model-development.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Module%204/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n",
    "</center>\n",
    "\n",
    "# Model Development\n",
    "\n",
    "Estimated time needed: **30** minutes\n",
    "\n",
    "## Objectives\n",
    "\n",
    "After completing this lab you will be able to:\n",
    "\n",
    "*   Develop prediction models\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>In this section, we will develop several models that will predict the price of the car using the variables or features. This is just an estimate but should give us an objective idea of how much the car should cost.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some questions we want to ask in this module\n",
    "\n",
    "<ul>\n",
    "    <li>Do I know if the dealer is offering fair value for my trade-in?</li>\n",
    "    <li>Do I know if I put a fair value on my car?</li>\n",
    "</ul>\n",
    "<p>In data analytics, we often use <b>Model Development</b> to help us predict future observations from the data we have.</p>\n",
    "\n",
    "<p>A model will help us understand the exact relationship between different variables and how these variables are used to predict the result.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import libraries:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the data and store it in dataframe `df`:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object. Click <a href=\"https://cocl.us/DA101EN_object_storage?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\">HERE</a> for free storage.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</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>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</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>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</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>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</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>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</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>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</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>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \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  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# path of data \n",
    "path = 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>1. Linear Regression and Multiple Linear Regression</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Linear Regression</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>One example of a Data  Model that we will be using is:</p>\n",
    "<b>Simple Linear Regression</b>\n",
    "\n",
    "<br>\n",
    "<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n",
    "<ul>\n",
    "    <li>The predictor/independent variable (X)</li>\n",
    "    <li>The response/dependent variable (that we want to predict)(Y)</li>\n",
    "</ul>\n",
    "\n",
    "<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Y: Response \\ Variable\\\\\\\\\n",
    "X: Predictor \\ Variables\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Linear Function</b>\n",
    "$$\n",
    "Yhat = a + b  X\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li>a refers to the <b>intercept</b> of the regression line, in other words: the value of Y when X is 0</li>\n",
    "    <li>b refers to the <b>slope</b> of the regression line, in other words: the value with which Y changes when X increases by 1 unit</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Let's load the modules for linear regression:</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:35: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:597: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, fit_path=True,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:836: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, fit_path=True,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:862: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, positive=False):\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1097: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  max_n_alphas=1000, n_jobs=None, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1344: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  max_n_alphas=1000, n_jobs=None, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1480: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, positive=False):\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:152: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  precompute=False, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:320: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, random_state=None,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:580: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=4 * np.finfo(np.float).eps, n_jobs=None,\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Create the linear regression object:</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How could \"highway-mpg\" help us predict car price?</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this example, we want to look at how highway-mpg can help us predict car price.\n",
    "Using simple linear regression, we will create a linear function with \"highway-mpg\" as the predictor variable and the \"price\" as the response variable.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[['highway-mpg']]\n",
    "Y = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using highway-mpg:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can output a prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
