IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork_labs_jupyterlite_files_DA0101EN-5-Review-Model-Evaluation-and-Refinement-20230323-1679529600.ipynb

{
  "metadata": {
    "kernelspec": {
      "name": "python",
      "display_name": "Pyolite",
      "language": "python"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "python",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8"
    }
  },
  "nbformat_minor": 4,
  "nbformat": 4,
  "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\nEstimated time needed: **30** minutes\n\n## Objectives\n\nAfter completing this lab you will be able to:\n\n*   Evaluate and refine prediction models\n",
      "metadata": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h4>Setup</h4>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "you are running the lab in your  browser, so we will install the libraries using `piplite`\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "#you are running the lab in your  browser, so we will install the libraries using ``piplite``\nimport piplite\nimport micropip\nawait piplite.install(['pandas'])\nawait piplite.install(['matplotlib'])\nawait piplite.install(['scipy'])\nawait piplite.install(['seaborn'])\nawait micropip.install(['ipywidgets'],keep_going=True)\nawait micropip.install(['tqdm'],keep_going=True)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "#install specific version of libraries used in lab\n#! mamba install pandas==1.3.3 -y\n#! mamba install numpy=1.21.2 -y\n#! mamba install sklearn=0.20.1 -y\n#! mamba install   ipywidgets=7.4.2 -y\n#! mamba install tqdm",
      "metadata": {
        "trusted": true
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "import pandas as pd\nimport numpy as np",
      "metadata": {
        "trusted": true
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "This function will download the dataset into your browser\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "#This function will download the dataset into your browser \n\nfrom pyodide.http import pyfetch\n\nasync def download(url, filename):\n    response = await pyfetch(url)\n    if response.status == 200:\n        with open(filename, \"wb\") as f:\n            f.write(await response.bytes())",
      "metadata": {
        "trusted": true
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "import pandas as pd\nimport numpy as np\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "path = 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/module_5_auto.csv'",
      "metadata": {
        "trusted": true
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "you will need to download the dataset; if you are running locally, please comment out the following\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "#you will need to download the dataset; if you are running locally, please comment out the following \nawait download(path, \"auto.csv\")\npath=\"auto.csv\"",
      "metadata": {
        "trusted": true
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "\ndf = pd.read_csv(path)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "df.to_csv('module_5_auto.csv')",
      "metadata": {
        "trusted": true
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "First, let's only use numeric data:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "df=df._get_numeric_data()\ndf.head()",
      "metadata": {
        "trusted": true
      },
      "execution_count": 10,
      "outputs": [
        {
          "execution_count": 10,
          "output_type": "execute_result",
          "data": {
            "text/plain": "   Unnamed: 0.1  Unnamed: 0  symboling  normalized-losses  wheel-base  \\\n0             0           0          3                122        88.6   \n1             1           1          3                122        88.6   \n2             2           2          1                122        94.5   \n3             3           3          2                164        99.8   \n4             4           4          2                164        99.4   \n\n     length     width  height  curb-weight  engine-size  ...  stroke  \\\n0  0.811148  0.890278    48.8         2548          130  ...    2.68   \n1  0.811148  0.890278    48.8         2548          130  ...    2.68   \n2  0.822681  0.909722    52.4         2823          152  ...    3.47   \n3  0.848630  0.919444    54.3         2337          109  ...    3.40   \n4  0.848630  0.922222    54.3         2824          136  ...    3.40   \n\n   compression-ratio  horsepower  peak-rpm  city-mpg  highway-mpg    price  \\\n0                9.0       111.0    5000.0        21           27  13495.0   \n1                9.0       111.0    5000.0        21           27  16500.0   \n2                9.0       154.0    5000.0        19           26  16500.0   \n3               10.0       102.0    5500.0        24           30  13950.0   \n4                8.0       115.0    5500.0        18           22  17450.0   \n\n   city-L/100km  diesel  gas  \n0     11.190476       0    1  \n1     11.190476       0    1  \n2     12.368421       0    1  \n3      9.791667       0    1  \n4     13.055556       0    1  \n\n[5 rows x 21 columns]",
            "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Unnamed: 0.1</th>\n      <th>Unnamed: 0</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>...</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>0</td>\n      <td>0</td>\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>...</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>1</td>\n      <td>1</td>\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>...</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>2</td>\n      <td>2</td>\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>...</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>3</td>\n      <td>3</td>\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>...</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>4</td>\n      <td>4</td>\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>...</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<p>5 rows × 21 columns</p>\n</div>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Libraries for plotting:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from ipywidgets import interact, interactive, fixed, interact_manual",
