDBucU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "yhat_test1=poly1.predict(x_test_pr1)\n",
        "\n",
        "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n",
        "\n",
        "DistributionPlot(y_test, yhat_test1, \"Actual Values (Test)\", \"Predicted Values (Test)\", Title)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 714
        },
        "id": "DmxxQveSBuc2",
        "outputId": "0249204b-a586-40c2-876a-8584d421deed"
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.8/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
            "  warnings.warn(msg, FutureWarning)\n",
            "/usr/local/lib/python3.8/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
            "  warnings.warn(msg, FutureWarning)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
        "<h1> Question  #4f): </h1>\n",
        "\n",
        "<b>Using the distribution plot above, describe (in words) the two regions where the predicted prices are less accurate than the actual prices.</b>\n",
        "\n",
        "</div>\n"
      ],
      "metadata": {
        "id": "GTydC_kwBuc6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        " # The predicted value is higher than actual value for cars where the price $10,000 range, conversely the predicted price is lower than the price cost in the $30,000 to $40,000 range. \n",
        "    \n",
        "     # As such the model is not as accurate in these ranges.\n"
      ],
      "metadata": {
        "trusted": true,
        "id": "hze4g5HOBuc7"
      },
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "<h2 id=\"ref3\">Part 3: Ridge Regression</h2> \n"
      ],
      "metadata": {
        "id": "KibBwuDSBuc7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this section, we will review Ridge Regression and see how the parameter alpha changes the model. Just a note, here our test data will be used as validation data.\n"
      ],
      "metadata": {
        "id": "PZebhQnbBudb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's perform a degree two polynomial transformation on our data.\n"
      ],
      "metadata": {
        "id": "rfMyQLjUBudb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pr=PolynomialFeatures(degree=2)\n",
        "x_train_pr=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])\n",
        "x_test_pr=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])"
      ],
      "metadata": {
        "trusted": true,
        "id": "X6wG0rFbBudc"
      },
      "execution_count": 52,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's import  <b>Ridge</b>  from the module <b>linear models</b>.\n"
      ],
      "metadata": {
        "id": "QoHo6J8qBudd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.linear_model import Ridge"
      ],
      "metadata": {
        "trusted": true,
        "id": "jDfN4NnwBudk"
      },
      "execution_count": 53,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's create a Ridge regression object, setting the regularization parameter (alpha) to 0.1\n"
      ],
      "metadata": {
        "id": "_8CKmcUUBudl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "RigeModel=Ridge(alpha=1)"
      ],
      "metadata": {
        "trusted": true,
        "id": "_0A2HTgJBudv"
      },
      "execution_count": 54,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Like regular regression, you can fit the model using the method <b>fit</b>.\n"
      ],
      "metadata": {
        "id": "7lF5C-_2Budw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "RigeModel.fit(x_train_pr, y_train)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SdDr2-cVBud9",
        "outputId": "f521815b-f86a-46c4-f147-90156a224635"
      },
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ridge(alpha=1)"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Similarly, you can obtain a prediction:\n"
      ],
      "metadata": {
        "id": "U0S2pDORBud-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "yhat = RigeModel.predict(x_test_pr)"
      ],
      "metadata": {
        "trusted": true,
        "id": "M1gHcO8sBueJ"
      },
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's compare the first five predicted samples to our test set:\n"
      ],
      "metadata": {
        "id": "7PwCB21wBueQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('predicted:', yhat[0:4])\n",
        "print('test set :', y_test[0:4].values)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CuWk789PBueZ",
        "outputId": "71b6834e-521b-4cee-93a4-64a02182bb4a"
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "predicted: [ 6570.82441941  9636.2489147  20949.92322737 19403.60313256]\n",
            "test set : [ 6295. 10698. 13860. 13499.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We select the value of alpha that minimizes the test error. To do so, we can use a for loop. We have also created a progress bar to see how many iterations we have completed so far.\n"
      ],
      "metadata": {
        "id": "yfVNbGF7Bueg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from tqdm import tqdm\n",
        "\n",
        "Rsqu_test = []\n",
        "Rsqu_train = []\n",
        "dummy1 = []\n",
        "Alpha = 10 * np.array(range(0,1000))\n",
        "pbar = tqdm(Alpha)\n",
        "\n",
        "for alpha in pbar:\n",
        "    RigeModel = Ridge(alpha=alpha) \n",
        "    RigeModel.fit(x_train_pr, y_train)\n",
        "    test_score, train_score = RigeModel.score(x_test_pr, y_test), RigeModel.score(x_train_pr, y_train)\n",
        "    \n",
        "    pbar.set_postfix({\"Test Score\": test_score, \"Train Score\": train_score})\n",
        "\n",
        "    Rsqu_test.append(test_score)\n",
        "    Rsqu_train.append(train_score)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lk5H5Wz6Buei",
        "outputId": "61733e17-b51c-42e3-e37d-dae268850fe8"
      },
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 1000/1000 [00:04<00:00, 205.31it/s, Test Score=0.564, Train Score=0.859]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can plot out the value of R^2 for different alphas:\n"
      ],
      "metadata": {
        "id": "a3IealP9Buen"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "width = 12\n",
        "height = 10\n",
        "plt.figure(figsize=(width, height))\n",
        "\n",
        "plt.plot(Alpha,Rsqu_test, label='validation data  ')\n",
        "plt.plot(Alpha,Rsqu_train, 'r', label='training Data ')\n",
        "plt.xlabel('alpha')\n",
        "plt.ylabel('R^2')\n",
        "plt.legend()"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 624
        },
        "id": "ZE-g55DOBuer",
        "outputId": "481865b2-cc98-4a6b-b63f-152008c57184"
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7ff20954ca30>"
            ]
          },
          "metadata": {},
          "execution_count": 59
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Figure 4**: The blue line represents the R^2 of the validation data, and the red line represents the R^2 of the training data. The x-axis represents the different values of Alpha.\n"
