model-evaluation-and-refinement.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/Logos/organization_logo/organization_logo.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": [
    "<h1>Table of content</h1>\n",
    "<ul>\n",
    "    <li><a href=\"#ref1\">Model Evaluation </a></li>\n",
    "    <li><a href=\"#ref2\">Over-fitting, Under-fitting and Model Selection </a></li>\n",
    "    <li><a href=\"#ref3\">Ridge Regression </a></li>\n",
    "    <li><a href=\"#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\">HERE</a> for free storage.\n"
   ]
  },
  {
   "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://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/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 lets only use numeric data \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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       "    }\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",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <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",
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       "    <tr>\n",
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       "      <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",
       "      <td>2</td>\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",
       "      <td>3</td>\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",
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       "      <td>4</td>\n",
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       "      <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>"
      ],
      "text/plain": [
       "   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": [
    "%%capture\n",
    "! pip install ipywidgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": 7,
   "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": 8,
   "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": [
    "<h1 id=\"ref1\">Part 1: Training and Testing</h1>\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</b>:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_data = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "drop price data in x data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": 11,
   "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 set to 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 data set 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_train_1\" , \"x_test_1\", \"y_train_1\" and  \"y_test_1\".</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "x_train_1,x_test_1,y_train_1,y_test_1 = train_test_split(x_data,y_data,test_size=0.4,random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\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])\n",
    "\n",
    "-->\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": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We create a Linear Regression object:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "lre=LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we fit the model using the feature horsepower \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 15,
     "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": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.36358755750788263"
      ]
     },
     "execution_count": 16,