      "metadata": {
        "trusted": true
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "<h2>Functions for Plotting</h2>\n",
      "metadata": {}
    },
    {
      "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
      },
      "execution_count": 12,
      "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    #testing data \n    # lr:  linear regression object \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
      },
      "execution_count": 13,
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "y_data = df['price']",
      "metadata": {
        "trusted": true
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Drop price data in dataframe **x_data**:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "x_data=df.drop('price',axis=1)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 15,
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.model_selection import train_test_split\n\n\nx_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.10, random_state=1)\n\n\nprint(\"number of test samples :\", x_test.shape[0])\nprint(\"number of training samples:\",x_train.shape[0])\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 16,
      "outputs": [
        {
          "name": "stdout",
          "text": "number of test samples : 21\nnumber of training samples: 180\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "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": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nx_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0) \nprint(\"number of test samples :\", x_test1.shape[0])\nprint(\"number of training samples:\",x_train1.shape[0])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 17,
      "outputs": [
        {
          "name": "stdout",
          "text": "number of test samples : 81\nnumber of training samples: 120\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nx_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0) \nprint(\"number of test samples :\", x_test1.shape[0])\nprint(\"number of training samples:\",x_train1.shape[0])\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's import <b>LinearRegression</b> from the module <b>linear_model</b>.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.linear_model import LinearRegression",
      "metadata": {
        "trusted": true
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We create a Linear Regression object:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lre=LinearRegression()",
      "metadata": {
        "trusted": true
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We fit the model using the feature \"horsepower\":\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lre.fit(x_train[['horsepower']], y_train)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 20,
      "outputs": [
        {
          "execution_count": 20,
          "output_type": "execute_result",
          "data": {
            "text/plain": "LinearRegression()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Let's calculate the R^2 on the test data:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lre.score(x_test[['horsepower']], y_test)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 21,
      "outputs": [
        {
          "execution_count": 21,
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.3635875575078824"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can see the R^2 is much smaller using the test data compared to the training data.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "lre.score(x_train[['horsepower']], y_train)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 22,
      "outputs": [
        {
          "execution_count": 22,
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.6619724197515103"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1> Question  #2): </h1>\n<b> \nFind the R^2  on the test data using 40% of the dataset for testing.\n</b>\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nx_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0)\nlre.fit(x_train1[['horsepower']],y_train1)\nlre.score(x_test1[['horsepower']],y_test1)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 23,
      "outputs": [
        {
          "execution_count": 23,
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.7139364665406973"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nx_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0)\nlre.fit(x_train1[['horsepower']],y_train1)\nlre.score(x_test1[['horsepower']],y_test1)\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2>Cross-Validation Score</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's import <b>model_selection</b> from the module <b>cross_val_score</b>.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.model_selection import cross_val_score",
      "metadata": {
        "trusted": true
      },
      "execution_count": 24,
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "Rcross = cross_val_score(lre, x_data[['horsepower']], y_data, cv=4)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 25,
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "Rcross",
      "metadata": {
        "trusted": true
      },
      "execution_count": 26,
      "outputs": [
        {
          "execution_count": 26,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([0.7746232 , 0.51716687, 0.74785353, 0.04839605])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can calculate the average and standard deviation of our estimate:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "print(\"The mean of the folds are\", Rcross.mean(), \"and the standard deviation is\" , Rcross.std())",
      "metadata": {
        "trusted": true
      },
      "execution_count": 27,
      "outputs": [
        {
          "name": "stdout",
          "text": "The mean of the folds are 0.5220099150421197 and the standard deviation is 0.29118394447560203\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "-1 * cross_val_score(lre,x_data[['horsepower']], y_data,cv=4,scoring='neg_mean_squared_error')",
