model-evaluation-and-refinement.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Module%205/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n",
    "</center>\n",
    "\n",
    "# Model Evaluation and Refinement\n",
    "\n",
    "Estimated time needed: **30** minutes\n",
    "\n",
    "## Objectives\n",
    "\n",
    "After completing this lab you will be able to:\n",
    "\n",
    "*   Evaluate and refine prediction models\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Import clean data \n",
    "path = 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/module_5_auto.csv'\n",
    "df = pd.read_csv(path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_csv('module_5_auto.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's only use numeric data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <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",
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       "      <td>48.8</td>\n",
       "      <td>2548</td>\n",
       "      <td>130</td>\n",
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       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
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       "      <td>48.8</td>\n",
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       "      <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",
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       "      <td>1</td>\n",
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       "      <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",
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       "    <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",
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       "      <td>1</td>\n",
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       "      <td>99.4</td>\n",
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       "      <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",
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       "   Unnamed: 0  Unnamed: 0.1  symboling  normalized-losses  wheel-base  \\\n",
       "0           0             0          3                122        88.6   \n",
       "1           1             1          3                122        88.6   \n",
       "2           2             2          1                122        94.5   \n",
       "3           3             3          2                164        99.8   \n",
       "4           4             4          2                164        99.4   \n",
       "\n",
       "     length     width  height  curb-weight  engine-size  ...  stroke  \\\n",
       "0  0.811148  0.890278    48.8         2548          130  ...    2.68   \n",
       "1  0.811148  0.890278    48.8         2548          130  ...    2.68   \n",
       "2  0.822681  0.909722    52.4         2823          152  ...    3.47   \n",
       "3  0.848630  0.919444    54.3         2337          109  ...    3.40   \n",
       "4  0.848630  0.922222    54.3         2824          136  ...    3.40   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm  city-mpg  highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0        21           27  13495.0   \n",
       "1                9.0       111.0    5000.0        21           27  16500.0   \n",
       "2                9.0       154.0    5000.0        19           26  16500.0   \n",
       "3               10.0       102.0    5500.0        24           30  13950.0   \n",
       "4                8.0       115.0    5500.0        18           22  17450.0   \n",
       "\n",
       "   city-L/100km  diesel  gas  \n",
       "0     11.190476       0    1  \n",
       "1     11.190476       0    1  \n",
       "2     12.368421       0    1  \n",
       "3      9.791667       0    1  \n",
       "4     13.055556       0    1  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df=df._get_numeric_data()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Libraries for plotting:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact, interactive, fixed, interact_manual"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Functions for Plotting</h2>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "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()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_data = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Drop price data in dataframe **x_data**:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_data=df.drop('price',axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we randomly split our data into training and testing data using the function <b>train_test_split</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 21\n",
      "number of training samples: 180\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.10, random_state=1)\n",
    "\n",
    "\n",
    "print(\"number of test samples :\", x_test.shape[0])\n",
    "print(\"number of training samples:\",x_train.shape[0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 81\n",
      "number of training samples: 120\n"
     ]
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "\n",
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0) \n",
    "print(\"number of test samples :\", x_test1.shape[0])\n",
    "print(\"number of training samples:\",x_train1.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0) \n",
    "print(\"number of test samples :\", x_test1.shape[0])\n",
    "print(\"number of training samples:\",x_train1.shape[0])\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import <b>LinearRegression</b> from the module <b>linear_model</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:35: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:597: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, fit_path=True,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:836: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, fit_path=True,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:862: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, positive=False):\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1097: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  max_n_alphas=1000, n_jobs=None, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1344: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  max_n_alphas=1000, n_jobs=None, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1480: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, positive=False):\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:152: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  precompute=False, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:320: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, random_state=None,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:580: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=4 * np.finfo(np.float).eps, n_jobs=None,\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a Linear Regression object:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "lre=LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We fit the model using the feature \"horsepower\":\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lre.fit(x_train[['horsepower']], y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2 on the test data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3635875575078824"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lre.score(x_test[['horsepower']], y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the R^2 is much smaller using the test data compared to the training data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6619724197515103"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lre.score(x_train[['horsepower']], y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #2): </h1>\n",
