c07-data-analysis-with-python/res/5-Review-Model-Evaluation-and-Refinement.ipynb

{
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    "kernelspec": {
      "name": "python",
      "display_name": "Pyolite",
      "language": "python"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "python",
        "version": 3
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      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8"
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    "metadata": {
      "interpreter": {
        "hash": "ac2eaa0ea0ebeafcc7822e65e46aa9d4f966f30b695406963e145ea4a91cd4fc"
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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\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\nawait piplite.install(['pandas'])\nawait piplite.install(['matplotlib'])\nawait piplite.install(['scipy'])\nawait piplite.install(['seaborn'])\nawait piplite.install(['ipywidgets'])\nawait piplite.install(['tqdm'])",
      "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": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "import pandas as pd\nimport numpy as np",
      "metadata": {
        "trusted": true
      },
      "execution_count": 2,
      "outputs": [
        {
          "name": "stderr",
          "text": "/lib/python3.9/site-packages/pandas/compat/__init__.py:124: UserWarning: Could not import the lzma module. Your installed Python is incomplete. Attempting to use lzma compression will result in a RuntimeError.\n  warnings.warn(msg)\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "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": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "import pandas as pd\nimport numpy as np\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 4,
      "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": 5,
      "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": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "\ndf = pd.read_csv(path)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "df.to_csv('module_5_auto.csv')",
      "metadata": {
        "trusted": true
      },
      "execution_count": 8,
      "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": 9,
      "outputs": [
        {
          "execution_count": 9,
          "output_type": "execute_result",
          "data": {
            "text/plain": "   Unnamed: 0  Unnamed: 0.1  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</th>\n      <th>Unnamed: 0.1</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": 10,
      "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": 11,
      "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": 12,
      "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": 13,
      "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": 14,
      "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": 15,
      "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=0.40, 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=0.40, random_state=0)\nlre.fit(x_train1[['horsepower']], y_train1)\nlre.score(x_test1[['horsepower']], y_test1)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 24,