      "metadata": {
        "trusted": true
      },
      "execution_count": 28,
      "outputs": [
        {
          "execution_count": 28,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([20254142.84026702, 43745493.26505171, 12539630.34014929,\n       17561927.72247586])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1> Question  #3): </h1>\n<b> \nCalculate 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": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nRc=cross_val_score(lre,x_data[['horsepower']], y_data,cv=2)\nRc.mean()",
      "metadata": {
        "trusted": true
      },
      "execution_count": 29,
      "outputs": [
        {
          "execution_count": 29,
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.5166761697127429"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nRc=cross_val_score(lre,x_data[['horsepower']], y_data,cv=2)\nRc.mean()\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.model_selection import cross_val_predict",
      "metadata": {
        "trusted": true
      },
      "execution_count": 30,
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "yhat = cross_val_predict(lre,x_data[['horsepower']], y_data,cv=4)\nyhat[0:5]",
      "metadata": {
        "trusted": true
      },
      "execution_count": 31,
      "outputs": [
        {
          "execution_count": 31,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([14141.63807508, 14141.63807508, 20814.29423473, 12745.03562306,\n       14762.35027598])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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\nLet'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": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "lr = LinearRegression()\nlr.fit(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_train)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 32,
      "outputs": [
        {
          "execution_count": 32,
          "output_type": "execute_result",
          "data": {
            "text/plain": "LinearRegression()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Prediction using training data:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "yhat_train = lr.predict(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\nyhat_train[0:5]",
      "metadata": {
        "trusted": true
      },
      "execution_count": 33,
      "outputs": [
        {
          "execution_count": 33,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([ 7426.6731551 , 28323.75090803, 14213.38819709,  4052.34146983,\n       34500.19124244])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Prediction using test data:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "yhat_test = lr.predict(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\nyhat_test[0:5]",
      "metadata": {
        "trusted": true
      },
      "execution_count": 34,
      "outputs": [
        {
          "execution_count": 34,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([11349.35089149,  5884.11059106, 11208.6928275 ,  6641.07786278,\n       15565.79920282])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "import matplotlib.pyplot as plt\n%matplotlib inline\nimport seaborn as sns",
      "metadata": {
        "trusted": true
      },
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Let's examine the distribution of the predicted values of the training data.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "import matplotlib.pyplot as plt\nimport seaborn as sns\n\nsns.displot(y_train, kde=True, color=\"r\", label=\"Actual Values (Train)\")\nsns.displot(yhat_train, kde=True, color=\"b\", label=\"Predicted Values (Train)\")\nplt.title(\"Distribution Plot of Predicted Value Using Training Data vs Training Data Distribution\")\nplt.xlabel(\"Values\")\nplt.legend()\nplt.show()\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x6639478>",
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 500x500 with 1 Axes>",
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 500x500 with 0 Axes>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "import seaborn as sns\nimport matplotlib.pyplot as plt\n\ndef DistributionPlot(y_test, yhat_test, ActualName, PredictName, Title):\n    sns.displot(y_test, color=\"r\", label=ActualName)\n    sns.displot(yhat_test, color=\"b\", label=PredictName)\n    plt.title(Title)\n    plt.legend()\n    plt.show()\n\nTitle='Distribution Plot of Predicted Values Using Test Data vs Data Distribution of Test Data'\nDistributionPlot(y_test, yhat_test, \"Actual Values (Test)\", \"Predicted Values (Test)\", Title)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x681a140>",
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 500x500 with 1 Axes>",
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 500x500 with 0 Axes>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.preprocessing import PolynomialFeatures",
      "metadata": {
        "trusted": true
      },
      "execution_count": 42,
      "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": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's use 55 percent of the data for training and the rest for testing:\n",
      "metadata": {}
    },
    {
      "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
      },
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We will perform a degree 5 polynomial transformation on the feature <b>'horsepower'</b>.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "pr = PolynomialFeatures(degree=5)\nx_train_pr = pr.fit_transform(x_train[['horsepower']])\nx_test_pr = pr.fit_transform(x_test[['horsepower']])\npr",
      "metadata": {
        "trusted": true
      },
      "execution_count": 44,
      "outputs": [
        {
          "execution_count": 44,
          "output_type": "execute_result",
          "data": {
            "text/plain": "PolynomialFeatures(degree=5)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Now, let's create a Linear Regression model \"poly\" and train it.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "poly = LinearRegression()\npoly.fit(x_train_pr, y_train)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 45,
      "outputs": [
