4 - Model Development.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 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": 2,
   "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",
    "#!pip install sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2022-01-01\">HERE</a> for free storage.\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>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": 4,
     "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> 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": 5,
   "metadata": {},
   "outputs": [],
   "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": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 6,
     "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": 7,
   "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can output a prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
       "       20345.17153508])"
      ]
     },
     "execution_count": 9,
     "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": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.305858157386"
      ]
     },
     "execution_count": 10,
     "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": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-821.73337832])"
      ]
     },
     "execution_count": 11,
     "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": [
    "<b>Create a linear regression object called \"lm1\".</b>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm1 = LinearRegression()\n",
    "lm1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Train the model using \"engine-size\" as the independent variable and \"price\" as the dependent variable?</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X1 = df[['engine-size']]\n",
    "Y1 = df['price']\n",
    "\n",
    "lm1.fit(X1,Y1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Find the slope and intercept of the model.</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([166.86001569])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Slope\n",
    "lm1.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7963.338906281049"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Intercept\n",
    "lm1.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>What is the equation of the predicted line? You can use x and yhat or \"engine-size\" or \"price\".</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Equation\n",
    "\n",
    " Price = 166.86*engine size - 7963.3389"
   ]
  },
  {
   "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": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using the four above-mentioned variables.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 20,
     "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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15806.624626329198"
      ]
     },
     "execution_count": 21,
     "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": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([53.49574423,  4.70770099, 81.53026382, 36.05748882])"
      ]
     },
     "execution_count": 22,
     "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": [
    "<b> Let's 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\"</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm2 = LinearRegression()\n",
    "lm2.fit(df[['normalized-losses','highway-mpg']],df['price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Find the coefficients and intercept of the model</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[   1.49789586 -820.45434016]\n",
      "38201.31327245728\n"
     ]
    }
   ],
   "source": [
    "print(lm2.coef_)\n",
    "print(lm2.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>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": 25,
   "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": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 48193.11264544412)"
      ]
     },
     "execution_count": 26,
     "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": "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": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 47414.1)"
      ]
     },
     "execution_count": 27,
     "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": [
    "<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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','highway-mpg','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692  compared to \"peak-rpm\" which is approximate -0.101616. "
   ]
  },
  {
   "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": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Alvaro\\anaconda3\\lib\\site-packages\\seaborn\\_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
      "  warnings.warn(\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": [
    "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": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_hat = lm.predict(Z)"
   ]
  },
  {
