DA0101EN-Review-Model-Evaluation-and-Refinement.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "    <a href=\"http://cocl.us/DA0101EN_NotbookLink_Top\">\n",
    "         <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/TopAd.png\" width=\"750\" align=\"center\">\n",
    "    </a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.bigdatauniversity.com\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/CCLog.png\" width=300, align=\"center\"></a>\n",
    "\n",
    "<h1 align=center><font size=5>Data Analysis with Python</font></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Module 5: Model Evaluation and Refinement</h1>\n",
    "\n",
    "We have built models and made predictions of vehicle prices. Now we will determine how accurate these predictions are. "
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/cognitive_class_DA0101EN_objectstorage\">HERE</a> for free storage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_csv('module_5_auto.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " First lets only use numeric data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Unnamed: 0.1</th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>...</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>48.8</td>\n",
       "      <td>2548</td>\n",
       "      <td>130</td>\n",
       "      <td>...</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>48.8</td>\n",
       "      <td>2548</td>\n",
       "      <td>130</td>\n",
       "      <td>...</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <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",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>0.922222</td>\n",
       "      <td>54.3</td>\n",
       "      <td>2824</td>\n",
       "      <td>136</td>\n",
       "      <td>...</td>\n",
       "      <td>3.40</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "<p>5 rows × 21 columns</p>\n",
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      "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": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df=df._get_numeric_data()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Libraries for plotting "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "! pip install ipywidgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\LENOVO\\Anaconda3\\lib\\site-packages\\IPython\\html.py:14: ShimWarning: The `IPython.html` package has been deprecated since IPython 4.0. You should import from `notebook` instead. `IPython.html.widgets` has moved to `ipywidgets`.\n",
      "  \"`IPython.html.widgets` has moved to `ipywidgets`.\", ShimWarning)\n"
     ]
    }
   ],
   "source": [
    "from IPython.display import display\n",
    "from IPython.html import widgets \n",
    "from IPython.display import display\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Functions for plotting</h2>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_data = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "drop price data in x data"
   ]
  },
  {
   "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>. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 31\n",
      "number of training samples: 170\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=0.15, 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. "
   ]
  },
  {
   "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",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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",
    "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": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 81\n",
      "number of training samples: 120\n"
     ]
    }
   ],
   "source": [
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size=0.4, random_state=0) \n",
    "print(\"number of test samples :\", x_test1.shape[0])\n",
    "print(\"number of training samples:\",x_train1.shape[0])"
   ]
  },
  {
   "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",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import <b>LinearRegression</b> from the module <b>linear_model</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We create a Linear Regression object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "lre=LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we fit the model using the feature horsepower "
   ]
  },
  {
   "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": [
    "lre.fit(x_train[['horsepower']], y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's Calculate the R^2 on the test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.707688374146705"
      ]
     },
     "execution_count": 28,
     "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6449517437659684"
      ]
     },
     "execution_count": 29,
     "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 21\n",
      "number of training samples: 180\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.7340722810055448"
      ]
     },
     "execution_count": 34,
     "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=0.1, random_state=0) \n",
    "print(\"number of test samples :\", x_test1.shape[0])\n",
    "print(\"number of training samples:\",x_train1.shape[0])\n",
    "lre.fit(x_train1[['horsepower']],y_train1)\n",
    "lre.score(x_test1[['horsepower']], y_test1)"
   ]
  },
  {
   "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",
    "-->"
   ]
  },
  {
   "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. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Cross-validation Score</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets import <b>model_selection</b> from the module <b>cross_val_score</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.7746232 , 0.51716687, 0.74785353, 0.04839605])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rcross"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can calculate the average and standard deviation of our estimate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "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'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20254142.84026704, 43745493.2650517 , 12539630.34014932,\n",
       "       17561927.72247591])"
      ]
     },
     "execution_count": 39,
     "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.443196127755029"
      ]
     },
     "execution_count": 40,
     "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[1]"
   ]
  },
  {
   "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[1]\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 to get a prediction while the rest of the folds are used as test data. First import the function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([14141.63807508, 14141.63807508, 20814.29423473, 12745.03562306,\n",
       "       14762.35027598])"
      ]
     },
     "execution_count": 43,
     "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>"
   ]
  },
  {
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 41,
     "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11927.70699817, 11236.71672034,  6436.91775515, 21890.22064982,\n",
       "       16667.18254832])"
      ]
     },
     "execution_count": 44,
     "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: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11349.16502418,  5914.48335385, 11243.76325987,  6662.03197043,\n",
       "       15555.76936275])"
      ]
     },
     "execution_count": 48,
     "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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. "
   ]
  },
  {
   "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. "
   ]
  },
  {
   "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": [
    "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. "
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use 55 percent of the data for testing and the rest for training:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "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>. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "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. "
   ]
  },
  {
   "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. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " R^2 of the training data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly.score(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " R^2 of the test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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."