        {
          "execution_count": 45,
          "output_type": "execute_result",
          "data": {
            "text/plain": "LinearRegression()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can see the output of our model using the method \"predict.\" We assign the values to \"yhat\".\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "yhat = poly.predict(x_test_pr)\nyhat[0:5]",
      "metadata": {
        "trusted": true
      },
      "execution_count": 46,
      "outputs": [
        {
          "execution_count": 46,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([ 6728.58641321,  7307.91998787, 12213.73753589, 18893.37919224,\n       19996.10612156])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Let's take the first five predicted values and compare it to the actual targets.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "print(\"Predicted values:\", yhat[0:4])\nprint(\"True values:\", y_test[0:4].values)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 47,
      "outputs": [
        {
          "name": "stdout",
          "text": "Predicted values: [ 6728.58641321  7307.91998787 12213.73753589 18893.37919224]\nTrue values: [ 6295. 10698. 13860. 13499.]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train, y_test, poly,pr)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 1200x1000 with 1 Axes>",
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "ename": "<class 'pandas.errors.InvalidIndexError'>",
          "evalue": "(slice(None, None, None), None)",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "File \u001b[0;32m/lib/python3.10/site-packages/pandas/core/indexes/base.py:3621\u001b[0m, in \u001b[0;36mIndex.get_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m   3620\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m-> 3621\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_engine\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_loc\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcasted_key\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   3622\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mKeyError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m err:\n",
            "File \u001b[0;32m/lib/python3.10/site-packages/pandas/_libs/index.pyx:136\u001b[0m, in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
            "File \u001b[0;32m/lib/python3.10/site-packages/pandas/_libs/index.pyx:142\u001b[0m, in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
            "\u001b[0;31mTypeError\u001b[0m: '(slice(None, None, None), None)' is an invalid key",
            "\nDuring handling of the above exception, another exception occurred:\n",
            "\u001b[0;31mInvalidIndexError\u001b[0m                         Traceback (most recent call last)",
            "Cell \u001b[0;32mIn[48], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mPollyPlot\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx_train\u001b[49m\u001b[43m[\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mhorsepower\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx_test\u001b[49m\u001b[43m[\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mhorsepower\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my_train\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my_test\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mpoly\u001b[49m\u001b[43m,\u001b[49m\u001b[43mpr\u001b[49m\u001b[43m)\u001b[49m\n",
            "Cell \u001b[0;32mIn[13], line 19\u001b[0m, in \u001b[0;36mPollyPlot\u001b[0;34m(xtrain, xtest, y_train, y_test, lr, poly_transform)\u001b[0m\n\u001b[1;32m     14\u001b[0m xmin\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mmin\u001b[39m([xtrain\u001b[38;5;241m.\u001b[39mvalues\u001b[38;5;241m.\u001b[39mmin(), xtest\u001b[38;5;241m.\u001b[39mvalues\u001b[38;5;241m.\u001b[39mmin()])\n\u001b[1;32m     16\u001b[0m x\u001b[38;5;241m=\u001b[39mnp\u001b[38;5;241m.\u001b[39marange(xmin, xmax, \u001b[38;5;241m0.1\u001b[39m)\n\u001b[0;32m---> 19\u001b[0m \u001b[43mplt\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mplot\u001b[49m\u001b[43m(\u001b[49m\u001b[43mxtrain\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my_train\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mro\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlabel\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mTraining Data\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m     20\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(xtest, y_test, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mgo\u001b[39m\u001b[38;5;124m'\u001b[39m, label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mTest Data\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m     21\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(x, lr\u001b[38;5;241m.\u001b[39mpredict(poly_transform\u001b[38;5;241m.\u001b[39mfit_transform(x\u001b[38;5;241m.\u001b[39mreshape(\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m1\u001b[39m))), label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mPredicted Function\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
            "File \u001b[0;32m/lib/python3.10/site-packages/matplotlib/pyplot.py:2757\u001b[0m, in \u001b[0;36mplot\u001b[0;34m(scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   2755\u001b[0m \u001b[38;5;129m@_copy_docstring_and_deprecators\u001b[39m(Axes\u001b[38;5;241m.\u001b[39mplot)\n\u001b[1;32m   2756\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mplot\u001b[39m(\u001b[38;5;241m*\u001b[39margs, scalex\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, scaley\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, data\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[0;32m-> 2757\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m gca()\u001b[38;5;241m.\u001b[39mplot(\n\u001b[1;32m   2758\u001b[0m         \u001b[38;5;241m*\u001b[39margs, scalex\u001b[38;5;241m=\u001b[39mscalex, scaley\u001b[38;5;241m=\u001b[39mscaley,\n\u001b[1;32m   2759\u001b[0m         \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m({\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdata\u001b[39m\u001b[38;5;124m\"\u001b[39m: data} \u001b[38;5;28;01mif\u001b[39;00m data \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;28;01melse\u001b[39;00m {}), \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
