5 - Model Evaluation and Refinement.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "    <a href=\"https://skills.network/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2022-01-01\" target=\"_blank\">\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\"  />\n",
    "    </a>\n",
    "</p>\n",
    "\n",
    "In this notebook we will evaluate and refine prediction models\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object. Click <a href=\"https://cocl.us/DA101EN_object_storage?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2022-01-01\">HERE</a> for free storage.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#install specific version of libraries used in lab\n",
    "#! mamba install pandas==1.3.3 -y\n",
    "#! mamba install numpy=1.21.2 -y\n",
    "#! mamba install sklearn=0.20.1 -y\n",
    "#!pip install   ipywidgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# Import clean data \n",
    "path = 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/module_5_auto.csv'\n",
    "df = pd.read_csv(path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_csv('module_5_auto.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's only use numeric data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Unnamed: 0.1</th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>...</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>48.8</td>\n",
       "      <td>2548</td>\n",
       "      <td>130</td>\n",
       "      <td>...</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>0.890278</td>\n",
       "      <td>48.8</td>\n",
       "      <td>2548</td>\n",
       "      <td>130</td>\n",
       "      <td>...</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>0.909722</td>\n",
       "      <td>52.4</td>\n",
       "      <td>2823</td>\n",
       "      <td>152</td>\n",
       "      <td>...</td>\n",
       "      <td>3.47</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>0.919444</td>\n",
       "      <td>54.3</td>\n",
       "      <td>2337</td>\n",
       "      <td>109</td>\n",
       "      <td>...</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>0.922222</td>\n",
       "      <td>54.3</td>\n",
       "      <td>2824</td>\n",
       "      <td>136</td>\n",
       "      <td>...</td>\n",
       "      <td>3.40</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 21 columns</p>\n",
       "</div>"
      ],
      "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": [
    "from ipywidgets import interact, interactive, fixed, interact_manual"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Functions for Plotting</h2>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def DistributionPlot(RedFunction, BlueFunction, RedName, BlueName, Title):\n",
    "    width = 12\n",
    "    height = 10\n",
    "    plt.figure(figsize=(width, height))\n",
    "\n",
    "    ax1 = sns.distplot(RedFunction, hist=False, color=\"r\", label=RedName)\n",
    "    ax2 = sns.distplot(BlueFunction, hist=False, color=\"b\", label=BlueName, ax=ax1)\n",
    "\n",
    "    plt.title(Title)\n",
    "    plt.xlabel('Price (in dollars)')\n",
    "    plt.ylabel('Proportion of Cars')\n",
    "\n",
    "    plt.show()\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PollyPlot(xtrain, xtest, y_train, y_test, lr,poly_transform):\n",
    "    width = 12\n",
    "    height = 10\n",
    "    plt.figure(figsize=(width, height))\n",
    "    \n",
    "    \n",
    "    #training data \n",
    "    #testing data \n",
    "    # lr:  linear regression object \n",
    "    #poly_transform:  polynomial transformation object \n",
    " \n",
    "    xmax=max([xtrain.values.max(), xtest.values.max()])\n",
    "\n",
    "    xmin=min([xtrain.values.min(), xtest.values.min()])\n",
    "\n",
    "    x=np.arange(xmin, xmax, 0.1)\n",
    "\n",
    "\n",
    "    plt.plot(xtrain, y_train, 'ro', label='Training Data')\n",
    "    plt.plot(xtest, y_test, 'go', label='Test Data')\n",
    "    plt.plot(x, lr.predict(poly_transform.fit_transform(x.reshape(-1, 1))), label='Predicted Function')\n",
    "    plt.ylim([-10000, 60000])\n",
    "    plt.ylabel('Price')\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref1\">Part 1: Training and Testing</h2>\n",
    "\n",
    "<p>An important step in testing your model is to split your data into training and testing data. We will place the target data <b>price</b> in a separate dataframe <b>y_data</b>:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_data = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Drop price data in dataframe **x_data**:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_data=df.drop('price',axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we randomly split our data into training and testing data using the function <b>train_test_split</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 21\n",
      "number of training samples: 180\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.10, random_state=1)\n",
    "\n",
    "\n",
    "print(\"number of test samples :\", x_test.shape[0])\n",
    "print(\"number of training samples:\",x_train.shape[0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The <b>test_size</b> parameter sets the proportion of data that is split into the testing set. In the above, the testing set is 10% of the total dataset.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>We use the function \"train_test_split\" to split up the dataset such that 40% of the data samples will be utilized for testing. Set the parameter \"random_state\" equal to zero. The output of the function should be the following:  \"x_train1\" , \"x_test1\", \"y_train1\" and  \"y_test1\".</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 81\n",
      "number of training samples: 120\n"