     "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6619724197515104"
      ]
     },
     "execution_count": 17,
     "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 90% of the data for training data\n",
    "</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "x_train_1,x_test_1,y_train_1,y_test_1 = train_test_split(x_data,y_data,test_size=0.1,random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.1, random_state=0)\n",
    "lre.fit(x_train1[['horsepower']],y_train1)\n",
    "lre.score(x_test1[['horsepower']],y_test1)\n",
    "\n",
    "-->\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": [
    "Lets import <b>model_selection</b> from the module <b>cross_val_score</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We input the object, the feature in this case ' horsepower', the target data (y_data). The parameter 'cv'  determines the number of folds; in this case 4. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "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 in the fold:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.7746232 , 0.51716687, 0.74785353, 0.04839605])"
      ]
     },
     "execution_count": 21,
     "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": 22,
   "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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20254142.84026704, 43745493.2650517 , 12539630.34014932,\n",
       "       17561927.72247591])"
      ]
     },
     "execution_count": 23,
     "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, find the average R^2 for the second fold utilizing the horsepower as a feature : \n",
    "</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5166761697127429"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "Rscore = cross_val_score(lre, x_data[['horsepower']], y_data, cv=2)\n",
    "Rscore.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "Rc=cross_val_score(lre,x_data[['horsepower']], y_data,cv=2)\n",
    "Rc.mean()\n",
    "\n",
    "-->\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, using one fold for testing and the other folds are used for training.  First import the function:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_predict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We input the object, the feature in this case <b>'horsepower'</b> , the target data <b>y_data</b>. The parameter 'cv' determines the number of folds; in this case 4. We can produce an output:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([14141.63807508, 14141.63807508, 20814.29423473, 12745.03562306,\n",
       "       14762.35027598])"
      ]
     },
     "execution_count": 26,
     "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": [
    "<h1 id=\"ref2\">Part 2: Overfitting, Underfitting and Model Selection</h1>\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; 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": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 27,
     "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": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 7426.6731551 , 28323.75090803, 14213.38819709,  4052.34146983,\n",
       "       34500.19124244])"
      ]
     },
     "execution_count": 28,
     "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": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11349.35089149,  5884.11059106, 11208.6928275 ,  6641.07786278,\n",