            "File \u001b[0;32m/lib/python3.10/site-packages/matplotlib/axes/_axes.py:1632\u001b[0m, in \u001b[0;36mAxes.plot\u001b[0;34m(self, scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1390\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m   1391\u001b[0m \u001b[38;5;124;03mPlot y versus x as lines and/or markers.\u001b[39;00m\n\u001b[1;32m   1392\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   1629\u001b[0m \u001b[38;5;124;03m(``'green'``) or hex strings (``'#008000'``).\u001b[39;00m\n\u001b[1;32m   1630\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m   1631\u001b[0m kwargs \u001b[38;5;241m=\u001b[39m cbook\u001b[38;5;241m.\u001b[39mnormalize_kwargs(kwargs, mlines\u001b[38;5;241m.\u001b[39mLine2D)\n\u001b[0;32m-> 1632\u001b[0m lines \u001b[38;5;241m=\u001b[39m [\u001b[38;5;241m*\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_lines(\u001b[38;5;241m*\u001b[39margs, data\u001b[38;5;241m=\u001b[39mdata, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)]\n\u001b[1;32m   1633\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m line \u001b[38;5;129;01min\u001b[39;00m lines:\n\u001b[1;32m   1634\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39madd_line(line)\n",
            "File \u001b[0;32m/lib/python3.10/site-packages/matplotlib/axes/_base.py:312\u001b[0m, in \u001b[0;36m_process_plot_var_args.__call__\u001b[0;34m(self, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m    310\u001b[0m     this \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m args[\u001b[38;5;241m0\u001b[39m],\n\u001b[1;32m    311\u001b[0m     args \u001b[38;5;241m=\u001b[39m args[\u001b[38;5;241m1\u001b[39m:]\n\u001b[0;32m--> 312\u001b[0m \u001b[38;5;28;01myield from\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_plot_args\u001b[49m\u001b[43m(\u001b[49m\u001b[43mthis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
            "File \u001b[0;32m/lib/python3.10/site-packages/matplotlib/axes/_base.py:487\u001b[0m, in \u001b[0;36m_process_plot_var_args._plot_args\u001b[0;34m(self, tup, kwargs, return_kwargs)\u001b[0m\n\u001b[1;32m    484\u001b[0m         kw[prop_name] \u001b[38;5;241m=\u001b[39m val\n\u001b[1;32m    486\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(xy) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m2\u001b[39m:\n\u001b[0;32m--> 487\u001b[0m     x \u001b[38;5;241m=\u001b[39m \u001b[43m_check_1d\u001b[49m\u001b[43m(\u001b[49m\u001b[43mxy\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    488\u001b[0m     y \u001b[38;5;241m=\u001b[39m _check_1d(xy[\u001b[38;5;241m1\u001b[39m])\n\u001b[1;32m    489\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
            "File \u001b[0;32m/lib/python3.10/site-packages/matplotlib/cbook/__init__.py:1327\u001b[0m, in \u001b[0;36m_check_1d\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m   1321\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m warnings\u001b[38;5;241m.\u001b[39mcatch_warnings(record\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m) \u001b[38;5;28;01mas\u001b[39;00m w:\n\u001b[1;32m   1322\u001b[0m     warnings\u001b[38;5;241m.\u001b[39mfilterwarnings(\n\u001b[1;32m   1323\u001b[0m         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124malways\u001b[39m\u001b[38;5;124m\"\u001b[39m,\n\u001b[1;32m   1324\u001b[0m         category\u001b[38;5;241m=\u001b[39m\u001b[38;5;167;01mWarning\u001b[39;00m,\n\u001b[1;32m   1325\u001b[0m         message\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mSupport for multi-dimensional indexing\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m-> 1327\u001b[0m     ndim \u001b[38;5;241m=\u001b[39m \u001b[43mx\u001b[49m\u001b[43m[\u001b[49m\u001b[43m:\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mNone\u001b[39;49;00m\u001b[43m]\u001b[49m\u001b[38;5;241m.\u001b[39mndim\n\u001b[1;32m   1328\u001b[0m     \u001b[38;5;66;03m# we have definitely hit a pandas index or series object\u001b[39;00m\n\u001b[1;32m   1329\u001b[0m     \u001b[38;5;66;03m# cast to a numpy array.\u001b[39;00m\n\u001b[1;32m   1330\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(w) \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m0\u001b[39m:\n",
            "File \u001b[0;32m/lib/python3.10/site-packages/pandas/core/frame.py:3505\u001b[0m, in \u001b[0;36mDataFrame.__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m   3503\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcolumns\u001b[38;5;241m.\u001b[39mnlevels \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m   3504\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_getitem_multilevel(key)\n\u001b[0;32m-> 3505\u001b[0m indexer \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcolumns\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_loc\u001b[49m\u001b[43m(\u001b[49m\u001b[43mkey\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   3506\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m is_integer(indexer):\n\u001b[1;32m   3507\u001b[0m     indexer \u001b[38;5;241m=\u001b[39m [indexer]\n",
            "File \u001b[0;32m/lib/python3.10/site-packages/pandas/core/indexes/base.py:3628\u001b[0m, in \u001b[0;36mIndex.get_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m   3623\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mKeyError\u001b[39;00m(key) \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01merr\u001b[39;00m\n\u001b[1;32m   3624\u001b[0m     \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m:\n\u001b[1;32m   3625\u001b[0m         \u001b[38;5;66;03m# If we have a listlike key, _check_indexing_error will raise\u001b[39;00m\n\u001b[1;32m   3626\u001b[0m         \u001b[38;5;66;03m#  InvalidIndexError. Otherwise we fall through and re-raise\u001b[39;00m\n\u001b[1;32m   3627\u001b[0m         \u001b[38;5;66;03m#  the TypeError.\u001b[39;00m\n\u001b[0;32m-> 3628\u001b[0m         \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_check_indexing_error\u001b[49m\u001b[43m(\u001b[49m\u001b[43mkey\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   3629\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m\n\u001b[1;32m   3631\u001b[0m \u001b[38;5;66;03m# GH#42269\u001b[39;00m\n",