      "outputs": [
        {
          "execution_count": 24,
          "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": 25,
      "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": 26,
      "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": 27,
      "outputs": [
        {
          "execution_count": 27,
          "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": 28,
      "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": 29,
      "outputs": [
        {
          "execution_count": 29,
          "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 \nRcross1 = cross_val_score(lre, x_data[['horsepower']], y_data, cv=2)\nprint(Rcross1)\nprint(\"The mean of the folds are\", Rcross1.mean(), \"and the standard deviation is\" , Rcross1.std())",
      "metadata": {
        "trusted": true
      },
      "execution_count": 30,
      "outputs": [
        {
          "name": "stdout",
          "text": "[0.59015621 0.44319613]\nThe mean of the folds are 0.5166761697127429 and the standard deviation is 0.07348004195771385\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "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": 31,
      "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": 32,
      "outputs": [
        {
          "execution_count": 32,
          "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": 33,
      "outputs": [
        {
          "execution_count": 33,
          "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": 34,
      "outputs": [
        {
          "execution_count": 34,
          "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": 35,
      "outputs": [
        {
          "execution_count": 35,
          "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": 36,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Let's examine the distribution of the predicted values of the training data.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "Title = 'Distribution  Plot of  Predicted Value Using Training Data vs Training Data Distribution'\nDistributionPlot(y_train, yhat_train, \"Actual Values (Train)\", \"Predicted Values (Train)\", Title)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 37,
      "outputs": [
        {
          "name": "stderr",
          "text": "/lib/python3.9/site-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/lib/python3.9/site-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": "stream"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x4fb4728>",
            "image/png": 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"
          },
          "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": "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\nDistributionPlot(y_test,yhat_test,\"Actual Values (Test)\",\"Predicted Values (Test)\",Title)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 38,
      "outputs": [
        {
          "name": "stderr",
          "text": "/lib/python3.9/site-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/lib/python3.9/site-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": "stream"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x55d57b0>",
            "image/png": 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"
          },
          "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": 39,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "<h4>Overfitting</h4>\n<p><b>Overfitting occurs when the model fits the noise</b>, 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": 40,
      "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": 41,
      "outputs": [
        {
          "execution_count": 41,
          "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": 42,
      "outputs": [
        {
          "execution_count": 42,
          "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": 43,
      "outputs": [
        {
          "execution_count": 43,
          "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": 44,
      "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": 45,
      "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": {}
    },
    {
      "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": 46,
      "outputs": [
        {
          "execution_count": 46,
          "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": 47,
      "outputs": [
        {
          "execution_count": 47,
          "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": 48,
      "outputs": [
        {
          "execution_count": 48,
          "output_type": "execute_result",
          "data": {
            "text/plain": "Text(3, 0.75, 'Maximum R^2 ')"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": 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bOGNUPw7t35NbH1/UohtSWv5ygTCzNiGJ684YwYp3N/PgrOVpx7E24AJhZm1m/Ig+jB20Dz96opotLXhGieUnFwgzazOSuH7CCN6s3cJ9Ly5LO47tIRcIM2tTxw3rzTFD9uW2JxezeZt7EYUspwVC0pmSFkiqlnRDA+O/Iml28jNXUr2kfZszrZnlr+vPGMk7G7byi7/XpB3F9kDOCoSkYuA24CxgFHCppFHZbSLiexExJiLGADcCT0fE2uZMa2b566iKfTlpRB9uf3oxG7bWpR3HWimXPYhxQHVELImIbcD9wPm7aX8pcF8rpzWzPHPdhBG8u2k79zy3NO0o1kq5LBD9gexr3VYkwz5EUlfgTOB3rZh2kqQqSVWrV6/e49Bm1jbGDOzF6R/px50zllC7eXvacawV8uUk9bnAcxGxtqUTRsSdEVEZEZV9+vTJQTQza63rJoxg/ZY67npmSdpRrBVyWSBWAgOz3g9IhjXkEv55eKml05pZnhp1YA/OPvQAfvZcDWs3bks7jrVQLgvETGC4pMGSysgUgUd3bSSpJ3Ay8PuWTmtm+e9Lpw9n47Y67pixOO0o1kI5KxARUQdMAR4D5gMPRMQ8SZMlTc5q+nFgakRsbGraXGU1s9wZ3q875x9+ID//Ww2r3tuSdhxrAXWkh41XVlZGVVVV2jHMbBdL39nI6Tc9zaePHcQ3zh2ddhzLImlWRFQ2NC5fTlKbWQc2uHc5nzyyP796YRlv1m5OO441kwuEmbWLq08dTkRw25PVaUexZnKBMLN2MXDfrlx81EB+M3M5y9duSjuONYMLhJm1mymnDEcSP3xiUdpRrBlcIMys3ezfszOXHz2I3720kqXvbGx6AkuVC4SZtavPjx9KWXERt05fmHYUa4ILhJm1qz7dO/Hp4wbx+zlvsOjt99KOY7vhAmFm7W7ySUMpLyvhZvci8poLhJm1u33Ky7ji+Ar+/OpbzHujNu041ggXCDNLxWdPHEKPziXcPM29iHzlAmFmqejZpZRJJw1h+vxVzF6+Lu041gAXCDNLzWeOH8w+XUu5yb2IvOQCYWap6daphM+PH8qMhauZWdPi54VZjrlAmFmq/uWYCvp078R/PraAjnR36Y7ABcLMUtWlrJirxg/lhaVr+dviNWnHsSwuEGaWukvGHcQBPTvz/anuReQTFwgzS13n0mKmnDqMl5at46mFq9OOYwkXCDPLCxeNHcjAfbtw09SF7kXkCRcIM8sLZSVFXHPqcF5dWcvUf7yddhzDBcLM8sjHj+jPkN7l3DxtITt2uBeRNhcIM8sbJcVFfPH04bz21nv86dU3046z18tpgZB0pqQFkqol3dBIm/GSZkuaJ+nprOE1kl5NxlXlMqeZ5Y9zDzuQEf26cfP0hdTV70g7zl4tZwVCUjFwG3AWMAq4VNKoXdr0An4MnBcRo4GLdpnNKRExJiIqc5XTzPJLUZG4bsIIlqzeyO9nv5F2nL1aLnsQ44DqiFgSEduA+4Hzd2nzKeChiFgGEBGrcpjHzArER0fvz+gDe3Dr44vY7l5EanJZIPoDy7Per0iGZRsB7CPpKUmzJH06a1wAU5PhkxpbiKRJkqokVa1e7eunzToCKdOLWLZ2E7+btSLtOHuttE9SlwBjgbOBjwJfkzQiGXdCRBxJ5hDVVZJOamgGEXFnRFRGRGWfPn3aJbSZ5d6pB/dlzMBe/ODxRWytq087zl4plwViJTAw6/2AZFi2FcBjEbExIt4BZgCHA0TEyuT3KuBhMoeszGwvIYnrzxjBG7Vb+M3M5U1PYG0ulwViJjBc0mBJZcAlwKO7tPk9cIKkEkldgaOB+ZLKJXUHkFQOnAHMzWFWM8tDJwzrzbjB+/KjJ6rZst29iPaWswIREXXAFOAxYD7wQETMkzRZ0uSkzXzgr8ArwIvATyNiLtAPeFbSnGT4nyLir7nKamb5SRLXTxjBqve2cu/zr6cdZ6+jjnTPk8rKyqiq8lcmzDqay3/6AvPfXM+Mr55CeaeStON0KJJmNfZVgrRPUpuZNem6M0awZuM27vlbTdpR9iouEGaW9448aB9OPbgvd85Ywvot29OOs9dwgTCzgnDdhBHUbt7OXc8sTTvKXsMFwswKwiH9e3Lm6P352bNLWbdpW9px9gouEGZWMK6dMIIN2+q4c8aStKPsFVwgzKxgjNy/O+cediB3P1fDOxu2ph2nw3OBMLOC8sXTh7O1rp7bn1qcdpQOzwXCzArK0D7d+PgRA/jl86/z9votacfp0FwgzKzgfPG04dTvCG57sjrtKB2aC4SZFZyD9uvKRZUDue/FZax4d1PacTosFwgzK0hXnzoMIX70hHsRueICYWYF6cBeXfjU0Qfx4KwVvL5mY9pxOiQXCDMrWF8YP5SSInHr44vSjtIhuUCYWcHq26MzE4+r4JGXV1K9akPacTocFwgzK2hXnjSEzqXF3DJ9YdpROhwXCDMraPt168QVxw/mj6+8yfw316cdp0NxgTCzgvffTxxC984l3DzNvYi25AJhZgWvZ9dSPnfCEKb+421eXVGbdpwOwwXCzDqEK06ooFfXUr4/bUHaUToMFwgz6xC6dy7lypOG8tSC1cx6fW3acTqEnBYISWdKWiCpWtINjbQZL2m2pHmSnm7JtGZm2SYeN4je3cr4/lSfi2gLOSsQkoqB24CzgFHApZJG7dKmF/Bj4LyIGA1c1Nxpzcx21bWshM+PH8bfFq/h74vXpB2n4OWyBzEOqI6IJRGxDbgfOH+XNp8CHoqIZQARsaoF05qZfchlRx9Evx6duGnaAiIi7TgFLZcFoj+wPOv9imRYthHAPpKekjRL0qdbMC0AkiZJqpJUtXr16jaKbmaFqnNpMVNOHc7MmneZseidtOMUtLRPUpcAY4GzgY8CX5M0oiUziIg7I6IyIir79OmTi4xmVmAurhxI/15duGmqexF7IpcFYiUwMOv9gGRYthXAYxGxMSLeAWYAhzdzWjOzBpWVFHHNacOYs6KW6fNXNT2BNSiXBWImMFzSYEllwCXAo7u0+T1wgqQSSV2Bo4H5zZzWzKxRnzhyABX7deWmaQvZscO9iNbIWYGIiDpgCvAYmZ3+AxExT9JkSZOTNvOBvwKvAC8CP42IuY1Nm6usZtbxlBYX8cXThzP/zfX8dd5baccpSOpIx+cqKyujqqoq7RhmlifqdwQfvWUGAI996SSKi5RyovwjaVZEVDY0Lu2T1GZmOVNcJK49fQTVqzbwhzlvpB2n4LhAmFmHdtYh+3Pw/t25ZfpC6up3pB2noLhAmFmHVlQkrj9jJDVrNvHQS74YsiV2WyAkFUu6UtK3JB2/y7j/ldtoZmZt4/SP9OXwAT259fFFbKtzL6K5mupB3AGcDKwBfiDppqxxn8hZKjOzNiSJ684Yycp1m/lN1fKmJzCg6QIxLiI+FRG3kPmOQjdJD0nqBPhyADMrGCcN703loH247YlqtmyvTztOQWiqQJTtfBERdRExCZgNPAF0y2EuM7M2lelFjOCt9Vv49QvL0o5TEJoqEFWSzsweEBH/DtwNVOQqlJlZLhw3tDfHDd2PHz9VzaZtdWnHyXu7LRARcXlE/LWB4T+NiNLcxTIzy43rzxjBOxu28Yu/v552lLzXrMtckwf4mJkVvLGD9mX8yD7c/vRi3tuyPe04ea3JAiGpO5mb6pmZdQjXTRjBuk3bufu5mrSj5LWmvgdxADAduLN94piZ5d5hA3oxYVQ/fvLMEmo3uRfRmKZ6EM8A34kI32rbzDqU6yaM4L0tdfzkmSVpR8lbTRWId2nkUZ9mZoXsIwf04OzDDuDu55ayZsPWtOPkpaYKxHjgLElXtUMWM7N2de3pw9m8vZ47ZrgX0ZCmLnPdCJwHHNE+cczM2s+wvt25YEx/fvH3Gla9tyXtOHmnyauYIqI+Ij7XHmHMzNrbNacNZ3t98OMnF6cdJe+06nbfkookXdbWYczM2ltF73IuGjuAX7+wjDfWbU47Tl5p6jLXHpJulPQjSWco42pgCfDf2ieimVluTTl1GEHwoyer046SV5rqQfwSGAm8CnwOeBK4ELggIs7PcTYzs3YxYJ+uXHLUQTwwcznL1mxKO07eaKpADImIz0TEHcClwCjgoxExO+fJzMza0ZRTh1FcJH7wxKK0o+SNpgrE+18xjIh6YEVENPtUv6QzJS2QVC3phgbGj5dUK2l28vP1rHE1kl5Nhlc1d5lmZq3Rr0dnLj9mEA+9tIIlqzekHScvNFUgDpe0Pvl5Dzhs52tJ63c3YXKDv9uAs8j0PC6VNKqBps9ExJjk5993GXdKMryyuStkZtZanx8/lE4lxdwy3b0IaPp7EMUR0SP56R4RJVmvezQx73FAdUQsiYhtwP2Az1uYWd7q3a0Tnzm+gj+88gYL3nov7Tipa9Vlrs3UH8h++OsKGr5tx7GS5kj6i6TRWcMDmCpplqRJjS1E0iRJVZKqVq9e3TbJzWyvNenEIZSXlXDL9IVpR0ldLgtEc7wEDIqIw4EfAo9kjTshIo4kc4jqKkknNTSDiLgzIiojorJPnz45D2xmHds+5WV89oTB/GXuW8xdWZt2nFTlskCsBAZmvR+QDHtfRKyPiA3J6z8DpZJ6J+9XJr9XAQ+TOWRlZpZznz1xMD27lHLztL27F5HLAjETGC5psKQy4BLgA7cNl7S/JCWvxyV51kgqTx5UhKRy4Axgbg6zmpm9r0fnUiadNITHX1vFS8veTTtOanJWICKiDpgCPAbMBx6IiHmSJkuanDS7EJgraQ7wA+CSiAigH/BsMvxF4E8NPRvbzCxXPnNcBfuWl+3VvQhl9scdQ2VlZVRV+SsTZtY2fjJjCd/+83x+M+kYjh6yX9pxckLSrMa+SpD2SWozs7x1+TGD6Nu9E9+ftpCO9GG6uVwgzMwa0aWsmKtOGcaLS9fyXPWatOO0OxcIM7PduGTcQA7s2Zn/nLpgr+tFuECYme1Gp5Jirj5tOLOXr+PJBavSjtOuXCDMzJpw4dgBHLRvV74/de86F+ECYWbWhNLiIr542nDmvbGex+a9lXacduMCYWbWDBcc0Z8hfcq5adpC6nfsHb0IFwgzs2YoLhJfOn0EC9/ewB9feSPtOO3CBcLMrJnOOfQARvbrzq3TF1FXvyPtODnnAmFm1kxFReLaCSNY8s5GHpnd8XsRLhBmZi3w0dH9OKR/D259fCHbO3gvwgXCzKwFJHH9hJEsX7uZB6tWpB0np1wgzMxaaPzIPhxxUC9++MQitmyvTztOzrhAmJm1kCS+fMZI3qzdwv0vLks7Ts64QJiZtcJxQ/fj6MH7cttTi9m8rWP2IlwgzMxaQRLXnzGS1e9t5ZfP16QdJydcIMzMWmnc4H05cXhvbn96CRu21qUdp825QJiZ7YHrzxjJ2o3b+PnfatKO0uZcIMzM9sCYgb04/SN9uePpxdRu3p52nDblAmFmtoeunTCC9VvquOvZpWlHaVM5LRCSzpS0QFK1pBsaGD9eUq2k2cnP15s7rZlZvhh9YE/OOmR/fvbsUt7duC3tOG0mZwVCUjFwG3AWMAq4VNKoBpo+ExFjkp9/b+G0ZmZ54doJI9i4rY47ZixJO0qbyWUPYhxQHRFLImIbcD9wfjtMa2bW7kb06855hx/Iz/9Ww+r3tqYdp03kskD0B5ZnvV+RDNvVsZLmSPqLpNEtnNbMLG988bThbKvfwX89tTjtKG0i7ZPULwGDIuJw4IfAIy2dgaRJkqokVa1evbqt85mZNduQPt34xBH9ufeF13mrdkvacfZYLgvESmBg1vsBybD3RcT6iNiQvP4zUCqpd3OmzZrHnRFRGRGVffr0acv8ZmYtds1pw9mxI/jRk4vSjrLHclkgZgLDJQ2WVAZcAjya3UDS/pKUvB6X5FnTnGnNzPLRwH27cvFRA/nNzOWseHdT2nH2SM4KRETUAVOAx4D5wAMRMU/SZEmTk2YXAnMlzQF+AFwSGQ1Om6usZmZtacqpw5DEDx+vTjvKHlFEpJ2hzVRWVkZVVVXaMczM+Oaj8/jl86/z+HUnU9G7PO04jZI0KyIqGxqX9klqM7MO6QunDKW0WNz6eOGei3CBMDPLgb7dOzPx2Aoemb2SRW+/l3acVnGBMDPLkStPHkrX0mJumV6YvQgXCDOzHNm3vIwrThjMn159k3+8sT7tOC3mAmFmlkOfO2EI3TuXcNO0hWlHaTEXCDOzHOrZtZRJJw5h+vy3mbN8XdpxWsQFwswsx/71hMHs07W04HoRLhBmZjnWrVMJk08eytMLV1NVszbtOM3mAmFm1g4+fWwFvbt14vtTC6cX4QJhZtYOupQV84XxQ/n7kjX8rfqdtOM0iwuEmVk7+dTRB7F/j858f9pCCuE2Ry4QZmbtpHNpMVNOHcas19/l6YX5//waFwgzs3b03yoHMmCfLtxUAL0IFwgzs3ZUVlLENacN55UVtUz7x9tpx9ktFwgzs3b2iSP6M7h3OTdNW8iOHfnbi3CBMDNrZyXFRXzp9OG89tZ7/Hnum2nHaZQLhJlZCs457ECG9+3GzdMWUp+nvQgXCDOzFBQXiWsnjGDx6o38fvbKtOM0yAXCzCwlZ47en1EH9ODWxxexvX5H2nE+xAXCzCwlRUXiugkjeH3NJn43a0XacT7EBcLMLEWnfaQvhw/sxQ+fqGZrXX3acT4gpwVC0pmSFkiqlnTDbtodJalO0oVZw2okvSpptqSqXOY0M0uLJK6fMIKV6zbzwMzlacf5gJwVCEnFwG3AWcAo4FJJoxpp9x/A1AZmc0pEjImIylzlNDNL24nDe3NUxT788IlqtmzPn15ELnsQ44DqiFgSEduA+4HzG2h3NfA7YFUOs5iZ5S1JXH/GSFa9t5V7n3897Tjvy2WB6A9k95dWJMPeJ6k/8HHgvxqYPoCpkmZJmtTYQiRNklQlqWr16vy/+ZWZWUOOGbIfxw/bj/96ajEbt9alHQdI/yT1LcC/RURD13edEBFHkjlEdZWkkxqaQUTcGRGVEVHZp0+fHEY1M8ut6yaMZM3Gbfz87zVpRwFyWyBWAgOz3g9IhmWrBO6XVANcCPxY0gUAEbEy+b0KeJjMISszsw5r7KB9OGVkH+54egnrt2xPO05OC8RMYLikwZLKgEuAR7MbRMTgiKiIiArgt8AXIuIRSeWSugNIKgfOAObmMKuZWV64bsJIajdv52fPLk07Su4KRETUAVOAx4D5wAMRMU/SZEmTm5i8H/CspDnAi8CfIuKvucpqZpYvDh3Qk4+O7sddzyxl3aZtqWZRvj+woiUqKyujqspfmTCzwvbaW+s569Zn+ML4oXzlowfndFmSZjX2VYK0T1KbmdkuDt6/B+ccdiB3P1fDmg1bU8vhAmFmloe+dPpwtmyv5/anF6eWwQXCzCwPDe3TjQuO6M8v/v46b6/fkkoGFwgzszz1xdOGU78j+PGT1aks3wXCzCxPDdqvnIsqB3Dfi8tZuW5zuy/fBcLMLI9NOXU4AD96YlG7L9sFwswsj/Xv1YVLxw3kwaoVvL5mY7su2wXCzCzPXXXKMIqLxK2Pt28vwgXCzCzP9e3RmU8fO4hHXl5J9aoN7bZcFwgzswIw+eShdC4tbtdehAuEmVkB2K9bJz5zXAV/mPMGr721vl2W6QJhZlYgJp00hO6dSrh52sJ2WZ4LhJlZgejVtYzPnjiYx+a9zasranO+PBcIM7MCcsUJg+nVtZSbpi3I+bJcIMzMCkiPzqVMOmkITy5YzazX383pslwgzMwKzMRjK9ivvCznvQgXCDOzAlPeqYTPjx/Kc9Vr+PviNTlbjguEmVkBuvyYQfTr0Ymbpi0gV08GdYEwMytAnUuLueqUYcyseZdnFr2Tk2W4QJiZFaiLjxpI/15d+P60hTnpRbhAmJkVqE4lxVw7YQSH9e/J1rodbT7/nBYISWdKWiCpWtINu2l3lKQ6SRe2dFozs73ZhWMH8K0LDqFzaXGbzztnBUJSMXAbcBYwCrhU0qhG2v0HMLWl05qZWe7ksgcxDqiOiCURsQ24Hzi/gXZXA78DVrViWjMzy5FcFoj+wPKs9yuSYe+T1B/4OPBfLZ02ax6TJFVJqlq9evUehzYzs4y0T1LfAvxbRLT67EpE3BkRlRFR2adPn7ZLZma2lyvJ4bxXAgOz3g9IhmWrBO6XBNAb+JikumZOa2ZmOZTLAjETGC5pMJmd+yXAp7IbRMTgna8l3QP8MSIekVTS1LRmZpZbOSsQEVEnaQrwGFAM/Cwi5kmanIy/vaXT5iqrmZl9mHJ1D480VFZWRlVVVdoxzMwKhqRZEVHZ4LiOVCAkrQZeb+XkvYHc3NCk/XWUdeko6wFel3zUUdYD9mxdBkVEg1f4dKgCsSckVTVWRQtNR1mXjrIe4HXJRx1lPSB365L2Za5mZpanXCDMzKxBLhD/dGfaAdpQR1mXjrIe4HXJRx1lPSBH6+JzEGZm1iD3IMzMrEEuEGZm1qC9qkBI+pmkVZLmNjJekn6QPKToFUlHtnfG5mrGuoyXVCtpdvLz9fbO2BySBkp6UtI/JM2T9MUG2hTEdmnmuuT9dpHUWdKLkuYk6/G/G2hTKNukOeuS99skm6RiSS9L+mMD49p2u0TEXvMDnAQcCcxtZPzHgL8AAo4BXkg78x6sy3gy97ZKPWsT63EAcGTyujuwEBhViNulmeuS99sl+Tt3S16XAi8AxxToNmnOuuT9Ntkl73XArxvK3NbbZa/qQUTEDGDtbpqcD/wiMp4Hekk6oH3StUwz1qUgRMSbEfFS8vo9YD4ffvZHQWyXZq5L3kv+zhuSt6XJz65XsxTKNmnOuhQMSQOAs4GfNtKkTbfLXlUgmqHZDyoqEMcmXeu/SBqddpimSKoAjiDzKS9bwW2X3awLFMB2SQ5jzCbzpMdpEVGw26QZ6wIFsE0StwBfBRp7hk6bbhcXiI7rJTL3WDkc+CHwSLpxdk9SNzKPnv1SRKxPO8+eaGJdCmK7RER9RIwh8yyWcZIOSTlSqzVjXQpim0g6B1gVEbPaa5kuEB/UYR5UFBHrd3atI+LPQKmk3inHapCkUjI71F9FxEMNNCmY7dLUuhTSdgGIiHXAk8CZu4wqmG2yU2PrUkDb5HjgPEk1wP3AqZLu3aVNm24XF4gPehT4dHIlwDFAbUS8mXao1pC0v5R5VJ+kcWS29Zp0U31YkvEuYH5E3NRIs4LYLs1Zl0LYLpL6SOqVvO4CTABe26VZoWyTJtelELYJQETcGBEDIqKCzEPUnoiIy3dp1qbbJZdPlMs7ku4jc8VCb0krgG+QOWlFZB5g9GcyVwFUA5uAf00nadOasS4XAp9X5hGum4FLIrnMIc8cD/wL8GpynBjgfwAHQcFtl+asSyFslwOAn0sqJrOzfCAi/qgPPuyrULZJc9alELZJo3K5XXyrDTMza5APMZmZWYNcIMzMrEEuEGZm1iAXCDMza5ALhJmZNcgFwqwdSPqmpC+nncOsJVwgzNpY8iWlPfq/JWmv+o6S5ScXCLNWkHSdpLnJz5ckVUhaIOkXwFxgoKT/KWmhpGeBkVnTDpX0V0mzJD0j6eBk+D2Sbpf0AvDddNbM7J/8KcWshSSNJfMN1aPJ3Hf/BeBpYDgwMSKeT9pcAowh8//sJWDnTdbuBCZHxCJJRwM/Bk5Nxg0AjouI+nZaHbNGuUCYtdwJwMMRsRFA0kPAicDryT34Sd4/HBGbkjaPJr+7AccBDya3/wHolDXvB10cLF+4QJi1nY3NaFMErEtuP93aeZi1C5+DMGu5Z4ALJHWVVA58PBmWbUbSpouk7sC5kLm1NLBU0kXw/gntw9sxu1mzuUCYtVDyWNF7gBfJnH/4KfBuA21+A8wh84zgmVmjLwM+K2kOMI/MYyLN8o7v5mpmZg1yD8LMzBrkAmFmZg1ygTAzswa5QJiZWYNcIMzMrEEuEGZm1iAXCDMza9D/B6fvTcb7wY/RAAAAAElFTkSuQmCC\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": {}
    },
    {
      "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": "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
      },
      "execution_count": 49,
      "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": 50,
      "outputs": [
        {
          "execution_count": 50,
          "output_type": "execute_result",
          "data": {
            "text/plain": "<function __main__.f(order, test_data)>"
          },
          "metadata": {}
        },
        {
          "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  #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 \npr1 = PolynomialFeatures(degree=2)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 51,