       "       15565.79920282])"
      ]
     },
     "execution_count": 29,
     "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 matplotlibb library for plotting.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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": 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 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 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": 32,
   "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": [
    "Figur 2: Plot of predicted value using the test data compared to the test data. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing Figure 1 and Figure 2; it is evident the distribution of the test data in Figure 1 is much better at fitting the data. This difference in Figure 2 is apparent where the ranges are from 5000 to 15 000. This is where the distribution shape is exceptionally 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": 33,
   "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, not the underlying process. Therefore when testing your model using the test-set, your model does not perform as well as 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": 34,
   "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>'horse power'</b>. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=5, include_bias=True, interaction_only=False,\n",
       "                   order='C')"
      ]
     },
     "execution_count": 35,
     "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": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 36,
     "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.\" then assign the values to \"yhat\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6728.60486749,  7307.93778255, 12213.74792967, 18893.34125061,\n",
       "       19996.06555028])"
      ]
     },
     "execution_count": 37,
     "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": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted values: [ 6728.60486749  7307.93778255 12213.74792967 18893.34125061]\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": 39,
   "metadata": {
    "scrolled": false
   },
   "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": [
    "Figur 4 A polynomial regression model, 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": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5567716898927437"
      ]
     },
     "execution_count": 40,
     "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": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-29.871035846525604"
      ]
     },
     "execution_count": 41,
     "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 plot the results:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(3, 0.75, 'Maximum R^2 ')"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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J4kcvqhfRkSggRKTVcrMy+Np5I/jrmnL+uuajqMuRNqKAEJE2cdXpgzmmWw73vLiKjnKHhqOdAkJE2kROZjrTzx9ByYadvLxavYiOQAEhIm3mS8WDGNijE/e8uFK9iA5AASEibSYrI42ZEwp5Z3MF81Zsj7ocaSUFhIi0qctPHUhB71zumbuKWj2APKWFGhBmdqGZrTSzUjO7LcHw2Wb2dvBaZWa74oZNM7PVwWtamHWKSNvJSE/j5guKWLFtN39574Ooy5FWCC0gzCwdeAC4CBgJTDWzkfHjuPst7j7a3UcDPwGeCabtBdwBnA6MAe4ws55h1SoibeuzJw+gsG8XZs9b1aynMkpyCbMHMQYodfe17l4FPAFc1sD4U4HfBe8/A8x19x3uvhOYC1wYYq0i0obS04ybLyiidPtenntna9TlSAuFGRADgU1xnzcHbZ9iZkOAocD85kxrZtebWYmZlZSVlbVJ0SLSNi468RiO79+Ne+etorqmNupypAXCDIhED2g+Ul9zCvC0u9c0Z1p3f8jdi929OC8vr4VlikgY0tKMWROLWF++j2fe2hJ1OdICYQbEZmBQ3Od84Eh9zSl8snupudOKSJK64Pi+nJzfnfteWk1VtXoRqSbMgFgCFJrZUDPLIhYCc+qPZGbHAj2B1+OaXwAmmVnP4OD0pKBNRFKImTFr0rFs2bWfJ0s2NT6BJJXQAsLdq4EZxDbsK4Cn3H25md1pZpPjRp0KPOFxl126+w7gLmIhswS4M2gTkRRzTmEfiof05P75qzlwqKbxCSRpWEe5HL64uNhLSkqiLkNEEnh9TTlTf76Y71w6kn8+e2jU5UgcM1vq7sWJhulKahEJ3ZnDe3PW8N7898JS9lVVR12ONJECQkTaxa2TivhobxW/en1D1KVIEykgRKRdnDakF+cdm8fPFq1hz4FDUZcjTaCAEJF2M2tiEbv2HeKR19ZHXYo0gQJCRNrNqPweTBrZj5+/spaKfepFJDsFhIi0q1smFrHnQDU/f2Vt1KVIIxQQItKuju/fjUtG9eeR19ZRvvdg1OVIAxQQItLubrmgkP2HanjwZfUikpkCQkTa3Yi+Xfnc6IH86vX1bN99IOpy5AgUECISiZkXFHKoxvnpwjVRlyJHoIAQkUgM6d2ZK07L57dvbGTrrv1RlyMJKCBEJDIzzh+B49y/oDTqUiQBBYSIRCa/Zy5TxwzmqSWb2Fi+L+pypB4FhIhEavr4EaSnGT+evzrqUqQeBYSIRKpftxz+6YwhPPPWZtaU7Y26HImjgBCRyN143nByMtO5b556EclEASEikevTJZtpZxXw3LtbWfnBnqjLkYACQkSSwg3nDKNLVgaz566KuhQJKCBEJCn0yM3i2rOH8r/LP+C9LRVRlyMoIEQkifzzuKF075SpXkSSUECISNLolpPJ9ecM46W/b+etjTujLueoF2pAmNmFZrbSzErN7LYjjPNFM3vfzJab2W/j2mvM7O3gNSfMOkUkeVxzVgG9O2epF5EEQgsIM0sHHgAuAkYCU81sZL1xCoHbgbHufgJwc9zg/e4+OnhNDqtOEUkunbMz+Np5w3ll9Ue8sbY86nKOamH2IMYApe6+1t2rgCeAy+qN81XgAXffCeDu20OsR0RSxJfPGELfrtn8aO4q3D3qco5aYQbEQGBT3OfNQVu8IqDIzF4zs8VmdmHcsBwzKwnaP5doBmZ2fTBOSVlZWdtWLyKRyclMZ/r4Eby5bgevlaoXEZUwA8IStNX/KZABFALnAVOBh82sRzBssLsXA1cC95rZ8E99mftD7l7s7sV5eXltV7mIRG7KmEEM6J7DD19cqV5ERMIMiM3AoLjP+cDWBOP8yd0Pufs6YCWxwMDdtwZ/1wILgVNCrFVEkkx2RjrfmFDI25t2sWCl9j5HIcyAWAIUmtlQM8sCpgD1z0Z6FhgPYGZ9iO1yWmtmPc0sO659LPB+iLWKSBL6wmn5DO6Vy49e1LGIKIQWEO5eDcwAXgBWAE+5+3Izu9PM6s5KegEoN7P3gQXAt9y9HDgeKDGzd4L2u91dASFylMlMT2PmhEKWb93NC8s/iLqco451lFQuLi72kpKSqMsQkTZWU+tMnL2IjDTjLzPPIT0t0eFNaSkzWxoc7/0UXUktIkktPc245YIiVn24l+ffrX8YU8KkgBCRpHfJSf057piu3DdvNdU1tVGXc9RQQIhI0ktLM26ZWMTajyr547ItUZdz1FBAiEhKmDSyHycN7M6P56/mkHoR7UIBISIpwcyYNbGITTv28/uSzVGXc1RQQIhIyjjv2DxOHdyDn8xfzYFDNVGX0+EpIEQkZZgZt046lm0VB3jizY1Rl9PhKSBEJKWcNbw3pw/txf0L1rC/Sr2IMCkgRCSl1PUiPtp7kMcXr4+6nA5NASEiKWfM0F6MK+zDzxatZe/B6qjL6bAUECKSkm6ddCw7Kqt49LV1UZfSYSkgRCQljR7UgwuO78tDL6+lYv+hqMvpkBQQIpKybplYxO4D1fziVfUiwqCAEJGUdcKA7lx80jH88tV17KysirqcDkcBISIp7eYLiqisqubBl9dGXUqHo4AQkZRW1K8rl508gMf+up6yPQejLqdDUUCISMqbeUERVTW1/PfCNVGX0qEoIEQk5Q3t05nLTxnIr9/YwAcVB6Iup8NQQIhIh3DThELcnfsXrI66lA5DASEiHcKgXrl8sXgQTy7ZxKYd+6Iup0MINSDM7EIzW2lmpWZ22xHG+aKZvW9my83st3Ht08xsdfCaFmadItIxzDh/BGbGT+arF9EWQgsIM0sHHgAuAkYCU81sZL1xCoHbgbHufgJwc9DeC7gDOB0YA9xhZj3DqlVEOob+3Ttx1emD+cNbW1j/UWXU5aS8MHsQY4BSd1/r7lXAE8Bl9cb5KvCAu+8EcPftQftngLnuviMYNhe4MMRaRaSD+Np5w8lMN+57Sb2I1gozIAYCm+I+bw7a4hUBRWb2mpktNrMLmzEtZna9mZWYWUlZWVkbli4iqapv1xymnVXAs29vYfWHe6IuJ6WFGRCWoM3rfc4ACoHzgKnAw2bWo4nT4u4PuXuxuxfn5eW1slwR6ShuOGc4uZnp3DtPvYjWCDMgNgOD4j7nA1sTjPMndz/k7uuAlcQCoynTiogk1KtzFteePZT/+ds2lm+tiLqclBVmQCwBCs1sqJllAVOAOfXGeRYYD2BmfYjtcloLvABMMrOewcHpSUGbiEiTXDduGN1yMpg9V72IlgotINy9GphBbMO+AnjK3Zeb2Z1mNjkY7QWg3MzeBxYA33L3cnffAdxFLGSWAHcGbSIiTdK9UyZfHTeMeSs+5J1Nu6IuJyWZ+6d27aek4uJiLykpiboMEUkiew9WM+4/53NSfg9+de2YqMtJSma21N2LEw3TldQi0mF1yc7gxnOH8/KqMkrWaydEcykgRKRDu/rMAvp0yeZHL66KupSUo4AQkQ6tU1Y608cP5/W15fy19KOoy0kpDQaEmaWb2Q1mdpeZja037F/DLU1EpG1MHTOY/t1z+NHcVXSU467tobEexIPAuUA58GMzuydu2OWhVSUi0oZyMtOZcf4Ilm7YycJVuutCUzUWEGPc/Up3v5fYjfO6mNkzZpZN4qudRUSS0hWnDSK/ZydmqxfRZI0FRFbdG3evdvfrgbeB+UCXMAsTEWlLWRlp3DShkHc3VzD3/Q+jLiclNBYQJXE30APA3e8EHgEKwipKRCQMl58ykKF9OnPP3FXU1qoX0ZgGA8Ldv+zu/5ug/WF3zwyvLBGRtpeRnsbNFxTy9w/28Of3tkVdTtJr0mmuwcN/RERS3qWjBlDUrwuz566iRr2IBjUaEGbWFfhTO9QiIhK69DTjlguKWFNWyZ/e3hJ1OUmtsesg+gPzgIfapxwRkfB95oRjGNm/G/e9tJpDNbVRl5O0GutBvALc7e71b9MtIpKy0tKMWycVsaF8H39YujnqcpJWYwGxkwSP+hQRSXXnH9eX0YN68JP5pRysrom6nKTUWECcB1xkZtPboRYRkXZjZsyaWMSWXft5csmmqMtJSo2d5loJTAZOaZ9yRETaz7jCPowp6MX980s5cEi9iPoaPYvJ3Wvc/br2KEZEpD2ZGbMmFbF9z0F+vXhD1OUknRbd7ju4y+tVbV2MiEh7O2NYb84e0Yf/XriGyoPVUZeTVBo7zbWbmd1uZveb2SSL+QawFvhi+5QoIhKuWZOKKK+s4rHX10ddSlJprAfxOHAs8DfgOuBF4AvAZe5+Wci1iYi0i1MH92T8sXk8uGgtuw8cirqcpNFYQAxz92vc/UFgKlAMXOrub4dfmohI+5k18Vgq9h/il6+ui7qUpNFYQHwcpe5eA6xz9z1N/XIzu9DMVppZqZndlmD4NWZWZmZvB6/r4obVxLXrQj0RCdVJ+d35zAn9+MUr69i1ryrqcpJCYwFxspntDl57gFF1781sd0MTBjf4ewC4CBgJTDWzkQlGfdLdRwevh+Pa98e1T27OQomItMQtE4vYW1XNQy+vjbqUpNDYdRDp7t4teHV194y4990a+e4xQKm7r3X3KuAJQMctRCRpHXdMNy4dNYBH/7qe8r0Hoy4nci06zbWJBgLxlyduJvFtOz5vZu+a2dNmNiiuPcfMSsxssZl9LtEMzOz6YJySsjI9Z1ZEWu/mCwo5cKiGny1aE3UpkQszIBI9s7r+zdefAwrcfRSxu8Y+FjdssLsXA1cC95rZ8E99mftD7l7s7sV5eXltVbeIHMWG53XhH0/J51evb+DD3QeiLidSYQbEZiC+R5APbI0fwd3L3b2uH/dz4LS4YVuDv2uBheh2HyLSTmZOKKSm1vnpgtKoS4lUmAGxBCg0s6FmlgVMAQ47Gyl43kSdycCKoL2nmWUH7/sAY4H3Q6xVRORjg3vnckVxPr97cxNbdu2PupzIhBYQ7l4NzABeILbhf8rdl5vZnWZWd1bSTWa23MzeAW4CrgnajwdKgvYFxJ5JoYAQkXYz4/xCAO6fvzriSqJj7h3jmazFxcVeUlISdRki0oHc8af3+M0bG3np1nMZ0rtz1OWEwsyWBsd7PyXMXUwiIilt+vgRpKcZ9710dPYiFBAiIkfQt1sOV585hGeXbaF0+96oy2l3CggRkQbceO5wcjLTuXfeqqhLaXcKCBGRBvTuks1Xxhbw/Lvb+PsHDd5hqMNRQIiINOKr44bRNTuD2XOPrl6EAkJEpBE9crO4btwwXlj+IX/bXBF1Oe1GASEi0gTXnl1Aj9xM7pm7MupS2o0CQkSkCbrmZHL9OcNYsLKMpRt2Rl1Ou1BAiIg00TVnFdCnS9ZR04tQQIiINFFuVgY3njuc10rLeX1NedTlhE4BISLSDF8+Ywj9umVzz9yVdJRbFR2JAkJEpBlyMtOZMX4ES9bv5JXVH0VdTqgUECIizfTFfxjEwB6d+NGLHbsXoYAQEWmm7Ix0bpowgnc2V/DSiu1RlxMaBYSISAtcfmo+Q3rncs/cVdTWdsxehAJCRKQFMtPTmDmhkPe37eZ/l38QdTmhUECIiLTQZaMHMjyvM7PnrqKmA/YiFBAiIi2UnmbcMrGI1dv38vy7W6Mup80pIEREWuHiE/tz3DFduXfeaqpraqMup00pIEREWiEtzZg1sYh1H1XyzLItUZfTpkINCDO70MxWmlmpmd2WYPg1ZlZmZm8Hr+vihk0zs9XBa1qYdYqItMbEkf0Yld+d++atpqq64/QiQgsIM0sHHgAuAkYCU81sZIJRn3T30cHr4WDaXsAdwOnAGOAOM+sZVq0iIq1hFutFbNm1n6dKNkVdTpsJswcxBih197XuXgU8AVzWxGk/A8x19x3uvhOYC1wYUp0iIq12blEepw3pyf3zSzlwqCbqctpEmAExEIiP0s1BW32fN7N3zexpMxvUzGlFRJKCmXHrpCI+2H2A376xMepy2kSYAWEJ2uqfKPwcUODuo4B5wGPNmBYzu97MSsyspKysrFXFioi01lnD+3DmsN78dOEa9lVVR11Oq4UZEJuBQXGf84HDThR293J3Pxh8/DlwWlOnDaZ/yN2L3b04Ly+vzQoXEWmpWycV8dHeg/zq9Q1Rl9JqYQbEEqDQzIaaWRYwBZgTP7CC3JcAAAz1SURBVIKZ9Y/7OBlYEbx/AZhkZj2Dg9OTgjYRkaRWXNCLc4vyeHDRGvYeTO1eRGgB4e7VwAxiG/YVwFPuvtzM7jSzycFoN5nZcjN7B7gJuCaYdgdwF7GQWQLcGbSJiCS9WROL2LnvEI+8ui7qUlrFOsq9zIuLi72kpCTqMkREALjusRLeWFfOq98+n+65mVGXc0RmttTdixMN05XUIiIhmDWxiD0Hqnn41bVRl9JiCggRkRCMHNCNS07qzy9fXceOyqqoy2kRBYSISEhumVjI/kM1PLhoTdSltIgCQkQkJCP6duWy0QN57PX1bN9zIOpymk0BISISopkTCjlU4/x0Qer1IhQQIiIhKujTmS+cms9v39jItor9UZfTLAoIEZGQfWPCCBzn/vmlUZfSLAoIEZGQ5ffMZco/DObJJZvYtGNf1OU0mQJCRKQdTB8/grQ048cvrY66lCZTQIiItINjuufw5dOH8Ie3NrO2bG/U5TSJAkJEpJ187bzhZGekc1+K9CIUECIi7SSvazbTzipgzjtbWfXhnqjLaZQCQkSkHd1wzjA6Z2Uwe+6qqEtplAJCRKQd9eycxbVnD+Uv733Ae1sqoi6nQQoIEZF29s9nD6VbTvL3IhQQIiLtrHunTG44dzgv/X07yzbujLqcI1JAiIhE4JqzCujVOYt7krgXoYAQEYlA5+wMbjx3GK+s/og31yXnE5UVECIiEfmnMwrI65rND19cSTI+/lkBISISkU5Z6Uw/bzhvrtvBa6XlUZfzKQoIEZEITT19MAO65/CjucnXiwg1IMzsQjNbaWalZnZbA+N9wczczIqDzwVmtt/M3g5ePwuzThGRqGRnpDPj/EKWbdzFwpVlUZdzmNACwszSgQeAi4CRwFQzG5lgvK7ATcAb9QatcffRwevGsOoUEYnaFcX5DOrVKel6EWH2IMYApe6+1t