     ]
    }
   ],
   "source": [
    "x_train1, x_test1, y_train1, y_test1 = train_test_split(x_data, y_data, test_size = 0.4, random_state=0)\n",
    "\n",
    "print(\"number of test samples :\", x_test1.shape[0])\n",
    "print(\"number of training samples:\",x_train1.shape[0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import <b>LinearRegression</b> from the module <b>linear_model</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a Linear Regression object:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "lre=LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We fit the model using the feature \"horsepower\":\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lre.fit(x_train[['horsepower']], y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2 on the test data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3635875575078824"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lre.score(x_test[['horsepower']], y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the R^2 is much smaller using the test data compared to the training data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6619724197515103"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lre.score(x_train[['horsepower']], y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> \n",
    "Find the R^2  on the test data using 40% of the dataset for testing.\n",
    "</b>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7139364665406973"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lre1 = LinearRegression()\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",
    "\n",
    "lre1.fit(x_train1[['horsepower']], y_train1)\n",
    "\n",
    "lre1.score(x_test1[['horsepower']], y_test1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes you do not have sufficient testing data; as a result, you may want to perform cross-validation. Let's go over several methods that you can use for cross-validation.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Cross-Validation Score</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import <b>model_selection</b> from the module <b>cross_val_score</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We input the object, the feature (\"horsepower\"), and the target data (y_data). The parameter 'cv' determines the number of folds. In this case, it is 4.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "Rcross = cross_val_score(lre, x_data[['horsepower']], y_data, cv=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The default scoring is R^2. Each element in the array has the average R^2 value for the fold:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.7746232 , 0.51716687, 0.74785353, 0.04839605])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Rcross"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can calculate the average and standard deviation of our estimate:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the folds are 0.522009915042119 and the standard deviation is 0.2911839444756029\n"
     ]
    }
   ],
   "source": [
    "print(\"The mean of the folds are\", Rcross.mean(), \"and the standard deviation is\" , Rcross.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use negative squared error as a score by setting the parameter  'scoring' metric to 'neg_mean_squared_error'.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20254142.84026704, 43745493.2650517 , 12539630.34014931,\n",
       "       17561927.72247591])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-1 * cross_val_score(lre,x_data[['horsepower']], y_data,cv=4,scoring='neg_mean_squared_error')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> \n",
    "Let's calculate the average R^2 using two folds, then find the average R^2 for the second fold utilizing the \"horsepower\" feature: \n",
    "</b>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.59015621 0.44319613]\n",
      "0.5166761697127429\n"
     ]
    }
   ],
   "source": [
    "Rcross1 = cross_val_score(lre, x_data[['horsepower']], y_data, cv=2)\n",
    "print(Rcross1)\n",
    "print(Rcross1.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also use the function 'cross_val_predict' to predict the output. The function splits up the data into the specified number of folds, with one fold for testing and the other folds are used for training. First, import the function:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_predict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We input the object, the feature <b>\"horsepower\"</b>, and the target data <b>y_data</b>. The parameter 'cv' determines the number of folds. In this case, it is 4. We can produce an output:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([14141.63807508, 14141.63807508, 20814.29423473, 12745.03562306,\n",
       "       14762.35027598])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = cross_val_predict(lre,x_data[['horsepower']], y_data,cv=4)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref2\">Part 2: Overfitting, Underfitting and Model Selection</h2>\n",
    "\n",
    "<p>It turns out that the test data, sometimes referred to as the \"out of sample data\", is a much better measure of how well your model performs in the real world.  One reason for this is overfitting.\n",
    "\n",
    "Let's go over some examples. It turns out these differences are more apparent in Multiple Linear Regression and Polynomial Regression so we will explore overfitting in that context.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create Multiple Linear Regression objects and train the model using <b>'horsepower'</b>, <b>'curb-weight'</b>, <b>'engine-size'</b> and <b>'highway-mpg'</b> as features.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = LinearRegression()\n",