            "File \u001b[0;32m/lib/python3.10/site-packages/pandas/core/indexes/base.py:5637\u001b[0m, in \u001b[0;36mIndex._check_indexing_error\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m   5633\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_check_indexing_error\u001b[39m(\u001b[38;5;28mself\u001b[39m, key):\n\u001b[1;32m   5634\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m is_scalar(key):\n\u001b[1;32m   5635\u001b[0m         \u001b[38;5;66;03m# if key is not a scalar, directly raise an error (the code below\u001b[39;00m\n\u001b[1;32m   5636\u001b[0m         \u001b[38;5;66;03m# would convert to numpy arrays and raise later any way) - GH29926\u001b[39;00m\n\u001b[0;32m-> 5637\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m InvalidIndexError(key)\n",
            "\u001b[0;31mInvalidIndexError\u001b[0m: (slice(None, None, None), None)"
          ],
          "output_type": "error"
        }
      ]
    },
    {
      "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": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "markdown",
      "source": "R^2 of the training data:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "poly.score(x_train_pr, y_train)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 49,
      "outputs": [
        {
          "execution_count": 49,
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.5567716897754004"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "R^2 of the test data:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "poly.score(x_test_pr, y_test)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 50,
      "outputs": [
        {
          "execution_count": 50,
          "output_type": "execute_result",
          "data": {
            "text/plain": "-29.87099623387278"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "Rsqu_test = []\n\norder = [1, 2, 3, 4]\nfor 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\nplt.plot(order, Rsqu_test)\nplt.xlabel('order')\nplt.ylabel('R^2')\nplt.title('R^2 Using Test Data')\nplt.text(3, 0.75, 'Maximum R^2 ')    ",
      "metadata": {
        "trusted": true
      },
      "execution_count": 51,
      "outputs": [
        {
          "execution_count": 51,
          "output_type": "execute_result",
          "data": {
            "text/plain": "Text(3, 0.75, 'Maximum R^2 ')"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 640x480 with 1 Axes>",
            "image/png": 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"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": {}
    },
    {
      "cell_type": "markdown",
      "source": "The following function will be used in the next section. Please run the cell below.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.preprocessing import PolynomialFeatures\nfrom sklearn.linear_model import LinearRegression\n\n# Generate some sample data\nx = np.linspace(0, 10, 100)\ny = np.sin(x) + np.random.normal(0, 0.1, size=len(x))\n\n# Split data into training and test sets\nx_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n\n# Create polynomial features for training and test sets\npoly = PolynomialFeatures(degree=2)\nX_train_poly = poly.fit_transform(x_train.reshape(-1, 1))\nX_test_poly = poly.transform(x_test.reshape(-1, 1))\n\n# Fit linear regression model to training data\nlin_reg = LinearRegression()\nlin_reg.fit(X_train_poly, y_train)\n\n# Predict on test data and calculate R^2 score\ny_pred = lin_reg.predict(X_test_poly)\nr2_score = lin_reg.score(X_test_poly, y_test)\n\n# Plot the test data and polynomial fit\nplt.scatter(x_test, y_test)\nplt.plot(x_test, y_pred, color='red')\nplt.title(f\"Polynomial Regression (degree=2)\\nTest R^2 score: {r2_score:.2f}\")\nplt.show()\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x66a2588>",
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 640x480 with 0 Axes>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": "import matplotlib.pyplot as plt\ndef f(order, test_data):\n    x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n    # Create polynomial features for training and test sets\n    poly = PolynomialFeatures(degree=2)\n    X_train_poly = poly.fit_transform(x_train.reshape(-1, 1))\n    X_test_poly = poly.transform(x_test.reshape(-1, 1))\n\n    # Fit linear regression model to training data\n    lin_reg = LinearRegression()\n    lin_reg.fit(X_train_poly, y_train)\n\n    # Predict on test data and calculate R^2 score\n    y_pred = lin_reg.predict(X_test_poly)\n    r2_score = lin_reg.score(X_test_poly, y_test)\n\n    # Plot the test data and polynomial fit\n    plt.scatter(x_test, y_test)\n    plt.plot(x_test, y_pred, color='red')\n    plt.title(f\"Polynomial Regression (degree=2)\\nTest R^2 score: {r2_score:.2f}\")\n    plt.show()\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 53,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "The following interface allows you to experiment with different polynomial orders and different amounts of data.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "interact(f, order=(0, 6, 1), test_data=(0.05, 0.95, 0.05))",
      "metadata": {
        "trusted": true
      },
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x7bd1520>",
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "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": "3d65b408de584e83985060af35585421"
            }
          },
          "metadata": {}
        },
        {
          "execution_count": 54,
          "output_type": "execute_result",
          "data": {
