navidfrb/model-development.ipynb

## model-development.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "    <a href=\"https://cocl.us/corsera_da0101en_notebook_top\">\n",
    "         <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/TopAd.png\" width=\"750\" align=\"center\">\n",
    "    </a>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/CCLog.png\" width = 300, align = \"center\"></a>\n",
    "\n",
    "<h1 align=center><font size=5>Data Analysis with Python</font></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Module 4: Model Development</h1>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some questions we want to ask in this module\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>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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "load data and store in dataframe df:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                9.0       154.0    5000.0       19          26  16500.0   \n",
       "3               10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                8.0       115.0    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# path of data \n",
    "path = 'https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>1. Linear Regression and Multiple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Linear Regression</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<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",
    "\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",
    "$$\n",
    "Yhat = a + b  X\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li>a refers to the <b>intercept</b> of the regression line0, 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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Lets load the modules for linear regression</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Create the linear regression object</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How could Highway-mpg help us predict car price?</h4>"
   ]
  },
  {
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "X = df[['highway-mpg']]\n",
    "Y = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using highway-mpg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can output a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
       "       20345.17153508])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "Yhat[0:5]   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>What is the value of the intercept (a)?</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.3058581574"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>What is the value of the Slope (b)?</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-821.73337832])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What is the final estimated linear model we get?</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, we should get a final linear model with the structure:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b  X\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plugging in the actual values we get:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>price</b> = 38423.31 - 821.73 x  <b>highway-mpg</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 a): </h1>\n",
    "\n",
    "<b>Create a linear regression object?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1 = LinearRegression()\n",
    "lm1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm1 = LinearRegression()\n",
    "lm1 \n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question #1 b): </h1>\n",
    "\n",
    "<b>Train the model using 'engine-size' as the independent variable and 'price' as the dependent variable?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.fit(df[['highway-mpg']], df[['price']])\n",
    "lm1                        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm1.fit(df[['highway-mpg']], df[['price']])\n",
    "lm1\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 c):</h1>\n",
    "\n",
    "<b>Find the slope and intercept of the model?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Slope</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-821.73337832]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.coef_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Intercept</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([38423.30585816])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# Slope \n",
    "lm1.coef_\n",
    "# Intercept\n",
    "lm1.intercept_\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 d): </h1>\n",
    "\n",
    "<b>What is the equation of the predicted line. You can use x and yhat or 'engine-size' or 'price'?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# You can type you answer here\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# using X and Y  \n",