    "lr.fit(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction using training data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 7426.6731551 , 28323.75090803, 14213.38819709,  4052.34146983,\n",
       "       34500.19124244])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat_train = lr.predict(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "yhat_train[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction using test data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11349.35089149,  5884.11059106, 11208.6928275 ,  6641.07786278,\n",
       "       15565.79920282])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat_test = lr.predict(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "yhat_test[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's perform some model evaluation using our training and testing data separately. First, we import the seaborn and matplotlib library for plotting.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's examine the distribution of the predicted values of the training data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Alvaro\\anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "C:\\Users\\Alvaro\\anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Title = 'Distribution  Plot of  Predicted Value Using Training Data vs Training Data Distribution'\n",
    "DistributionPlot(y_train, yhat_train, \"Actual Values (Train)\", \"Predicted Values (Train)\", Title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 1: Plot of predicted values using the training data compared to the actual values of the training data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far, the model seems to be doing well in learning from the training dataset. But what happens when the model encounters new data from the testing dataset? When the model generates new values from the test data, we see the distribution of the predicted values is much different from the actual target values.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Alvaro\\anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "C:\\Users\\Alvaro\\anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n",
    "DistributionPlot(y_test,yhat_test,\"Actual Values (Test)\",\"Predicted Values (Test)\",Title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 2: Plot of predicted value using the test data compared to the actual values of the test data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing Figure 1 and Figure 2, it is evident that the distribution of the test data in Figure 1 is much better at fitting the data. This difference in Figure 2 is apparent in the range of 5000 to 15,000. This is where the shape of the distribution is extremely different. Let's see if polynomial regression also exhibits a drop in the prediction accuracy when analysing the test dataset.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Overfitting</h4>\n",
    "<p>Overfitting occurs when the model fits the noise, but not the underlying process. Therefore, when testing your model using the test set, your model does not perform as well since it is modelling noise, not the underlying process that generated the relationship. Let's create a degree 5 polynomial model.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use 55 percent of the data for training and the rest for testing:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.45, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will perform a degree 5 polynomial transformation on the feature <b>'horsepower'</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=5)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr = PolynomialFeatures(degree=5)\n",
    "x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "x_test_pr = pr.fit_transform(x_test[['horsepower']])\n",
    "pr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's create a Linear Regression model \"poly\" and train it.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly = LinearRegression()\n",
    "poly.fit(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the output of our model using the method \"predict.\" We assign the values to \"yhat\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6728.70501896,  7308.02845162, 12213.7843307 , 18893.19108677,\n",
       "       19995.88963424])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = poly.predict(x_test_pr)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take the first five predicted values and compare it to the actual targets.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted values: [ 6728.70501896  7308.02845162 12213.7843307  18893.19108677]\n",
      "True values: [ 6295. 10698. 13860. 13499.]\n"
     ]
    }
   ],
   "source": [
    "print(\"Predicted values:\", yhat[0:4])\n",
    "print(\"True values:\", y_test[0:4].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the function \"PollyPlot\" that we defined at the beginning of the lab to display the training data, testing data, and the predicted function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train, y_test, poly,pr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 3: A polynomial regression model where red dots represent training data, green dots represent test data, and the blue line represents the model prediction.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the estimated function appears to track the data but around 200 horsepower, the function begins to diverge from the data points.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R^2 of the training data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5567716902635091"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly.score(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R^2 of the test data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-29.871418859187518"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly.score(x_test_pr, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see the R^2 for the training data is 0.5567 while the R^2 on the test data was -29.87.  The lower the R^2, the worse the model. A negative R^2 is a sign of overfitting.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how the R^2 changes on the test data for different order polynomials and then plot the results:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(3, 0.75, 'Maximum R^2 ')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Rsqu_test = []\n",