            "text/plain": "<function __main__.f(order, test_data)>"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 640x480 with 0 Axes>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nfrom sklearn.preprocessing import PolynomialFeatures\n\npr1 = PolynomialFeatures(degree=2)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\npr1=PolynomialFeatures(degree=2)\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \n# Assuming that you have imported the necessary libraries and read the dataset into a variable named 'df'\n\n# Split the data into training and testing sets\nfrom sklearn.model_selection import train_test_split\nX = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]\ny = df['price']\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)\n\n# Create a PolynomialFeatures object of degree two\nfrom sklearn.preprocessing import PolynomialFeatures\npr1 = PolynomialFeatures(degree=2)\n\n# Transform the training data\nX_train_pr = pr1.fit_transform(X_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n\n# Transform the testing data\nX_test_pr = pr1.fit_transform(X_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nx_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.2, random_state=0)\n\nx_train_pr1=pr1.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n\nx_test_pr1=pr1.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<!-- The answer is below:\n\nx_train_pr1=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\nx_test_pr1=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n\n-->\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1> Question  #4c): </h1>\n<b> \nHow many dimensions does the new feature have? Hint: use the attribute \"shape\".\n</b>\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nX_train_pr.shape[1]\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 60,
      "outputs": [
        {
          "execution_count": 60,
          "output_type": "execute_result",
          "data": {
            "text/plain": "15"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nx_train_pr1.shape #there are now 15 features\n\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1> Question  #4d): </h1>\n\n<b> \nCreate a linear regression model \"poly1\". Train the object using the method \"fit\" using the polynomial features.</b>\n</div>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \n# import LinearRegression\nfrom sklearn.linear_model import LinearRegression\n\n# create a linear regression object\npoly1 = LinearRegression()\n\n# train the model using the training data with polynomial features\npoly1.fit(X_train_pr, y_train)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 61,
      "outputs": [
        {
          "execution_count": 61,
          "output_type": "execute_result",
          "data": {
            "text/plain": "LinearRegression()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\npoly1=LinearRegression().fit(x_train_pr1,y_train)\n\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \n# Transform the testing data using the existing polynomial features object \"pr1\"\nX_test_poly = pr1.transform(X_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n\n# Predict the output on the polynomial features\nyhat_test_poly = poly1.predict(X_test_poly)\n\n# Display the distribution plot of predicted test output vs actual test data\nTitle = 'Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\nDistributionPlot(y_test, yhat_test_poly, \"Actual Values (Test)\", \"Predicted Values (Test)\", Title)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x8827028>",
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 500x500 with 1 Axes>",
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 500x500 with 0 Axes>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nyhat_test1=poly1.predict(x_test_pr1)\n\nTitle='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n\nDistributionPlot(y_test, yhat_test1, \"Actual Values (Test)\", \"Predicted Values (Test)\", Title)\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \n#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. As such the model is not as accurate in these ranges.\nprint(\"predicted values:\", yhat[0:4])\nprint(\"True values:\", y_test[0:4].values)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 65,
      "outputs": [
        {
          "name": "stdout",
          "text": "predicted values: [ 6728.58641321  7307.91998787 12213.73753589 18893.37919224]\nTrue values: [ 6295. 10698. 13860. 13499.]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nprint(\"predicted values:\",yhat[0:4])\nprint(\"True values:\",y_test[0:4].values)\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2 id=\"ref3\">Part 3: Ridge Regression</h2> \n",
      "metadata": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's perform a degree two polynomial transformation on our data.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "pr=PolynomialFeatures(degree=2)\nfrom sklearn.preprocessing import PolynomialFeatures\n\npoly = PolynomialFeatures(degree=2)\nX_train_poly = poly.fit_transform(X_train)\nX_test_poly = poly.transform(X_test)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 67,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Let's import  <b>Ridge</b>  from the module <b>linear models</b>.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.linear_model import Ridge",
      "metadata": {
        "trusted": true
      },
      "execution_count": 68,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Let's create a Ridge regression object, setting the regularization parameter (alpha) to 0.1\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "RigeModel=Ridge(alpha=1)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 69,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Like regular regression, you can fit the model using the method <b>fit</b>.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.linear_model import Ridge\n\n# Create a Ridge regression object with alpha=0.1\nridge = Ridge(alpha=0.1)\n\n# Fit the model to the training data\nridge.fit(X_train_poly, y_train)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 76,
      "outputs": [
        {
          "name": "stderr",
          "text": "/lib/python3.10/site-packages/sklearn/linear_model/_ridge.py:157: LinAlgWarning: Ill-conditioned matrix (rcond=7.29129e-17): result may not be accurate.\n  return linalg.solve(A, Xy, sym_pos=True, overwrite_a=True).T\n",
          "output_type": "stream"
        },
        {
          "execution_count": 76,
          "output_type": "execute_result",
          "data": {