    "<b> \n",
    "Find the R^2  on the test data using 40% of the dataset for testing.\n",
    "</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7139364665406973"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0)\n",
    "lre.fit(x_train1[['horsepower']],y_train1)\n",
    "lre.score(x_test1[['horsepower']],y_test1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0)\n",
    "lre.fit(x_train1[['horsepower']],y_train1)\n",
    "lre.score(x_test1[['horsepower']],y_test1)\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Cross-Validation Score</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import <b>model_selection</b> from the module <b>cross_val_score</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:437: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  fold_sizes = np.full(n_splits, n_samples // n_splits, dtype=np.int)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n"
     ]
    }
   ],
   "source": [
    "Rcross = cross_val_score(lre, x_data[['horsepower']], y_data, cv=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The default scoring is R^2. Each element in the array has the average R^2 value for the fold:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.7746232 , 0.51716687, 0.74785353, 0.04839605])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rcross"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can calculate the average and standard deviation of our estimate:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the folds are 0.522009915042119 and the standard deviation is 0.2911839444756029\n"
     ]
    }
   ],
   "source": [
    "print(\"The mean of the folds are\", Rcross.mean(), \"and the standard deviation is\" , Rcross.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use negative squared error as a score by setting the parameter  'scoring' metric to 'neg_mean_squared_error'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:437: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  fold_sizes = np.full(n_splits, n_samples // n_splits, dtype=np.int)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([20254142.84026704, 43745493.2650517 , 12539630.34014931,\n",
       "       17561927.72247591])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-1 * cross_val_score(lre,x_data[['horsepower']], y_data,cv=4,scoring='neg_mean_squared_error')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #3): </h1>\n",
    "<b> \n",
    "Calculate the average R^2 using two folds, then find the average R^2 for the second fold utilizing the \"horsepower\" feature: \n",
    "</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:437: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  fold_sizes = np.full(n_splits, n_samples // n_splits, dtype=np.int)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.5166761697127429"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "Rc=cross_val_score(lre,x_data[['horsepower']], y_data,cv=2)\n",
    "Rc.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "Rc=cross_val_score(lre,x_data[['horsepower']], y_data,cv=2)\n",
    "Rc.mean()\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_predict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:437: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  fold_sizes = np.full(n_splits, n_samples // n_splits, dtype=np.int)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([14141.63807508, 14141.63807508, 20814.29423473, 12745.03562306,\n",
       "       14762.35027598])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = cross_val_predict(lre,x_data[['horsepower']], y_data,cv=4)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref2\">Part 2: Overfitting, Underfitting and Model Selection</h2>\n",
    "\n",
    "<p>It turns out that the test data, sometimes referred to as the \"out of sample data\", is a much better measure of how well your model performs in the real world.  One reason for this is overfitting.\n",
    "\n",
    "Let's go over some examples. It turns out these differences are more apparent in Multiple Linear Regression and Polynomial Regression so we will explore overfitting in that context.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LinearRegression()\n",
    "lr.fit(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction using training data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 7426.6731551 , 28323.75090803, 14213.38819709,  4052.34146983,\n",
       "       34500.19124244])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat_train = lr.predict(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "yhat_train[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction using test data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11349.35089149,  5884.11059106, 11208.6928275 ,  6641.07786278,\n",
       "       15565.79920282])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat_test = lr.predict(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "yhat_test[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine the distribution of the predicted values of the training data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Title = 'Distribution  Plot of  Predicted Value Using Training Data vs Training Data Distribution'\n",
    "DistributionPlot(y_train, yhat_train, \"Actual Values (Train)\", \"Predicted Values (Train)\", Title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 1: Plot of predicted values using the training data compared to the actual values of the training data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n",
    "DistributionPlot(y_test,yhat_test,\"Actual Values (Test)\",\"Predicted Values (Test)\",Title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 2: Plot of predicted value using the test data compared to the actual values of the test data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use 55 percent of the data for training and the rest for testing:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.45, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will perform a degree 5 polynomial transformation on the feature <b>'horsepower'</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=5, include_bias=True, interaction_only=False)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr = PolynomialFeatures(degree=5)\n",