      "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 \nx_train_pr1 = pr1.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\nx_test_pr1 = pr1.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 52,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\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_pr1.shape",
      "metadata": {
        "trusted": true
      },
      "execution_count": 53,
      "outputs": [
        {
          "execution_count": 53,
          "output_type": "execute_result",
          "data": {
            "text/plain": "(110, 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\npoly1 = LinearRegression()\npoly1.fit(x_train_pr1,y_train)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 54,
      "outputs": [
        {
          "execution_count": 54,
          "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 \nyhat_test1 = poly1.predict(x_test_pr1)\nDistributionPlot(y_test, yhat_test1, \"Actual Values (Test)\", \"Predicted Values (Test)\", Title)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 56,
      "outputs": [
        {
          "name": "stderr",
          "text": "/lib/python3.9/site-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/lib/python3.9/site-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": "stream"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<pyolite.display.Image at 0x5f4d6f8>",
            "image/png": 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"
          },
          "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": "markdown",
      "source": "# Write your code below and press Shift+Enter to execute \nhigh in $10000, low in 30000-40000",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\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.\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)\nx_train_pr=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])\nx_test_pr=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 57,
      "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": 58,
      "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": 59,
      "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": "RigeModel.fit(x_train_pr, y_train)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 60,
      "outputs": [
        {
          "execution_count": 60,
          "output_type": "execute_result",
          "data": {
            "text/plain": "Ridge(alpha=1)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Similarly, you can obtain a prediction:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "yhat = RigeModel.predict(x_test_pr)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 61,
      "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": 62,
      "outputs": [
        {
          "name": "stdout",
          "text": "predicted: [ 6570.82441941  9636.24891471 20949.92322738 19403.60313255]\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 tqdm import tqdm\n\nRsqu_test = []\nRsqu_train = []\ndummy1 = []\nAlpha = 10 * np.array(range(0,1000))\npbar = tqdm(Alpha)\n\nfor 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