    "Yhat=-7963.34 + 166.86*X\n",
    "\n",
    "Price=-7963.34 + 166.86*engine-size\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Multiple Linear Regression</h4>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Y: Response \\ Variable\\\\\n",
    "X_1 :Predictor\\ Variable \\ 1\\\\\n",
    "X_2: Predictor\\ Variable \\ 2\\\\\n",
    "X_3: Predictor\\ Variable \\ 3\\\\\n",
    "X_4: Predictor\\ Variable \\ 4\\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "a: intercept\\\\\n",
    "b_1 :coefficients \\ of\\ Variable \\ 1\\\\\n",
    "b_2: coefficients \\ of\\ Variable \\ 2\\\\\n",
    "b_3: coefficients \\ of\\ Variable \\ 3\\\\\n",
    "b_4: coefficients \\ of\\ Variable \\ 4\\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equation is given by"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
    "$$"
   ]
  },
  {
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(Z, df['price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the value of the intercept(a)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15806.62462632922"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the values of the coefficients (b1, b2, b3, b4)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([53.49574423,  4.70770099, 81.53026382, 36.05748882])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " What is the final estimated linear model that we get?"
   ]
  },
  {
   "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?"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #2 a): </h1>\n",
    "Create and train a Multiple Linear Regression model \"lm2\" where the response variable is price, and the predictor variable is 'normalized-losses' and  'highway-mpg'.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm2=LinearRegression()\n",
    "lm2.fit(df[['normalized-losses','highway-mpg']], df['price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm2 = LinearRegression()\n",
    "lm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  #2 b): </h1>\n",
    "<b>Find the coefficient of the model?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1.49789586, -820.45434016])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm2.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm2.coef_\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>2)  Model Evaluation using Visualization</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've developed some models, how do we evaluate our models and how do we choose the best one? One way to do this is by using visualization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "import the visualization package: seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the visualization package: seaborn\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Regression Plot</h3>"
   ]
  },
  {
   "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>scatter plot</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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's visualize Horsepower as potential predictor variable of price:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 48273.70336436886)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 20\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",
    "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. Let's compare this plot to the regression plot of \"peak-rpm\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 47422.919330307624)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x720 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 the 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 \"highway-mpg\" increases.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #3:</h1>\n",
    "<b>Given the regression plots above is \"peak-rpm\" or \"highway-mpg\" more strongly correlated with \"price\". Use the method  \".corr()\" to verify your answer.</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "\"The highway-mpg has stronger corrolation\"\n",
    "df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692  compared to   \"peak-rpm\" which is approximate     -0.101616. You can verify it using the following command:\n",
    "df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Residual Plot</h3>\n",
    "\n",
    "<p>A good way to visualize the variance of the data is to use a residual plot.</p>\n",
    "\n",
    "<p>What is a <b>residual</b>?</p>\n",
    "\n",
    "<p>The difference between the observed value (y) and the predicted value (Yhat) is called the residual (e). When we look at a regression plot, the residual is the distance from the data point to the fitted regression line.</p>\n",