      ],
      "metadata": {
        "id": "Y5QsccnNBue1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here the model is built and tested on the same data, so the training and test data are the same.\n",
        "\n",
        "The red line in Figure 4 represents the R^2 of the training data. As alpha increases the R^2 decreases. Therefore, as alpha increases, the model performs worse on the training data\n",
        "\n",
        "The blue line represents the R^2 on the validation data. As the value for alpha increases, the R^2 increases and converges at a point.\n"
      ],
      "metadata": {
        "id": "8Oo7zVeQBue2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
        "<h1> Question  #5): </h1>\n",
        "\n",
        "Perform Ridge regression. Calculate the R^2 using the polynomial features, use the training data to train the model and use the test data to test the model. The parameter alpha should be set to 10.\n",
        "\n",
        "</div>\n"
      ],
      "metadata": {
        "id": "-A125kOkBue2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "RigeModel = Ridge(alpha=10) \n",
        "RigeModel.fit(x_train_pr, y_train)\n",
        "RigeModel.score(x_test_pr, y_test)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5TVf0GS9Bue3",
        "outputId": "d9118209-6909-4701-88d0-47a5495901fa"
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5418576440206702"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "<h2 id=\"ref4\">Part 4: Grid Search</h2>\n"
      ],
      "metadata": {
        "id": "bSOsRZZGBufB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The term alpha is a hyperparameter. Sklearn has the class <b>GridSearchCV</b> to make the process of finding the best hyperparameter simpler.\n"
      ],
      "metadata": {
        "id": "Vb6zvEqJBufI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's import <b>GridSearchCV</b> from  the module <b>model_selection</b>.\n"
      ],
      "metadata": {
        "id": "-VmrGOtmBufI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import GridSearchCV"
      ],
      "metadata": {
        "trusted": true,
        "id": "EN2ICYaPBufK"
      },
      "execution_count": 61,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We create a dictionary of parameter values:\n"
      ],
      "metadata": {
        "id": "V2e3CSycBufL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "parameters1= [{'alpha': [0.001,0.1,1, 10, 100, 1000, 10000, 100000, 100000]}]\n",
        "parameters1"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7Hjf7kRHBufR",
        "outputId": "496b744f-2cff-417a-aff8-a3d5a9ac641d"
      },
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000, 100000]}]"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Create a Ridge regression object:\n"
      ],
      "metadata": {
        "id": "pdYoQrRJBufS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "RR=Ridge()\n",
        "RR"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jBKkle85Bufb",
        "outputId": "02a7e8ed-46bc-4ab0-b948-33bf04539feb"
      },
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ridge()"
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Create a ridge grid search object:\n"
      ],
      "metadata": {
        "id": "MSXtwIxrBufc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Grid1 = GridSearchCV(RR, parameters1,cv=4)"
      ],
      "metadata": {
        "trusted": true,
        "id": "riFK8oUOBuff"
      },
      "execution_count": 64,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "Fit the model:\n"
      ],
      "metadata": {
        "id": "eHtOcjepBufj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Grid1.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_data)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AWf5PIEtBufn",
        "outputId": "8c5b825f-91d8-4aa0-c620-5cd71082b970"
      },
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "GridSearchCV(cv=4, estimator=Ridge(),\n",
              "             param_grid=[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000,\n",
              "                                    100000]}])"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The object finds the best parameter values on the validation data. We can obtain the estimator with the best parameters and assign it to the variable BestRR as follows:\n"
      ],
      "metadata": {
        "id": "jEbRqF5UBufo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "BestRR=Grid1.best_estimator_\n",
        "BestRR"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8ft2qywcBufp",
        "outputId": "3b6fa6b7-5cc4-4e82-8b70-e092bd0ae130"
      },
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ridge(alpha=10000)"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We now test our model on the test data:\n"
      ],
      "metadata": {
        "id": "zKlLPmbwBufr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "BestRR.score(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_test)"
      ],
      "metadata": {
        "trusted": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DcpkXynmBuf6",
        "outputId": "fed5e002-d114-45d0-8a91-dc7994d277b4"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8411649831036151"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Thank you for completing this lab!\n",
        "\n",
        "## Author\n",
        "\n",
        "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Joseph Santarcangelo</a>\n",
        "\n",
        "### Other Contributors\n",
        "\n",
        "<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
        "\n",
        "Bahare Talayian\n",
        "\n",
        "Eric Xiao\n",
        "\n",
        "Steven Dong\n",
        "\n",
        "Parizad\n",
        "\n",
        "Hima Vasudevan\n",
        "\n",
        "<a href=\"https://www.linkedin.com/in/fiorellawever/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Fiorella Wenver</a>\n",
        "\n",
        "<a href=\"https:// https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
        "\n",
        "## Change Log\n",
        "\n",
        "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                  |\n",
        "| ----------------- | ------- | ---------- | ----------------------------------- |\n",
        "| 2022-08-23        | 2.4     | Malika     | Updated packages by adding keep_going=True |\n",
        "| 2020-10-30        | 2.3     | Lakshmi    | Changed URL of csv                  |\n",
        "| 2020-10-05        | 2.2     | Lakshmi    | Removed unused library imports      |\n",
        "| 2020-09-14        | 2.1     | Lakshmi    | Made changes in OverFitting section |\n",
        "| 2020-08-27        | 2.0     | Lavanya    | Moved lab to course repo in GitLab  |\n",
        "\n",
        "<hr>\n",
        "\n",
        "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
      ],
      "metadata": {
        "id": "sD7kibwcBuf7"
      }
    }
  ]
}