       "       20345.17153508])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "Yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>What is the value of the intercept (a)?</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.3058581574"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>What is the value of the slope (b)?</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-821.73337832])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What is the final estimated linear model we get?</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, we should get a final linear model with the structure:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b  X\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plugging in the actual values we get:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Price</b> = 38423.31 - 821.73 x <b>highway-mpg</b>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 a): </h1>\n",
    "\n",
    "<b>Create a linear regression object called \"lm1\".</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1 = LinearRegression()\n",
    "lm1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "lm1 = LinearRegression()\n",
    "lm1\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question #1 b): </h1>\n",
    "\n",
    "<b>Train the model using \"engine-size\" as the independent variable and \"price\" as the dependent variable?</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "\n",
    "X = df[[\"engine-size\"]]\n",
    "Y = df[['price']]\n",
    "\n",
    "lm1.fit(X,Y)\n",
    "lm1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "lm1.fit(df[['engine-size']], df[['price']])\n",
    "lm1\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 c):</h1>\n",
    "\n",
    "<b>Find the slope and intercept of the model.</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Slope</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[166.86001569]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Intercept</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7963.33890628])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "# Slope \n",
    "lm1.coef_\n",
    "\n",
    "# Intercept\n",
    "lm1.intercept_\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 d): </h1>\n",
    "\n",
    "<b>What is the equation of the predicted line? You can use x and yhat or \"engine-size\" or \"price\".</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "yhat = lm1.intercept_ + lm1.coef_*X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "# using X and Y  \n",
    "Yhat=-7963.34 + 166.86*X\n",
    "\n",
    "Price=-7963.34 + 166.86*engine-size\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Multiple Linear Regression</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>What if we want to predict car price using more than one variable?</p>\n",
    "\n",
    "<p>If we want to use more variables in our model to predict car price, we can use <b>Multiple Linear Regression</b>.\n",
    "Multiple Linear Regression is very similar to Simple Linear Regression, but this method is used to explain the relationship between one continuous response (dependent) variable and <b>two or more</b> predictor (independent) variables.\n",
    "Most of the real-world regression models involve multiple predictors. We will illustrate the structure by using four predictor variables, but these results can generalize to any integer:</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Y: Response \\ Variable\\\\\\\\\n",
    "X\\_1 :Predictor\\ Variable \\ 1\\\\\\\\\n",
    "X\\_2: Predictor\\ Variable \\ 2\\\\\\\\\n",
    "X\\_3: Predictor\\ Variable \\ 3\\\\\\\\\n",
    "X\\_4: Predictor\\ Variable \\ 4\\\\\\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "a: intercept\\\\\\\\\n",
    "b\\_1 :coefficients \\ of\\ Variable \\ 1\\\\\\\\\n",
    "b\\_2: coefficients \\ of\\ Variable \\ 2\\\\\\\\\n",
    "b\\_3: coefficients \\ of\\ Variable \\ 3\\\\\\\\\n",
    "b\\_4: coefficients \\ of\\ Variable \\ 4\\\\\\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equation is given by:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b\\_1 X\\_1 + b\\_2 X\\_2 + b\\_3 X\\_3 + b\\_4 X\\_4\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From the previous section  we know that other good predictors of price could be:</p>\n",
    "<ul>\n",
    "    <li>Horsepower</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Highway-mpg</li>\n",
    "</ul>\n",
    "Let's develop a model using these variables as the predictor variables.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using the four above-mentioned variables.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(Z, df['price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the value of the intercept(a)?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15806.624626329194"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the values of the coefficients (b1, b2, b3, b4)?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([53.49574423,  4.70770099, 81.53026382, 36.05748882])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the final estimated linear model that we get?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, we should get a final linear function with the structure:\n",
    "\n",
    "$$\n",
    "Yhat = a + b\\_1 X\\_1 + b\\_2 X\\_2 + b\\_3 X\\_3 + b\\_4 X\\_4\n",
    "$$\n",
    "\n",
    "What is the linear function we get in this example?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Price</b> = -15678.742628061467 + 52.65851272 x <b>horsepower</b> + 4.69878948 x <b>curb-weight</b> + 81.95906216 x <b>engine-size</b> + 33.58258185 x <b>highway-mpg</b>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #2 a): </h1>\n",
    "Create and train a Multiple Linear Regression model \"lm2\" where the response variable is \"price\", and the predictor variable is \"normalized-losses\" and  \"highway-mpg\".\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "variables = df[['normalized-losses', 'highway-mpg']]\n",
    "\n",
    "lm2 = LinearRegression()\n",