2rgCeAyxKMdxfwAyD1HtgqItIGMtPTmDmhiPe27OaF5R9GXc7HwgyIgcCmuM+bg7aPmdkpwCB3fz7B9EPNbJmZLTKzcYlmYGbXm1mJmZWUlSVX10xEpDk+N3oAw/p0ZvbcVdTWJkcvIsyAsARtHy+1maUBs4FbE4y3DRjs7qcAs4Dfmlm3T32Z+0PuXuzuxXl5eW1UtohI+8tIT+PmiUWs/HAPz/9tW9TlAOEGxGZgUNznfGBr3OeuwInAQjNbD5wBzDGzYnc/6O7lAO6+FFgDFIVYq4hI5C49qT/H9uvKvfNWUV1TG3U5oQbEEqDQzIaaWRYwBZhTN9DdK9y9j7sXuHsBsBiY7O4lZpYXHOTGzIYBhcDaEGsVEYlcWppxy8RC1pZV8uzbWxufIOx6wvpid68GZgAvACuAp9x9uZndaWaTG5n8HOBdM3sHeBq40d2T81p0EZE29JkTjuGEAd348UurORRxL8KS6ZSq1iguLvaSkpKoyxARabX5f/+Qax8t4T8uP4mpYwaHOi8zW+ruxYmG6UpqEZEkM/7YvpwyuAc/eWk1B6trIqtDASEikmTMjFsnHsvWigM88eamxicIiQJCRCQJjR3RmzFDe3H/glL2V0XTi1BAiIgkoVgvooiyPQf59eINkdSggBARSVKnD+vNuMI+/PeiNVQerG73+SsgRESS2KyJReyorOLRv65v93krIEREktgpg3sy4bi+PLhoDRX7D7XrvBUQIiJJ7paJRew+UM0vXl3XrvNVQIiIJLkTB3bnohOP4ZevrmNnZVW7zVcBISKSAm6ZWERlVTUPvdJ+t6VTQIiIpICifl357KgBPPraesr2HGyXeSogRERSxM0XFHKwuoafLVrTLvNTQIiIpIhheV24/NR8Hl+8gQ8qwn9KswJCRCSFzJxQSG2t88CC0tDnpYAQEUkhg3rl8sV/GMQTSzayeee+UOelgBARSTEzxo/AMH7yUri9CAWEiEiKGdCjE1eePpin39rM+o8qQ5uPAkJEJAV9ffxwMtON+15aHdo8FBAiIimob9ccrj6zgGff3kLp9j2hzEMBISKSom44Zxi5menMnhdOLyIjlG8VEZHQ9e6SzdfHj+DAoRrcHTNr0+8PtQdhZhea2UozKzWz2xoY7wtm5mZWHNd2ezDdSjP7TJh1ioikqunjR3DrpGPbPBwgxB6EmaUDDwATgc3AEjOb4+7v1xuvK3AT8EZc20hgCnACMACYZ2ZF7h7Ng1lFRI5CYfYgxgCl7r7W3auAJ4DLEox3F/ADIP668cuAJ9z9oLuvA0qD7xMRkXYSZkAMBDbFfd4ctH3MzE4BBrn7882dNpj+ejMrMbOSsrKytqlaRESAcAMi0Q4x/3igWRowG7i1udN+3OD+kLsXu3txXl5eiwsVEZFPC/Msps3AoLjP+cDWuM9dgROBhcHBlWOAOWY2uQnTiohIyMLsQSwBCs1sqJllETvoPKduoLtXuHsfdy9w9wJgMTDZ3UuC8aaYWbaZDQUKgTdDrFVEROoJrQfh7tVmNgN4AUgHfunuy83sTqDE3ec0MO1yM3sKeB+oBqbrDCYRkfZl7p/atZ+SiouLvaSkJOoyRERSipktdffihMM6SkCYWRmwoRVf0Qf4qI3KiVJHWQ7QsiSrjrIsHWU5oHXLMsTdE57l02ECorXMrORIKZpKOspygJYlWXWUZekoywHhLYtu1iciIgkpIEREJCEFxCceirqANtJRlgO0LMmqoyxLR1kOCGlZdAxCREQSUg9CREQSUkCIiEhCR1VAmNkvzWy7mb13hOFmZj8OHlT0rpmd2t41NlUTluU8M6sws7eD13fbu8amMLNBZrbAzFaY2XIzm5lgnJRYL01clqRfL2aWY2Zvmtk7wXL8W4Jxss3syWCdvGFmBe1faeOauCzXmFlZ3Dq5Lopam8rM0s1smZnVvwt2268Xdz9qXsA5wKnAe0cYfjHwF2J3kz0DeCPqmluxLOcBz0ddZxOWoz9wavC+K7AKGJmK66WJy5L06yX4d+4SvM8k9jCvM+qN83XgZ8H7KcCTUdfdimW5Brg/6lqbsUyzgN8m+u+ordfLUdWDcPeXgR0NjHIZ8CuPWQz0MLP+7VNd8zRhWVKCu29z97eC93uAFXz62R8psV6auCxJL/h33ht8zAxe9c9muQx4LHj/NDDBwnjmZSs1cVlShpnlA5cADx9hlDZdL0dVQDRBkx5UlELODLrWfzGzE6IupjFBd/gU4h4/G0i59dLAskAKrJdgN8bbwHZgrrsfcZ24ezVQAfRu3yqbpgnLAvD5YPfl02Y2KMHwZHEv8G2g9gjD23S9KCAO16QHFaWIt4jdY+Vk4CfAsxHX0yAz6wL8AbjZ3XfXH5xgkqRdL40sS0qsF3evcffRxJ7FMsbMTqw3SsqskyYsy3NAgbuPAubxyS/wpGJmlwLb3X1pQ6MlaGvxelFAHK7DPKjI3XfXda3d/c9Appn1ibishMwsk9gG9Tfu/kyCUVJmvTS2LKm0XgDcfRewELiw3qCP14mZZQDdSfJdnkdaFncvd/eDwcefA6e1c2lNNRaYbGbrgSeA883s1/XGadP1ooA43Bzg6uCsmTOACnffFnVRLWFmx9TtezSzMcTWdXm0VX1aUOMvgBXufs8RRkuJ9dKUZUmF9WJmeWbWI3jfCbgA+Hu90eYA04L3XwDme3BkNJk0ZVnqHc+aTOzYUdJx99vdPd9jD1ibQuzf/Mv1RmvT9RLmI0eTjpn9jthZJH3MbDNwB7GDVrj7z4A/EztjphTYB3wlmkob14Rl+QLwNTOrBvYDU5Lxf2Biv4r+CfhbsJ8Y4F+AwZBy66Upy5IK66U/8JiZpRMLsKfc/Xk7/GFfvwAeN7NSYr9Qp0RXboOasiw3WexRx9XEluWayKptgTDXi261ISIiCWkXk4iIJKSAEBGRhBQQIiKSkAJCREQSUkCIiEhCCgiRdhDcMfT+qOsQaQ4FhEgbCy7oa9X/W8FVsCKRUkCItICZzTKz94LXzWZWYLHnQPyU2P2WBpnZV8xslZktInYRXd20eWb2BzNbErzGBu3fM7OHzOxF4FfRLJnIJ/QrRaSZzOw0Yldzn07s5mhvAIuAY4GvuPvXg9s3/Bux+/pUAAuAZcFX3AfMdvdXzWww8AJwfDDsNOBsd9/fXssjciQKCJHmOxv4o7tXApjZM8A4YEPwvAqIhcdCdy8LxnkSKAqGXQCMjLtNfzcz6xq8n6NwkGShgBBpviM9gKWy3ucj3ccmDTizfhAEgVH/O0Qio2MQIs33MvA5M8s1s87APwKv1BvnDeA8M+sd3AL8irhhLwIz6j6Y2eiwCxZpCfUgRJrJ3d8ys0eBN4Omh4Gd9cbZZmbfA14HthE7cJ0eDL4JeMDM3iX2/+DLwI3hVy7SPLqbq4iIJKRdTCIikpACQkREElJAiIhIQgoIERFJSAEhIiIJKSBERCQhBYSIiCT0/wF3lmkd+dGdngAAAABJRU5ErkJggg==\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 four.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function will be used in the next section; please run the cell.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "74cd370af129440ea0958b076f734cde",