   ]
  },
  {
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function will be used in the next section; please run the cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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",
    "</div>"
   ]
  },
  {
   "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",
    "-->"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "x_train_pr1=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "\n",
    "x_test_pr1=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\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",
    "-->"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "There are now 15 features: x_train_pr1.shape \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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "poly1=linear_model.LinearRegression().fit(x_train_pr1,y_train)\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>"
   ]
  },
  {
   "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_train_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",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #4f): </h1>\n",
    "\n",
    "<b>Use the distribution plot to determine the two regions were the predicted prices are less accurate than the actual prices.</b>\n",
    "</div>"
   ]
  },
  {
   "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 lower than actual value for cars where the price  $ 10,000 range, conversely the predicted price is larger 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",
    "<img src = \"https://ibm.box.com/shared/static/c35ipv9zeanu7ynsnppb8gjo2re5ugeg.png\" width = 700, align = \"center\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref3\">Part 3: Ridge regression</h2> "
   ]
  },
  {
   "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's perform a degree two polynomial transformation on our data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "RigeModel.fit(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Similarly, you can obtain a prediction: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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 Alfa that minimizes the test error, for example, we can use a for loop. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Rsqu_test = []\n",
    "Rsqu_train = []\n",
    "dummy1 = []\n",
    "ALFA = 10 * np.array(range(0,1000))\n",
    "for alfa in ALFA:\n",
    "    RigeModel = Ridge(alpha=alfa) \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 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "\n",
    "plt.plot(ALFA,Rsqu_test, label='validation data  ')\n",
    "plt.plot(ALFA,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 test data, and the red line represents the R^2 of the training data. The x-axis represents the different values of Alfa "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The red line in figure 6 represents the  R^2 of the test data, as Alpha increases the R^2 decreases; therefore as Alfa increases the model performs worse on the test data.  The blue line represents the R^2 on the validation data, as the value for Alfa increases the R^2 decreases.   "
   ]
  },
  {
   "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",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "RigeModel = Ridge(alpha=0) \n",
    "RigeModel.fit(x_train_pr, y_train)\n",
    "RigeModel.score(x_test_pr, y_test)\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref4\">Part 4: Grid Search</h2>"
   ]
  },
  {
   "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import <b>GridSearchCV</b> from  the module <b>model_selection</b>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a dictionary of parameter values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "RR=Ridge()\n",
    "RR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a ridge grid search object "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Grid1 = GridSearchCV(RR, parameters1,cv=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "BestRR=Grid1.best_estimator_\n",
    "BestRR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We now test our model on the test data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n"
   ]
  },
  {
   "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",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Thank you for completing this notebook!</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "\n",
    "    <p><a href=\"https://cocl.us/DA0101EN_NotbookLink_Top_bottom\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/BottomAd.png\" width=\"750\" align=\"center\"></a></p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>About the Authors:</h3>\n",
    "\n",
    "This notebook was written by <a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>, <a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>, Bahare Talayian, Eric Xiao, Steven Dong, Parizad, Hima Vsudevan and <a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a> and <a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "<p><a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a> is a Data Scientist at IBM, and holds a PhD in Electrical Engineering. His research focused on using Machine Learning, Signal Processing, and Computer Vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "<p>Copyright &copy; 2018 IBM Developer Skills Network. This notebook and its source code are released under the terms of the <a href=\"https://cognitiveclass.ai/mit-license/\">MIT License</a>.</p>"
   ]
  }
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