    "\n",
    "<p>So what is a <b>residual plot</b>?</p>\n",
    "\n",
    "<p>A residual plot is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n",
    "\n",
    "<p>What do we pay attention to when looking at a residual plot?</p>\n",
    "\n",
    "<p>We look at the spread of the residuals:</p>\n",
    "\n",
    "<p>- If the points in a residual plot are <b>randomly spread out around the x-axis</b>, then a <b>linear model is appropriate</b> for the data. 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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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, which leads us to believe that maybe a non-linear model is more appropriate for this data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression</h3>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First lets make a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "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>horsepower</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>highway-mpg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>111.0</td>\n",
       "      <td>2548</td>\n",
       "      <td>130</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>111.0</td>\n",
       "      <td>2548</td>\n",
       "      <td>130</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>154.0</td>\n",
       "      <td>2823</td>\n",
       "      <td>152</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>102.0</td>\n",
       "      <td>2337</td>\n",
       "      <td>109</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>115.0</td>\n",
       "      <td>2824</td>\n",
       "      <td>136</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>114.0</td>\n",
       "      <td>2952</td>\n",
       "      <td>141</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>160.0</td>\n",
       "      <td>3049</td>\n",
       "      <td>141</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>134.0</td>\n",
       "      <td>3012</td>\n",
       "      <td>173</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>106.0</td>\n",
       "      <td>3217</td>\n",
       "      <td>145</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>114.0</td>\n",
       "      <td>3062</td>\n",
       "      <td>141</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>201 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     horsepower  curb-weight  engine-size  highway-mpg\n",
       "0         111.0         2548          130           27\n",
       "1         111.0         2548          130           27\n",
       "2         154.0         2823          152           26\n",
       "3         102.0         2337          109           30\n",
       "4         115.0         2824          136           22\n",
       "..          ...          ...          ...          ...\n",
       "196       114.0         2952          141           28\n",
       "197       160.0         3049          141           25\n",
       "198       134.0         3012          173           23\n",
       "199       106.0         3217          145           27\n",
       "200       114.0         3062          141           25\n",
       "\n",
       "[201 rows x 4 columns]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_hat = lm.predict(Z)\n",
    "Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qRGFhIQ888ACQvKBeltGjR1NUVPSlfUVFRV9alTTdhTmi3g9Y6Zxb7ZzbDxQBw484ZjjwhPPeApqaWZtKzh0OjAu+HgeMiNtf5Jzb55xbA6wMrmPBq5GZGXAUsCGEzysi1fGb38A//gG/+hX06QOjRsHPf+4DvIiIZJ1Zs2Zx0UUXsXbtWh5++GH+8Ic/UFBQwOzZs5kyZQo/+clPKCgoYNWqVaxatYqhQ4dy6qmnMmDAAD744AMA1qxZwxlnnEHfvn258847y7zPZZddxosvvsi+ffsAWLt2LRs2bKB///7s2rWLc889lz59+nDKKafwwgsvlFtnzA033MDjjz8OwPz58zn77LM59dRTOf/88w+vRvrAAw/QvXt3evbsyahRo2r8s6pT4yuUry3wcdz3xcBpCRzTtpJzWznnNgI45zaaWcu4a7115LWcc2+a2feB94DdwArg+rIKNrNr8CP7dOjQIYGPKCI18uKLcNddMGYM3Hkn3HorXH893H03vP8+jB8PjRpFXaWISMa75RZYuDC51ywogPvvr/iYvXv3UlBQAEB+fj6TJ08+/F6nTp249tprady4MT/+8Y8BGDZsGBdddBGXXXYZAOeeey4PP/wwnTt35u233+a6665j5syZ3HzzzXz/+99nzJgxPPjgg2Xeu3nz5vTr149p06YxfPhwioqKuOKKKzAz6tevz+TJkznqqKPYunUrp59+OsOGDcOP6VbswIED3Hjjjbzwwgu0aNGCp59+mjvuuIPHHnuMe+65hzVr1lCvXj127NiRyI+xQmEG9bI+qUvwmETOTeh+ZpYHfB/oDawG/gTcDvz2Kwc791fgrwCFhYWV3U9EauLDD+HKK/0o+sMPgxnUqwePPAK9esFNN8Hvf+8DvIiIZKRY60t17Nq1izfeeINvfOMbh/fFRsdff/11nn32WQCuuuoqbr311jKvEWt/iQX1xx57DADnHD/72c+YM2cOtWrVYv369ZSUlNC6detK61q+fDnvv/8+Q4YMAeDQoUO0adMGgJ49e3LllVcyYsQIRowYUdFlEhJmUC8G2sd9346vtpyUd0zdCs4tMbM2wWh6G2BzJdcqAHDOrQIws4kEfe0iEpG9e+GSSyAvD557Dho0+OI9M7jxRnj+eXj8cd8Gk8AIh4iIlK+yke90VFpaStOmTcsN+omMfo8YMYIf/vCHLFiwgL1799Knj5+3ZPz48WzZsoX58+eTl5dHp06d+Pzzz790bp06dSiNa8OMve+co0ePHrz55ptfud9LL73EnDlzmDJlCr/5zW9YsmQJdepUP26H2aP+LtDZzPLNrC7+Qc8pRxwzBRgTzP5yOrAzaGup6NwpwNjg67HAC3H7R5lZPTPLxz+g+g6wHuhuZi2C44YAy5L9YUWkCl58EZYuhcceg44dyz7m6qth9WqYOzelpYmISOo0adKEzz77rMzvjzrqKPLz83nmmWcAH5AXLVoEwFlnnXX4QdHx48eXe/3GjRszaNAgvvOd73zpIdKdO3fSsmVL8vLyePXVV1m3bt1Xzu3YsSNLly5l37597Ny5kxkzZgBw0kknsWXLlsNB/cCBAyxZsoTS0lI+/vhjBg8ezL333suOHTvYtWtXTX484QV159xB/Owq0/HBeKJzbomZXWtm1waHTcW3o6wEHgGuq+jc4Jx7gCFmtgIfuu8JzlkCTASWAtOA651zh5xzG4BfAXPMbDF+hP2/wvrcIpKAqVPhmGPgwgvLP+bSS6FJE/jb31JXl4iIpNTFF1/M5MmTKSgo4LXXXmPUqFH87ne/o3fv3qxatYrx48fz6KOP0qtXL3r06HH4oc8//vGPPPjgg/Tt25edO3dWeI/Ro0ezaNGiLz3ceeWVVzJv3jwKCwsZP348Xbt2/cp57du35/LLLz/cztK7d28A6taty6RJk7j11lvp1asXBQUFvPHGGxw6dIhvfetbnHLKKfTu3Zsf/OAHNG3atEY/H3NOrdhlKSwsdPPmzYu6DJHsU1oKxx0HgwfDhAkVH/vd70JREWzaBGk0r62ISCZYtmwZ3bp1i7oMiVPWv4mZzXfOFZZ1vFYmFZHU+ve/oaSk4tH0mKuvht27fR+7iIhIjlFQF5HUmjrVPxw6dGjlx551Fpx4otpfREQkJymoi0hqTZ0K/fpBixaVH2vmR9VnzYI1a8KuTEQk66jFOX1U599CQV1EUmfLFnj77cTaXmLGjPGB/YknwqtLRCQL1a9fn23btimspwHnHNu2baN+/fpVOi/MedRFRL5s+nRwrmpBvX17+NrX/Jzqd94JtTS+ICKSiHbt2lFcXMyWLVuiLkXwvzi1a9euSucoqItI6kydCq1a+dVIq+Lqq/0qprNn+9liRESkUnl5eeTn50ddhtSAhqZEJDUOHYJp0+CCC6o+Kj5iBNSv7xdKEhERyREK6iKSGm+/Ddu3V63tJaZhQzjtNJgzJ/l1iYiIpCkFdRFJjalToXZtGDKkeucPGODnYI9balpERCSbKaiLSGq89JKfF726yykPHOjbZ958M7l1iYiIpCkFdREJ34YNsHAhfP3r1b/GGWf4EfnXXkteXSIiImlMQV1Ewvf66357zjnVv0bjxn62GPWpi4hIjlBQF5Hwvfeen+nl5JNrdp2BA/1Dqfv2JacuERGRNKagLiLhW7wYTjrJT7FYEwMG+JD+7rvJqUtERCSNKaiLSPgWL4ZTTqn5dfr391u1v4iISA5QUBeRcH32GaxZAz171vxazZtDjx56oFRERHKCgrqIhOv99/02GUEdfJ/666/7qRpFRESymIK6iITrvff8NhmtL+D71D/7DBYtSs71RERE0pSCuoiEa/FiaNIEOnZMzvUGDPBb9amLiEiWU1AXkXDFHiQ1S8712rWD/Hz1qYuISNZTUBeR8DjnW1+S1Z8eM3CgH1F3LrnXFRERSSMK6iISnuJi2LEjnKC+dSt88EFyrysiIpJGFNRFJDyLF/ttsh4kjYn1qav9RUREspiCuoiEJ9kzvsSceKKfU10rlIqISBZTUBeR8CxeDB06wNFHJ/e6ZtC7N/z738m9roiISBpRUBeR8CxenPz+9Jjevf2I/YED4VxfREQkYgrqIhKOfftg+fLwgnpBAezfrwdKRUQkaymoi0g4PvgADh5Mfn96TO/efqv2FxERyVIK6iISjtiML2GNqHfpAg0awMKF4VxfREQkYgrqIhKO996DunWhc+dwrl+7tv8lQCPqIiKSpRTURSQcixdD9+6QlxfePXr39iPqWqFURESykIK6iITjvffCa3uJKSjwK5+uWxfufURERCKgoC4iybd1K2zYEN6DpDF6oFRERLKYgrqIJF9YK5Ie6eSToVYtBXUREclKCuoiknwrVvhtt27h3qdhQ+jaVTO/iIhIVlJQF5HkW7PGP0Tatm349+rdWyPqIiKSlRTURST5Vq+Gjh39FIphKyiA4mLfFy8iIpJFFNRFJPlWr4bjj0/NvWIPlKr9RUREsoyCuogkXyqDekGB36r9RUREsoyCuogk186d8MknkJ+fmvs1bw7t22tEXUREso6Cuogk15o1fpuqEXXQA6UiIpKVFNRFJLlWr/bbVAb1ggJYvhz27EndPUVEREKmoC4iyRVFUO/dG0pLv1hoSUREJAsoqItIcq1ZA02b+leq6IFSERHJQgrqIpJcqZzxJaZjR/+LwaJFqb2viIhIiBTURSS5ogjqZtCjByxZktr7ioiIhEhBXUSSp7QU1q5NfVAH6N7dB3XnUn9vERGRECioi0jybNgA+/enbg71eD16+PnbN29O/b1FRERCoKAuIskTxYwvMT16+K3aX0REJEsoqItI8iioi4iIJI2Cuogkz+rVUKsWdOiQ+nu3bg3HHKOgLiIiWUNBXUSSZ/VqaNcO6tZN/b0184uIiGQZBXURSZ41a6Jpe4nRzC8iIpJFFNRFJHmimEM9Xo8esH07lJREV4OIiEiSKKiLSHLs2QObNkUf1EHtLyIikhVCDepmNtTMlpvZSjO7rYz3zcweCN5fbGZ9KjvXzJqZ2ctmtiLYHhP33u3B8cvN7PxgXxMzWxj32mpm94f5uUVy0po1fhvFHOoxCuoiIpJFQgvqZlYbeBC4AOgOjDaz7kccdgHQOXhdAzyUwLm3ATOcc52BGcH3BO+PAnoAQ4G/mFlt59xnzrmC2AtYBzwX0scWyV2xoB7liHqrVtCsmYK6iIhkhTBH1PsBK51zq51z+4EiYPgRxwwHnnDeW0BTM2tTybnDgXHB1+OAEXH7i5xz+5xza4CVwXUOM7POQEvgtWR+UBEh2jnUYzTzi4iIZJEwg3pb4OO474uDfYkcU9G5rZxzGwGCbcsq3G808LRzZU8JYWbXmNk8M5u3ZcuWCj6aiHzF6tXQqBG0aBFtHZr5RUREskSYQd3K2HfkfznLOyaRc6tzv1HAhPIu4Jz7q3Ou0DlX2CLqsCGSaVav9v3pVtb/KaZQjx6wY4d/sFVERCSDhRnUi4H2cd+3AzYkeExF55YE7TEE282J3M/MegF1nHPzq/NhRKQSUc+hHqMHSkVEJEuEGdTfBTqbWb6Z1cWPZk854pgpwJhg9pfTgZ1BO0tF504BxgZfjwVeiNs/yszqmVk+/gHVd+LuNZoKRtNFpAaci34O9RgFdRERyRJ1wrqwc+6gmd0ATAdqA48555aY2bXB+w8DU4EL8Q9+7gG+XdG5waXvASaa2X8AHwHfCM5ZYmYTgaXAQeB659yhuJIuD+4lIsm2ebOfRz0dgnrLltC8uYK6iIhkvNCCOoBzbio+jMfvezjuawdcn+i5wf5twLnlnHM3cHc576VBghDJUrEZX6KcQz1GM7+IiEiW0MqkIlJz6bDYUTzN/CIiIllAQV1Eaq642G87dIi2jpgePWDnTti4MepKREREqk1BXURqrrgYjjoKmjSJuhJPD5SKiEgWUFAXkZorLoZ27aKu4gsK6iIikgUU1EWk5tavh7ZHLgQcoZYt4dhjFdRFRCSjKaiLSM2l24g6QLdu8MEHUVchIiJSbQrqIlIzBw74hzbTMagvWxZ1FSIiItWmoC4iNbNpk58GMZ1aXwC6doVt22DLlqgrERERqRYFdRGpmfXr/TYdR9RBo+oiIpKxFNRFpGZic6ina1BXn7qIiGQoBXURqZl0Dert20PDhhpRFxGRjKWgLiI1s3491KsHzZpFXcmX1aoFJ52koC4iIhlLQV1EaiY2NaNZ1JV8laZoFBGRDKagLiI1k45zqMd06wbr1sHu3VFXIiIiUmUK6iJSM+kc1Lt29dvly0O7xa5dMG+e7wA6dCi024iISA5SUBeR6isthQ0b0m8O9ZgQZ35xDiZN8m3wffv631Xq1fO3fOWVpN9ORERykIK6iFTf1q2wf3/6jqifeCLUrp30B0rXrYOLL4ZvfANatoSnnoKHHoJbb/Wt+uedBz//ORw8mNTbiohIjqkTdQEiksHSdWrGmHr14PjjkxrUd+yAgQP9oqe//z3ceCPUifv/pHfcATfdBHffDbNn+1H3Vq2SdnsREckhGlEXkepL96AOvhclSUHdObj2Wt+PPmMG/OAHXw7p4Kdu/7//g/HjYf58GDEC9u1Lyu1FRCTHKKiLSPWtX++36dqjDj6or1iRlD6UJ5+Ep5+GX/0KTjut4mO/+U34+9/hrbd8uHeuxrcXEZEco6AuItVXXOx7wNO5t6NrVzhwAFavrtFlVq+G66+H/v3httsSO2fkSPjlL+Hxx+H++2t0exERyUEK6iJSfcXFcNxxPqynq9jMLzVof3EOrrrKPyj65JNV+7i/+AVcein8+Mfw8svVLkFERHKQgrqIVN/69endnw5fzKVegykap02DN96A++6Djh2rdm6tWjBunP994eqrYfv2apchIiI5RkFdRKqvuDi9+9MBjj7aj/rXYET93nv9xxw7tnrnN27sw3pJCfzwh9UuQ0REcoyCuohUj3PpvSppvK5dqx3U582DWbP8DC9161a/hFNP9fOsP/44/POf1b+OiIjkDgV1EamenTth9+7MCOqxKRqrMfXK734HRx0F3/tezcv4xS+ge3e45hr/4xMREamIgrqIVE9sasZMCeqffQYbN1bptNWr/YJF3/++D2po4NwAACAASURBVOs1Va8e/O1vsGED/OQnNb+eiIhkNwV1Eame2GJH6d6jDl88UFrF9pff/97P8HLTTckrpV8/36f+yCMwd27yrisiItlHQV1EqicTViWNqcYUjdu2wWOP+WkZjzsuueXcdRd06OAXQtq/P7nXFhGR7KGgLiLVE2t9SXaKDUObNr53pQpTNBYVwd69yR1Nj2nUCP78Z1iyBP7wh+RfX0REsoOCuohUT3GxX5G0JlOhpIrZFw+UJmjCBOjRA3r1Cqekiy+GSy6BX/0K1qwJ5x4iIpLZFNRFpHoyYQ71eFWYovGjj+D112H06HBL+uMffQ/8DTdUa0IaERHJcgrqIlI9mTKHeky3bn7WlwTmRSwq8ttRo8ItqX17+M1vYOpUePrpcO8lIiKZR0FdRKpn/frMC+qQUJ/6hAl+dpYTTgi5JuDGG/29brwRtmwJ/34iIpI5FNRFpOr27IFPPsmsoJ7gFI0ffAALF4bf9hJTuzY8+qgf6L/lltTcU0REMoOCuohUXWzGl0zqUT/+eP/gayVBfcIE/+zp5ZenqC7g5JPhjjvgqafgxRdTd18REUlvCuoiUnWZNId6TJ060Llzha0vzvmgPnhw6medvP12H9ivvRZ27EjtvUVEJD0pqItI1cVG1DMpqEOlM78sWAArVqSu7SVe3bp+gaVNm+A//kOzwIiIiIK6iFTHhg1+26ZNtHVUVbdusGoV7NtX5tvPPed7xi+9NMV1Bfr2hXvu8XX86U/R1CAiIulDQV1Eqm7jRr+8ZpMmUVdSNd26QWkprFxZ5tsvvQT9+0OzZimuK86PfuQXQ/rxj+Gdd6KrQ0REoqegLiJVt2lT5o2mwxdTNJbR/rJ+PSxaBBdemOKajmAG48b5HvnLL/eT64iISG5SUBeRqtu4MTODepcufltGUJ861W+jDuoAxxwDEyf6DqOLL4Zdu6KuSEREoqCgLiJVt2kTtG4ddRVV16gRdOxYblDv0AF69IigrjL06+dnoHn7bR/W9+yJuiIREUk1BXURqbpMHVEH3/5yxBSN+/bBK6/40XSziOoqw8iR8Pe/w+zZMGIEfP551BWJiEgqKaiLSNXs2QOffpqZI+rgp2j84AP/UGngtdd8e8nXvx5hXeUYPdpP2/jyy3D++V9MuCMiItlPQV1EqmbTJr/N5BH1vXvho48O75o6FerV8wsdpaOrr4bx42HePCgogGnToq5IRERSQUFdRKomFtQzdUQ9NvNLXPvLSy/5kN6oUUQ1JeCb3/RBvXVruOAC+MEPYPv2qKsSEZEwKaiLSNVs3Oi3mTyiDocfKF25Ej78MD1me6lMt27+4dJrr4X774fjj/cLJOlBUxGR7KSgLiJVk+kj6sceC82bHw7q6TQtYyIaNICHHoKFC+Gss+D22+GEE+Avf4H9+6OuTkREkklBXUSqZuNGqF3bB95M1a3b4aA+bZqfXv2EEyKuqYp69YIXX/QPwnbuDNdf7z/Wk09+6TlZERHJYArqIlI1mzZBy5Y+rGeqYIrGAwdgzhz42teiLqj6+vf30zdOnQpHHQVXXeV72GN/+BARkcyloC4iVZPJc6jHdO0KW7fyzr92sHs3nHtu1AXVjJkP5/Pn+7aY116Dnj39Q7IiIpK5FNRFpGoydVXSeMEDpTOe24kZDBoUbTnJUquWf9B03jz/u9RFF8Hvfhd1VSIiUl0K6iJSNdkwoh4E9Zlz8+jdG5o1i7ieJOve3c8Oc/nl8NOfwnPPRV2RiIhUh4K6iCTu0CHYvDnzR9Q7dGBP/Wa8uaplxre9lKd+fRg3Dk4/3fetL1gQdUUiIlJVCuoikritW31Yz/QR9Vq1mHvc5ew/VIdzzom6mPDUrw/PP+9noxw27Isp8EVEJDOEGtTNbKiZLTezlWZ2Wxnvm5k9ELy/2Mz6VHaumTUzs5fNbEWwPSbuvduD45eb2flx++ua2V/N7EMz+8DMRob5uUWyVqbPoR5nZv0LyWM/AwZEXUm4WrWCf/wDduyAK68E56KuSEREEhVaUDez2sCDwAVAd2C0mXU/4rALgM7B6xrgoQTOvQ2Y4ZzrDMwIvid4fxTQAxgK/CW4DsAdwGbnXJfgerOT/oFFckGmr0oaZ8bOUzmdt2h06NOoSwldr15+BdNXX4WXX466GhERSVSYI+r9gJXOudXOuf1AETD8iGOGA0847y2gqZm1qeTc4cC44OtxwIi4/UXOuX3OuTXAyuA6AN8B/hvAOVfqnNua7A8rkhOyZER9+3aYv6EN5zDz8MJH2e5734MOHeDnP9eouohIpggzqLcFPo77vjjYl8gxFZ3byjm3ESDYtqzoWmbWNPj+N2a2wMyeMbNWZRVsZteY2Twzm7dly5ZEPqNIbomNqGd4UJ89G5wzzmUGLFkSdTkpUa8e/PKX8O67MGVK1NWIiEgiwgzqVsa+I8dxyjsmkXMTvV8doB3wunOuD/AmcF9ZF3DO/dU5V+icK2zRokUltxPJQZs2+eUvGzaMupIamTEDGjZ0nFZvUc4EdYAxY6BzZ7jzTigtjboaERGpTJhBvRhoH/d9O2BDgsdUdG5J0B5DsN1cybW2AXuAycH+Z4A+iEjVZcMc6sDMmTBggFG32wmwdGnU5aRMnTrwq1/Be+/BM89EXY2IiFQmzKD+LtDZzPLNrC7+Qc8j/+A6BRgTzP5yOrAzaGep6NwpwNjg67HAC3H7R5lZPTPLxz+g+o5zzgH/AAYFx50L5M5/mUWSKQtWJd282WfzwYOBHj1yakQd4Ior4OSTfRuMetVFRNJbaEHdOXcQuAGYDiwDJjrnlpjZtWZ2bXDYVGA1/sHPR4DrKjo3OOceYIiZrQCGBN8TvD8RH8KnAdc75w4F59wK3GVmi4GrgB+F9blFsloWjKjPDuZ8GjQIH9Q//hg+zf6ZX2Jq1YKf/ASWL4c334y6GhERqUidMC/unJuKD+Px+x6O+9oB1yd6brB/G35UvKxz7gbuLmP/OmBgVWoXkTJkwYj67NnQqBH06QNsCmZ9XbYMTjst0rpSacQIvxhSURGceWbU1YiISHm0MqmIJGbXLv/K8BH1WbPgrLMgLw8/og451/5y1FHw9a/DxIlw8GDU1YiISHkU1EUkMVkwh/rWrT6TDxoU7MjP90PLORbUAUaPhpKSL1qBREQk/Sioi0hismBV0jlz/Pbss4MdtWtDt245GdQvvBCaNIEJE6KuREREyqOgLiKJyYIR9Vmz/BTwhYVxO7t3z6kpGmMaNPC96s8+C/v3R12NiIiURUFdRBKTBSPqs2f7hyfr1o3bmYMzv8SMGgU7dsD06VFXIiIiZVFQF5HEbNrkn8Bs1izqSqpl2zZYvDiuPz0m9kBpDo6qDxkCzZur/UVEJF0pqItIYjZuhFat/ETcGei11/z2cH96TA4H9bw8uOwyeOEF2L076mpERORImflfXBFJvU2bMrrtZdYs35fdt+8Rb3TqlLMzv4AP6nv2aPYXEZF0pKAuIonZuDGjHySdPRvOOAPq1TvijRye+QX8nPJ16/pfZEREJL0oqItIYjZuzNgR9e3bYdGiMvrTY3r0yMnWF/B/ZTj9dHj11agrERGRIymoi0jlDh6ELVsydkT9tdfAuTL602O6d8/ZmV/A/wKzYAHs3Bl1JSIiEk9BXUQqt3mzT7oZOqI+e7ZveenXr5wDcviBUvBBvbQU5s6NuhIREYmnoC4ilcvwxY5mzfL96fXrl3NALKjnaJ/66aerT11EJB0pqItI5TJ4saMdO2DhwgraXsDP/NKgQc6OqMf61BXURUTSi4K6iFQug0fU5871bR3lPkgKfuaXrl1zdkQdYPBg9amLiKQbBXURqVwsqLdqFW0d1TB7tm/rOO20Sg485RS/dGmOivWpxxaGEhGR6Cmoi0jlSkrg6KMraPJOX7Nm+baOBg0qObBXL9/is2VLKspKO6ef7h+4VfuLiEj6UFAXkcqVlGTkaPqnn/p2jgr702N69vTbHB1Vr19ffeoiIulGQV1EKpehQT2h/vSYXr38NkeDOvif07//7R/AFRGR6Cmoi0jlMjSoz54NeXl+pLhSLVr4h2UXLQq9rnQ1eLD61EVE0omCuohULoOD+mmnQcOGCZ7Qq1dOj6j36+cnwHn77agrERERUFAXkcrs3w/bt2dcUP/sM5g3L8H+9JiePf0UjQcOhFZXOmvQALp39339IiISPQV1EanY5s1+m2FB/fXX4dChKgb1Xr38LyYffhhaXemuTx+YPx+ci7oSERFRUBeRipWU+G2GBfVXX/X96WedVYWTYjO/5HCfep8+/nez2GK0IiISHQV1EalYhgb1GTPgjDOq0J8OfnXSvLyc7lPv08dv1f4iIhI9BXURqVgGBvXt233QPOecKp6Yl+ebtHN4RL1XLzDz0zSKiEi0FNRFpGIZGNRnz/Y91lUO6pDzM780aQJdumhEXUQkHSioi0jFSkqgceMq9pBEa+ZMX+5pp1Xj5J49YcMG2Lo16XVlij59FNRFRNKBgrqIVKykBFq2jLqKKpkxAwYMgLp1q3GyViilTx/46KOc/l1FRCQtKKiLSMUybLGjTZtg6dJqtr2AZn7hiwdK1acuIhItBXURqViGBfVXX/Xbagf1li2hdeucHlHv3dtv1f4iIhItBXURqViGBfWZM6Fp0y/CZrX07JnTI+rHHAP5+QrqIiJRU1AXkfIdPAjbtmVUUJ8xAwYNgtq1a3CRnj1hyRL/+XOUHigVEYmegrqIlG/LFj/PYYYE9TVr/KvabS8xvXrB/v2wfHlS6spEvXvDypWwc2fUlYiI5C4FdREpX4bNoV7j/vSY2AOlOdynHnugdOHCaOsQEcllCuoiUr4MC+r/+pd/DrR79xpeqGtXv0ppDvepx4K62l9ERKKjoC4i5du82W8zIKgfOgQvvwznnw9mNbxY3brQrVtOB/VWraBNG42oi4hESUFdRMqXQSPq8+bBJ5/A0KFJumDv3n4iceeSdMHMc/LJfk56ERGJhoK6iJSvpATq14cmTaKupFLTpvmR9CFDknTBwkL/+devT9IFM0+3brBsWU7/riIiEikFdREpX2wO9Rr3koRv+nTo2xeaN0/SBQsL/XbevCRdMPN06wa7d8PHH0ddiYhIblJQF5HyZchiR598Am+/ncS2F/BTNNapA+++m8SLZpZu3fx22bJo6xARyVUK6iJSvgwJ6q+8AqWl/kHSpGnQwDdp5/CIemz2HAV1EZFoKKiLSPkyJKhPnw5Nm0K/fkm+cGGhD+o52qTdooVvJdIDpSIi0VBQF5GylZb6lUnTPKg75x8kHTLEd6okVWGh76tZsybJF84csQdKRUQk9RTURaRs27b5yclbtoy6kgq9/z5s2JDktpeYvn39NsfbX5Yuzdk/KoiIREpBXUTKliFzqE+f7rehBPWTT/aLH+VwUO/Wzf9RYcuWqCsREck9CuoiUrYMCer//Cf06AHt2oVw8bp1/ewvOR7UQe0vIiJRUFAXkbJlQFDfvh1mz4aLLw7xJn37wvz5vmc/Bymoi4hER0FdRMqWAUF96lTfRj98eIg3KSyETz+FFStCvEn6at8eGjdWUBcRiYKCuoiUraQE8vLgmGOirqRczz8PrVuHMC1jvBxfodQMunbVFI0iIlFQUBeRspWU+BlfzKKupEz79vlpGYcNg1ph/n+ybt384kc5vkKpRtRFRFJPQV1Eypbmix3NnAm7doXc9gJ+cvY+fXJ2RB38FI3r1/sOIBERSR0FdREpW5oH9RdegEaN4JxzUnCzwkL497/h4MEU3Cz96IFSEZFoKKiLSNnSOKiXlsKUKTB0KNSvn4IbFhbCnj05m1QV1EVEoqGgLiJf5Rxs3py2QX3ePNi4MQVtLzE5vkLp8cf7KeUV1EVEUivUoG5mQ81suZmtNLPbynjfzOyB4P3FZtansnPNrJmZvWxmK4LtMXHv3R4cv9zMzo/bPyvYtzB4pfea6CJR274dDhxI26D+wgtQuzZ8/espumHnztCkSc4G9Tp1oEsXzfwiIpJqoQV1M6sNPAhcAHQHRptZ9yMOuwDoHLyuAR5K4NzbgBnOuc7AjOB7gvdHAT2AocBfguvEXOmcKwhem5P9eUWySprPof7CCzBwIDRrlqIb1qoFp56a8zO/fPBB1FWIiOSWMEfU+wErnXOrnXP7gSLgyD9UDweecN5bQFMza1PJucOBccHX44ARcfuLnHP7nHNrgJXBdUSkqtI4qC9dCkuWwCWXpPjGp5/uHyjdsyfFN04PnTvD2rX+Dy0iIpIaYQb1tsDHcd8XB/sSOaaic1s55zYCBNtYG0tl9/tb0PZyp1nZE0Ob2TVmNs/M5m3ZsqWyzyeSvdI4qD/9tB/g/sY3UnzjAQP8rC9vv53iG6eHE0/0H/+jj6KuREQkd4QZ1MsKwy7BYxI5tyr3u9I5dwowIHhdVdYFnHN/dc4VOucKW7RoUcntRLJYmgZ156CoCAYN8iuSptSZZ/rFn157LcU3Tg8nnui3K1dGW4eISC4JM6gXA+3jvm8HbEjwmIrOLQnaYwi2sX7zcs9xzq0Ptp8BT6GWGJGKbd7sh62bN4+6ki9ZuBA+/BBGjYrg5k2bwimnwNy5Edw8egrqIiKpF2ZQfxfobGb5ZlYX/6DnlCOOmQKMCWZ/OR3YGbSzVHTuFGBs8PVY4IW4/aPMrJ6Z5eMfUH3HzOqY2bEAZpYHXAS8H8YHFskaJSXQooUP62mkqMjPQHLppREVMGAAvPlmTi581Lo1NGyooC4ikkqh/VfYOXcQuAGYDiwDJjrnlpjZtWZ2bXDYVGA1/sHPR4DrKjo3OOceYIiZrQCGBN8TvD8RWApMA653zh0C6gHTzWwxsBBYH9xLRMqThosdOef704cMiXCgv39/2LXLD+3nGDM/qq6gLiKSOnXCvLhzbio+jMfvezjuawdcn+i5wf5twLnlnHM3cPcR+3YDp1a1dpGcloZB/e23Yd06+PWvIyxiwAC/nTvXr1aaY048UXOpi4ikUnr9XVtE0kMaBvWiIqhXL4WrkZalbVvIz8/pB0pXr4ZDh6KuREQkNyioi8iXOecfJk2joH7oEEycCBdeCEcfHXEx/fv7oO4qm4gq+5x4IuzfD8XFUVciIpIbKg3qZtbIzGoFX3cxs2HBQ5kiko127YK9e6Fly8qPTZFZs2DjxohmeznSgAGwZYuffibHaOYXEZHUSmREfQ5Q38zaAjOAbwOPh1mUiEQoDedQHzfOj6QPGxZ1JXy5Tz3HKKiLiKRWIkHdnHN7gEuBPznnLgG6h1uWiEQmzYL6p5/CpEl+NL1+/airAU46CY49Nif71Nu29c8JKKiLiKRGQkHdzM4ArgReCvaFOluMiEQozYL6pEm+E+fqq6OuJGD2RZ96jqlVC044QUFdRCRVEgnqNwO3A5ODedCPB14NtywRiczmYLHfNAnq48ZBly5w2mlRVxJnwAA//cmGIxdbzn6aS11EJHUqDOpmVhu42Dk3zDn3PwDOudXOuZtSUp2IpF5sRL1Fi2jrAFatgjlz/Gi6WdTVxMnxPvVVq6C0NOpKRESyX4VBPVjZU4sFieSSkhJo1gzyop/c6YknfEC/6qqoKzlCQQE0bJiT7S8nnuhbkTZujLoSEZHsl0iv+b/NbArwDLA7ttM591xoVYlIdNJksaPSUh/Uv/Y1aNcu6mqOkJcHZ5yRs0EdfPtL27bR1iIiku0S6VFvBmwDzgEuDl4XhVmUiEQoTYL6nDmwdm0aPUR6pMGDYdGiL3r6c4SmaBQRSZ1KR9Sdc99ORSEikiZKSuDU6DveHn8cmjSBESOirqQcQ4fCz38O//oXfOtbUVeTMu3b+z8oKKiLiISv0qBuZvWB/wB6AIdnMXbOfSfEukQkKps3R74q6a5dflrG0aN9K3ha6t3b/5z++c+cCup16kB+voK6iEgqJNL68negNXA+MBtoB3wWZlEiEpHPP/crDEXc+vLss7B7dxq3vYCfVPz882H6dDh0KOpqUkpTNIqIpEYiQf1E59ydwG7n3Djg68Ap4ZYlIpFIk8WOHn/ch8Ezz4y0jMoNHQrbtsH8+VFXklKxoO5c1JWIiGS3RIL6gWC7w8xOBo4GOoVWkYhEJw2C+po1MGsWjB2bZnOnl+W883yR06ZFXUlKnXCCb0/KsedoRURSLpGg/lczOwb4OTAFWArcG2pVIhKNNAjqf/+7z75jxkRWQuKOPRb69vV96jkkP99v16yJtg4RkWxXaVB3zv2fc267c26Oc+5451xL59zDqShORFIsNkQaUVAvLfVtL4MHQ4cOkZRQdUOHwjvv+BaYHBEL6mvXRlqGiEjWKzeom9kPzew/yth/o5ndEm5ZIhKJ2Ih6RLO+zJ3rR2nT+iHSI11wgf8N4+WXo64kZTp18luNqIuIhKuiEfXv4Gd8OdJfg/dEJNuUlPjJyxs0iOT248ZB48Zw6aWR3L56+vaFZs1yqk+9cWNo0UJBXUQkbBUFdeec21/Gzn1Auj/iJSLVEeGqpHv3+rnTR46ERo0iKaF6atf2D5VOm+ZH1nNEfr6CuohI2CrsUTezr/wXu6x9IpIlIgzqL77op3DPyLWDhg71P7tFi6KuJGUU1EVEwldRUP8d8JKZnW1mTYLXIOAfwH0pqU5EUmvz5siC+pNPQps2/kHSjHP++X6bQ7O/5OfDRx/l3FpPIiIpVW5Qd849AdwJ/BpYC6wBfgX8Mlj4SESyTUlJJA+Sbt0KU6fCN7/pO0kyTuvW0Lt3TvWp5+fDgQOwfn3UlYiIZK8KW1+cc/90zp3tnGvunDs2+Dp3hoxEcsmBA36KwQhG1J95Bg4ehKuuSvmtk+fCC+GNN3JmFSDN/CIiEr5EFjwSkVywZYvfRhDUn3wSTj4ZevZM+a2T5/LLfR/Is89GXUlKaNEjEZHwKaiLiBfRqqSrV/uB6G99y69ImrFOOQW6dYOioqgrSYkOHfy/l4K6iEh4Klrw6OZge1bqyhGRyES0KumTT/rtN7+Z0tsmnxmMHg2vvQbFxVFXE7p69aBtWwV1EZEwVTSi/u1g+6dUFCIiEYtgVVLn4Kmn4OyzoX37lN02PFdc4T/UxIlRV5IS+fmwdm3UVYiIZK+KgvoyM1sLnGRmi+Ne75nZ4hTVJyKpEkHry7JlsHy5b+/OCl26QJ8+OdP+ornURUTCVae8N5xzo82sNTAdGJa6kkQkEiUlUL8+NGmSsls++6zvGLnkkpTdMnyjRsFPfwqrVsEJJ0RdTajy8/30jPv2+VYYERFJrsqmZ9zknOsFbASaBK8Nzrl1qShORFIotippCp/ofPZZOOMMv9BR1rjiCr99+ulo60iB/Hzf6fPRR1FXIiKSnSqd9cXMzgZWAA8CfwE+NLOBYRcmIimW4lVJV62CRYtg5MiU3TI1OnSAs87KifYXTdEoIhKuRKZn/D1wXrDY0UDgfOAP4ZYlIimX4lVJn3vOby+