            "text/plain": "Ridge(alpha=0.1)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Similarly, you can obtain a prediction:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "X_test = X_test.reset_index(drop=True)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 77,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Let's compare the first five predicted samples to our test set:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "print('predicted:', yhat[0:4])\nprint('test set :', y_test[0:4].values)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 78,
      "outputs": [
        {
          "name": "stdout",
          "text": "predicted: [ 6728.58641321  7307.91998787 12213.73753589 18893.37919224]\ntest set : [ 6295. 10698. 13860. 13499.]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.metrics import mean_squared_error\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 81,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We can plot out the value of R^2 for different alphas:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.preprocessing import PolynomialFeatures\n\n# Define degree of polynomial features\ndegree = 2\n\n# Create a PolynomialFeatures object\npoly_features = PolynomialFeatures(degree=degree)\n\n# Transform the validation data to polynomial features\nX_val_poly = poly_features.fit_transform\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 86,
      "outputs": []
    },
    {
      "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": {}
    },
    {
      "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\nThe 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\nThe 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": {}
    },
    {
      "cell_type": "markdown",
      "source": "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n<h1> Question  #5): </h1>\n\nPerform 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": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute \nfrom sklearn.linear_model import Ridge\nfrom sklearn.metrics import r2_score\nfrom sklearn.preprocessing import PolynomialFeatures\nimport numpy as np\n\n# Create polynomial features\npoly = PolynomialFeatures(degree=2)\nX_train_poly = poly.fit_transform(X_train)\nX_test_poly = poly.transform(X_test)\n\n# Create Ridge regression object with alpha=10\nridge = Ridge(alpha=10)\n\n# Fit the model to the training data\nridge.fit(X_train_poly, y_train)\n\n# Make predictions on the test data\ny_pred = ridge.predict(X_test_poly)\n\n# Calculate the R^2 score on the test data\nr2 = r2_score(y_test, y_pred)\nprint(\"R^2 score on test data:\", r2)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 87,
      "outputs": [
        {
          "name": "stdout",
          "text": "R^2 score on test data: 0.7500742509959217\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nRigeModel = Ridge(alpha=10) \nRigeModel.fit(x_train_pr, y_train)\nRigeModel.score(x_test_pr, y_test)\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2 id=\"ref4\">Part 4: Grid Search</h2>\n",
      "metadata": {}
    },
    {
      "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": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's import <b>GridSearchCV</b> from  the module <b>model_selection</b>.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "from sklearn.model_selection import GridSearchCV",
      "metadata": {
        "trusted": true
      },
      "execution_count": 88,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We create a dictionary of parameter values:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "parameters1= [{'alpha': [0.001,0.1,1, 10, 100, 1000, 10000, 100000, 100000]}]\nparameters1",
      "metadata": {
        "trusted": true
      },
      "execution_count": 89,
      "outputs": [
        {
          "execution_count": 89,
          "output_type": "execute_result",
          "data": {
            "text/plain": "[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000, 100000]}]"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Create a Ridge regression object:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "RR=Ridge()\nRR",
      "metadata": {
        "trusted": true
      },
      "execution_count": 90,
      "outputs": [
        {
          "execution_count": 90,
          "output_type": "execute_result",
          "data": {
            "text/plain": "Ridge()"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Create a ridge grid search object:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Grid1 = GridSearchCV(RR, parameters1,cv=4)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 91,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "\nFit the model:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Grid1.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_data)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 92,
      "outputs": [
        {
          "execution_count": 92,
          "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": {}
        }
      ]
    },
    {
      "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": {}
    },
    {
      "cell_type": "code",
      "source": "BestRR=Grid1.best_estimator_\nBestRR",
      "metadata": {
        "trusted": true
      },
      "execution_count": 93,
      "outputs": [
        {
          "execution_count": 93,
          "output_type": "execute_result",
          "data": {
            "text/plain": "Ridge(alpha=10000)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We now test our model on the test data:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "BestRR.score(x_test, y_test)",
      "metadata": {},
      "execution_count": null,
      "outputs": []
    },
    {
      "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\">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\">Mahdi Noorian PhD</a>\n\nBahare Talayian\n\nEric Xiao\n\nSteven Dong\n\nParizad\n\nHima 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\">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| 2023-09-09        | 2.5     | Nafisa Idris  | Updated the code and answered the questions and pushed the changes to the relevant Github repository |\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": {}
    }
  ]
}