       "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": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "pr1 = PolynomialFeatures(degree=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "pr1=PolynomialFeatures(degree=2)\n",
    "\n",
    "-->\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\" \n",
    "?</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train_pr1 = pr1.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "x_test_pr1 = pr1.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\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"
   ]
  },
  {
   "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": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(110, 15)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train_pr1.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    " x_train_pr1.shape #There are now 15 features:\n",
    "\n",
    "-->\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\" and train the object using the method \"fit\" using the polynomial features?</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly1 = LinearRegression()\n",
    "poly1.fit(x_train_pr1,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "poly1=LinearRegression().fit(x_train_pr1,y_train)\n",
    "\n",
    "-->\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 output vs the test data?</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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": [
    "yhat_test_pr1 = poly1.predict(x_test_pr1)\n",
    "DistributionPlot(y_test,yhat_test_pr1,\"Actual Values (Test)\", \"Predicted Values (Test)\", Title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "yhat_test1=poly1.predict(x_test_pr1)\n",
    "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n",
    "DistributionPlot(y_test, yhat_test1, \"Actual Values (Test)\", \"Predicted Values (Test)\", Title)\n",
    "\n",
    "-->\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, explain in words about the two regions were the predicted prices are less accurate than the actual prices</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\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"
   ]
  },
  {
   "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 we will see how the parameter Alfa 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 to 0.1 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "RigeModel=Ridge(alpha=0.1)"
   ]
  },
  {
   "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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\ridge.py:147: LinAlgWarning: Ill-conditioned matrix (rcond=1.02972e-16): result may not be accurate.\n",
      "  overwrite_a=True).T\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=0.1, 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: [ 6567.83081933  9597.97151399 20836.22326844 19347.69543463]\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, for example, we can use a for loop. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "Rsqu_test = []\n",