    "\n",
    "order = [1, 2, 3, 4]\n",
    "for n in order:\n",
    "    pr = PolynomialFeatures(degree=n)\n",
    "    \n",
    "    x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "    \n",
    "    x_test_pr = pr.fit_transform(x_test[['horsepower']])    \n",
    "    \n",
    "    lr.fit(x_train_pr, y_train)\n",
    "    \n",
    "    Rsqu_test.append(lr.score(x_test_pr, y_test))\n",
    "\n",
    "plt.plot(order, Rsqu_test)\n",
    "plt.xlabel('order')\n",
    "plt.ylabel('R^2')\n",
    "plt.title('R^2 Using Test Data')\n",
    "plt.text(3, 0.75, 'Maximum R^2 ')    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see the R^2 gradually increases until an order three polynomial is used. Then, the R^2 dramatically decreases at an order four polynomial.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function will be used in the next section. Please run the cell below.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(order, test_data):\n",
    "    x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=test_data, random_state=0)\n",
    "    pr = PolynomialFeatures(degree=order)\n",
    "    x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "    x_test_pr = pr.fit_transform(x_test[['horsepower']])\n",
    "    poly = LinearRegression()\n",
    "    poly.fit(x_train_pr,y_train)\n",
    "    PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train,y_test, poly, pr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following interface allows you to experiment with different polynomial orders and different amounts of data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c378e1f1246c4de7993657f850ac3ec3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=3, description='order', max=6), FloatSlider(value=0.45, description='tes…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.f(order, test_data)>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interact(f, order=(0, 6, 1), test_data=(0.05, 0.95, 0.05))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>We can perform polynomial transformations with more than one feature. Create a \"PolynomialFeatures\" object \"pr1\" of degree two.</b>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "pr1 = PolynomialFeatures(degree=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> \n",
    " Transform the training and testing samples for the features 'horsepower', 'curb-weight', 'engine-size' and 'highway-mpg'. Hint: use the method \"fit_transform\".</b>"
   ]
  },
  {
   "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_test[['horsepower','curb-weight','engine-size','highway-mpg']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> \n",
    "How many dimensions does the new feature have? Hint: use the attribute \"shape\".\n",
    "</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(110, 15)\n",
      "(91, 15)\n"
     ]
    }
   ],
   "source": [
    "print(x_train_pr1.shape)\n",
    "print(x_test_pr1.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> \n",
    "Create a linear regression model \"poly1\". Train the object using the method \"fit\" using the polynomial features.</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly1 = LinearRegression()\n",
    "\n",
    "poly1.fit(x_train_pr1,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Use the method  \"predict\" to predict an output on the polynomial features, then use the function \"DistributionPlot\" to display the distribution of the predicted test output vs. the actual test data.</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Alvaro\\anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "C:\\Users\\Alvaro\\anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "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_test1 = poly1.predict(x_test_pr1)\n",
    "\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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref3\">Part 3: Ridge Regression</h2> \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, we will review Ridge Regression and see how the parameter alpha changes the model. Just a note, here our test data will be used as validation data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's perform a degree two polynomial transformation on our data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "x_train_pr=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])\n",
    "x_test_pr=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import  <b>Ridge</b>  from the module <b>linear models</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a Ridge regression object, setting the regularization parameter (alpha) to 0.1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "RigeModel=Ridge(alpha=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:\\Users\\Alvaro\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_ridge.py:147: LinAlgWarning: Ill-conditioned matrix (rcond=1.02972e-16): result may not be accurate.\n",
      "  return linalg.solve(A, Xy, sym_pos=True,\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=0.1)"
      ]
     },