    "x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "x_test_pr = pr.fit_transform(x_test[['horsepower']])\n",
    "pr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's create a Linear Regression model \"poly\" and train it.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly = LinearRegression()\n",
    "poly.fit(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the output of our model using the method \"predict.\" We assign the values to \"yhat\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6728.73285076,  7308.05589332, 12213.80614303, 18893.13997531,\n",
       "       19995.82734265])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = poly.predict(x_test_pr)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take the first five predicted values and compare it to the actual targets.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted values: [ 6728.73285076  7308.05589332 12213.80614303 18893.13997531]\n",
      "True values: [ 6295. 10698. 13860. 13499.]\n"
     ]
    }
   ],
   "source": [
    "print(\"Predicted values:\", yhat[0:4])\n",
    "print(\"True values:\", y_test[0:4].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train, y_test, poly,pr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R^2 of the training data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5567716902237296"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly.score(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R^2 of the test data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-29.87158580724305"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly.score(x_test_pr, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how the R^2 changes on the test data for different order polynomials and then plot the results:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(3, 0.75, 'Maximum R^2 ')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Rsqu_test = []\n",
    "\n",
    "order = [1, 2, 3, 4]\n",
    "for n in order:\n",
    "    pr = PolynomialFeatures(degree=n)\n",
    "    \n",
    "    x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "    \n",
    "    x_test_pr = pr.fit_transform(x_test[['horsepower']])    \n",
    "    \n",
    "    lr.fit(x_train_pr, y_train)\n",
    "    \n",
    "    Rsqu_test.append(lr.score(x_test_pr, y_test))\n",
    "\n",
    "plt.plot(order, Rsqu_test)\n",
    "plt.xlabel('order')\n",
    "plt.ylabel('R^2')\n",
    "plt.title('R^2 Using Test Data')\n",
    "plt.text(3, 0.75, 'Maximum R^2 ')    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function will be used in the next section. Please run the cell below.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following interface allows you to experiment with different polynomial orders and different amounts of data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e3b9eacc49e24753b7b934421d532a67",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=3, description='order', max=6), FloatSlider(value=0.45, description='tes…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.f(order, test_data)>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(f, order=(0, 6, 1), test_data=(0.05, 0.95, 0.05))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "pr1=PolynomialFeatures(degree=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "pr1=PolynomialFeatures(degree=2)\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "x_train_pr1=pr1.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "\n",
    "x_test_pr1=pr1.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "x_train_pr1=pr1.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "\n",
    "x_test_pr1=pr1.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!-- The answer is below:\n",
    "\n",
    "x_train_pr1=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "x_test_pr1=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #4c): </h1>\n",
    "<b> \n",
    "How many dimensions does the new feature have? Hint: use the attribute \"shape\".\n",
    "</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(110, 15)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "x_train_pr1.shape #there are now 15 features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "x_train_pr1.shape #there are now 15 features\n",
    "\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #4d): </h1>\n",
    "\n",
    "<b> \n",
    "Create a linear regression model \"poly1\". Train the object using the method \"fit\" using the polynomial features.</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "poly1=LinearRegression().fit(x_train_pr1,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "poly1=LinearRegression().fit(x_train_pr1,y_train)\n",
    "\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "\n",
    "\n",
    "yhat_test1=poly1.predict(x_test_pr1)\n",
    "\n",
    "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n",
    "\n",
    "DistributionPlot(y_test, yhat_test1, \"Actual Values (Test)\", \"Predicted Values (Test)\", Title)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "yhat_test1=poly1.predict(x_test_pr1)\n",
    "\n",
    "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n",
    "\n",
    "DistributionPlot(y_test, yhat_test1, \"Actual Values (Test)\", \"Predicted Values (Test)\", Title)\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "\n",
    "#The predicted value is higher than actual value for cars where the price $10,000 range, \n",
    "#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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref3\">Part 3: Ridge Regression</h2> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's perform a degree two polynomial transformation on our data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "x_train_pr=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])\n",
    "x_test_pr=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import  <b>Ridge</b>  from the module <b>linear models</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a Ridge regression object, setting the regularization parameter (alpha) to 0.1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "RigeModel=Ridge(alpha=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Like regular regression, you can fit the model using the method <b>fit</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=1, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RigeModel.fit(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, you can obtain a prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "yhat = RigeModel.predict(x_test_pr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare the first five predicted samples to our test set:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted: [ 6570.82441941  9636.24891471 20949.92322737 19403.60313255]\n",
      "test set : [ 6295. 10698. 13860. 13499.]\n"
     ]
    }
   ],
   "source": [
    "print('predicted:', yhat[0:4])\n",
    "print('test set :', y_test[0:4].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:04<00:00, 244.47it/s, Test Score=0.564, Train Score=0.859]\n"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm\n",