    "Rsqu_train = []\n",
    "dummy1 = []\n",
    "Alpha = 10 * np.array(range(0,1000))\n",
    "for alpha in Alpha:\n",
    "    RigeModel = Ridge(alpha=alpha) \n",
    "    RigeModel.fit(x_train_pr, y_train)\n",
    "    Rsqu_test.append(RigeModel.score(x_test_pr, y_test))\n",
    "    Rsqu_train.append(RigeModel.score(x_train_pr, y_train))"
   ]
  },
  {
   "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 0x28af2b13fc8>"
      ]
     },
     "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 6**: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 6 represents the R^2 of the test data.  \n",
    "As Alpha increases the R^2 decreases.  \n",
    "Therefore as Alpha increases the model performs worse on the test data.  \n",
    "\n",
    "The blue line represents the R^2 on the validation data.  \n",
    "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 and calculate the R^2 using the polynomial features, use the training data to train the model and 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": [
       "0.5418576440211109"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "Rige = Ridge(alpha=10) \n",
    "Rige.fit(x_train_pr, y_train)\n",
    "Rige.score(x_test_pr, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "RigeModel = Ridge(alpha=10) \n",
    "RigeModel.fit(x_train_pr, y_train)\n",
    "RigeModel.score(x_test_pr, y_test)\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref4\">Part 4: Grid Search</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The term Alfa 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 regions 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the model \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_search.py:814: 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": [
       "GridSearchCV(cv=4, error_score='raise-deprecating',\n",
       "             estimator=Ridge(alpha=1.0, copy_X=True, fit_intercept=True,\n",
       "                             max_iter=None, normalize=False, random_state=None,\n",
       "                             solver='auto', tol=0.001),\n",
       "             iid='warn', n_jobs=None,\n",
       "             param_grid=[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000,\n",
       "                                    100000]}],\n",
       "             pre_dispatch='2*n_jobs', refit=True, return_train_score=False,\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": [
       "0.841164983103615"
      ]
     },
     "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": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_search.py:814: 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, normalize=True,\n",
       "      random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "parameters2 = [{'alpha':[0.001,0.1,1, 10, 100, 1000,10000,100000,100000],'normalize':[True,False]}]\n",
    "gridSrch = GridSearchCV(Ridge(),parameters2,cv=4)\n",
    "gridSrch.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']],y_data)\n",
    "gridSrch.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\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_\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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