     "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 20836.22326843 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. To do so, we can use a for loop. We have also created a progress bar to see how many iterations we have completed so far.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:05<00:00, 177.72it/s, Test Score=0.564, Train Score=0.859]\n"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm\n",
    "\n",
    "Rsqu_test = []\n",
    "Rsqu_train = []\n",
    "dummy1 = []\n",
    "Alpha = 10 * np.array(range(0,1000))\n",
    "pbar = tqdm(Alpha)\n",
    "\n",
    "for alpha in pbar:\n",
    "    RigeModel = Ridge(alpha=alpha) \n",
    "    RigeModel.fit(x_train_pr, y_train)\n",
    "    test_score, train_score = RigeModel.score(x_test_pr, y_test), RigeModel.score(x_train_pr, y_train)\n",
    "    \n",
    "    pbar.set_postfix({\"Test Score\": test_score, \"Train Score\": train_score})\n",
    "\n",
    "    Rsqu_test.append(test_score)\n",
    "    Rsqu_train.append(train_score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot out the value of R^2 for different alphas:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x203aedad910>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtcAAAJNCAYAAAD6c1l4AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAA4eElEQVR4nO3de5hlZWHn+9/bdenqK91Agwi03RoUaEAuFaLBUYjRoBPjJSbBy0Q8E4lEJ5k8GQaSSWLUJ2dyToyjjhpDHGcyDonHoCjmMd4yGNTgSDeicvHCTWhJoAGBvndV13v+2HtX766uvu61u7qrP5/n2c9ee112vZul8nXVW3uVWmsAAIDezZnpAQAAwGwhrgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAhgzM9gCYde+yxdcWKFTM9DAAAZrE1a9Y8UmtdNt22WRXXK1asyOrVq2d6GAAAzGKllB/ubptpIQAA0BBxDQAADRHXAADQkFk15xoAYCaNjY1l7dq12bJly0wPhQaMjIzkpJNOytDQ0D4fI64BABqydu3aLFq0KCtWrEgpZaaHQw9qrXn00Uezdu3arFy5cp+PMy0EAKAhW7ZsyTHHHCOsZ4FSSo455pj9/i2EuAYAaJCwnj0O5FyKawCAI9jChQuTJA8++GBe/epXT7vPhRdeuNd7ibznPe/Jpk2bJl+/9KUvzeOPP97YODs6492dxx9/PB/84Acb/7n7SlwDAJCnPvWpufbaaw/4+Klx/dnPfjZLlixpYGT7R1wDANCIK6+8cqew/KM/+qP82Z/9WTZs2JAXvvCFOffcc3PmmWfm05/+9C7H3nfffTnjjDOSJJs3b84ll1ySs846K7/yK7+SzZs3T+53+eWXZ3R0NKtWrcrb3va2JMn73ve+PPjgg7noooty0UUXJWndOfuRRx5Jkrz73e/OGWeckTPOOCPvec97Jn/eaaedlje96U1ZtWpVXvziF+/0czruvffePPe5z81P/uRP5g/+4A8m1+/uM1111VW5++67c/bZZ+eKK67Yp8/eqFrrrHmcd955FQBgptxxxx0z+vNvueWW+vznP3/y9WmnnVZ/+MMf1rGxsfrEE0/UWmtdt25dfcYznlEnJiZqrbUuWLCg1lrrvffeW1etWlVrrfXP/uzP6hvf+MZaa63f+ta36sDAQL355ptrrbU++uijtdZax8fH6wte8IL6rW99q9Za69Oe9rS6bt26yZ/deb169ep6xhln1A0bNtT169fX008/vd5yyy313nvvrQMDA/Wb3/xmrbXWX/qlX6of/ehHd/lML3vZy+pf/dVf1Vprff/73z853t19pu7Psaf99tV05zTJ6rqbHvVVfAAAffD2z9yeOx58stH3PP2pi/O2l63a7fZzzjknDz/8cB588MGsW7cuS5cuzfLlyzM2Npbf+73fy4033pg5c+bkRz/6UR566KE85SlPmfZ9brzxxvzmb/5mkuSss87KWWedNbnt4x//eK6++uqMj4/nn//5n3PHHXfstH2qr371q3nlK1+ZBQsWJEle9apX5Stf+Up+4Rd+IStXrszZZ5+dJDnvvPNy33337XL81772tXziE59Ikvybf/NvcuWVVyZpXSCe7jNNtbv9dvfZeyWuAQBmkVe/+tW59tpr8y//8i+55JJLkiTXXHNN1q1blzVr1mRoaCgrVqzY61fMTfdNGffee2/e9a535eabb87SpUtz6aWX7vV9Whd6pzd37tzJ5YGBgWmnhexuLPv6mQ7ks/dCXAMA9MGerjD30yWXXJI3velNeeSRR/KP//iPSZInnngixx13XIaGhnLDDTfkhz/84R7f4/nPf36uueaaXHTRRbntttvy7W9/O0ny5JNPZsGCBTnqqKPy0EMP5e///u9z4YUXJkkWLVqU9evX59hjj93lvS699NJcddVVqbXmuuuuy0c/+tF9/jwXXHBBPvaxj+X1r399rrnmmsn1u/tMnXHsbb9+EdcAALPIqlWrsn79+px44ok54YQTkiSve93r8rKXvSyjo6M5++yzc+qpp+7xPS6//PK88Y1vzFlnnZWzzz47559/fpLk2c9+ds4555ysWrUqT3/603PBBRdMHnPZZZflJS95SU444YTccMMNk+vPPffcXHrppZPv8Wu/9ms555xzpp0CMp33vve9ee1rX5v3vve9+cVf/MXJ9bv7TMccc0wuuOCCnHHGGXnJS16SK6+8cr8+e6/Kni7VH25GR0fr3r6DEQCgX+68886cdtppMz0MGjTdOS2lrKm1jk63v6/iAwCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi47tXmzcmLX5x89rMzPRIA4Aj3+OOP54Mf/OABHfvSl740jz/++B73+cM//MN86UtfOqD3n2rFihU588wzc+aZZ+b000/P7//+72fr1q17PKaXz3ewiOtePfBA8sUvJq98ZesZAGCG7Ck+t2/fvsdjP/vZz2bJkiV73Ocd73hHfvZnf/ZAh7eLG264Id/5znfyjW98I/fcc08uu+yyPe4vro8EnXvTDwwkL3950r7NKADAwXbVVVfl7rvvztlnn50rrrgiX/7yl3PRRRflta99bc4888wkySte8Yqcd955WbVqVa6++urJY1esWJFHHnkk9913X0477bS86U1vyqpVq/LiF784mzdvTpJceumlufbaayf3f9vb3pZzzz03Z555Zr773e8mSdatW5cXvehFOffcc/Prv/7redrTnpZHHnlkj+NeuHBhPvShD+VTn/pUHnvssWzYsCEvfOELJ9/705/+9LSfb3f7zSRx3avOry8+8IFk5crkX//r5J/+aWbHBAAckf7kT/4kz3jGM3LrrbfmT//0T5Mk3/jGN/LHf/zHueOOO5IkH/nIR7JmzZqsXr0673vf+/Loo4/u8j4/+MEP8pa3vCW33357lixZkk984hPT/rxjjz02t9xySy6//PK8613vSpK8/e1vz8/8zM/klltuyStf+crcf//9+zT2xYsXZ+XKlfnBD36QkZGRXHfddbnllltyww035Hd+53dSa93l8+1uv5k0OKM/fTboxPVJJyVf+lLyghckP/dzyX/9r8kb3pCUMrPjAwBmxr//98mttzb7nmefnbznPft1yPnnn5+VK1dOvn7f+96X6667LknywAMP5Ac/+EGOOeaYnY5ZuXJlzj777CTJeeedl/vuu2/a937Vq141uc8nP/nJJMlXv/rVyfe/+OKLs3Tp0n0eayeMa635vd/7vdx4442ZM2dOfvSjH+Whhx6adv/p9nvKU56yzz+zaa5c96ozLWRkJDnhhOTLX07OOy954xtb00TavyIBAJgJCxYsmFz+8pe/nC996Uu56aab8q1vfSvnnHNOtnRapsvcuXMnlwcGBjI+Pj7te3f2697nQK8cr1+/Pvfdd1+e+cxn5pprrsm6deuyZs2a3HrrrTn++OOnHee+7ncwuXLdq86V685/CJ/61OQf/iF597uTd7wjWbUqueSS5M1vTp73PFeyAeBIsZ9XmJuwaNGirF+/frfbn3jiiSxdujTz58/Pd7/73Xz9619vfAzPe97z8vGPfzxXXnllvvCFL+THP/7xXo/ZsGFDfuM3fiOveMUrsnTp0jzxxBM57rjjMjQ0lBtuuCE//OEPk+z6+Xa330xy5bpX3VeuOwYGkiuuSO6+O/mt30r+7u+S5z8/Oe205Hd/N7nppmQvf7ELALC/jjnmmFxwwQU544wzcsUVV+yy/eKLL874+HjOOuus/MEf/EGe85znND6Gt73tbfnCF76Qc889N3//93+fE044IYsWLZp234suuihnnHFGzj///Cxfvjx/8Rd/kSR53etel9WrV2d0dDTXXHNNTj311Gk/3+72m0llpid9N2l0dLSuXr364P7Qv/7r5HWva03/eNazpt9n48bk4x9PPvrR5MYbW2G9cGHynOckF1zQmkZy+umtP4ic4//vAMDh6s4778xpp50208OYUVu3bs3AwEAGBwdz00035fLLL8+tTc89P4imO6ellDW11tHp9jctpFdTp4VMZ8GC1hzsN74xefzx5POfb0X2176WvPOdycREa79581pXt5/1rORpT0uWL9/xvHx5smiRaSUAwCHt/vvvzy//8i9nYmIiw8PD+cu//MuZHtJBJa57Nd20kD1ZsiT5lV9pPZJk/frkttuS229P7rij9fz1ryd/+7fJ1D8eGBlJjjsuWbZs58exxyZHHZUsXtx67l7uPA861QBA/51yyin55je/OdPDmDGKq1f7cuV6TxYtSp773Naj2/btyb/8S3L//TseDz/ceqxb13rceWfredOmvf+cefOS+fN3PLpf727bvHnJ8HDrMXfujuXpXu9tn8HB1lx0V94BgFlMXPdqf69c76uBgeTEE1uPqeE91ebNyZNPJk88seO5e7nzvHlzK8Q3bdqxvHFj8sgju65v34mpcQMDrdDuPKa+nvrY2/ap+wwM7HjMmdN6dJanPu/run5s6zxKmf55T9v6+dx5AHDAaq0p/rd0VjiQv00U173q9cp1E+bNaz2OP76595yYaH22bdt2fuzLuuleb9/emuayu8f+bN+yZffbx8ZaY+88tm+f/rl7eRb9UW9j+hHv+xr2u3sk+7bfwX6vQ/39ZmJsnX26993TOsc45mAdcxCMjIzk0UcfzTHHHBOBfXirtebRRx/NyH5eQBXXvdq6tXXFdLZ9y8ecOTuifbardffhvacoP