    "lm2.fit(variables, df['price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "lm2 = LinearRegression()\n",
    "lm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n",
    "\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  #2 b): </h1>\n",
    "<b>Find the coefficient of the model.</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1.49789586, -820.45434016])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm2.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "lm2.coef_\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>2. Model Evaluation Using Visualization</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've developed some models, how do we evaluate our models and choose the best one? One way to do this is by using a visualization.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the visualization package, seaborn:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the visualization package: seaborn\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Regression Plot</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When it comes to simple linear regression, an excellent way to visualize the fit of our model is by using <b>regression plots</b>.</p>\n",
    "\n",
    "<p>This plot will show a combination of a scattered data points (a <b>scatterplot</b>), as well as the fitted <b>linear regression</b> line going through the data. This will give us a reasonable estimate of the relationship between the two variables, the strength of the correlation, as well as the direction (positive or negative correlation).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize **highway-mpg** as potential predictor variable of price:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 48257.47314782687)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see from this plot that price is negatively correlated to highway-mpg since the regression slope is negative.\n",
    "\n",
    "One thing to keep in mind when looking at a regression plot is to pay attention to how scattered the data points are around the regression line. This will give you a good indication of the variance of the data and whether a linear model would be the best fit or not. If the data is too far off from the line, this linear model might not be the best model for this data.\n",
    "\n",
    "Let's compare this plot to the regression plot of \"peak-rpm\".</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 47414.1)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing the regression plot of \"peak-rpm\" and \"highway-mpg\", we see that the points for \"highway-mpg\" are much closer to the generated line and, on average, decrease. The points for \"peak-rpm\" have more spread around the predicted line and it is much harder to determine if the points are decreasing or increasing as the \"peak-rpm\" increases.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #3:</h1>\n",
    "<b>Given the regression plots above, is \"peak-rpm\" or \"highway-mpg\" more strongly correlated with \"price\"? Use the method  \".corr()\" to verify your answer.</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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>peak-rpm</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>-0.058598</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             peak-rpm  highway-mpg     price\n",
       "peak-rpm     1.000000    -0.058598 -0.101616\n",
       "highway-mpg -0.058598     1.000000 -0.704692\n",
       "price       -0.101616    -0.704692  1.000000"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df[['peak-rpm', 'highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "# The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692  compared to \"peak-rpm\" which is approximate -0.101616. You can verify it using the following command:\n",
    "\n",
    "df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Residual Plot</h3>\n",
    "\n",
    "<p>A good way to visualize the variance of the data is to use a residual plot.</p>\n",
    "\n",
    "<p>What is a <b>residual</b>?</p>\n",
    "\n",
    "<p>The difference between the observed value (y) and the predicted value (Yhat) is called the residual (e). When we look at a regression plot, the residual is the distance from the data point to the fitted regression line.</p>\n",
    "\n",
    "<p>So what is a <b>residual plot</b>?</p>\n",
    "\n",
    "<p>A residual plot is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n",
    "\n",
    "<p>What do we pay attention to when looking at a residual plot?</p>\n",
    "\n",
    "<p>We look at the spread of the residuals:</p>\n",
    "\n",
    "<p>- If the points in a residual plot are <b>randomly spread out around the x-axis</b>, then a <b>linear model is appropriate</b> for the data.\n",
    "\n",
    "Why is that? Randomly spread out residuals means that the variance is constant, and thus the linear model is a good fit for this data.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "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": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.residplot(df['highway-mpg'], df['price'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>What is this plot telling us?</i>\n",
    "\n",
    "<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, leading us to believe that maybe a non-linear model is more appropriate for this data.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n",
    "\n",
    "<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>. We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's make a prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_hat = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": [
    "plt.figure(figsize=(width, height))\n",
    "\n",
    "\n",
    "ax1 = sns.distplot(df['price'], hist=False, color=\"r\", label=\"Actual Value\")\n",
    "sns.distplot(Y_hat, hist=False, color=\"b\", label=\"Fitted Values\" , ax=ax1)\n",