      },
      "execution_count": 63,
      "outputs": [
        {
          "name": "stderr",
          "text": "<ipython-input-63-e0c60797668d>:7: TqdmMonitorWarning: tqdm:disabling monitor support (monitor_interval = 0) due to:\ncan't start new thread\n  pbar = tqdm(Alpha)\n100%|##########| 1000/1000 [00:03<00:00, 301.20it/s, Test Score=0.564, Train Score=0.859]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can plot out the value of R^2 for different alphas:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "width = 12\nheight = 10\nplt.figure(figsize=(width, height))\n\nplt.plot(Alpha,Rsqu_test, label='validation data  ')\nplt.plot(Alpha,Rsqu_train, 'r', label='training Data ')\nplt.xlabel('alpha')\nplt.ylabel('R^2')\nplt.legend()",
      "metadata": {
        "trusted": true
      },
      "execution_count": 64,
      "outputs": [
        {
          "execution_count": 64,
          "output_type": "execute_result",
          "data": {
            "text/plain": "<matplotlib.legend.Legend at 0x62941d0>"
          },
          "metadata": {}
        },
        {
          "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": {}
    },
    {
      "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 \n\nRigeModel1 = Ridge(alpha=10) \nRigeModel1.fit(x_train_pr, y_train)\nyhat1 = RigeModel1.predict(x_test_pr)\nRigeModel1.score(x_test_pr, y_test)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 67,
      "outputs": [
        {
          "execution_count": 67,
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.5418576440208844"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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": 68,
      "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": 69,
      "outputs": [
        {
          "execution_count": 69,
          "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": 70,
      "outputs": [
        {
          "execution_count": 70,
          "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": 71,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Fit 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": 72,
      "outputs": [
        {
          "execution_count": 72,
          "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": 73,
      "outputs": [
        {
          "execution_count": 73,
          "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[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_test)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 74,
      "outputs": [
        {
          "execution_count": 74,
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.8411649831036152"
          },
          "metadata": {}
        }
      ]
    },
    {
      "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\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\" 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| 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": {}
    },
    {
      "cell_type": "code",
      "source": "",
      "metadata": {},
      "execution_count": null,
      "outputs": []
    }
  ]
}