9D9u6N+uuc9bTvcn/e2z+4enfO0P4/dveeBvFfTYztY7wfsqqmIn+45yUlLl2btlVdm3dOf3lzYz/R7zPTP39N7LVzYevTJyMhITjrppP06Rlz3asuW5qeEcHCVsmMqCcxGBzP8O/t077undY5xzOF4zHTP7eWhJCu///3k+9/f92OnvEdPz7PpPfblvX71V5PXvz6HEnHdq61bZ3ZKCMDeHORfiwMcyWbZXIYZIK4BAGgT170yLQQAgDZx3StXrgEAaBPXvXLlGgCANnHdK1euAQBo62tcl1IuLqV8r5RyVynlqmm2H1VK+Uwp5VullNtLKW/s2nZfKeU7pZRbSymr+znOnhx/fLJixUyPAgCAQ0DfvoqvlDKQ5ANJXpRkbZKbSynX11rv6NrtLUnuqLW+rJSyLMn3SinX1Fq3tbdfVGt9pF9jbMRHPzrTIwAA4BDRzyvX5ye5q9Z6TzuWP5bk5VP2qUkWldb9QRcmeSzJeB/HBAAAfdPPuD4xyQNdr9e213V7f5LTkjyY5DtJfqvWOtHeVpN8oZSyppRyWR/HCQAAjehnXE93O7A65fXPJbk1yVOTnJ3k/aWUxe1tF9Raz03ykiRvKaU8f9ofUsplpZTVpZTV69ata2TgAABwIPoZ12uTnNz1+qS0rlB3e2OST9aWu5Lcm+TUJKm1Pth+fjjJdWlNM9lFrfXqWutorXV02bJlDX8EAADYd/2M65uTnFJKWVlKGU5ySZLrp+xzf5IXJkkp5fgkz0pyTyllQSllUXv9giQvTnJbH8cKAAA969u3hdRax0spb03y+SQDST5Sa729lPLm9vYPJXlnkv9RSvlOWtNIrqy1PlJKeXqS61p/55jBJH9da/1cv8YKAABNKLVOnQZ9+BodHa2rVx+6X4kNAMDhr5SyptY6Ot02d2gEAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhvQ1rkspF5dSvldKuauUctU0248qpXymlPKtUsrtpZQ37uuxAABwqOlbXJdSBpJ8IMlLkpye5DWllNOn7PaWJHfUWp+d5MIkf1ZKGd7HYwEA4JDSzyvX5ye5q9Z6T611W5KPJXn5lH1qkkWllJJkYZLHkozv47EAAHBI6Wdcn5jkga7Xa9vrur0/yWlJHkzynSS/VWud2MdjAQDgkNLPuC7TrKtTXv9ckluTPDXJ2UneX0pZvI/Htn5IKZeVUlaXUlavW7fuwEcLAAA96mdcr01yctfrk9K6Qt3tjUk+WVvuSnJvklP38dgkSa316lrraK11dNmyZY0NHgAA9lc/4/rmJKeUUlaWUoaTXJLk+in73J/khUlSSjk+ybOS3LOPxwIAwCFlsF9vXGsdL6W8Ncnnkwwk+Uit9fZSypvb2z+U5J1J/kcp5TtpTQW5stb6SJJMd2y/xgoAAE0otU47lfmwNDo6WlevXj3TwwAAYBYrpayptY5Ot80dGgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAhfY3rUsrFpZTvlVLuKqVcNc32K0opt7Yft5VStpdSjm5vu6+U8p32ttX9HCcAADRhsF9vXEoZSPKBJC9KsjbJzaWU62utd3T2qbX+aZI/be//siS/XWt9rOttLqq1PtKvMQIAQJP6eeX6/CR31VrvqbVuS/KxJC/fw/6vSfI3fRwPAAD0VT/j+sQkD3S9Xttet4tSyvwkFyf5RNfqmuQLpZQ1pZTL+jZKAABoSN+mhSQp06yru9n3ZUm+NmVKyAW11gdLKccl+WIp5bu11ht3+SGt8L4sSZYvX97rmAEA4ID188r12iQnd70+KcmDu9n3kkyZElJrfbD9/HCS69KaZrKLWuvVtdbRWuvosmXLeh40AAAcqH7G9c1JTimlrCylDKcV0NdP3amUclSSFyT5dNe6BaWURZ3lJC9OclsfxwoAAD3r27SQWut4KeWtST6fZCDJR2qtt5dS3tze/qH2rq9M8oVa68auw49Pcl0ppTPGv661fq5fYwUAgCaUWnc3DfrwMzo6Wlev9pXYAAD0TyllTa11dLpt7tAIAAANEdcAANAQcQ0AAA0R1wAA0BBxDQAADRHXAADQEHENAAANEdcAANAQcQ0AAA0R1wAA0BBxDQAADRHXAADQEHENAAANEdcAANAQcQ0AAA0R1wAA0BBxDQAADRHXAADQEHENAAANEdcAANAQcQ0AAA0R1wAA0BBxDQAADRHXAADQEHENAAANEdcAANAQcQ0AAA0R1wAA0BBxDQAADRHXAADQEHENAAANEdcAANAQcQ0AAA0R1wAA0BBxDQAADRHXAADQEHENAAANEdcAANAQcQ0AAA0R1wAA0BBxDQAADRHXAADQEHENAAANEdcAANAQcQ0AAA0R1wAA0BBxDQAADRHXAADQEHENAAANEdcAANAQcQ0AAA0R1wAA0BBxDQAADelrXJdSLi6lfK+Uclcp5apptl9RSrm1/bitlLK9lHL0vhwLAACHmr7FdSllIMkHkrwkyelJXlNKOb17n1rrn9Zaz661np3kd5P8Y631sX05FgAADjX9vHJ9fpK7aq331Fq3JflYkpfvYf/XJPmbAzwWAABmXD/j+sQkD3S9Xttet4tSyvwkFyf5xP4eCwAAh4p+xnWZZl3dzb4vS/K1Wutj+3tsKeWyUsrqUsrqdevWHcAwAQCgGf2M67VJTu56fVKSB3ez7yXZMSVkv46ttV5dax2ttY4uW7ash+ECAEBv+hnXNyc5pZSyspQynFZAXz91p1LKUUlekOTT+3ssAAAcSgb79ca11vFSyluTfD7JQJKP1FpvL6W8ub39Q+1dX5nkC7XWjXs7tl9jBQCAJpRadzcN+vAzOjpaV69ePdPDAABgFiulrKm1jk63zR0aAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCF7jOtSykAp5ddLKe8spVwwZdvv93doAABweNnbleu/SPKCJI8meV8p5d1d217Vt1EBAMBhaG9xfX6t9bW11vck+akkC0spnyylzE1S+j46AAA4jOwtroc7C7XW8VrrZUluTfK/kyzs47gAAOCws7e4Xl1Kubh7Ra31HUn+e5IV/RoUAAAcjvYY17XW19daPzfN+g/XWof6NywAADj87NNX8ZVSBvo9EAAAONztNa5LKYuSfPogjAUAAA5re/ue6xOSfCnJ1QdnOAAAcPga3Mv2ryS5otZ6/cEYDAAAHM72Ni3kx0lOPBgDAQCAw93e4vrCJC8ppbzlIIwFAAAOa3v7Kr6NSX4hyTkHZzgAAHD42tuc69Ratyf5tYMwFgAAOKzt0/dcT1VKGSilvK7pwQAAwOFsb1/Ft7iU8rullPeXUl5cWv5dknuS/PLBGSIAABwe9jYt5KNpfWPITWlNDbkiyXCSl9dab+3v0AAA4PCyt7h+eq31zCQppXw4ySNJltda1/d9ZAAAcJjZ25zrsc5C+w8b7xXWAAAwvb1duX52KeXJ9nJJMq/9uiSptdbFfR0dAAAcRvYY17XWgYM1EAAAONwd0FfxAQAAuxLXAADQEHENAAANEdcAANAQcQ0AAA0R1wAA0BBxDQAADRHXAADQEHENAAAN6Wtcl1IuLqV8r5RyVynlqt3sc2Ep5dZSyu2llH/sWn9fKeU77W2r+zlOAABowh5vf96LUspAkg8keVGStUluLqVcX2u9o2ufJUk+mOTiWuv9pZTjprzNRbXWR/o1RgAAaFI/r1yfn+SuWus9tdZtST6W5OVT9nltkk/WWu9Pklrrw30cDwAA9FU/4/rEJA90vV7bXtftmUmWllK+XEpZU0r51a5tNckX2usv6+M4AQCgEX2bFpKkTLOuTvPzz0vywiTzktxUSvl6rfX7SS6otT7YniryxVLKd2utN+7yQ1rhfVmSLF++vNEPAAAA+6OfV67XJjm56/VJSR6cZp/P1Vo3tudW35jk2UlSa32w/fxwkuvSmmayi1rr1bXW0Vrr6LJlyxr+CAAAsO/6Gdc3JzmllLKylDKc5JIk10/Z59NJ/lUpZbCUMj/JTyW5s5SyoJSyKElKKQuSvDjJbX0cKwAA9Kxv00JqreOllLcm+XySgSQfqbXeXkp5c3v7h2qtd5ZSPpfk20kmkny41npbKeXpSa4rpXTG+Ne11s/1a6wAANCEUuvUadCHr9HR0bp6ta/EBgCgf0opa2qto9Ntc4dGAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaIi4BgCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIawAAaEhf47qUcnEp5XullLtKKVftZp8LSym3llJuL6X84/4cCwAAh5LBfr1xKWUgyQeSvCjJ2iQ3l1Kur7Xe0bXPkiQfTHJxrfX+Uspx+3osAAAcavp55fr8JHfVWu+ptW5L8rEkL5+yz2uTfLLWen+S1Fof3o9jAQDgkNLPuD4xyQNdr9e213V7ZpKlpZQvl1LWlFJ+dT+OBQCAQ0rfpoUkKdOsq9P8/POSvDDJvCQ3lVK+vo/Htn5IKZcluSxJli9ffsCDBQCAXvXzyvXaJCd3vT4pyYPT7PO5WuvGWusjSW5M8ux9PDZJUmu9utY6WmsdXbZsWWODBwCA/dXPuL45ySmllJWllOEklyS5fso+n07yr0opg6WU+Ul+Ksmd+3gsAAAcUvo2LaTWOl5KeWuSzycZSPKRWuvtpZQ3t7d/qNZ6Zynlc0m+nWQiyYdrrbclyXTH9musAADQhFLrtFOZD0ujo6N19erVMz0MAABmsVLKmlrr6HTb3KERAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAh4hoAABoirgEAoCHiGgAAGiKuAQCgIeIaAAAaIq4BAKAhgzM9AAAASJJaa7Ztn8iWsYlsHduezWPbs2VsIlvGtrce4zuWt45N5PSnLs4ZJx4108PeibgGAGBatdZsnQza9vP4lOAdm8jW8dby5m3dAdx63jrN/ps7gTy+8/ot49tT676P77d/9pniGgCA3oxvbwXq5vYV3M3tsN2xrr28bUfIbunapxO7m3dat3PkduJ3f2K329BAycjQQPsxJyODO5YXjQzm2IVzW+uHBjKvs097/7mDc6Y9dt7wnMztep8l84eb/QfbAHENANCAWmvGttedY7YrXqdG8M77TOwcxZ2rwF1XejePbc+Wba0rx2Pb9794S0nmTYZsK07nDbdeLxoZzLJFc3eJ3JHBOZm7m8gdGRxob9t5/87ywJzSh3/Khz5xDQDMetsnaraMbc+mbTvidtO28Z2u9nZidnN30G6bEsFjE5OB2x3JnekQ2yf2P3oH5pTJ4O1E67zh1usl84dbETy0Y93kvkMDGRnecdV33i7rBrrWzcnwwJyUcmQG78EkrgGAGbd9ou64qrttezaNje9Y3rYjfjdtG8/msYls3ja+0/rNewjnTdta0xv2V2daw2TYDnbCdU6OWTCckSU7x2z3Vd95UwJ3ZDKOd43goQFf3jabiGsAYK868btp23i2bJvIprFW3G5px++msc7yeNfy9umXu8O5HccHEr/zh3eE77yhgdbr4YEcu3A484fn77R+pP28Y3lwp/U7xfBwa3rDoOjlAIhrAJglOl9jtnnb9mzctj2btrYCeOO28Wza2grZzrpN28azsR24G7eOT26bXDflyu+2/Yzfzvze7nCdNzyYeUNzctyikV2CeMfy4I7ldujuvDw4eYXYFAcOReIaAA6yTgRv2rojYjd2rvpOWbe5HcE7orgdy539t23f6Zjx/ZjzOzRQMn94MAvagbtgbitcly2am+XD8zO/c9V3eCDzhwa7lgemLA9m3vCcncJ47qD45cgkrgFgDyba0yE2bh3Phnbgbtg6vtPrTZ34nebqb+uKcfu5K4z35w/fdhfBxy0amZzqMH94MAvm7pjusGB4sL3vQOYNTb9teNC0B2iauAZgVtk+UVtTHrZub8fveDuGt3ctj2fD1k4I71je0H69cWsrpjvTJfb1e373GMHHiGA4EohrAGbU+PaJbNy2I2Y7yzvCuGtbe3nDtvFWGO8U0K1tm8e27/PPnt8O4AWd57mDWbZwblYcM5iFcwczf3gwC+fu2LZgbit4F84dzPy5rW2tmBbBQIu4BmC/1Vonp0es37JjisT6La3nDVvGWq87V4m3TNnetW5fvyWilGRB+6pvK4hby09dMtK+GrwjdhdOieHWtsHMnzswuW3+0EDmHKE3uQD6R1wDHEHGtk9k4zSRu779vHHrjuUNW8d2CuKNXftu3DqefZkyPDw4J4vmDmbhSCtuF84dzAlHjUwG7mToDg/stK5zRbk7iOcNDfgDOeCQ19e4LqVcnOS9SQaSfLjW+idTtl+Y5NNJ7m2v+mSt9R3tbfclWZ9ke5LxWutoP8cKcCibmKhZv3U867eMZf2W8Ty5ufW8fmv7eUsngseycev2yeUNU64a78tV4lKShcM7gnjB3MEsGhnMUxa3onjhyOBkMHcCeNHIYBbOHepabm0zTQI40vQtrkspA0k+kORFSdYmubmUcn2t9Y4pu36l1vrzu3mbi2qtj/RrjAAHw8REzYZtnQAe2+n5ye5Q3jL1eTxPtpc3bB3f688ZHpiz0xXihSODOX7RSJ6xrB3IXet3CuKR1nSKzrLpEgAHrp9Xrs9Pclet9Z4kKaV8LMnLk0yNa4BDVq01G7dt3yl8n9y8I3qnRvGT08Txhq3je/22iaGBksUjQ1k0MphF7ecVx87PopGhrvWDu+yzeN6ObXMHBw7OPxQAdqufcX1ikge6Xq9N8lPT7PfcUsq3kjyY5D/UWm9vr69JvlBKqUn+otZ6dR/HCsxi28Yn8uSWsTyxeSxPbm4/bxmffP3k5rGu7e31XfvvbW7x4Jyyc/CODGX50fO7Xk8XwzsHsxtuAMwO/Yzr6f4tMfVfUbckeVqtdUMp5aVJPpXklPa2C2qtD5ZSjkvyxVLKd2utN+7yQ0q5LMllSbJ8+fLGBg8cOjpXj5/YPJYnNo1NG8pP7vR651De21ezzR2ck8XzhnLUvKEsHhnMsQuH8/RlC9qvh7J4XncM7wjm1lXkIbdhBmBSP+N6bZKTu16flNbV6Um11ie7lj9bSvlgKeXYWusjtdYH2+sfLqVcl9Y0k13iun1F++okGR0d3ffbXQEHVSeQH9+0LY9vasXv45vG8vjm1usnt3SuIu965fjJLeN7vJtdKcmiuYNdgTyUpx+7MIvnDU6+Pmp++3neUHu/1v6LR4YyMmQ6BQDN6Gdc35zklFLKyiQ/SnJJktd271BKeUqSh2qttZRyfpI5SR4tpSxIMqfWur69/OIk7+jjWHs2vn0if/mVe3PzfY/lrJOOyqU/vSJL5g/P9LCgcRMTNeu3jE9G8eObx/L4pm07YrkdzE9Ms218D4E8PDhn8srxUfOGcvSC4aw8dkFXEHeF8mQgt54Xzh3MgD/AA+AQ0Le4rrWOl1LemuTzaX0V30dqrbeXUt7c3v6hJK9OcnkpZTzJ5iSXtEP7+CTXtX/NOpjkr2utn+vXWJvwwS/fnXd/8ftZccz83PC9h/ORr96b/3jxqXnt+cv91T2HpPHtE63obYfvE51YbkfxE5u2TW7rfv3E5rE9/nHewrmtCF4yv/U49SmLc9T8oSzprJs33PV6OEvmtyLZ1WMAZoNS9/Yn7IeR0dHRunr16oP+c7eMbc+57/xiLnzWsnzwdeflu//yZN7xmTvyT3c/mp9csTT/+VVn5ieOW3TQx8WRodaazWPb89jGVhw/tnFbfrxpW368cVse29S6ctzZ1rna/MSmsazfw1e7lZIsHunE8FCOmj/cFcdTXs8fylHzdkTy0IDvNQZgdiulrNndPVjcobEB/3T3I9m0bXt+5Sdbf1B56lMW55pf+6lcu2Zt/vizd+al7/1qfuOiZ+TyC5/hq7LYo8685B93AnnT2I7ljdvy2E7rxibXbdvDjUGWzB/K0vYV4uMWjeSZxy1qXzke7orj9lXkdjAvGhkyzQIADoC4bsBNdz+auYNz8pynHz25rpSSXxo9ORedelze8Zk78p4v/SB/9+1/zp+86syMrjh6D+/GbFFrzYat4/nxxrH8eFMrgltXkbuCedO2ye2d5W3bpw/lUpIl84aydMFwls4fzolL5uXMExdn6fzh9rqhruXhHL1gOEfNE8kAcDCJ6wbcs25jVh67YNqr0scunJv3veacvPLcE/P7192WV3/oprzm/JPz1p85JScumTcDo+VA1Frz5JbxnaZYPNYVyI9t3Hn6RSekx7ZPP+1qTslOUbz86Pl59klLdkTyZCC3g3n+cBYLZQA45InrBtz7yMacesKe51Rf9Kzj8oXffn7e/cXv53/edF/+dvXavOKcE3PpT6/IGScedZBGSrIjlH+8mzj+8eTzjukXj2/atttvuhiYU9oB3IriFcfOz7kLlmTJ/OEc3X1VuRPM84ezaGTQH7oCwCwkrns0tn0i9z+2KS858yl73XfB3MH8wc+fnn/7vJW5+sZ78rGb78+1a9bmjBMX5xfPPSkvXvUUV7P30/6H8rY9fiXc0EDJkvk7plj8xHELd55y0Z5usWR+66vili4YzqK5g24gAgAkEdc9e+jJLRmfqDl56fx9PuapS+blj35hVX77Z5+ZT936o/zNN+7P2z9zR97+mTty+gmL8zOnHpefXHl0zl2+JItGhvo4+kPLtvHWV8O1Hq3vRp4ayj/e2JpysS+hPDinZOmC1pXiJfOHJkO587oTx0snrzC3vi9ZKAMAB0pc96hz17jhwf3/+rGj5g/lDT+9Im/46RW5e92GfOmOh/LFOx7Kn//j3Xn/DXdlTkmeefyiPOsp7cfxi7Li2AV56lHzMm/40PvWkVprto5PZP2W8WzcOj55h73O3fg6j85NRTrbnmx/1/Kmbbu/RXUnlLuvKC/pmpN8dDuSJ+N5wZArygDAQSeue9S5aDqnx4h7xrKFecYLFubXX/CMbNg6nlvvfzzfuO+xfHvt47n53sfy6Vt3unN8jl4wnKcuGclxi0ba3zu846vV5g8PZHhwTuYODmTu4JzMHZyT4cE5GZhT2uOtmahJrclErZPPW8e3Z8vYRLaOb8/WsYlsGduereMT2TreWt4yNpGNW8ezYdt4NmwZz4atrYhe37W8pzvwJcnIUOsufEvmtb7J4uSj5+eo9p32Op+j87pzlz5TLwCAw4W47tFE+yY8TXbfwrmDed4px+Z5pxw7ue7JLWP5wUPr88Bjm/OjxzfnwfbjoSe35PsPrd/rTUF6NTinZO7gnCwcGcyCuYNZNHcwC0cGc8yC+Vk4suN197aFc7tuOtK+TbW78AEAs5m47lGdjOv+XlVdPDKU8552dM572u73GWvfznrzts4V5+3ZNj6Rbe2rz9snakppXWWffG6PfU5JRoYGMneodcV7ZGjnK9+D7roHALBX4rpHO6aFzOw4kmRoYE6OXTh3pocBAHDEcjmyR7WhOdcAABz+xHWPOnOuD4Ur1wAAzCxx3aOJgzTnGgCAQ5+47lFnWoi0BgBAXPfInGsAADrEdY8m51z7JwkAcMSThD0y5xoAgA5x3aMJc64BAGgT1z2qk1/FJ68BAI504rpH7QvX4hoAAHHdq4kJN5EBAKBFXPdocs61K9cAAEc8cd2jOvltITM8EAAAZpy47pE51wAAdIjrHk3eREZbAwAc8cR1j8y5BgCgQ1z3aMKcawAA2sR1j9xEBgCADnHdo3Zbm3MNAIC47tXEZFyrawCAI5247pE51wAAdIjrHk3eRCbqGgDgSCeuezQ559o/SQCAI54k7JE51wAAdIjrHrlDIwAAHeK6R524jjnXAABHPHHdI99zDQBAh7juUY07NAIA0CKuezQx0XoW1wAAiOseuYkMAAAd4rpHnTnX4hoAAHHdI3OuAQDoENc9chMZAAA6xHWP3EQGAIAOcd2jCfeQAQCgTVz3qFZzrgEAaBHXParmXAMA0Caue2TONQAAHeK6RxOT33OtrgEAjnTiukfVHRoBAGgT1z0y5xoAgA5x3SNzrgEA6OhrXJdSLi6lfK+Uclcp5apptl9YSnmilHJr+/GH+3rsocIdGgEA6Bjs1xuXUgaSfCDJi5KsTXJzKeX6WusdU3b9Sq315w/w2BnXuXINAAD9vHJ9fpK7aq331Fq3JflYkpcfhGMPKjeRAQCgo59xfWKSB7per22vm+q5pZRvlVL+vpSyaj+PnXE7/qBxZscBAMDM69u0kCTT5ebUORS3JHlarXVDKeWlST6V5JR9PLb1Q0q5LMllSbJ8+fIDHuyBMucaAICOfl65Xpvk5K7XJyV5sHuHWuuTtdYN7eXPJhkqpRy7L8d2vcfVtdbRWuvosmXLmhz/PpnwPdcAALT1M65vTnJKKWVlKWU4ySVJru/eoZTylNK+tWEp5fz2eB7dl2MPFTtuIqOuAQCOdH2bFlJrHS+lvDXJ55MMJPlIrfX2Usqb29s/lOTVSS4vpYwn2Zzkktqq1WmP7ddYe1FjvjUAAC39nHPdmerx2SnrPtS1/P4k79/XYw9FE7Wabw0AQBJ3aOzZRPXHjAAAtIjrHk3UOv13mwAAcMQR1z2q1ZxrAABaxHWPqjnXAAC0iesemXMNAECHuO7RRK1uIAMAQBJx3TN/zwgAQIe47lGtNXP8RSMAABHXPTPnGgCADnHdo9YdGmd6FAAAHArEdY8mamLWNQAAibhugCvXAAC0iOseTUyYcw0AQIu47pE51wAAdIjrHk3UpLhyDQBAxHXPqjs0AgDQJq57VGPONQAALeK6R+ZcAwDQIa575A6NAAB0iOseTdTqHjIAACQR171z5RoAgDZx3SNzrgEA6BDXPWrFtboGAEBc98xNZAAA6BDXPaq1+ntGAACSiOue1ZrM8U8RAICI656Zcw0AQIe47pE51wAAdIjrHk2Ycw0AQJu4boDvuQYAIBHXPTPnGgCAjsGZHsDh7oSj5mVs+8RMDwMAgEOAuO7Ru37p2TM9BAAADhGmhQAAQEPENQAANERcAwBAQ8Q1AAA0RFwDAEBDxDUAADREXAMAQEPENQAANERcAwBAQ8Q1AAA0RFwDAEBDxDUAADREXAMAQEPENQAANERcAwBAQ8Q1AAA0RFwDAEBDxDUAADREXAMAQEPENQAANERcAwBAQ8Q1AAA0RFwDAEBDSq11psfQmFLKuiQ/nIEffWySR2bg53JwOc9HBuf5yOA8z37O8ZFhps7z02qty6bbMKvieqaUUlbXWkdnehz0l/N8ZHCejwzO8+znHB8ZDsXzbFoIAAA0RFwDAEBDxHUzrp7pAXBQOM9HBuf5yOA8z37O8ZHhkDvP5lwDAEBDXLkGAICGiOselFIuLqV8r5RyVynlqpkeD/unlHJyKeWGUsqdpZTbSym/1V5/dCnli6WUH7Sfl3Yd87vt8/29UsrPda0/r5Tynfa295VSykx8JqZXShkopXyzlPJ37dfO8SxUSllSSrm2lPLd9n+vn+tczy6llN9u/+/1