   "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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NCralAvyYuKOO8ivHzgV7LhEREQECDMfOuTnOuV7OuV5AX2AzoF0NJPWNH+/DatDhGHxrxbJl/gJAERERCVyi2iqOBOY75/ISdD6R4EQvxjvooODPddRR/l6tFSIiIgmRqHB8JvBCad8ws8vMbIKZTVi5cmWCyhGpgnHj/BbPjRoFf662baFbN7/hiIiIiAQu8HBsZtWB4cDLpX3fOfeIc66fc65fs2bNgi5HpGqc8yvHiWipiBo0yG8lXVycuHOKiIhkqESsHB8PTHLOLU/AuUSCtXix7wE++ODEnfPww2HtWj/zWERERAKViHB8FmW0VIiknHHj/H0iV44HDvT3X36ZuHOKiIhkqEDDsZnVBo4GXgvyPCIJM24cVK8OBx6YuHO2bw+tWikci4iIJEBOkAd3zm0GmgR5DpGE+v576NnTB+REMfOrx19+6Xueg9x4REREJMNphzyRipg2DfbfP/HnHTgQCgshT9MQRUREgqRwLBKrVav8xXhhhOPDD/f3aq0QEREJlMKxSKymTfP3YYTjnj2hQQP46qvEn1tERCSDKByLxCrMcJydDYceqpVjERGRgCkci8Rq2jRo2hRatAjn/AMHwqxZvr1DREREAqFwLBKrqVP9qnFY0yKifcdffx3O+UVERDKAwrFILIqL/Q51YbRURB10kB8hp75jERGRwCgci8Ri4ULYtCnccFyzJvTuDWPHhleDiIhImlM4FolFmBfjlTRgAEyYANu3h1uHiIhImlI4FolFNBzvt1+4dQwYAFu2wPTp4dYhIiKSphSORWIxbRp07Ah164ZbR//+/v6778KtQ0REJE0pHIvEIqxto/fUvj3ss4/CsYiISEAUjkX2pqgI5s1LjnBs5lePdVGeiIhIIBSORfZm1izYuRMOOCDsSrwBA2DOHFizJuxKRERE0o7CscjeTJ3q75Nh5Rh8OAYYNy7cOkRERNKQwrHI3sycCdWqQefOYVfi9evn2yvUdywiIhJ3CsciezN3rg/GOTlhV+LVr+9HyqnvWEREJO4UjkX2Zs4c6NYt7Cp217+/Xzl2LuxKRERE0kqSLIWJJKkdO+CHH2D48EofYulSeOcdKCiAwkJo0ACuugo6dKhCXQMGwGOP+SkaXbtW4UAiIiJSksKxSHkWLfJbNVdy5fitt+DCC2H1at8m3Lw5/Pgj3H8/nHUW/OEPlTx09KK8sWMVjkVEROJIbRUi5Zkzx99XMIAWFcHVV8PJJ0NuLnz/PWzd6leRFy6Ea66B11/319Z9800l6urRA2rXhgkTKvFiERERKYvCsUh5ouG4gsu7l1wCDz4I114L334LBx7oB14AtG4Nd9/tD92yJRx3XCUGT2RnQ58+CsciIiJxpnAsUp65c6FxY2jaNOaXPPssPPcc3HYb3Hsv1KhR+vNat4YxY/xu0MceW4mxxX37wuTJvi9aRERE4kLhWKQ8FZxUsWAB/PKXcPjh8Pvf7/350YDctKlvwVi9ugK19esHW7bA7NkVeJGIiIiUR+FYpDwVCMc7dsC550JWll89zs6O7RRt28Irr8DKlb4NI2Z9+/p7tVaIiIjEjcKxSFnWr/dX0MUYjh980PcX//vf/iK8iujdG265BZ55xo99i0nXrlC3LkycWLGTiYiISJkUjkXKMneuv49hUsXWrXDXXTBkCJx5ZuVO94c/wP77w+WXw5o1MbxAF+WJiIjEncKxSFmi4TiGleOnn4YlS+Dmmyt/uurV4YknYPlyuOGGGF/Ut6+fE6eL8kREROJC4VikLHPm+Abizp3LfdrOnfD3v/ucetRRVTtl375+PvLjj+/K5uXq188PVZ45s2onFhEREUDhWKRsc+ZA+/Zlz2KLeOUVv8P0Lbf4XfCq6qaboGZNuP32GJ7cr5+/V2uFiIhIXCgci5QlhkkVzsEdd0D37jBiRHxO27w5XHUVPP88zJq1lyd37gz16ikci4iIxInCsUhpiot9X8NewvFHH8GUKXDjjb4DI15+9zuoUwf+/Oe9PDEry/diaGKFiIhIXCgci5SmsBA2b97rpIqnnvIb6J19dnxP37QpXHMN/O9/MG3aXp7ct69P6Nu2xbcIERGRDKRwLFKaGCZVbNoEb74Jp5/uJ03E2/XXQ/368Je/7OWJ/fr5WXIzZsS/CBERkQyjcCxSmnnz/H2XLmU+5e23/eLyWWcFU0LjxnDppfDqq34hu0zRi/LUWiEiIlJlCscipZk/30+paN26zKc8/7z/9sCBwZVx5ZW+/fmRR8p5UqdO0KCBLsoTERGJA4VjkdIsWAAdOpR5ld3q1fDBB343vHheiLenTp3guON8OC6zpdjM9x0rHIuIiFSZwrFIaebP98m0DK++Ctu3B9dSUdKvfgXLlsHrr5fzpH79YOpU33ssIiIilaZwLLIn5/zKcceOZT7lhRf8IIs+fYIv57jj/CL2Qw+V86S+fX1anz49+IJERETSmMKxyJ5WrYING8pcOS4shM8+86vG8dgRb2+ys33v8ZdfljPWTRfliYiIxIXCscie5s/392WsHL/1ll9c/sUvElfSRRf5LaUffriMJ3ToAI0aqe9YRESkihSORfa0YIG/L2Pl+MMPoX17v2V0ojRpAiNHwosvlnFhni7KExERiQuFY5E9RVeOO3T42be2b4fRo+GYYxLTUlHSuefCmjXw/vtlPKFfP99zXFSU0LpERETSicKxyJ4WLIBWraBWrZ99a+xY3458zDGJL+voo6FZM3j22TKeEL0ob6/7TYuIiEhZFI5F9lTOGLePPvJzjY88MsE1ATk5/iLAt9+GtWtLeUL0ojy1VoiIiFSawrHInubPL/NivA8/hP79oWHDxJYUNWqUH2X8yiulfDM31zcna2KFiIhIpSkci5S0ZQssWVLqyvHq1TB+fDgtFVF9+0K3bmW0VuiiPBERkSpTOBYpaeFCf19KOP70Uz/CLcxwbOYvzPv8c8jPL+UJ0YvytmxJeG0iIiLpQOFYpKToGLdS2io++ggaNICDD05wTXs45xx///zzpXyzb1/YudNvJS0iIiIVpnAsUlJ0jNseK8fO+XB85JH+wrgwdegAAwaU0Xfct6+/V9+xiIhIpSgci5Q0fz7UrQtNm+728Jw5vo0hzJaKkkaO9Pk3L2+Pb7Rrp4vyREREqkDhWKSkBQv8qvEeO3x88YW/Hzo0hJpKMXKkv3/99T2+Eb0oT+FYRESkUhSORUoqY8bxN9/4DTg6dw6hplJ06gQHHgivvlrKN/v2hRkztFOeiIhIJSgci0QVF/tpFaVcjPfNN3DooYnfMro8I0fC11/DsmV7fKNvX9ixQxfliYiIVILCsUjUkiV+h409Vo5XrYJ58+CQQ0KqqwwjR/oLBd98c49v6KI8ERGRSlM4FomKjnHr0GG3h7/91t8femiC69mL/faDLl3gtdf2+EZuLjRurHAsIiJSCQrHIlHR0Q97hONvvvHj2/r1C6Gmcpj51ePRo2HNmj2+oYvyREREKkXhWCRq0SJ/367dbg9/8w306QO1aiW+pL0ZOdK3F7/99h7f6NvX75Sni/JEREQqROFYJGrRImjRAmrW/Omh7dth/Pjk6zeOOuggaNWqjHC8YwdMmxZKXSIiIqlK4VgkKi8P2rff7aEpU2DLluTrN44yg2HD/O5927eX+IYuyhMREakUhWORqEWLfhaOv/nG3ydrOAY44QRYvx6++qrEg+3bQ6NGMGlSWGWJiIikpEDDsZk1NLNXzGy2mc0ysyT9cFoyXnGx3x86N3e3h7/9Ftq2hTZtQqorBkcdBdWrw7vvlnhQF+WJiIhUStArx/cDHzjnugMHArMCPp9I5Sxd6vsSSlk5TtZ+46i6deGII/YIx+DD8bRpfnaziIiIxCSwcGxm9YFBwGMAzrltzrm1QZ1PpEqikypKhOPCQr+YnMwtFVEnnACzZ/vdr3/Sp48P/NOnh1aXiIhIqgly5bgjsBJ4wswmm9mjZlZnzyeZ2WVmNsHMJqxcuTLAckTKEZ1xXKKtYvx4f9+/fwj1VNAJJ/j73VaPdVGeiIhIhQUZjnOAPsDDzrnewCbgpj2f5Jx7xDnXzznXr1mzZgGWI1KO6MpxiXA8aRJkZcEBB4RTUkV07gxdu+4Rjjt2hIYNFY5FREQqIMhwXAAUOOfGRv78Cj4siySfRYugWTOoXfunhyZPhu7dd3soqZ1wAnz2GWzcGHnAzLdWKByLiIjELLBw7JxbBiw2s26Rh44EZgZ1PpEqKWXG8eTJ0Lt3OOVUxgknwLZt8OmnJR6MXpS3bVtodYmIiKSSoKdVXA08Z2ZTgV7AXwM+n0jl7DHjeOVKf0FeKoXjgQP95IoPPijxYN++PhjrojwREZGYBBqOnXPfR/qJD3DOjXDOrQnyfCKV4tzPZhxPnuzvUykcV68OQ4b43fJ+oovyREREKkQ75IksXw5FRbutHEfDca9eoVRUacccAwsWlBjp1qkTNGigcCwiIhIjhWORUmYcT57sF5IbNw6loko75hh//9PqsS7KExERqRCFY5FSZhyn2sV4UV26+B/jZ60VU6fqojwREZEYKByL7DHjeONGmDcvNcOxGRx7LIwe7TfHA3ZdlDdjRqi1iYiIpAKFY5FFi3z/RL16AEyZ4q/RS8VwDL61Yv16GDcu8oAuyhMREYmZwrHIHjOOU3FSRUlDh/qd/X5qrejUCerX91v+iYiISLkUjkX2mHE8eTI0bQqtW4dWUZU0agQHH1wiHGdl6aI8ERGRGCkcS2Zzzq8cl3IxnlmIdVXRMcf4too10cniffv6fpGfGpFFRESkNArHktlWrYLNm38Kx9HN5FK1pSLqmGOguLjEVtJ9+8LWrTBTO7iLiIiUR+FYMlt+vr+PhONZs/ziaqqH4/79/fWFo0dHHtBFeSIiIjFROJbMtnixv2/XDtg17axnz5DqiZOcHBg4sEQ47tzZp2WFYxERkXIpHEtmi64ct20L+HCckwNdu4ZYU5wMHQpz5sCSJeiiPBERkRgpHEtmW7wYatb04ynw4bhLF6hePeS64mDoUH8/ZkzkgehFeTt2hFaTiIhIslM4lsyWn+9XjSOjKWbMgP32C7mmODnwQD/W7afWij59oKhIF+WJiIiUQ+FYMlt+/k/9xlu2wPz56ROOs7Jg8GBdlCciIlIRCseS2RYv/qnfePZsP/Y4XcIx+NaKRYtg4UJ8I3XdugrHIiIi5VA4lsy1fbu/Wm2PSRX77htiTXEW7TsePRq/lNy7t8KxiIhIORSOJXMtWeKXiiMrxzNn+kkVXbqEXFcc9egBzZvrojwREZFYKRxL5oqOcSuxcty1a3pMqogy86vHo0f73wPo29c3V8+aFXZpIiIiSUnhWDJXdAOQEjOO06nfOGrIEFi61M88/umivEmTQq1JREQkWSkcS+YqsQHI5s2wYEF6huPd+o67doU6ddR3LCIiUgaFY8lc+fnQuDHUrZuWkyqiOnb0nSNjxgDZ2f6ivAkTwi5LREQkKSkcS+YqMcYtOqkiHcNxtO94zBgoLgYOPhgmT/bTOkRERGQ3CseSuUpsADJjBlSrBp07h1xTQIYMgR9/hGnT8OG4qAimTw+7LBERkaSjcCyZq8TK8cyZvh23WrWQawrIkCH+fvRo4KCD/B/GjQutHhERkWSlcCyZacMGWLNmt5XjdGypiGrb1s9vHj0a6NABmjRROBYRESmFwrFkphJj3DZv9tsrp3M4Bt93/MUXsGOn+dYKhWMREZGfUTiWzBQNx+3aMXeun1TRo0e4JQVt6FBYvz4y4vjgg30vycaNYZclIiKSVBSOJTOVmHE8Z47/slu38MpJhMGD/f3o0fhwXFyszUBERET2oHAsmWnxYsjKglatmDvXP9SlS7glBW2ffaBnT12UJyIiUh6FY8lM+fnQqhVUq8acOf66vFq1wi4qeEOHwldfwdb6zfyFeQrHIiIiu1E4lsxUYozb3Lnp31IRNXQobNkCY8eii/JERERKoXAsmSmyAYhzMGeOn3GcCQYN8jvmffYZPhzn5cHy5WGXJSIikjQUjiXzOPfTyvGKFX6CQ6asHDdqBL16+a2kOfhg/+D48WGWJCIiklQUjiXzrFoFW7fuNqkiU1aOwe+W9+23UNSjN2Rnq7VCRESkBIVjyTwFBf6+TZufJlVkUjgePNj/bvDdtDp+fMXYsWGXJCIikjQUjiXzlAjHc+ZAjRo/7SKdEQYO9FPsPvsMGDDAh+Pi4rDLEhERSQoKx5J59lg57tzZdxdkioYNoXfvSN/xIYfAunUwe3bYZYmIiCQFhWPJPIsXQ04ONG+eUWPcShoyBL77Drb0OsQ/8O234RYkIiKSJBSOJfMUFECrVuxw2cyfn1n9xlGDB8O2bfDtqi5+hMV334VdkoiISFJQOJbMU1AAbdqwaBFs356ZK8c/9R1/br7vWCvHIiIigMKxZKJIOM7EMW5R9etD374l+o5nzvS9xyIiIhlO4Vgyi3M+HLdt+9MYt0xcOQbfdzx2LGzufZj/e9G8YxEREYVjyTCrV8OWLT+tHDduDE2ahF1UOAYP9m0l3+zs7/eUVmuFiIiIwrFkmD3GuGXqqjHA4Yf7EXafja8D++2ni/JERERQOJZMs8cGIJnYbxxVrx706xfpOx4wwIdjbQYiIiIZTuFYMkskHG9s1JYlSzI7HIPvOx43Djb1GQhr1vBTI7aIiEiGUjiWzLJ4MWRnM39TC8DvjpfJBg+GHTvg62qD/QNqrRARkQyncCyZpaAAWrZk/iK/X3Smh+PDDvObBX42v63fV/rrr8MuSUREJFQKx5JZIjOO58/3f+zUKdxywla3Lhx0EIz5zHxSVjgWEZEMp3AsmSUSjn/4wY9wa9Ag7ILCN2QIjB8PGw8aArNmwapVYZckIiISGoVjyRzO+Z7jtm2ZP1+rxlGDB8POnfBV3WP9A1o9FhGRDKZwLJlj7VrYvPmntopM7zeOOuwwqFYNPlvWHWrUgK++CrskERGR0CgcS+aIjHHb1qId+flaOY6qXRv694cxX+T4BmSFYxERyWAKx5I5IuE4L7sjxcUKxyUNHgwTJ8L6g46ECRP8CruIiEgGUjiWzBEJxz9sbQsoHJc0ZIjvO/6y/gl+8PG4cWGXJCIiEgqFY8kcixdDVhbz1zQGFI5LOuQQ3248euX+YKbWChERyVgKx5I5CgqgRQvmL8qmdm1o0SLsgpJHrVr+wrxPv64JPXsqHIuISMZSOJbMUWIDkE6d/AKp7DJ0KEyZAqv6HgvffOP7LERERDKMwrFkjhIbgKil4ueGDvX3n9UfDhs2wNSp4RYkIiISgkDDsZktMrNpZva9mU0I8lwie1VQQHHrtixYoHBcmoMOgnr14NPVvfwDX3wRaj0iIiJhSMTK8RDnXC/nXL8EnEukdBs2wIYNLKnbla1bFY5Lk5MDgwbB6HH1oEMH+PzzsEsSERFJOLVVSGYoLARgflYXQLvjleXII2HuXCg46BQfjouLwy5JREQkoYIOxw74yMwmmtllpT3BzC4zswlmNmHlypUBlyMZSzOOYxLtOx7dcCSsXq2+YxERyThBh+PDnHN9gOOBX5nZoD2f4Jx7xDnXzznXr1mzZgGXIxkrunK8cR9ycqBdu5DrSVL77w9Nm8LoaN/xZ5+FWY6IiEjCBRqOnXNLIvcrgNeBg4M8n0iZouF4ZX1yc31/rfxcVpbfLe/T7+rgOnaCMWPCLklERCShAgvHZlbHzOpFvwaOAaYHdT6RchUWQqNGzF+Uo37jvRg61HehzOvzCz+xQvOORUQkgwS5ctwc+MrMpgDjgHedcx8EeD6RshUU4Fq11ozjGBx9tL//uM4IWLvW7wwiIiKSIQILx865Bc65AyO3/Zxz/y+oc4nsVWEha5p3Z9066Ngx7GKSW6dO/u/oo6U9/QPqOxYRkQyiUW6SGQoLWVjvAMCP8JXyHX00jPm2Fts791DfsYiIZBSFY0l/27fD8uUsrNYVUDiOxTHH+H1Txva4QH3HIiKSURSOJf0tXQrOsbA4F1A4jsXQoX5yxcfVjof162Hy5LBLEhERSQiFY0l/kTFui7a2pGFDaNgw1GpSQsOGcPDB8FFeN//AJ5+EWo+IiEiiKBxL+ouE44VrG2nVuAKOPhrGTa7Omn0Pg48+CrscERGRhFA4lvQXDccraiscV8Axx0BxMYzpfCl89RVs2hR2SSIiIoFTOJb0V1CAq16DRYuzFY4roH9/qFcPPtp5pL+o8fPPwy5JREQkcArHkv4KC1nWohdFRaZwXAHVqvmtpD+e2Qpq1oSPPw67JBERkcApHEv6KyxkYaM+gCZVVNQxx8CChVl+K2n1HYuISAZQOJb0V1jIwlr7AgrHFXX88f7+/WajYOZMKCgItyAREZGAKRxLenPOh+PsTgC0bx9uOammY0fo1g3eW3mwf0CtFSIikuYUjiW9rV4NRUUs3NGW5s2hVq2wC0o9w4bBZxPrsmmfDgrHIiKS9hSOJb1Fx7ht3EctFZU0bBhs3WqM2fdXPhwXF4ddkoiISGAUjiW9RcPx6voKx5U0cCDUqQPvZZ0Iq1bBpElhlyQiIhIYhWNJb4WF7CCbxStqKBxXUo0acNRR8N68zjgM3n037JJEREQCo3As6a2ggALasHOnZhxXxbBhkLc4m1kHngnvvBN2OSIiIoFROJb0VljIwkZ9AY1xq4roSLf3Wl4EEybAsmXhFiQiIhIQhWNJb4WFLKx3AKBwXBVt28L++8N7P/b3D7z3XrgFiYiIBEThWNJbYSELa3QnK8sHPKm8YcPgy8l1WdtqX7VWiIhI2lI4lvRWUMBC2tO2LVSrFnYxqW34cNixw3i/x3V+pNvWrWGXJCIiEncKx5K+tmyB1atZuLWVWiriYMAAaN4cXi8aBhs3whdfhF2SiIhI3CkcS/pasgSAheubKBzHQVYWnHwyvD+lJUU1Gqi1QkRE0pLCsaSvwkKKqMHStbVp3z7sYtLDiBGwcaMx+oBrfTh2LuySRERE4krhWNJXQQGL8VfhKRzHx9ChUK8evFHjDFiwAGbMCLskERGRuFI4lvRVWEgeuQDk5oZcS5qoUcNPrXhzdjd2kg2vvRZ2SSIiInGlcCzpq7CQRTW6AwrH8TRiBKxYlc13B1wGr74adjkiIiJxpXAs6auwkLy6+5KdDW3ahF1M+jj+eD8W743GF8HUqfDDD2GXJCIiEjd7Dcdm9nczq29m1czsUzNbZWbnJqI4kSopKGBRThdat4acnLCLSR8NGsCRR8LrCw/EAbz+etgliYiIxE0sK8fHOOfWAycCBUBX4HeBViUSD4WF5Ll2uhgvACNHwvy8akzucbZaK0REJK3EEo6j+4oNA15wzq0OsB6R+CguhqVLySvaR/3GATj1VL8a/0LTq2HsWCgoCLskERGRuIglHL9lZrOBfsCnZtYMKAq2LJEqWrGC7TugYEMDheMANG4Mxx4LL87rSzGm1goREUkb5YZjM8sC3gYOAfo557YDm4GTE1CbSOUVFFBIa4pdltoqAnLWWVCwrBrftD9HrRUiIpI2yg3Hzrli4G7n3Brn3M7IY5ucc8sSUp1IZRUWsoj2gMa4BWX4cKhZM9Ja8cUXsHRp2CWJiIhUWSxtFR+Z2almZoFXIxIvJTYA0cpxMOrVg5NOgpcX9GGHy4KXXgq7JBERkSqLJRxfD7wMbDWz9Wa2wczWB1yXSNUUFpJnHQBo2zbkWtLYWWfBytU5jO50GbzwQtjliIiIVNlew7Fzrp5zLss5V905Vz/y5/qJKE6k0goKWFSrBy1b+i2PJRjHHw/168MLja6EceO0IYiIiKS8mHbIM7NGZnawmQ2K3oIuTKRKCgvJy+mkloqA1awJp5wCr83Zj83UghdfDLskERGRKollh7xLgC+AD4HbIvd/DrYskSoqLCRvZ2tdjJcAF1wA6zdk8WrXW+D558G5sEsSERGptFhWjq8BDgLynHNDgN7AykCrEqmi4oIl5G9pppXjBDjiCOjcGR51F8GsWTB1atgliYiIVFos4bjIOVcEYGY1nHOzgW7BliVSBevXs3RjXbYX52jlOAHM4KKL4It5rZib3UMX5omISEqLJRwXmFlD4A3gYzN7E1gSZFEiVaIZxwl3/vmQnQ2P594Gzz0HO3eGXZKIiEilxDKt4hTn3Frn3J+BPwKPASMCrkuk8jTjOOFatYJhw+Cp1Seyo2ApfPpp2CWJiIhUSpnh2MwOMrPjSz7mnPs88uX+gVYlUhUlwnG7diHXkkEuuQSWra3Fe3XOgCeeCLscERGRSilv5fguYFYpj8+MfE8kOUXaKpo1c9SpE3YxmWPYMGjRAv7b7GZ4/XVYuzbskkRERCqsvHDcxDm3aM8HnXM/AE0Cq0ikqgoKyKvWmdxc7XieSDk5/sK8d/N6smBrK808FhGRlFReOK5Vzve0HifJq7CQRVkddTFeCH71Kx+SH2hyu1orREQkJZUXjj8xs/9nZrstv5nZbcDoYMsSqTxXUEj+9pYKxyFo1Qp+8QvjsY1nsG7cbJg5M+ySREREKqS8cPwboCPwg5m9Grn9gJ9xfH1CqhOphFUFRWwprqlwHJLrroONW6vzaNZlWj0WEZGUU2Y4ds5tcs6dBRwNPBm5HeOcO9M5tzEx5YlU0Pbt5K+oCWhSRVj69IFBg+CBGjew44lnYOvWsEsSERGJWSxzjhc4596O3BYkoiiRSlu6lHzaAgrHYbr+esjf0ozXfxzoJ1eIiIikiFh2yBNJHSVmHKutIjwnngidOjnuqvEH3MP/DrscERGRmJW3CUiHRBYiEheFheTTjto1d9K4cdjFZK7sbLjxRmP81gN5/4vaMKu0kekiIiLJp7yV41cAzEz7wErqKCggn3a0a+swjTkO1QUXQId2O7nV/g/3n0fCLkdERCQm5YXjLDP7E9DVzK7f85aoAkUqpLCQfMslt2N22JVkvGrV4Nbbspno+vLmf1fAli1hlyQiIrJX5YXjM4EiIAeoV8pNJPkUFpKX1YF27bRsnAzOPRe6tNnMnzbfQPELL4VdjoiIyF7llPUN59wc4G9mNtU5934CaxKptC35K1mxs6kmVSSJnBz40x21OHfUgbz6l+c5/UKH+l1ERCSZxTKt4hszu8fMJkRud5tZg8ArE6mEgvxiQJMqksmZZxn7tlzNHxZexLbPvgm7HBERkXLFEo4fBzYAZ0Ru6wFteyXJxznyltUANOM4mWRnwz8eqs1cunH/NRqVLiIiyS2WcNzJOfenyGYgC5xzt+G3lRZJLqtXk7+9BaBwnGyOP6UmJ3Waye3TRrBkXEHY5YiIiJQplnC8xcwOj/7BzA4DdNm5JJ/IjGMzR5s2YRcje7r3iYZspxo3XLAi7FJERETKFEs4vgJ4yMwWmdki4EHg8lhPYGbZZjbZzN6pZI0isSkoII9cWjXdRrVqYRcje+o0sBW/7fEuz83qw1cf6/drERFJTnsNx865Kc65A4EDgAOcc72dc1MrcI5rAG2PJcGLrBy3axt2IVKWmx9oRVvyufz8LRQVhV2NiIjIz8WycgyAc269c259RQ5uZm2AE4BHK1qYSIVFwnFuZy0bJ6s6Rw7gP53/wcyljbn1jy7sckRERH4m5nBcSfcBNwDFZT3BzC6LjolbuXJlwOVIOisuWOJXjtsH/Z+1VJoZx//pYC7jP/zjbvj667ALEhER2V1gKcLMTgRWOOcmlvc859wjzrl+zrl+zZo1C6ocyQArFm5iGzU0qSLZnXEG/9jnLtrXXMb558PGjWEXJCIisktM4djMDjWzs83svOgthpcdBgyPXMT3IjDUzJ6tQq0i5crP8x/TawOQJFe9OvV+dR5PbDmTBQsc118fdkEiIiK77DUcm9kzwD+Aw4GDIrd+e3udc+5m51wb51x74ExgtHPu3KqVK1K2vOXaACRlXHEFR1T/jht6fcx//wvPPBN2QSIiIl5ODM/pB+zrnNPVM5K8tmwhf2NjQOE4JeyzD5x9Nn956TS+O+xHLr+8Gr16wf77h12YiIhkuljaKqYDLapyEufcZ865E6tyDJFyLfEX49WvtY2GDcMuRmJyzTXkbNnAi0MeoWFDOPVUWLcu7KJERCTTxRKOmwIzzexDM3sregu6MJEKiWwA0q75trArkVj16gVDh9LiiTt46dntLFgA554LO3eGXZiIiGSyWNoq/hx0ESJVVlhIPt3VUpFqfvMbOOEEBi55iX/+81x++Uu49lp44AEwC7s4ERHJRLHskPc5MBuoF7nNijwmkjyiG4B0qR52JVIRxx0HPXrAPfdw5RWO3/wGHnwQ7r8/7MJERCRTxTKt4gxgHHA6cAYw1sxOC7owkYrYtHAFP9KUdp0VjlNKVhZcdx1Mngyffcbf/+57j6+/Hl5/PeziREQkE8XSc/x74CDn3PnOufOAg4E/BluWSMXkz9sKaFJFSho1Cpo1g7vvJivLj3Xr3x/OOQfGjg27OBERyTSxhOMs59yKEn/+McbXiSRMfr6/1wYgKahmTfjVr+Ddd2HWLGrVgjffhBYt4KSTYOHCsAsUEZFMEkvI/SAyqeICM7sAeBd4L9iyRComb3lNQCvHKeuXv4QaNeC++wA/Bvm992DHDhg2DNasCbc8ERHJHLFckPc74BHgAOBA4BHn3I1BFyYSs+3byV/XgGzbScuWYRcjldKsGZx3Hjz9NKxcCUD37vDGG7BgAYwYAVu3hlqhiIhkiJjaI5xzrzrnrnfOXeec02UyklyWLSOftrRutJmcWIYTSnK6/nooKoJ//eunhwYNgiefhC++gPPPh+Li8MoTEZHMUGY4NrOvIvcbzGx9idsGM1ufuBJF9iKyAUhuy+1hVyJV0b07nHACPPQQbNny08NnnQV33gkvvQQ33RRifSIikhHKDMfOucMj9/Wcc/VL3Oo55+onrkSRvVi8mHza0a69do1Ieb/5jW+reO653R6+4QbflnzXXfDwwyHVJiIiGSGWOcfPxPKYSFh25hdSQBvada0ZdilSVYMH+22l77lntx4KM79r3gknwNVXw6efhlahiIikuVh6jvcr+QczywH6BlOOSMUtm7ueHVQjV+E49Zn51eNZs+CDD3b7VnY2PP+87744/XSYNy+kGkVEJK2V13N8s5ltAA4o2W8MLAfeTFiFInuR94PvNW6Xq7aKtPCLX0Dr1nD33T/7Vv368NZbfmO9E0+EtWsTX56IiKS38nqO7wAaAE/v0W/cxDl3c+JKFClffoH/z1gzjtNEtWrw61/D6NHw/fc/+3bHjvDaa37E2/nng3OJL1FERNJXuW0Vzrli/GxjkaSVv0IbgKSdyy6DOnV873EpBg2Cf/zDryKX8RQREZFKiaXn+DszOyjwSkQqY+dO8tY3pFHNzdSrF3YxEjcNG8LFF8MLL0BhYalP+fWvYeRIuPFG+PrrxJYnIiLpK5ZwPAT41szmm9lUM5tmZlODLkwkJsuXk+/a0q7p5rArkXi79lo/seKf/yz122bw+OPQvr1vU161KqHViYhImoolHB8PdAKGAicBJ0buRcJXUEA+7chtvSPsSiTeOnTwS8P/+Q9s2lTqUxo0gJdf9qORr7hC/cciIlJ1ew3Hzrk8oCE+EJ8ENIw8JhK+xYvJI5d27bPDrkSCcM01fiTFHpuClNS7N9x+O7z6Krz4YuJKExGR9BTLJiDXAM8B+0Ruz5rZ1UEXJhKLdfNWsI6GtOteO+xSJAiHHebT7wMPlLss/NvfwoAB8KtfwZIlCaxPRETSTixtFRcD/Z1ztzrnbgUGAJcGW5ZIbBbP9h+35/ZQOE5LZv7KuxkzYMyYMp+WnQ1PPQVFRX7QhdorRESksmIJxwbsLPHnnZHHREKXt9BvMawNQNLYmWdC06ZlXpgX1bUr3HknvPtuuV0YIiIi5YolHD8BjDWzP5vZbcB3wGPBliUSm/xC32usGcdprGZNvxz81luwcGG5T73qKjj4YN9msW5dguoTEZG0EssFefcAFwKrgR+BC51z9wVcl0hM8lfVolrWDlq0CLsSCdSVV/oWi3/9q9ynZWX5p6xYAX/6U4JqExGRtBLLynGUAQ61VEiyKC4mb31j2tZfR1ZF/kuW1NOmjR/r9thjsGVLuU/t29ePdfvnP2HKlATVJyIiaSOWaRW3Ak8BjYCmwBNm9oegCxPZq5UryXdtaNes/LAkaeLKK2HNGvjf//b61L/8BRo39tMriosTUJuIiKSNWNbbzgIOcs792Tn3J/y0inOCLUskBgUF5JFLbhuln4wweDB07w4PP7zXpzZuDH/7m99W+qWXgi9NRETSRyzheBFQs8SfawDzA6lGpAK2LypkCa1o1ykn7FIkEcx8v8TYsTB58l6ffsEFcOCB8Ic/wLZtwZcnIiLpIZZwvBWYYWZPmtkTwHRgo5k9YGYPBFueSNkKp6+hmGxy960TdimSKOefD7VqxbR6nJUFd9wBCxbAf/+bgNpERCQtxBKOXwduAcYAnwG/B94HJkZuIqHIm1MEQO5+9UKuRBKmYUM4+2w/yDiGWW3HHQdHHOG3l964MfjyREQk9cUyyu0p4AV2heHnnXNPRW9BFyhSlrxFfhu03A4aVZFRrrwSNm+GZ57Z61PNfO/xihVwzz0JqE1ERFJeLNMqBgPzgIeAfwFzzWxQsGWJ7F3+0moAtG0bciGSWH37Qr9+8J//xLRPdP/+fgrcXXfBqlUJqE9ERFJaLEtudwPHOOeOcM4NAo4F7g22LJG9y/uxLs1rrqVmzb0/V9LMpZfC9OkwfnxMT//LX2DTJrjvvmDLEhGR1BdLOK7mnJsT/YNzbi5QLbiSRGLgHHkbm5DbcH3YlUgYzjwTateGRx+N6ek9esBpp/mNQdauDbY0ERFJbbGE44lm9piZDY7c/osuxJOw/fgjea4t7ZpvDbsSCUP9+vCLX8ALL8R8pd0tt8D69fDQQwHXJiIiKS2WcHwFMAP4NXANMDPymEho3OIC8mlHbru995xKmrr0Uh+MY9gxD6BXLzjxRLj3Xk2uEBGRspUbjs0sC5jonLvHOTfSOXeKc+5e55yW6yRUK2esoIha5HatEXYpEpYBA2DffWNurQD4/e/hxx/9tXwiIiKlKTccO+eKgSlm1i5B9YjEJG/6BgBye9YNuRIJjRlccgl8+y3MmBHTSwYMgCOPhH/8A4qKAq5PRERSUixtFS3xO+R9amZvRW9BFyZSnry5/sOLdvs3DLcQCdeoUVCtGjz2WMwvuflmWLYMnn8+wLpERCRl5cTwnNsCr0KkgvIX+/vcjtnhFiLhatoUTjrJ75j3t7/5oLwXQ4fCAQf4sW4XXugXoEVERKLKXDk2s5pmdi1wOtAd+No593n0lqgCRUqTt6wm9bI30bBh2JVI6M4/32+B9+GHMT3dDK67DqZNg08/Dbg2ERFJOeW1VTwF9AOmAcfjNwMRSQp5a+qTW+dHrfoJHH88NGsGT8W+m/2ZZ8I++/jJFSIiIiWVF473dc6d65z7D3AaMDBBNYmUzznyNjejXRPN4xJ8K8XZZ8Nbb8Hq1TG9pGZN+OUv4b33YPbsgOsTEZGUUl443h79wjm3IwG1iMRm7VryXRtyW24LuxJJFuefD9u2wUsvxfySK6+EGjXg/vsDrEtERFJOeeH4QDNbH7ltAA6Ifm1m2rNXQrNx7hJW04Tc9rEMW5GM0KsX7L9/hVor9tkHzjnHv2TNmuBKExGR1FJmunDOZTvn6kdu9ZxzOSW+rp/IIkVKypvsPzpv17VmyJVI0jDzq8djx1aoT+Lqq2HLlgplahERSXNaepOUkz/T9xrnHtAg5EokqZxzDmRlwTPPxPySXr38xiD//jc47UQuIiIoHEsKypvvW+BzezcOuRJJKi1awFFHwQsvVCjpXnklzJkDY8YEWJuIiKQMhWNJOXmLs6jGNlq22/uGD5Jhzj4bFi70W0rH6PTToVEjv3osIiKicCwpJ29lLdrUWEmW/uuVPZ1yip/TVoG9oWvV8jvlvf46LF0aYG0iIpISFC8k5eSva0BuPY0XkFLUrw/Dh/uRbtu37/35EVdcATt2wGOPBVibiIikBIVjSTl5Rc3JbbYp7DIkWZ19NqxaBZ98EvNLunTx7cqPPAI7dwZYm4iIJD2FY0kp239czxLXktzWSjBShuOP903Ezz1XoZddfjksXgwffRRQXSIikhIUjiWlFExcTjHZtOuQHXYpkqyqV4fTToM33oBNsX/CMHw4NG0Kjz8eXGkiIpL8FI4lpeRP8b3GuT1qh1yJJLWzz/bB+O23Y35J9eowahS8+SasXBlgbSIiktQUjiWl5M3aDEBunyYhVyJJbeBAaN4cXnmlQi+7+GJ/Hd+zzwZUl4iIJD2FY0kpeQt8r3HbvvuEXIkktexsOPVUeO+9CrVW7Lcf9O/vp1ZoxzwRkcykcCwpJb8wm+ZZK6hZNyfsUiTZnX46bNkC775boZddfDHMmAHjxgVUl4iIJDWFY0kpeT/WJbe2GkIlBtHWipdfrtDLfvELqF1bM49FRDKVwrGklLyNjclttCHsMiQVZGfDyJEVbq2oX98vOr/4ImzeHGB9IiKSlAILx2ZW08zGmdkUM5thZrcFdS7JDG5nMfnbW9KuxbawS5FUcdppPuG+/36FXnbBBbBhg59cISIimSXIleOtwFDn3IFAL+A4MxsQ4Pkkza2ctYoiapGbG3YlkjIGDYJmzSrcWjFoELRrB08/HVBdIiKStAILx87bGPljtchN139LpeVN8L3Gud1qhlyJpIycHN9a8c47FeqRyMryM48/+giWLg2wPhERSTqB9hybWbaZfQ+sAD52zo0t5TmXmdkEM5uwUpP3pRx5032vce7+9UOuRFLK6adXqrVi1CgoLobnnw+oLhERSUqBhmPn3E7nXC+gDXCwmfUs5TmPOOf6Oef6NWvWLMhyJMXlzdsKQLuDmodciaSUI47w+0JXsLWiWzc/8/iZZwKqS0REklJCplU459YCnwHHJeJ8kp7y8416rKdh+4ZhlyKpJCcHTjnFt1Zs2VKhl553HkyZ4m8iIpIZgpxW0czMGka+rgUcBcwO6nyS/vKW1yS3xjIsy8IuRVLN6af7cW4ffFChl/3iF1CtmlaPRUQySZArxy2BMWY2FRiP7zl+J8DzSZrLW9uAdvXWhl2GpKIhQ6BJkwq3VjRpAiecAM89Bzt2BFSbiIgklSCnVUx1zvV2zh3gnOvpnLs9qHNJZsgvakZuM+3KIJUQba14++1KtVYsWwaffBJQbSIiklS0Q56khI2riljtGpPbZmfYpUiqOv102LgRPvywQi8bNgwaN9bMYxGRTKFwLCkhb/wKAHI75YRciaSsIUN8yn3llQq9rEYNOPNMeP11WL8+oNpERCRpKBxLSsj7fg0A7fatG3IlkrKqVYMRI+Ctt2Dr1gq99LzzoKgIXn01mNJERCR5KBxLSsif7XuNc/s0CbkSSWmnngobNsDo0RV62cEHQ9euaq0QEckECseSEvIWFlONbbTs0zLsUiSVDR0KderAm29W6GVmfvX4s88gLy+Y0kREJDkoHEtKyFuSQ5vspWTVqhF2KZLKataE44/34bi4uEIvPeccf//sswHUJSIiSUPhWFLColX1aF97ZdhlSDoYMcLPZhs3rkIva9/e70T99NPgXCCViYhIElA4lpSwaFNTOjRZF3YZkg6GDYPs7Aq3VgCMGgVz58L48QHUJSIiSUHhWJJe0RbH0h370L7ltrBLkXTQqBEMHgxvvFHhl552mu/M0HbSIiLpS+FYkl7elLUAtO9g4RYi6ePkk2H2bJgzp0Iva9DAv/SFF2CbflcTEUlLCseS9BZNWAVAh/1qh1yJpI2TT/b3lWyt+PFH+OCDONckIiJJQeFYkt6i6RsBaN+7UciVSNpo1w769KlUa8Uxx0CzZmqtEBFJVwrHkvQWztvhZxz3ax12KZJOTj4ZvvvOT66ogGrV4Oyz4e23