    "\n",
    "Rsqu_test = []\n",
    "Rsqu_train = []\n",
    "dummy1 = []\n",
    "Alpha = 10 * np.array(range(0,1000))\n",
    "pbar = tqdm(Alpha)\n",
    "\n",
    "for alpha in pbar:\n",
    "    RigeModel = Ridge(alpha=alpha) \n",
    "    RigeModel.fit(x_train_pr, y_train)\n",
    "    test_score, train_score = RigeModel.score(x_test_pr, y_test), RigeModel.score(x_train_pr, y_train)\n",
    "    \n",
    "    pbar.set_postfix({\"Test Score\": test_score, \"Train Score\": train_score})\n",
    "\n",
    "    Rsqu_test.append(test_score)\n",
    "    Rsqu_train.append(train_score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot out the value of R^2 for different alphas:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f9cf66495d0>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "\n",
    "plt.plot(Alpha,Rsqu_test, label='validation data  ')\n",
    "plt.plot(Alpha,Rsqu_train, 'r', label='training Data ')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('R^2')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the model is built and tested on the same data, so the training and test data are the same.\n",
    "\n",
    "The red line in Figure 4 represents the R^2 of the training data. As alpha increases the R^2 decreases. Therefore, as alpha increases, the model performs worse on the training data\n",
    "\n",
    "The blue line represents the R^2 on the validation data. As the value for alpha increases, the R^2 increases and converges at a point.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #5): </h1>\n",
    "\n",
    "Perform Ridge regression. Calculate the R^2 using the polynomial features, use the training data to train the model and use the test data to test the model. The parameter alpha should be set to 10.\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5418576440207269"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "RigeModel = Ridge(alpha=10) \n",
    "RigeModel.fit(x_train_pr, y_train)\n",
    "RigeModel.score(x_test_pr, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "RigeModel = Ridge(alpha=10) \n",
    "RigeModel.fit(x_train_pr, y_train)\n",
    "RigeModel.score(x_test_pr, y_test)\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref4\">Part 4: Grid Search</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import <b>GridSearchCV</b> from  the module <b>model_selection</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a dictionary of parameter values:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000, 100000]}]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parameters1= [{'alpha': [0.001,0.1,1, 10, 100, 1000, 10000, 100000, 100000]}]\n",
    "parameters1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a Ridge regression object:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RR=Ridge()\n",
    "RR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a ridge grid search object:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "Grid1 = GridSearchCV(RR, parameters1,cv=4, iid=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to avoid a deprecation warning due to the iid parameter, we set the value of iid to \"None\".\n",
    "\n",
    "Fit the model:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:437: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  fold_sizes = np.full(n_splits, n_samples // n_splits, dtype=np.int)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_search.py:821: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  dtype=np.int)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=4, error_score='raise-deprecating',\n",
       "       estimator=Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001),\n",
       "       fit_params=None, iid=None, n_jobs=None,\n",
       "       param_grid=[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000, 100000]}],\n",
       "       pre_dispatch='2*n_jobs', refit=True, return_train_score='warn',\n",
       "       scoring=None, verbose=0)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Grid1.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=10000, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BestRR=Grid1.best_estimator_\n",
    "BestRR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now test our model on the test data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8411649831036152"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BestRR.score(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #6): </h1>\n",
    "Perform a grid search for the alpha parameter and the normalization parameter, then find the best values of the parameters:\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:437: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  fold_sizes = np.full(n_splits, n_samples // n_splits, dtype=np.int)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_split.py:113: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  test_mask = np.zeros(_num_samples(X), dtype=np.bool)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_search.py:821: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  dtype=np.int)\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/model_selection/_search.py:841: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
      "  DeprecationWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "   normalize=True, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "\n",
    "parameters2= [{'alpha': [0.001,0.1,1, 10, 100, 1000,10000,100000,100000],'normalize':[True,False]} ]\n",
    "Grid2 = GridSearchCV(Ridge(), parameters2,cv=4)\n",
    "Grid2.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']],y_data)\n",
    "Grid2.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "parameters2= [{'alpha': [0.001,0.1,1, 10, 100, 1000,10000,100000,100000],'normalize':[True,False]} ]\n",
    "Grid2 = GridSearchCV(Ridge(), parameters2,cv=4)\n",
    "Grid2.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']],y_data)\n",
    "Grid2.best_estimator_\n",
    "\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thank you for completing this lab!\n",
    "\n",
    "## Author\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Joseph Santarcangelo</a>\n",
    "\n",
    "### Other Contributors\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
    "\n",
    "Bahare Talayian\n",
    "\n",
    "Eric Xiao\n",
    "\n",
    "Steven Dong\n",
    "\n",
    "Parizad\n",
    "\n",
    "Hima Vasudevan\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/fiorellawever/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Fiorella Wenver</a>\n",
    "\n",
    "<a href=\"https:// https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "## Change Log\n",
    "\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                  |\n",
    "| ----------------- | ------- | ---------- | ----------------------------------- |\n",
    "| 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"
   ]
  }
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