9NGW3TJ1Ro+C992DJkqgrCZWCuohIuBIJ6nnOueWxb5xzHwJ54ZUkIpGItb6kyHPPwamnfrHCZVa57DKoVSvrR9WPOw7y8hTURUTCkkhQn2dmj5rZoOD1CDA/7MJEJIVKS/3KpCkK6sXF8NZbWTqaDtC6NQweDBMm+CbuLFW7NnTsqKAuIhKWRIL694ElwE3AzcBS4NowixKRFNu2DQ4dSllQnzzZb7OuPz3eVVf5RvxZs6KuJFSaolFEJDyVBnXn3D7n3O+dc5c65y5xzv3BObcvFcWJSIqkeFXS556DHj3gpJNScrtoXH45NG8Of8ruNeM6dVJQFxEJSyIj6iKS7VK4Kum2bTBnTpbNnV6WBg3gu9+FF17I6vkL8/Nh61bYtSvqSkREso+CuoikdFXSV17xLfEXXRT6raL3/e/77UMPRVtHiGIzv6xdG2kZIiJZSUFdRFIa1KdNg2bNoLAw9FtFr2NHGDYMHnkEPv886mpCoSkaRUTCk8iCR13M7BEz+5eZzYy9UlGciKRISQnUqQPHHBPqbZzzQX3IED9jSE644Qbf75OlUzXGptdcp/WqRUSSrk4CxzwDPAw8AhwKtxwRiURssaNa4f6RbfFi2LQJhg4N9Tbp5ZxzoFs3/1Dp2LFgFnVFSdWyJdSvr9YXEZEwJPJf5YPOuYecc+845+bHXqFXJiKps3lzSh4knTbNb88/P/RbpQ8zP6q+YAG8/XbU1SSdme/wUVAXEUm+RIL6P8zsOjNrY2bNYq/QKxOR1EnRqqTTpkGvXtCmTei3Si9jxsBRR2XtVI2dOqn1RUQkDIkE9bHAT4A38CuSzgfmhVmUiKRYCoL6Z5/B3Lk51vYS07gxXH01PPNMVk7VqBF1EZFwJLLgUX4Zr+NTUZyIpIBzKQnqM2fCwYM5GtQBfvhDv7377mjrCEGnTn4u9d27o65ERCS7JDLrS56Z3WRmk4LXDWaWl4riRCQFdu6E/ftDD+rTpvmB5TPPDPU26atjR7jmGnjsMVi9Oupqkkozv4iIhCOR1peHgFOBvwSvU4N9IpINNm/22xAfJo1Ny3jOOVC3bmi3SX8/+5mfBvPXv466kqTq2NFv1f4iIpJciQT1vs65sc65mcHr20DfsAsTkRRJwWJHH37oQ1zOtr3EHHccXHcd/P3v8MEHUVeTNBpRFxEJRyJB/ZCZnRD7xsyOR/Opi2SPFAT1V1/12699LbRbZI5bb4UGDeCuu6KuJGlat/Z/KdGIuohIciUS1H8CvGpms8xsNjAT+FG4ZYlIyqQgqM+Z46dkPPHE0G6ROVq2hJtugqef9itAZYFataBDB42oi4gkWyKzvswAOgM3Ba+TnHOvhl2YiKRISYlftebYY0O5vHM+qA8cmHWLclbfj3/s51X/5S+jriRpOnXSiLqISLKVG9TN7JxgeynwdeBE4ATg68E+EckGmzf7kF6nTiiXX7MG1q+Hs88O5fKZqVkz+NGP8vOC9QAAIABJREFU4Pnn4fXXo64mKTSXuohI8lU0oh77z+rFZbwuCrkuEUmVkpJQZ3yZPdtvBw4M7RaZ6Uc/gnbt4IYb4FDmP/bTqZP/n9LevVFXIiKSPcodQnPOxf4m+2vn3Jr498wsP9SqRCR1Ql7saM4caN4cunUL7RaZqVEj+P3v4fLL4f/9Pz8bTAaLzfzy0Udw0kmRliIikjUSeZj02TL2TUrk4mY21MyWm9lKM7utjPfNzB4I3l9sZn0qO9fMmpnZy2a2ItgeE/fe7cHxy83s/DLuN8XM3k+kdpGckYKgPnCgf+BQjnDZZX5y+TvugC1boq6mRjSXuohI8lXUo97VzEYCR5vZpXGvq4H6lV3YzGoDDwIXAN2B0WbW/YjDLsA/qNoZuIZgIaVKzr0NmOGc6wzMCL4neH8U0AMYCvwluE6snkuBXZXVLZJzQgzqxcV+EU61vZTDDP70J9i1yy+GlME0l7qISPJVNMZ1Er4XvSlf7k/vA3wvgWv3A1Y651Y75/YDRcDwI44ZDjzhvLeApmbWppJzhwPjgq/HASPi9hc55/YFrTorg+tgZo2BHwK/TaBukdyxe7d/hRTU58zxWwX1CnTvDjffDI8+Cu+8E3U11Xbccf55ZI2oi4gkT0U96i+Y2YvArc65/6rGtdsCH8d9XwyclsAxbSs5t5VzbmNQ40Yziz0F1xZ4q4xrAfwG+F9gT0UFm9k1+JF9OnToUNGhItlh82a/Delh0jlz/CyEvXqFcvns8YtfwPjx/sHSt97KyD6h2rWhfXuNqIuIJFOF/zVwzh0ChlTz2mXNmOwSPCaRcxO6n5kVACc65yZXcj7Oub865wqdc4UtWrSo7HCRzBfyYkdz5kD//j7ESQWOOgruuw/efRcefjjqaqpNc6mLiCRXIsM2b5jZn81sgJn1ib0SOK8YaB/3fTtgQ4LHVHRuSdAeQ7DdXMm1zgBONbO1wP9v777jpKqv/4+/Dh0EBaSogHREsCBiQdQIQgALGGMiGmNNjNFEjabozxRNNfmmWRKNMcYSIxpjwQAaxYqCgIC70qQjvSgIFhaWz++PcycsuGV2du7U9/PxmMedvXPLZy7D7pnPPZ/zmQz0MrOXk2i/SOGLMVBfvx7mzVP99KSdfz4MHQo33OCF5/OQaqmLiKRXMoH6CfgAzZ/i6SO/A36bxH7TgZ5m1tXMGuEDPcfttc044MKo+svxwJYoraW6fccBF0XPLwKerrB+jJk1jspH9gSmhRDuCiEcFELoApwIvBtCOCWJ9osUvhgD9dde86Xy05Nk5r3pO3d6Ckwe6tIF1qyB7duz3RIRkcJQ41SEIYTBqRw4hLDTzL4FPAfUB+4LIcwxsyui1+8GJgCn4QM/PwYuqW7f6NC3Ao+Z2WXACuBL0T5zzOwxYC6wE7gqSt0RkarEmKP++uvQpAn0T+b+m7ju3eHmm+EHP4AnnoCz82sS6C5dIAR47z3o0SPbrRERyX8WQvWp32a2H/ATINEv9go+CdKWmNuWVQMGDAgzZszIdjNE4vXtb8NDD8HmzWk/9KBB3kk8eXLaD13YduyAY47ZnTu0337ZblHSXn4ZBg+GF16AU0/NdmtERPKDmb0VQhhQ2WvJpL7cB2wFvhw9PgT+nr7miUjWxFRDfccOmDkTjj027YcufA0bwr33+r/NDZ+ZJy6nJWqpK09dRCQ9kgnUu4cQfhLVNF8SQrgF6BZ3w0QkA2IK1EtL4dNP4bi9C7JKcgYM8Nrqd98Nb7yR7dYkrUMHryypQF1EJD2SCdQ/MbMTEz+Y2SDgk/iaJCIZE1Og/uabvlSgXgc//akXJv/mN32AaR5o2BA6dlQtdRGRdEkmUP8m8CczW2Zmy4E7gW/E2ywRyYgYA/V27bxcn6SoeXO47TYoKYHbb892a5KmWuoiIulTY6AeQpgdQjgSOAI4PIRwVAihJP6miUisysp8EGkMFV/efNN7062yacgkeWedBaefDj/5Caxcme3WJEW11EVE0qfGQN3M9jez24GXgZfM7DYz2z/2lolIvBKlGdPco755M8yfr4GkaWEGd9wB5eVw7bXZbk1SunTx+Zp27Mh2S0RE8l8yqS9jgQ3AF4FzouePxtkoEcmAmCY7SlQ1VX56mnTtCj/8Ifz73zBxYrZbU6POnWHXrry5ASAiktOSCdRbhxB+FkJYGj1+DrSMu2EiErOYAvXEQNJjjknrYYvbd78LvXvDVVfBJ7k9lj9RolEDSkVE6i6ZQP0lMxtjZvWix5eB8XE3TERiFmOg3rs3tNTX+fRp1Aj+/GdYuhT++Mdst6ZaqqUuIpI+yQTq3wD+CZRFj7HAdWa21cw+jLNxIhKjRI56GgeThrB7IKmk2eDBMHo0/OpXsGFDtltTpU6dPLVegbqISN0lU/WlRQihXgihQfSoF61rEULYNxONFJEYrFsHzZp5GcA0Wb7c438NJI3JrbfCxx/Dz3+e7ZZUqVEjOOggpb6IiKRDMj3qmNkoM/tt9Dgj7kaJSAbEUENdEx3FrHdv+NrXPA1m0aJst6ZKKtEoIpIeyZRnvBW4BpgbPa6J1olIPoshUJ82DZo0gSOOSOthpaKbb4bGjeGmm7Ldkip16aIedRGRdEimR/00YFgI4b4Qwn3AiGidiOSzGAL16dOhXz+fSl5icsABXgXmscd238LIMV26wHvvwc6d2W6JiEh+Syr1hT3LMe4XR0NEJMPWr0/rQNJdu2D2bDj66LQdUqpy/fX+Jev73/cRvDmmc2cP0levznZLRETyWzKB+q+AWWZ2v5k9ALwF/DLeZolIrMrLYePGtPaoL14MW7dC//5pO6RUpUULT4F59dWcnARJtdRFRNKj2kDdzAyYDBwPPBE9BoYQxmagbSISl40bvQs8jYH6zJm+POqotB1SqnPZZXDwwV4JJseolrqISHpUG6iHEALwVAhhTQhhXAjh6RDC2gy1TUTiEsNkR7NmeW56375pO6RUp2FDz1V/7TV4/fVst2YPBx/sSwXqIiJ1k0zqy1Qz02TgIoUkhkB95kw4/HCvoy0Zctll0KYN/PrX2W7JHpo08TGvSn0REambZAL1wXiwvtjMSsys1MxK4m6YiMQoMStpmgL1EDxQV9pLhjVrBldfDc88A++8k+3W7EG11EVE6i6ZQH0k0A0YApwJnBEtRSRfJXrU01T1ZeVK2LRJA0mz4qqrYJ994De/yXZL9qBa6iIidVdloG5mTczsWuB7eO30VSGE5YlHxlooIum