Yc2agGoTEZHQKBxL0lu0OJtcyye7qVaOJY5GjPAz2d5+u8IvHTXK70D98svxL0tERMKlcCxJb9GqOn7GsemCPImj/feHDh0q1Xfcpw/06KHWChGRdKRwLElv4YamtG+8PuwyJN2Y+daKTz6BjRsr/NJRo+Crr2DhwoDqExGRUCgcS1LbvBlW7GhCh1Zbwy5F0tGIEb4/4sMPK/zSc87xIVnbSYuIpBeFY0lqedP8inH7TvpPVQJw2GHQuHGlpla0a+f3EtF20iIi6UWJQ5LawvF+xnH7HppxLAHIyYGTToJ33oHt2yv88lGj4IcfYOzYAGoTEZFQKBxLUovOOO7Qt3HIlUjaGjEC1q6FL7+s8EtPPRVq1dKFeSIi6UThWJLaonnbqUERzftoxrEE5OijoWbNSrVW1K/vs/WLL2o7aRGRdKFwLElt4eIcci2frH2ahl2KpKs6dfy2d2++Wanm4VGjYPVqeO+9AGoTEZGEUziWpLZoZR061F6uGccSrOHDIT8fpk2r8EuPPhqaN1drhYhIulA4lqS2aGMTzTiW4J1wgr9/660KvzQnx28n/c472k5aRCQdKBxL0tq4EVbtaET7VmrmlIC1aAH9+1cqHINvrdi2Df73vzjXJSIiCadwLElr0czNAHToqJYKSYDhw2H8eFi6tMIv7dUL9tvPzzwWEZHUpnAsSWvh+JUAtN9XM44lAYYP9/fvvFPhl0a3k/7mG5g/P851iYhIQikcS9JaNM3POG7fp0nIlUhG2G8/aN++0q0V2k5aRCQ9KBxL0lo0bzu12Mw+vVqFXYpkAjO/evzJJ7B5c4Vf3qYNDB3qp1ZoO2kRkdSlcCxJa+HibNpbHtaiedilSKYYPhyKinxAroRRo3xbxbffxrkuERFJGIVjSVoLVtSjU+2lkKX/TCVBBg70295VsrVi5Ei/nbQuzBMRSV1KHZKUnIP5G5rRsfG6sEuRTFK9Ohx/PLz9NhQXV/jl9erBaaf57aS3bAmgPhERCZzCsSSlVatgY3EdOrbZGnYpkmmGD4cVK2DcuEq9/KKLYN06eP31ONclIiIJoXAsSWnBDL/s1rGT/hOVBDv+eMjO9qvHlTBoEHTsCI89Fue6REQkIZQ8JCktGLcKgI4H1A25Esk4jRr53uNK9h1nZcGFF8Lo0bBwYZxrExGRwCkcS1KaP9XPOO7Qf5+QK5GMNHw4TJ8OCxZU6uXnn+8nwz35ZHzLEhGR4CkcS1JaMK+Yliyh9r7twy5FMlF0t7xKtla0bQvHHANPPAE7d8axLhERCZzCsSSlBYXV6ZidB020O56EoFMn2HffSodj8BfmLV7s2ytERCR1KBxLUlrwY0M61lvlP5sWCcNJJ8Hnn8PatZV6+cknQ+PG8Oij8S1LRESCpXAsSWfrVigoakLH5pvCLkUy2fDhsGMHfPBBpV5eowacd54f6bZiRZxrExGRwCgcS9JZtNDhyKJTh4pvwiASN/37Q7NmVWqtuOwy2L5dF+aJiKQShWNJOgsmrgGgY48aIVciGS07G044Ad57zyfcSujRw889fuSRSm24JyIiIVA4lqTzUzju2yjkSiTjDR/ue46/+qrSh7jsMpg/H8aMiV9ZIiISHIVjSToLZm+lJlto0bd12KVIpjv6aN88XMkNQQBOPdUPXfnPf+JYl4iIBEbhWJLO/IVZdGQB1j437FIk09WtC0ce6fuOnavUIWrW9JuCvP46LF8e5/pERCTuFI4l6SxYXodONQt9qhAJ20kn+b6IWbMqfYhLL/WDL554Io51iYhIIBSOJak4BwvWNaFj43VhlyLinXiiv69Ca0X37jBkCDz8sHbMExFJdgrHklRWroRNxbXp2GZr2KWIeG3aQN++VQrHAFddBfn58M47capLREQCoXAsSWX+TB+KO3bODrkSkRKGD4fvvqvSbh7Dh0PbtvDgg3GsS0RE4k7hWJLKgvE/AtDxgLohVyJSwkkn+Z6fd9+t9CFycuDKK+GTT6rUviwiIgFTOJaksmDqRgA6HNQ05EpESujVy7dXVLG14pJLoHp1eOih+JQlIiLxp3AsSWX+vJ20opBaPdqHXYrILma+L+Kjj6CoqNKHadYMzjwTnnoK1q+PY30iIhI3CseSVOYtrkkXmw8tWoRdisjuTjoJNm+G0aOrdJirroKNG+HJJ+NTloiIxJfCsSSVeasa06XBCr9SJ5JMhgzxm4JUsbXioINgwAC4/36NdRMRSUYKx5I01q2Dldsa0LnFhrBLEfm5GjXg2GP9bnnFxVU61G9+AwsWVDlni4hIABSOJWnMm+u35+3SqXLb9IoEbvhwWLIEJk2q0mFOOQU6dIC7745TXSIiEjcKx5I0fpiwBoAuB9QKuRKRMgwbBllZfvW4CrKz4Zpr4OuvYezYONUmIiJxoXAsSWPeBL9ldKcBzUKuRKQMTZvCoYfGpR/ioougQQO455441CUiInGjcCxJY97MHbRhMbX37xR2KSJlGz4cvv/e7wVdBfXqweWXwyuvwKJFcalMRETiQOFYksa8/Op0sR/8HrsiyWr4cH//5ptVPtTVV/sujXvvrfKhREQkTgILx2bW1szGmNksM5thZtcEdS5JD/NWNaJz/ZV+n12RZNWtG+y7L7z2WpUP1aYNnHsu/Pe/sHJlHGoTEZEqC3LleAfwG+dcD2AA8Csz2zfA80kKW7MGftxWny6tNoZdisjejRwJX3wBq1ZV+VA33ug33bv//jjUJSIiVRZYOHbOLXXOTYp8vQGYBbQO6nyS2n6YFxnj1jnkQkRiccopftZxHC7M697dZ+0HH9SW0iIiySAhPcdm1h7oDfxsaJGZXWZmE8xswkp9rpix5o3TGDdJIb17Q25uXForAG6+2W+C8/DDcTmciIhUQeDh2MzqAq8C1zrnfrYu4px7xDnXzznXr1kzjfDKVPMmrsMoptMh+4Rdisjemfnl3o8/jstyb9++fvO9e+6BLVviUJ+IiFRaoOHYzKrhg/Fzzrn4LLFIWpo3aydtKKDmfhrjJili5EjYtg3efz8uh7v5ZlixAh59NC6HExGRSgpyWoUBjwGznHMacy/l+iG/Ol1svsa4Seo45BDYZ5+4tVYMGuRvd9yh1WMRkTAFuXJ8GDAKGGpm30duwwI8n6Sweasa0aXBcr+vrkgqyM6GESPg3Xf9uIkqMoPbboOlS+GRR6penoiIVE6Q0yq+cs6Zc+4A51yvyO29oM4nqWv1ali9vR5dWm0OuxSRihk5EjZt8r3HcTB4sL/deadWj0VEwqId8iR08+YUA9ClS8iFiFTUkCHQoAG8/nrcDnnbbbBsGfznP3E7pIiIVIDCsYRu3vi1AHQ+sE64hYhUVPXqcOKJfivpHTvicshBg2DoUL96vFkfpoiIJJzCsYRu3sT1GMV07K9RfpKCRo70vUFffBG3Q952GyxfDg89FLdDiohIjBSOJXRzZu6kAws1xk1S07HHQq1acW2tOPxwOP54P7li7dq4HVZERGKgcCyhm51Xi+5ZczXGTVJTnTpw3HE+HBcXx+2wf/0rrFkDd90Vt0OKiEgMFI4lVMXFMOfHJnRvuByy9J+jpKhTToHCQhg/Pm6H7NULzjoL7rvPj3cTEZHEUBqRUOXnQ1FxDbq305VHksJOPBFycuK2IUjU7bf7Tfj+8pe4HlZERMqhcCyhmj3dX+HfvWdOyJWIVEGjRn7ExGuvgXNxO2znznDppX5TkB9+iNthRUSkHArHEqrZ36wGoHv/BiFXIlJFp57qE+zUqXE97B//CDVqwI03xvWwIiJSBoVjCdXsSZtozI80Pbhj2KWIVM0pp/gtpV96Ka6HbdkSbrrJL0p/9llcDy0iIqVQOJZQzZqbTQ9mYd27hV2KSNU0a+ZbK/73v7i2VgD85jd+mMv118POnXE9tIiI7EHhWEI1e2kDutfOh/r1wy5FpOp+8QuYPx8mTYrrYWvVgr/9DSZPhqeeiuuhRURkDwrHEprVq2FFUQO6t1ofdiki8XHKKX5qxf/+F/dDn3kmDBgAv/89bNgQ98OLiEiEwrGEZs5s/9GzOiokbTRuDEcfHUhrhRncey8sWwZ33hnXQ4uISAkKxxKa2WPXAdC9b52QKxGJozPOgEWL4rohSNSAAXD22XD33ZCXF/fDi4gICscSotnj1lGdrbQ/tFXYpYjEz4gRUK1a3KdWRN15p99M8qabAjm8iEjGUziW0MyeWUwX5pHTs3vYpYjET8OGcOyxvrWiuDjuh2/bFn77W3jxRfjmm7gfXkQk4ykcS2hm59emR/Y8aKWVY0kzZ50FBQXw1VeBHP6GG/z/bK67LpD8LSKS0RSOJRTbtsH8dU3pvs9qf6WRSDo5+WSoUweeey6Qw9etC3fcAePGabSbiEi8KRxLKH74AXa6bLp33BZ2KSLxV6eO7z1++WX/m2AAzj0XDjnEbyu9Zk0gpxARyUgKxxKK2ZO3AND9wBohVyISkLPP9qn1gw8COXxWFvzrX/Djj/CHPwRyChGRjKRwLKGY9fVqALoe2jTkSkQCcvTR0LRpYK0VAL16wa9+BQ8/DBMnBnYaEZGMonAsoZg+eTvtWUi93p3DLkUkGNWq+e2k33oL1ge3C+Ttt0OzZj4k6+I8EZGqUziWUEybX4uezIDOCseSxs45B4qK4I03AjtFw4Zw110wdiw88URgpxERyRgKx5Jw27bBnFVN2L9xIVSvHnY5IsEZMAA6dIBnnw30NKNGweGH+4vzfvwx0FOJiKQ9hWNJuDlzYIfLoWfnorBLEQmWmU+un3zi5x4HeJqHHoK1a+H3vw/sNCIiGUHhWBJu+gQfivfvp0kVkgHOOw+cg2eeCfQ0BxwAV18NjzwC48cHeioRkbSmcCwJN+2L1eSwnW6DmoddikjwOnWCQYPgySd9SA7QbbdB8+bwy1/Czp2BnkpEJG0pHEvCTZ+8g27MoXqfnmGXIpIYF1wAc+fCd98Fepr69eHuu2HCBPj3vwM9lYhI2lI4loSbtrAO+2fPhI4dwy5FJDFOOw1q1/arxwE76yw46ii45RZYsiTw04mIpB2FY0moDRtg0fom9Gy+CrKzwy5HJDHq1fMB+cUXYcuWQE9l5jcF2boVrr020FOJiKQlhWNJqBkz/P3+3beHW4hIol1wgd8MJMCZx1GdO8Mf/wgvvwzvvRf46URE0orCsSTUtG82ANBzQN2QKxFJsCOOgPbt4bHHEnK63/0OevTwF+dt2pSQU4qIpAWFY0mo6V+vpQ4baT+oXdiliCRWVhZcfDF8+inMnx/46apX9xfl5eX5LaZFRCQ2CseSUNOmwX7MIOvA/cMuRSTxLrzQ99o/+mhCTjdokM/jd98NU6cm5JQiIilP4VgSavriBuxfY54fxiqSaVq3hhNPhMcf9/uoJ8Df/gaNGsHll0NxcUJOKSKS0hSOJWGWL4eVRfXp2Watv6ReJBNddhmsWAFvvZWQ0zVpAvfc40csP/JIQk4pIpLSFI4lYaZP9ctW+6ujQjLZscdC27YJTarnngtDh8JNN8HSpQk7rYhISlI4loSZ+vkaAHoe3jDcQkTClJ0Nl1wCH38MCxYk5JTR2cdFRXDddQk5pYhIylI4loSZ9PUWWlFI80M7hV2KSLguvthPr0jg6nHXrn7XvJdegg8+SNhpRURSjsKxJMykmTXowyTo2TPsUkTC1bo1jBgB//1v4DvmlXTjjdCtm599vHlzwk4rIpJSFI4lITZtgtkrGtOncZ7fSlck0119NaxeDS+8kLBT1qgB//kPLFyo2cciImVROJaEmDoVismmz76JWyUTSWpHHOGvTn3gAXAuoae98EI/+3jKlISdVkQkZSgcS0JM+tLvX9tnoLaNFgH8VXJXX+0T6ldfJfTUd90FjRv76wJ37EjoqUVEkp7CsSTEpDFracpK2gzpEnYpIsnjnHP8Dh3//GdCT9ukiV+wnjAB7r8/oacWEUl6CseSEJOm5tCXiVjfPmGXIpI8atf2y7evvQaLFyf01GecASedBH/8I8yfn9BTi4gkNYVjCdzWrTB9aRP6NJjvP8sVkV1++Uvfc5zg1WMz+Ne/ICfHb9qXwLZnEZGkpnAsgZs+HXa4HPp01+wokZ9p3x5OP92PkVi3LqGnbtMG/v53GD0annwyoacWEUlaCscSuElf+wkVfQ6rHXIlIknqd7+D9esTuilI1GWXwcCBcP31sGxZwk8vIpJ0FI4lcJM+XUMD1tLhyI5hlyKSnPr2hSOPhPvu831ICZSVtWsvkquvTuipRUSSksKxBG7i5Cz6MEkX44mU54YbYMkSeP75hJ+6Wze49VZ45RV4442En15EJKkoHEugtm+HqYWN6VN3LjRvHnY5Isnr6KPhwAP9EOLi4oSf/ne/86f/5S9h7dqEn15EJGkoHEugZs2CrcXV6dNlY9iliCQ3M796PGsWvPVWwk9frRo8+igsXw433pjw04uIJA2FYwnUxG98/2SfQ2uGXIlICjjjDOjcGW6/PZTZav36wXXX+esCP/884acXEUkKCscSqG/fX0ND1tD1qHZhlyKS/HJy4A9/gMmT4e23Qynh9tuhY0e49FJ/kZ6ISKZROJZAfTs+hwF8R9ZBfcMuRSQ1nHMOdOoEt90Wyupx7dp+5XjePF+CiEimUTiWwKxbBzOWNuaQ+jOhdeuwyxFJDTk58Pvfw6RJ8M47oZRw5JFw8cX+2sCxY0MpQUQkNArHEpixY8GRxSG99NmsSIWcey506BDa6jHA3Xf732nPP1/tFSKSWRSOJTDffrgeo5j+xzcOuxSR1FKtmu89njgxtMHDDRrA44/DnDl+IVtEJFMoHEtgvv10Mz2ZTv0h6jcWqbDzzoPu3eHmm2HHjlBKOOooP/f4vvvgiy9CKUFEJOECC8dm9riZrTCz6UGdQ5JXcTF8N7sBh2SNg969wy5HJPXk5MAdd/il28cfD62Mv/3Nd3hccAFs1LhyEckAQa4cPwkcF+DxJYnNng3rttbikI7LoXr1sMsRSU0nnwyHHgp/+hNs2hRKCXXrwpNPwqJFfo8SEZF0F1g4ds59AawO6viS3L75fDsAhwzMCbkSkRRmBn//Oyxb5nsbQjJwoN8c5OGH4eOPQytDRCQhQu85NrPLzGyCmU1YuXJl2OVInHz73hoa8yNdh3UOuxSR1HbYYX4F+W9/8yE5JH/5i2+BvugiP6ZRRCRdhR6OnXOPOOf6Oef6NWvWLOxyJE6+HZ/NIXyLHXpI2KWIpL6//x2KivzFeSGpVcu3VyxZAldfHVoZIiKBCz0cS/pZswZmLW/CIQ1nQatWYZcjkvq6dvV9DU8+Cd99F1oZ/fv7sW7PPAPPPx9aGSIigVI4lriL/n/3Ib23hluISDr5wx+gZUu/bFtcHFoZt97qrxG84gpYsCC0MkREAhPkKLcXgG+BbmZWYGYXB3UuSS5j3tpANbYxYJg2/xCJm3r1/H7OEyaEOtotJ8evGmdlwVlnwfbtoZUiIhKIIKdVnOWca+mcq+aca+Oceyyoc0lyGf3hNg7hW2oP6R92KSLp5eyz4fDD4aabIMQLmHNz4b//hXHj/JQ5EZF0orYKias1a2DSwkYcWfNr6NUr7HJE0osZ/PvfsH49XHttqKWcfjpccgnceSd8+mmopYiIxJXCscTV55+DI4uh/TZAdnbY5Yikn/32g1tu8b0N774bain33QfdusGoUaEuZIuIxJXCscTV6DfXU5tNHHxK67BLEUlfN98M++4LV14JGzaEVkadOvDCC/Djj37+sXOhlSIiEjcKxxJXoz/eyUC+pPrRR4Rdikj6qlEDHn0UCgrgxhtDLaVXL3+d4DvvwAMPhFqKiEhcKBxL3CxfDjMKGzG0zjj/0a+IBOeQQ3zf8cMPw/vvh1rK1VfD8OHw29/CN9+EWoqISJUpHEvcjBntP1MdOmCzn/MkIsH661+hZ0+48EJYsSK0MszgqaegXTt/oV6IpYiIVJkSjMTN6DfW05A19B7ZIexSRDJDzZrw3HN+TMwll4Ta9NuwIbz6KqxeDWeeCTt2hFaKiEiVKBxL3IweA4P5jOwjB4ddikjmOOAAP0/t7bf9mLcQ9erlSxgzxg/UEBFJRQrHEhd5eTB/ZQOG1p8IXbuGXY5IZrnmGjj2WN+DPGFCqKWcfz788pf+Ir3nngu1FBGRSlE4lrj44H3/ce5Rg7b5BkQRSZysLHj2WWjRAk47zc9WC9F998ERR/hOj5CzuohIhSkcS1y89fwGOvED3Ud0D7sUkczUtCm88gosXQrnngs7d4ZWSrVq8PLL0Lw5jBgBy5aFVoqISIUpHEuVbdoEn35bm+G8hZ0wLOxyRDLXQQf5YcMffAC33hpqKc2awZtv+msFhw+HzZtDLUdEJGYKx1JlH38MW3fkcFK3ef5jXREJz2WXwaWX+jFvTz4ZaikHHuh30JswwS9mFxeHWo6ISEwUjqXK3vrfFhqwlsN/oS2jRUJnBg89BEcd5UPymDGhljN8ONx7L7z+OtxwQ6iliIjEROFYqmTnTr9t7DDeo9rJaqkQSQrVqvn+465dYeRImDkz1HJ+/Wu46iq4+2548MFQSxER2SuFY6mSceNg5YZanNTwK+jdO+xyRCSqQQN4912/UcjRR8OCBaGVYuZXj08+2Qfll14KrRQRkb1SOJYqefuNneSwneOGV9cIN5Fk0769vyigqAiOPBIKCkIrJSfH9x8ffjiMGuXLEhFJRgrHUiVv/W8LA/mSRqcODbsUESlNz57w4Yd+9vFRR4U6V61WLXjrLejeHU45xX/yJCKSbBSOpdLmz4cZi+pyUvb7flVKRJJTv36+xWLxYhg0CPLzQyulYUM/aW6fffymft9/H1opibFtm/+FZM4cmDEDpk6F6dP9e7B2bajzqEWkdDlhFyCp68UXHGCMPHwF1KkTdjkiUp6BA30vw7Bh/utPP4XOnUMppVUrGD3a5/Sjj4bPPoP99gullPjYts1f9Pj99zBtGvzwAyxcCIsWwYYN5b82JwfatIHcXH8BZa9efgZe795Qu3YCiheRPZlzLuwaftKvXz83QXuNpgTnoEfHIpovGsvn/54Nl18edkkiEotJk/ySbU6OHzXTt29opcyb57eZds4H5G7dQiulYrZs8QV//jl89ZUf5Lx1q/9erVrQqRN07Oh7vps1gyZN/AWSOTmQne0HPm/YAOvWwYoVfhU5Lw9mzYLVq/1xqlWD/v1h8GA4/ngYMMBvEy4icWFmE51z/Ur9nsKxVMaECX4zrkeyruDSFf/P/+MvIqlh1iwfuFauhGef9Q3AIZk5E4YM8dfzjh4N++4bWinly8/3rSnvvusL3bLFB9i+feGww/w/iL16+dX47OzKncM5KCyEyZN96P7sM5g40bdeNG/uh0afdZb/jUJBWaRKFI4l7q69xvHwA9tYdvR5NPpIc5lEUs7y5X622rhxcMcdfoeOkCbOzJoFQ4f6DPjJJ3DAAaGU8XPz5vlfHl591fcLg18RPuEEfxs0yK8UB2ndOnj/fXjjDR/MN26Etm39yI9LL/Wr0yJSYQrHElc7dkDrfbZx+Jq3efWZLX5fWBFJPVu2wIUX+sHDI0bA449Do0ahlDJ3rg/IW7b4C/YOOiiUMmDVKv/38cwzMHasX6E94gg48UQfiLt2DW9s5ebNftzHU0/BRx/5leYTT/Q7rBx9tMZpilRAeeFYn8tIhX3yCaxYU51zq/3PrzyJSGqqVcsPH77nHt9/3KcPjB8fSildu8IXX0D9+r7N4pNPEnjyoiJ4+WXfttCypQ+bW7bAXXf5CR+jR8P11/um6DADaO3acOaZfiV50SK45RYf4I891rd3vPKKpl+IxIHCsVTYs08X09DWMuykbKhXL+xyRKQqzOC66+DLL/2FYoceCrfe6icwJFjHjvD119Chg1+kfeWVAE9WXOwvqLv0UmjRAs44w/f3XncdTJnib7/9rR+tkYzatoW//MX3Qj/+OGzaBKef7udaP/UUbN8edoUiKUvhWCpk40Z4/bViznAvUePc08MuR0TiZcAAP4rs7LPh//7Pz0YOoc2tVSu/gtyvn8+r998f5xPMng2//71P4oMH+5Xzk0/2Y+7y8+Hvf0+ipucY1KjhW2NmzvTtIDVqwAUXQJcu8O9/KySLVILCsVTIM8/A5q05nF/nVX+1u4ikj0aN/Krj22/73tuDD4ZLLvEX7yW4jI8/9pn12mvh17+uYrfAihXwwAO+kblHD7jzTr9N37PP+p/tqaf87oGVnTKRDLKz/W8Tkyf7FplWreDKK/34j5de8ivlIhIThWOJmXPwwH076Zs1iUN+0Q5q1gy7JBEJwokn+hES11/vg2OXLvDXv8L69QkroXZt31Zx3XXwz3/6aXN7209jNxs2+FXhE07wQfGaa3zCvuceKCjwV/2dc076bWBk5n/mr7/2IblWLd+nfPDBCW7kFkldCscSs08+gdlzs7mm+F7syivCLkdEgtSgAfzjH36r48GDfStC+/a+z3XNmoSUkJ3ts+yDD8J778Ehh/jN58q0cSO8+CKMHOn3pz77bL9d829/63+OSZN82m7ZMiH1hyoakidP9r/grFzpJ1occ4z/exCRMikcS8zuv9+xT/Yqzui7wDcEikj669bNjw8bPx4OPxz++Edo3dq3W0yenJASfvUr+PBDWLrUd0Z89FGJby5b5vu9Tj3V70Z31lnw7be+vi++8DvP3Xlniu9PXQXZ2XDeeTBnjv9NY9IkP9nizDP38puGSObSnGOJybx5ftTSrdzGbY+38xeAiEjmmTIFHnoInnvOz93t2dP3up5xRuD7Py9YACNOLmb6DONPh3zMHzbcSPa07/03W7TwAfmMM/yOdancPxykdev8JwL33OMnklx2mf+Fp0WLsCsTSShtAiJVdu218K9/7iCv3v60XDLRNwSKSOZau9YH5Jde8lsdO+fbLo46yu/m0a8fdOpUtW2Od+70iXjqVD/Pd+xYNo2bwZVF9/AM53Fko4k8d+XXND/1cL91s7ZUjt3SpX4qyX//6ydcXH+9bz+pXz/sykQSQuFYqmTdOmjbppjhm17k2esmwt13h12SiCSTwkK/vfEnn8CYMf4fDfBz0Hv29IOLc3P9hXENGvhbjRp+goJzfgV6zRp/KyjwI9UWLfKtAEVF/ljVq0Pv3jBgAO6oo3k870iu+m1NGjTwY36HDQvrh09x8+bBH/4A//sfNG3qv77iCv/+iKQxhWOpkltv9QsMk+lFr7kv+yvXRURKs2MHTJvm+5EnT4YZM3zQXbzYf29v6tXzQbpdOz92bb/9fMA+4ICfBbZp0/w1d9On+zz3j3+k3/CJhJkwAW66CT791H8CcPvt/i9X7SmSphSOpdJWrICOHR0n7HiLl4b8229bKiJSUTt3wo8/+nFw69b5flczf6tTBxo29Lc6dSq0RXNRkW+Zvftuv6/HI4/4rg6ppI8/9iF50iT/C8kdd/iZ9mFumy0SgPLCsRq0pFx33glbNjtu33qD/7hNRKQysrP9eLXOnf20hEMO8bvy9e/vV4bbtIG6dSscwmrWhLvugtGj/Z+PPBIuughWrw7gZ8gERx/tJ5O88IIfjXfCCf59eucd3wIjkgEUjqVMBQXwr385zq/xEt2GtvFXgIuIJKHBg32bxY03wtNP+8EZ//lPFXfWy1RZWX7U26xZ/i9xxQo46ST/S83rr2u3PUl7CsdSpv/7PyjeUcyfim6CP/0p7HJERMpVq5b/tGviRL9r8hVXQJ8+vo1WKqF6dT/qbe5ceOIJv+vgyJFw4IF+ZXn79rArFAmEwrGUasoUeOwxx+U1niR3cEcYNCjskkREYnLggfDZZ/Dyy77F+aij/MryF1+EXVmKqlYNLrjAryQ/+6y/sPLss/0Ukjvu8L3kImlE4Vh+ZudOuPRSaFJrC7dt/p0fVyEikkLM4LTTfJ574AE/Fe6II3xIfustdQZUSk4OnHOOn0Dy9tvQvTvccovvF7/sMj82RCQNKBzLz/zzn/56jPvdr2k8tLf/fxMRkRRUsyZcfbXfS+See/z9ySf7nuR77/XttFJBWVlw4ol+rvW0aTBqlN/Ce//9/W8g0RYMkRSlUW6ym0WL/FjRIU2m8PaSftjUKb55T0QkDWzf7q8pu/de+O47P0Tj+OPhrLP8faNGYVeYolatgkcf9TuyzJvnR/Kddppvxxg0SLsXStLRnGOJiXP+/xy+/nInMzZ3oN1vzvBT9UVE0tDMmfDUU76NdskSH5QPPxyOOcYP5znoIKhdO+wqU4xz8O238OST8OKLfgW5fXs44wx/Md9BBykoS1JQOJaY3Hkn3HwzPNj2Tn61858we7bfrUpEJI0VF8O4cb6N9p13YOpU/3i1an6Tvn339Z+otW8PrVv7W+PG/p/Hkpv2OedvO3f6a9bWr/c7Yq9du/ut5GPr1/v8uH79rtumTb6mPW/Z2X7n7YYNd7/fZx+/oWC7dtCpk28Frl49oX+Fpdu82W8r/vTTfmTIjh2+P/mUU3xQPvxw38csEgKFY9mrTz6BY4+FMw6cw/OTu2PPP+8/ZxQRyTCrV8M338DXX/ugPHOmbzkrTU6Ov/hv586KXeRXvboPtg0aQP36u9/q1PFBOCtr99v27X5zwXXrfLCO3i9fDlu27F5Tt26+BbhnT3/frx+0alWFv5SqWrPG/+bx2mvwwQd+a8MmTfwyffQWaoGSaRSOpVx5eX62e4uGW/guvzV1jznUL6Fou1AREcCv5hYUQGGhb8FYu9av+G7Y4FeLs7N33bKyfECtX9+v7jZqtGt37OitZs34/RPrnJ+mlpfnRxJPm+Zv06fvHuo7dfLtvwMH+vuOHUP6Z37TJh+Q33wTPvrIp3vwKf7YY/3svUMP1SeXEiiFYynTunUwZAjMn++Y0PhYumybAd9/D82ahV2aiIhU0fr1PiR/9x18+aW/RccSt2rlt9seNswv3DZuHEKBxcV+ef6jj+DDD+Grr2DbNv8bRq9ePskPHOhbMJo3D6FASVcKx1KqDRvguON8r91bg+/h+E9/C6NHa3SbiEiaKi72s5+//NJvlPLxx76NJCsLBgzwF2UPG+ZzaSjXzW3a5Htaokn+u+98CwZA164+JA8c6Ivt2lUX90mlKRzLz2ze7P8B/OoreOmiDzn1v8f5zT5uuy3s0kREJEF27vRz7d9/H957D6L/F9yqFZx0kr8NHeq35g7Ftm0wadKusPzVV75/GXzfSt++fgJG9NaunVoCJSYKx7KbNWvg1FPh88/h2V+P5az7D/HLBW++qSuHRUQy2PLlvh34nXf8/caNfpzdMcf4oHzCCSF3N0SXvseN87fx431bxvbt/vv77LN7WD7oILUJSqkUjuUnc+f6f+AWLoTHfzeLc//Ry//m/cknGugpIiI/2brVt168/bbfcnvxYr8oO2AADB/u/79k332TYKF261aYMsUH5eht1ix/pSL41eTevX2vSK9e/mutMGc8hWMBfG/ZGWf4xeHX/jyVgbcM9DMnv/wypCsxREQkFTjn82c0KEf/r7pjRx+SjznGT8CoWzfcOn+yYYNvxxg/3hc7ZQrMmbMrMDdsuHtY7tXLD7WuVi28miWhFI4z3KZNcNNN8OCDfublW1e8R4ffjITcXL9i3LZt2CWKiEgKWbLEt1689Zbf36OoyC+8DBjgJ2AceST0758km5FEbdrkZ9x9/72/TZ7sWzKiF/xVr+53eym5ynzggb63WdKOwnEGGz0aLr3Ut1H8+mrHX1s9SO2br4FDDvH/qjVpEnaJIiKSwrZs8QMmPvnEB+UJE/wCba1a0KcPHHzwrvbfTp2SrJthxw6YN29XWI7er1q16zmdOvmgfMABfhbzAQdAhw6alJHiFI4z0LRpfrX4vff8x15P3LuWQU9c6LfyHDkSnn02xMuPRUQkXa1Z43uVP//cdzVMmrRrcbZRI78w27UrdOkCnTv7+44dd9+KO1TOwdKluwfm77+H+fN3tWXUqeM/ii0ZmPffXy2KKUThOIOMHw/33gsvvui3Jb3lFriqw7vUuupi/y/WHXfAtdfqN14REUmI7dthxoxd18pNmQI//ODnK0eZ+fFxzZr9/NawoV/L2fNWo4ZvEY7lFt3mu0o2bfI/yNSpfgVq6lR/K/mDtG69e1g+4ADo3j3J+ksEFI7T3saNfkH44Yf9R1v16sGVV8KNw6bR+P/9xl+Jd8ABfrV4//3DLldERITVq31Hww8/+Pv8fFi5cvfbhg3xO19Ozs9Dc/XqfiEpus13dKvvxo2hRQto2dKH9pYt/ZS4n007ja4ylwzL06bBzJm7xsvl5PiAvOcqc5s2SdZjklkUjtPQhg2+v+uVV3ww3rzZfyx1za8dF+w3nvqP3gP/+5//X/of/+jTctJ8ZiUiIrJ3RUV+C+wtW35+27rV58/K3LZt23W/fr3/YHXNGli71t+XFsqzsvyM5/bt/a1DB3+Lft2uXYlhF9u3+9mpJVeZp03zvwFE1a3rQ3OPHrvfd+qkleYEUDhOA1u3+o+jvvzSX/DwxRf+f3uNGvnxbOccv5rDlrxM1mP/hYkT/dW1V17pG48bNgy7fBERkZSxbZvfEGXp0l23JUugsBAWLfIXuefn+x0Go7KyfFdFhw5+sSoanqNft2gBWevXwvTpPizPnu3nMc+eDQUFuw6Uk+MDcsnA3LWrP9A++2i1OU4UjlOIc/4i2Xnz/Kcykyb52/ff+4AM/hqAYcfuZFinORy65l2qffiOT83O+YnsV10Fo0Yl0cBJERGR9LJjhw/LCxf6WzQ0R2+Fhbs/v2ZNv8pcWnDu2GwD9ZfO2T0wz57tw0C0PQP8Zl0ll61LHqxNG98PovAck9DCsZkdB9wPZAOPOufuLO/5mRCOi4t9H9WSJbt+Gy0o8P/9z5vnP4VZu3bX8+vXd/TpUUTfdisZ2Gw2h20dTdM5X/sraDdt8k/q2dNPoDj1VN/HpP9hiIiIhKqoCPLyYMGCXYE5+vWCBbBu3e7Pb9zYbzvQsuWufucWzXbSwpbTcusiWmyaT8vVM6hTMAdbFDng+vW7H6R6df/Cks3S0a9btPAnadTI3zdsWEoTdeYIJRybWTYwFzgaKADGA2c552aW9ZowwnFxsf9YZMeOn9/KeryoaPe+p82bf/712rW7epei96tXw4oVu38MAz7Ltmvnx9l0bbuFrt//jy6bp9Bt9bd0WDmOLIp3PblePd/M37u3345o0KCQN7oXERGRilqz5ueBubDQL5otW+ZvO3b8/HXVqvlc27Cho0GdnTSsvpmGWetowDoa7lxNg20rqb15FbU2rKDm+hXU2ryKmhRRiy273eewg5w6NcluUJechv6WXb8OOXVqkFO3Jtl1apJTr5b/ul5tsurWxurU3jUmpHr1vd/n5EB2tu85ycoq++sQFvXKC8dB/spwMPCDc25BpIgXgZOBMsNxGI46CsaMie8xzfzVr9GrXhs1gm7d/H30t8GSv9S1aFHiWrlNxdDrL373ukN7QO5x/uvcXP9RSm6uxrCJiIikuOh0jD59Sv9+cbFfVFu2bFdgXrrUP7ZuHaxda6xbl8PatfUpXFufdevasnatX6SL2abIbcnen7qDbLJLLtbFy223wa23xv+4VRDkyvFpwHHOuUsifx4F9HfOXbXH8y4DLov8sRswJ5CCpCKaAqv2+ixJJL0nyUfvSXLR+5F89J4kH70nu+Q655qV9o0gV45LWyP/WRJ3zj0CPBJgHVJBZjahrI8aJBx6T5KP3pPkovcj+eg9ST56T2IT5OfzBUDbEn9uQ0wL9yIiIiIi4QgyHI8HuphZBzOrDpwJvBXg+UREREREqiSwtgrn3A4zuwr4ED/K7XHn3IygzidxpTaX5KP3JPnoPUkuej+Sj96T5KP3JAZJtQmIiIiIiEiYNBNMRERERCRC4VhEREREJELhWHZjZseZ2Rwz+8HMbgq7nnRiZo+b2Qozm17iscZm9rGZzYvcNyrxvZsj78McMzu2xON9zWxa5HsPmPmthcyshpm9FHl8rJm1T+gPmILMrK2ZjTGzWWY2w8yuiTyu9yUEZlbTzMaZ2ZTI+3Fb5HG9HyEzs2wzm2xm70T+rPckRGa2KPJ3+b2ZTYg8pvckThSO5Sfmt/x+CDge2Bc4y8z2DbeqtPIkcNwej90EfOqc6wJ8Gvkzkb/3M4H9Iq/5V+T9AXgYv3FOl8gtesyLgTXOuc7AvcDfAvtJ0scO4DfOuR7AAOBXkb97vS/h2AoMdc4dCPQCjjOzAej9SAbXALNK/FnvSfiGOOd6lZhbrPckThSOpaSftvx2zm0Dolt+Sxw4574AVu/x8MnAU5GvnwJGlHj8RefcVufcQuAH4GAzawnUd8596/zVtE/v8ZrosV4BjoyuAkjpnHNLnXOTIl9vwP+ff2v0voTCeRsjf6wWuTn0foTKzNoAJwCPlnhY70ny0XsSJwrHUlJrYHGJPxdEHpPgNHfOLQUf1IB9Io+X9V60jny95+O7vcY5twNYBzQJrPI0E/nYsDcwFr0voYl8fP89sAL42Dmn9yN89wE3AMUlHtN7Ei4HfGRmE83ssshjek/iJMjtoyX1xLTltyREWe9Fee+R3r9KMrO6wKvAtc659eUskOh9CZhzbifQy8waAq+bWc9ynq73I2BmdiKwwjk30cwGx/KSUh7TexJ/hznnlpjZPsDHZja7nOfqPakgrRxLSdryO/GWRz7aInK/IvJ4We9FQeTrPR/f7TVmlgM04OdtHLIHM6uGD8bPOedeizys9yVkzrm1wGf4Hki9H+E5DBhuZovwrXZDzexZ9J6Eyjm3JHK/Angd3xap9yROFI6lJG35nXhvAedHvj4feLPE42dGrhjugL9QYlzko7INZjYg0v913h6viR7rNGC00y4/5Yr8HT4GzHLO3VPiW3pfQmBmzSIrxphZLeAoYDZ6P0LjnLvZOdfGOdce//8Jo51z56L3JDRmVsfM6kW/Bo4BpqP3JH6cc7rp9tMNGAbMBeYDvw+7nnS6AS8AS4Ht+N/KL8b3cH0KzIvcNy7x/N9H3oc5wPElHu+H/4dwPvAgu3a6rAm8jL/YYhzQMeyfOdlvwOH4jwqnAt9HbsP0voT2fhwATI68H9OBWyOP6/1IghswGHhH70no70NHYErkNiP6/9V6T+J30/bRIiIiIiIRaqsQEREREYlQOBYRERERiVA4FhERERGJUDgWEREREYlQOBYRERERiVA4FhHZCzPbaWbfm9l0M3vZzGqX8bxv4nS+EWZ2a+TrK8zsvCoc60kzO20vz/nMzPpFvl5kZk0re74Sx7zKzC6s6nFERBJN4VhEZO+2OOd6Oed6AtuAK0p+08yyAZxzh8bpfDcA/4oc89/OuafjdNy4i/7spXgc+HUiaxERiQeFYxGRivkS6Gxmg81sjJk9D0wDMLON0SeZ2Q1mNs3MppjZnZHHOpnZB2Y20cy+NLPuex7czLoCW51zqyJ//rOZ/Tby9Wdm9jczG2dmc81sYCmvNzN70Mxmmtm7wD4lvnekmU2O1PW4mdUo7wc1szcitc4ws8tKPL7RzG43s7HAIWZ2Z+R8U83sHwDOuc3AIjM7OPa/WhGR8OWEXYCISKowsxzgeOCDyEMHAz2dcwv3eN7xwAigv3Nus5k1jnzrEeAK59w8M+uPXx0eusdpDgMmlVNGjnPuYDMbBvwJv8VySacA3YD9gebATOBxM6sJPAkc6Zyba2ZPA1cC95Vzroucc6sjWzmPN7NXnXM/AnWA6c65WyM/22NAd+eci27/HDEBGIjfYUtEJCVo5VhEZO9qmdn3+LCXjw+DAOP2DMYRRwFPRFZPiQTMusChwMuRY/0HaFnKa1sCK8up5bXI/USgfSnfHwS84Jzb6ZxbAoyOPN4NWOicmxv581OR55bn12Y2BfgOaAt0iTy+E3g18vV6oAh41MxGAptLvH4F0Gov5xARSSpaORYR2bstzrleJR8wM4BNZTzfALfHY1nA2j2PU9q5gAblfH9r5H4nZf8bvue5ozXFzMwG40P+IZHV78+AmpFvFznndgI453ZEWieOBM4ErmLXanhN/M8jIpIytHIsIhJ/HwEXRadamFlj59x6YKGZnR55zMzswFJeOwvoXIVzfwGcaWbZZtYSGBJ5fDbQ3syixx4FfF7OcRoAayLBuDswoLQnRVbEGzjn3gOuBXqV+HZXYHplfxARkTAoHIuIxJlz7gPgLWBCpIXit5FvnQNcHGlVmAGcXMrLvwB6W2RpuhJeB+bhLxJ8mEgAds4VARfi2zqmAcXAv8s5zgdAjplNBf4P31pRmnrAO5HnfQ5cV+J7hwGfVPLnEBEJhTlX2qdvIiISFjO7H3jbOZeywdLMegPXO+dGhV2LiEhFaOVYRCT5/BUodaORFNIU+GPYRYiIVJRWjkVEREREIrRyLCIiIiISoXAsIiIiIhKhcCwiIiIiEqFwLCIiIiISoXAsIiIiIhLx/wHHHmeWzaUmeQAAAABJRU5ErkJggg==\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> 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": 32,
   "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": 33,
   "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": 34,
   "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",
    "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": 35,
   "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": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 36,
     "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": [
    "<b>We will create 11 order polynomial model with the variables x and y from above.</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "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": [
    "f1 = np.polyfit(x,y,11)\n",
    "p1 = np.poly1d(f1)\n",
    "print(p1)\n",
    "\n",
    "PlotPolly(p1,x,y,'Highway MPG')"
   ]
  },
  {
   "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": 39,
   "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": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures()"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 42,
     "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": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 43,
     "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": 44,
   "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": 45,
   "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": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('scale', StandardScaler()),\n",
       "                ('polynomial', PolynomialFeatures(include_bias=False)),\n",
       "                ('model', LinearRegression())])"
      ]
     },
     "execution_count": 46,
     "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": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('scale', StandardScaler()),\n",
       "                ('polynomial', PolynomialFeatures(include_bias=False)),\n",
       "                ('model', LinearRegression())])"
      ]
     },
     "execution_count": 47,
     "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": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Let's create a pipeline that standardizes the data, then produce a prediction using a linear regression model using the features Z and target y.</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "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": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "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]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>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": 50,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.4965911884339175\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 \"highway_mpg_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": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output of the first four predicted value is:  [16236.50464347 16236.50464347 17058.23802179 13771.3045085 ]\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": 52,
   "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": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value is:  31635042.944639895\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": 54,
   "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": 55,
   "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": 56,
   "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": 57,
   "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": 58,
   "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": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20474146.426361218"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(df['price'], p(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>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": 60,
   "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": 61,
   "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": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 62,
     "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": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([37601.57247984, 36779.83910151, 35958.10572319, 35136.37234487,\n",
       "       34314.63896655])"
      ]
     },
     "execution_count": 63,
     "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": 64,
   "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",
    "\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"
   ]
  }
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