    "\n",
    "\n",
    "plt.title('Actual vs Fitted Values for Price')\n",
    "plt.xlabel('Price (in dollars)')\n",
    "plt.ylabel('Proportion of Cars')\n",
    "\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see that the fitted values are reasonably close to the actual values since the two distributions overlap a bit. However, there is definitely some room for improvement.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>3. Polynomial Regression and Pipelines</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Polynomial regression</b> is a particular case of the general linear regression model or multiple linear regression models.</p> \n",
    "<p>We get non-linear relationships by squaring or setting higher-order terms of the predictor variables.</p>\n",
    "\n",
    "<p>There are different orders of polynomial regression:</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><b>Quadratic - 2nd Order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X +b_2 X^2 \n",
    "$$\n",
    "\n",
    "<center><b>Cubic - 3rd Order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X +b_2 X^2 +b_3 X^3\\\\\\\\\n",
    "$$\n",
    "\n",
    "<center><b>Higher-Order</b>:</center>\n",
    "$$\n",
    "Y = a + b_1 X +b_2 X^2 +b_3 X^3 ....\\\\\\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We saw earlier that a linear model did not provide the best fit while using \"highway-mpg\" as the predictor variable. Let's see if we can try fitting a polynomial model to the data instead.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We will use the following function to plot the data:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PlotPolly(model, independent_variable, dependent_variabble, Name):\n",
    "    x_new = np.linspace(15, 55, 100)\n",
    "    y_new = model(x_new)\n",
    "\n",
    "    plt.plot(independent_variable, dependent_variabble, '.', x_new, y_new, '-')\n",
    "    plt.title('Polynomial Fit with Matplotlib for Price ~ Length')\n",
    "    ax = plt.gca()\n",
    "    ax.set_facecolor((0.898, 0.898, 0.898))\n",
    "    fig = plt.gcf()\n",
    "    plt.xlabel(Name)\n",
    "    plt.ylabel('Price of Cars')\n",
    "\n",
    "    plt.show()\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's get the variables:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df['highway-mpg']\n",
    "y = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's fit the polynomial using the function <b>polyfit</b>, then use the function <b>poly1d</b> to display the polynomial function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        3         2\n",
      "-1.557 x + 204.8 x - 8965 x + 1.379e+05\n"
     ]
    }
   ],
   "source": [
    "# Here we use a polynomial of the 3rd order (cubic) \n",
    "\n",
    "f = np.polyfit(x, y, 3)\n",
    "p = np.poly1d(f)\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the function:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "PlotPolly(p, x, y, 'highway-mpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.polyfit(x, y, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can already see from plotting that this polynomial model performs better than the linear model. This is because the generated polynomial function  \"hits\" more of the data points.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  #4:</h1>\n",
    "<b>Create 11 order polynomial model with the variables x and y from above.</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            11             10             9           8         7\n",
      "-1.243e-08 x  + 4.722e-06 x  - 0.0008028 x + 0.08056 x - 5.297 x\n",
      "          6        5             4             3             2\n",
      " + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n"
     ]
    },
    {
     "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": [
    "# Write your code below and press Shift+Enter to execute \n",
    "tf = np.polyfit(x, y, 11)\n",
    "tp = np.poly1d(tf)\n",
    "print(tp)\n",
    "\n",
    "PlotPolly(tp, x, y, 'Highway MPG')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "# Here we use a polynomial of the 11rd order (cubic) \n",
    "f1 = np.polyfit(x, y, 11)\n",
    "p1 = np.poly1d(f1)\n",
    "print(p1)\n",
    "PlotPolly(p1,x,y, 'Highway MPG')\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2) polynomial with two variables is given by:</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b\\_1 X\\_1 +b\\_2 X\\_2 +b\\_3 X\\_1 X\\_2+b\\_4 X\\_1^2+b\\_5 X\\_2^2\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can perform a polynomial transform on multiple features. First, we import the module:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a <b>PolynomialFeatures</b> object of degree 2:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_pr=pr.fit_transform(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the original data, there are 201 samples and 4 features.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the transformation, there are 201 samples and 15 features.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z_pr.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Pipeline</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Data Pipelines simplify the steps of processing the data. We use the module <b>Pipeline</b> to create a pipeline. We also use <b>StandardScaler</b> as a step in our pipeline.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create the pipeline by creating a list of tuples including the name of the model or estimator and its corresponding constructor.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We input the list as an argument to the pipeline constructor:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False))])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe=Pipeline(Input)\n",
    "pipe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we convert the data type Z to type float to avoid conversion warnings that may appear as a result of StandardScaler taking float inputs.\n",
    "\n",
    "Then, we can normalize the data,  perform a transform and fit the model simultaneously.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False))])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = Z.astype(float)\n",
    "pipe.fit(Z,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly,  we can normalize the data, perform a transform and produce a prediction  simultaneously.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #5:</h1>\n",
    "<b>Create a pipeline that standardizes the data, then produce a prediction using a linear regression model using the features Z and target y.</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13699.11161184, 13699.11161184, 19051.65470233, 10620.36193015,\n",
       "       15521.31420211, 13869.66673213, 15456.16196732, 15974.00907672,\n",
       "       17612.35917161, 10722.32509097])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "\n",
    "\n",
    "input_ = [('scale',StandardScaler()),('model',LinearRegression())]\n",
    "pipe1 = Pipeline(input_)\n",
    "\n",
    "pipe1.fit(Z,y)\n",
    "ypipe = pipe1.predict(Z)\n",
    "ypipe[0:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
    "\n",
    "pipe=Pipeline(Input)\n",
    "\n",
    "pipe.fit(Z,y)\n",
    "\n",
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:10]\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>4. Measures for In-Sample Evaluation</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n",
    "\n",
    "<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n",
    "<ul>\n",
    "    <li><b>R^2 / R-squared</b></li>\n",
    "    <li><b>Mean Squared Error (MSE)</b></li>\n",
    "</ul>\n",
    "\n",
    "<b>R-squared</b>\n",
    "\n",
    "<p>R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.</p>\n",
    "\n",
    "<p>The value of the R-squared is the percentage of variation of the response variable (y) that is explained by a linear model.</p>\n",
    "\n",
    "<b>Mean Squared Error (MSE)</b>\n",
    "\n",
    "<p>The Mean Squared Error measures the average of the squares of errors. That is, the difference between actual value (y) and the estimated value (ŷ).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 1: Simple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.7609686443622008\n"
     ]
    }
   ],
   "source": [
    "#highway_mpg_fit\n",
    "lm.fit(X, Y)\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(X, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that \\~49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\".\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output of the first four predicted value is:  [[13728.4631336 ]\n",
      " [13728.4631336 ]\n",
      " [17399.38347881]\n",
      " [10224.40280408]]\n"
     ]
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "print('The output of the first four predicted value is: ', Yhat[0:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import the function <b>mean_squared_error</b> from the module <b>metrics</b>:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the predicted results with the actual results:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value is:  15021126.025174143\n"
     ]
    }
   ],
   "source": [
    "mse = mean_squared_error(df['price'], Yhat)\n",
    "print('The mean square error of price and predicted value is: ', mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 2: Multiple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.8093562806577457\n"
     ]
    }
   ],
   "source": [
    "# fit the model \n",
    "lm.fit(Z, df['price'])\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(Z, df['price']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that \\~80.896 % of the variation of price is explained by this multiple linear regression \"multi_fit\".\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We produce a prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_predict_multifit = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We compare the predicted results with the actual results:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value using multifit is:  11980366.87072649\n"
     ]
    }
   ],
   "source": [
    "print('The mean square error of price and predicted value using multifit is: ', \\\n",
    "      mean_squared_error(df['price'], Y_predict_multifit))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 3: Polynomial Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let’s import the function <b>r2\\_score</b> from the module <b>metrics</b> as we are using a different function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We apply the function to get the value of R^2:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square value is:  0.674194666390652\n"
     ]
    }
   ],
   "source": [
    "r_squared = r2_score(y, p(x))\n",
    "print('The R-square value is: ', r_squared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that \\~67.419 % of the variation of price is explained by this polynomial fit.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>MSE</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the MSE:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20474146.426361214"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(df['price'], p(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>5. Prediction and Decision Making</h2>\n",
    "<h3>Prediction</h3>\n",
    "\n",
    "<p>In the previous section, we trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction. Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new input:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_input=np.arange(1, 100, 1).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the model:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X, Y)\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce a prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-7796.47889059],\n",