baWUvymljDjHs0Mp5SOllIdLKbd1rWvs3JZS5pZS/r/2+v9TSlnRr88irg9QKWUgyQeSvCTJ6UleU0o5fWZHxX4aT/I7tdbTkjwnyVva5/CqJP9Qaz0lyT+0X6e97ZIkq5JcnOSD7f8cJMmfJ7ksySntx8UH84OwV7+V5M6u187x7PTeJJ+rtZ6a5NlpnXPnepYopZyY5DeTjNZaz0gykNY5dI5nh/+RXc9Dk+f23yb5ca31J5L8lyT/T78+iLg+cOcnuavWek+tdVuSjyV5+QyPif1Qa/3nWust7eX1af2L+MS0zuNftXf7qySvaC+/PMnHaq1ba633JrkryfmllBOSLK613lRbf8TwP7uOYYaVUk5K8q+TfLhrtXM8y5RSFid5fpL/liS11m211sfjXM82g0nmlVIGk8xP8mCc41mh1npjksemrG7y3Ha/17VJXtiv31iI6wN3YpIHul6vba/jMNT+9dA5Sf5PkuNrrf+ctAI8yXHt3XZ3zk9sL09dz6HhPUn+Y5KJrnXO8ezz9CTrkvz39hSgD5dSFsS5njVqrT9K8q4k9yf55yRP1Fq/EOd4Nmvy3E4eU2sdT/JEkmP6MWhxfeCm+387vnrlMFRKWZjkE0n+fa31yT3tOs26uof1zLBSys8nebjWumZfD5lmnXN8eBhMcm6SP6+1npNkY9q/Qt4N5/ow055v+/IkK5M8NcmCUsrr93TINOuc49nhQM7tQTvv4vrArU1yctfrk9L69RSHkVLKUFphfU2t9ZPt1Q+1f7WU9vPD7fW7O+dr28tT1zPzLkjyC6WU+9KauvUzpZT/Fed4NlqbZG2t9f+0X1+bVmw717PHzya5t9a6rtY6luSTSX46zvFs1uS5nTymPa3oqOw6DaUR4vrA3ZzklFLKylLKcFoT66+f4TGxH9pzrf5bkjtrre/u2nR9kje0l9+Q5NNd6y9p/8XxyrT+UOIb7V9VrS+lPKf9nr/adQwzqNb6u7XWk2qtK9L67+j/rrW+Ps7xrFNr/ZckD5RSntVe9cIkd8S5nk3uT/KcUsr89rl5YVp/K+Mcz15Nntvu93p1Wv8+6M9vLGqtHgf4SPLSJN9PcneS/zTT4/HY7/P3vLR+JfTtJLe2Hy9Naw7WPyT5Qfv56K5j/lP7fH8vyUu61o8mua297f1p36DJ49B5JLkwyd+1l53jWfhIcnaS1e3/Tn8qyVLnenY9krw9yXfb5+ejSeY6x7PjkeRv0ppLP5bWVeZ/2+S5TTKS5G/T+uPHbyR5er8+izs0AgBAQ0wLAQCAhohrAABoiLgGAICGiGsAAGiIuAYAgIaIa4BZrpRyXynl2F73AWDvxDUAADREXAPMIqWUT5VS1pRSbi+lXDZl24pSyndLKX9VSvl2KeXaUsr8rl3+XSnlllLKd0opp7aPOb+U8k+llG+2n58VAHZLXAPMLv9XrfW8tO5S9pullGOmbH9WkqtrrWcleTLJb3Rte6TWem6SP0/yH9rrvpvk+bXWc5L8YZL/u6+jBzjMiWuA2eU3SynfSvL1JCcnOWXK9gdqrV9rL/+vJM/r2vbJ9vOaJCvay0cl+dtSym1J/kuSVf0YNMBsIa4BZolSyoVJfjbJc2utz07yzSQjU3are3i9tf28Pclge/mdSW6otZ6R5GXTvB8AXcQ1wOxxVJIf11o3tedMP2eafZaXUp7bXn5Nkq/uw3v+qL18aSOjBJjFxDXA7PG5JIOllG+ndcX569Psc2eSN7T3OTqt+dV78v8m+c+llK8lGWhysACzUal16m8IAZiNSikrkvxde4oHAH3gyjUAADTElWsAAGiIK9cAANAQcQ0AAA0R1wAA0BBxDQAADRHXAADQEHENAAAN+f8BNC/kvlkdhiMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "\n",
    "plt.plot(Alpha,Rsqu_test, label='validation data  ')\n",
    "plt.plot(Alpha,Rsqu_train, 'r', label='training Data ')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('R^2')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 4**: The blue line represents the R^2 of the validation data, and the red line represents the R^2 of the training data. The x-axis represents the different values of Alpha.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the model is built and tested on the same data, so the training and test data are the same.\n",
    "\n",
    "The red line in Figure 4 represents the R^2 of the training data. As alpha increases the R^2 decreases. Therefore, as alpha increases, the model performs worse on the training data\n",
    "\n",
    "The blue line represents the R^2 on the validation data. As the value for alpha increases, the R^2 increases and converges at a point.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We perform Ridge regression. Calculate the R^2 using the polynomial features, use the training data to train the model and use the test data to test the model. The parameter alpha should be set to 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5418576440207269"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RidgeModel = Ridge(alpha = 10)\n",
    "RidgeModel.fit(x_train_pr, y_train)\n",
    "RidgeModel.score(x_test_pr, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"ref4\">Part 4: Grid Search</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The term alpha is a hyperparameter. Sklearn has the class <b>GridSearchCV</b> to make the process of finding the best hyperparameter simpler.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import <b>GridSearchCV</b> from  the module <b>model_selection</b>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a dictionary of parameter values:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000, 100000]}]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parameters1= [{'alpha': [0.001,0.1,1, 10, 100, 1000, 10000, 100000, 100000]}]\n",
    "parameters1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a Ridge regression object:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge()"
      ]
     },
     "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": [
    "In order to avoid a deprecation warning due to the iid parameter, we set the value of iid to \"None\".\n",
    "\n",
    "Fit the model:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=4, estimator=Ridge(),\n",
       "             param_grid=[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000,\n",
       "                                    100000]}])"
      ]
     },
     "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)"
      ]
     },
     "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": [
       "0.8411649831036149"
      ]
     },
     "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": [
    "We perform a grid search for the alpha parameter and the normalization parameter, then find the best values of the parameters:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ridge(alpha=0.1, normalize=True)\n",
      "0.840859719294301\n"
     ]
    }
   ],
   "source": [
    "parameters2 = [{'alpha':[0.001, 0.1, 1, 10, 100, 1000, 10000, 100000], 'normalize':[True,False]}]\n",
    "\n",
    "Grid2 = GridSearchCV(Ridge(), parameters2, cv = 4)\n",
    "Grid2.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_data)\n",
    "\n",
    "print(Grid2.best_estimator_)\n",
    "\n",
    "print(Grid2.best_estimator_.score(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_test))\n"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "metadata": {
   "interpreter": {
    "hash": "ac2eaa0ea0ebeafcc7822e65e46aa9d4f966f30b695406963e145ea4a91cd4fc"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}