       "       [-7629.6188749 ],\n",
       "       [-7462.75885921],\n",
       "       [-7295.89884352],\n",
       "       [-7129.03882782]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat=lm.predict(new_input)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(new_input, yhat)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Decision Making: Determining a Good Model Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now that we have visualized the different models, and generated the R-squared and MSE values for the fits, how do we determine a good model fit?\n",
    "<ul>\n",
    "    <li><i>What is a good R-squared value?</i></li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>When comparing models, <b>the model with the higher R-squared value is a better fit</b> for the data.\n",
    "<ul>\n",
    "    <li><i>What is a good MSE?</i></li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>When comparing models, <b>the model with the smallest MSE value is a better fit</b> for the data.</p>\n",
    "\n",
    "<h4>Let's take a look at the values for the different models.</h4>\n",
    "<p>Simple Linear Regression: Using Highway-mpg as a Predictor Variable of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.49659118843391759</li>\n",
    "    <li>MSE: 3.16 x10^7</li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>Multiple Linear Regression: Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.80896354913783497</li>\n",
    "    <li>MSE: 1.2 x10^7</li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>Polynomial Fit: Using Highway-mpg as a Predictor Variable of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.6741946663906514</li>\n",
    "    <li>MSE: 2.05 x 10^7</li>\n",
    "</ul>\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Regression Model (SLR) vs Multiple Linear Regression Model (MLR)</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Usually, the more variables you have, the better your model is at predicting, but this is not always true. Sometimes you may not have enough data, you may run into numerical problems, or many of the variables may not be useful and even act as noise. As a result, you should always check the MSE and R^2.</p>\n",
    "\n",
    "<p>In order to compare the results of the MLR vs SLR models, we look at a combination of both the R-squared and MSE to make the best conclusion about the fit of the model.\n",
    "<ul>\n",
    "    <li><b>MSE</b>: The MSE of SLR is  3.16x10^7  while MLR has an MSE of 1.2 x10^7.  The MSE of MLR is much smaller.</li>\n",
    "    <li><b>R-squared</b>: In this case, we can also see that there is a big difference between the R-squared of the SLR and the R-squared of the MLR. The R-squared for the SLR (~0.497) is very small compared to the R-squared for the MLR (~0.809).</li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "This R-squared in combination with the MSE show that MLR seems like the better model fit in this case compared to SLR.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Model (SLR) vs. Polynomial Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li><b>MSE</b>: We can see that Polynomial Fit brought down the MSE, since this MSE is smaller than the one from the SLR.</li> \n",
    "    <li><b>R-squared</b>: The R-squared for the Polynomial Fit is larger than the R-squared for the SLR, so the Polynomial Fit also brought up the R-squared quite a bit.</li>\n",
    "</ul>\n",
    "<p>Since the Polynomial Fit resulted in a lower MSE and a higher R-squared, we can conclude that this was a better fit model than the simple linear regression for predicting \"price\" with \"highway-mpg\" as a predictor variable.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression (MLR) vs. Polynomial Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li><b>MSE</b>: The MSE for the MLR is smaller than the MSE for the Polynomial Fit.</li>\n",
    "    <li><b>R-squared</b>: The R-squared for the MLR is also much larger than for the Polynomial Fit.</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Conclusion</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing these three models, we conclude that <b>the MLR model is the best model</b> to be able to predict price from our dataset. This result makes sense since we have 27 variables in total and we know that more than one of those variables are potential predictors of the final car price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thank you for completing this lab!\n",
    "\n",
    "## Author\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Joseph Santarcangelo</a>\n",
    "\n",
    "### Other Contributors\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
    "\n",
    "Bahare Talayian\n",
    "\n",
    "Eric Xiao\n",
    "\n",
    "Steven Dong\n",
    "\n",
    "Parizad\n",
    "\n",
    "Hima Vasudevan\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/fiorellawever/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Fiorella Wenver</a>\n",
    "\n",
    "<a href=\"https:// https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "## Change Log\n",
    "\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                            |\n",
    "| ----------------- | ------- | ---------- | --------------------------------------------- |\n",
    "| 2020-10-30        | 2.2     | Lakshmi    | Changed url of csv                            |\n",
    "| 2020-09-09        | 2.1     | Lakshmi    | Fixes made in Polynomial Regression Equations |\n",
    "| 2020-08-27        | 2.0     | Lavanya    | Moved lab to course repo in GitLab            |\n",
    "\n",
    "<hr>\n",
    "\n",
    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
   ]
  }
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