3bp3nqLRsWfO2SUgMJFWgngWtW8Pll8M//5lTkXEiUN+1K9stERHJX9X1qD8ADABK8V7132WkRSISv3XrvDfdLC2HmzkT6tXTjKRZc911/g/w+99nuyX/07kz7NgBa9ZkuyUiIvmrukC9TwjhghDCX4BzgJMy1CYRiduaNXDggWk73KxZ0Lu3p0xLFnTsCBdcAH/9q5fezAGqpS4iUnfVBeo7Ek9CCJoIWqSQrF3rZTnSRANJc8D3vgeffAL33JPtlgDeow4aUCoiUhfVBepHmtmH0WMrcETiuZl9mKkGikgM0tijvm4drFql/PSsO/RQGDIE7r03JxLDE4G6etRFRFJXZaAeQqgfQtg3erQIITSo8HzfTDZSRNJoxw5Pj0hToD5rli8VqOeAyy+HpUth0qRst4R99oG2bdWjLiJSF8mUZxSRQrJ+vRc+T1PqSyJQ79cvLYeTujjrLJ8AKYfSXxSoi4ikToG6SLFJlOFIU4/6zJnQrVvaKj1KXTRuDBddBE89tbtWfhaplrqISN0oUBcpNmvX+jJNPeoaSJpjvv512LkT7r8/2y35X6AeQrZbIiKSnxSoixSbNPaob90KS5Yo7SWnHHIIfO5zXqoxy4NKO3eGTz/Nic59EZG8pEBdpNgkAvX27et8qHfe8aUmOsoxl18OixfDSy9ltRmqpS4iUjcK1EWKzdq1Pu1848Z1PlRpqS8PP7zOh5J0Ovts/zfO8qBS1VIXEakbBeoixSaNNdRLSqBFi90BmeSIJk18UOmTT3qVnyxRLXURkbpRoC5SbNauTWugfvjhUE+/SXLP17/uNfP/8Y+sNWHffb1jXz3qIiKp0Z9XkWKzZk1aKr6E4Kkvyk/PUYceCkcfDWPHZrUZqqUuIpI6BeoixSSEtKW+rFwJmzcrPz2njRkD06fDokVZa4JqqYuIpE6Bukgx2bwZysrSEqiXlPhSPeo57Nxzffnoo1lrQqJHXbXURURqT4G6SDFJlGZMQ+qLKr7kgU6d4MQTs5r+0qULfPwxbNqUtSaIiOQtBeoixSQxK2maetQPPhj226/Oh5I4jRnjBe8TRe8zLFFLXXnqIiK1p0BdpJiksUe9pERpL3nhnHO8LE+W0l9US11EJHUK1EWKSSJQr2OP+vbtsGCBAvW80L49DBkCjzySlURxzU4qIpI6BeoixWTtWmja1Atc18H8+bBzp/LT88Z558HixfDWWxk/dcuW/nFTj7qISO0pUBcpJoka6mZ1OowqvuSZL3wBGjbM2qDSLl0UqIuIpEKBukgxSVMN9dJSaNQIevVKQ5skfq1awYgRnqe+a1fGT69a6iIiqVGgLlJM1q5NW8WXPn2gQYM0tEkyY8wYn6XqjTcyfmrVUhcRSY0CdZFikkh9qSNVfMlDo0ZBkybwr39l/NRdusDWrT7floiIJE+Bukix+PRTj5Tq2KO+caPH+wrU80zz5jB0KIwbl/GubdVSFxFJjQJ1kWKRmOyojj3qmpE0j40e7dFyhic/Ui11EZHUKFAXKRZpqqGuii957IwzvOLP009n9LSqpS4ikhoF6iLFItGjXsdAvbQU2rb1eXQkzxxwABx3nKe/ZFDr1rDPPupRFxGpLQXqIsUi0aNex9SXkhJPe6ljKXbJllGjYPp0WL06Y6c0U4lGEZFUKFAXKRZr10K9etCuXcqHKC/39GalveSxUaN8+cwzGT2tJj0SEak9BeoixWLNGg/S69dP+RBLlsAnnyhQz2t9+kD37hlPf+ncGZYuzegpRUTyngJ1kWKRhhrqiYGkqviSx8y8V33SJNi2LWOn7dYNtmyBDz7I2ClFRPJerIG6mY0wswVmtsjMbqjkdTOz26PXS8ysf037mllrM3vezBZGy1YVXrsx2n6BmQ2vsP5ZM3vbzOaY2d1mlnqXoki+SsOspCUlnj3Tp0+a2iTZMXo0bN8O//1vxk7ZrZsvlyzJ2ClFRPJebIF6FAz/CRgJ9AHOM7O9/7yPBHpGj8uBu5LY9wZgUgihJzAp+pno9TFAX2AE8OcKAfmXQwhHAocBbYEvpf0Ni+S6NWvSUvGlZ09o1ixNbZLsGDQIWrXKaJnG7t19qUBdRCR5cfaoHwssCiEsCSGUAWOB0XttMxp4MLipQEszO7CGfUcDD0TPHwDOqrB+bAhhewhhKbAoOg4hhA+jbRoAjYDMTssnkm3l5bBuXdoqvkiea9AATj8dxo+HnTszcsquXX2pQF1EJHlxBuodgPcq/LwyWpfMNtXt2z6EsAYgWiZKWFR7PjN7DlgPbAUer6zBZna5mc0wsxkbNmyo6f2J5I9NmzxYr0OP+rZtsHixBpIWjNGj/XMxZUpGTteihdffX7w4I6cTESkIcQbqlVVZ3rsnu6ptktm3VucLIQwHDgQaA0MqO0AI4Z4QwoAQwoC2bdvWcDqRPJKGGupz5vhSgXqBGD4cGjXKaPWXbt3Uoy4iUhtxBuorgU4Vfu4I7D3DRlXbVLfvuig9hmi5PtnzhRA+Bcbx2RQckcKWhllJExVfFKgXiBYt4KST4NlnM3ZKBeoiIrUTZ6A+HehpZl3NrBE+0HPvrptxwIVR9ZfjgS1ROkt1+44DLoqeXwQ8XWH9GDNrbGZd8QGq08yseYXAvgFwGjA/jjcskrMSPep1DNSbN/d62FIgRozwGaxWrszI6bp3hxUrYMeOjJxORCTvxRaohxB2At8CngPmAY+FEOaY2RVmdkW02QRgCT7w86/AldXtG+1zKzDMzBYCw6KfiV5/DJgLPAtcFUIoB/YBxplZCfA23gN/d1zvWyQnpSH1pbTUB5LW0+wLhWPkSF8+91xGTtetmw+VeO+9mrcVERGvghKbEMIEPBivuO7uCs8DcFWy+0brNwGnVrHPL4Bf7LVuHXBMbdsuUlDWroV99025rmII3qP+5S+nuV2SXX36QMeOnv5y2WWxn65iLfXEcxERqZr6xkSKQR1nJV21ymeUVGnGAmPm6S/PP5+RMo2J4FyVX0REkqNAXaQYrFoFHfaujpq80lJfKlAvQCNGwJYtMHVq7Kc66CAvNKMBpSIiyVGgLlIMVq3yFIcUqeJLATv1VKhfPyPVX+rX94mPFKiLiCRHgbpIodu1q8496iUl0KkTtGyZxnZJbmjZEk44IWNlGlWiUUQkeQrURQrdhg2ef1zH1Bf1phewESPgrbdg/fqat60jBeoiIslToC5S6Fat8mWKgXpZGcybp0C9oI0Y4csMlGns1g02b4b334/9VCIieU+Bukihq2OgPn++d8grUC9g/fpBu3YZSX+pWKJRRESqp0BdpNAlAvUUB5MmBpKq4ksBq1cPhg/3HvXy8lhPpUBdRCR5CtRFCt3KlV5uo337lHYvLfWSer16pbldkltGjoRNm2DmzFhPo0BdRCR5CtRFCt2qVT7ZUf36Ke1eUuITWDZsmOZ2SW4ZNswnQJo4MdbTNG/uWTYK1EVEaqZAXaTQpaE0o9JeikCbNnD00T5LacxU+UVEJDkK1EUKXR0C9U2bYPVqDSQtGsOG+QylW7fGeppu3WDx4lhPISJSEBSoixS6OsxKWlrqSwXqRWLYMC/x88orsZ6mWzdYsQJ27Ij1NCIieU+Bukgh27YNtmxJuUc9UfFFgXqROOEEaNo09vSX7t19wtzly2M9jYhI3lOgLlLI6lhDvaTEU5dTLBgj+aZxYzj55NgD9R49fLloUaynERHJewrURQpZHQP10lLvTTdLY5sktw0b5lPRrlwZ2ykSpT7ffTe2U4iIFAQF6iKFrA6THZWXwzvvKO2l6Awd6stJk2I7Rdu2sO++sHBhbKcQESkICtRFClkdetSXLIGPP1ZpxqJz+OFe6DzG9Bcz71VXj7qISPUUqIsUspUroWVLaNas1rtqIGmRqlfPe9VfeAFCiO00PXuqR11EpCYK1EUKWR1qqJeWeszWp0+a2yS5b+hQWLfOc59i0rOnV33Zvj22U4iI5D0F6iKFrA6BekmJB1MpdMZLvhs2zJcxpr/06uUlGjVDqYhI1RSoixSyOkx2VFKi/PSi1bEj9O4da6Des6cvlacuIlI1BeoihWrnTli7NqUe9W3bfIp35acXsaFD4dVXY8tNSQTqylMXEamaAnWRQrV2recWpBCoz5njSwXqRWzYMC/7M2VKLIdv1con01KgLiJSNQXqIoWqDqUZExVflPpSxE45BerXjz1PXakvIiJVU6AuUqjqGKg3bw5duqS3SZJH9t0XjjvOyzTGRCUaRUSqp0BdpFDVYVbSxEDSevoNUdyGDYMZM+CDD2I5fM+e/jH96KNYDi8ikvf0Z1ikUK1aBY0aeSJwLYTgNdSVny4MG+bjHF58MZbD9+rly0WLYjm8iEjeU6AuUqhWroSDDvL52mth1SrvQFV+unDssdCiRWzpLyrRKCJSPQXqIoUqxcmOEgNJ1aMuNGzog0pjGlDao4cvlacuIlI5BeoihSrFQL201JfqURfA018WL4alS9N+6ObN/aaPAnURkcopUBcpRCGkPCtpSQl06gQtW8bQLsk/Q4f6Mqb0F5VoFBGpmgJ1kUK0ZYtPVpNi6ovSXuR/evf2z1FM6S8q0SgiUjUF6iKFaOVKX9YyUC8rg/nzFahLBWae/jJpEpSXp/3wvXrBhg2weXPaDy0ikvcUqIsUohQnO5o/H3buVKAuexk6FN5/H2bNSvuhE5Vf1KsuIvJZCtRFClGKgXqi4osGksoeYsxTT9RSX7Ag7YcWEcl7CtRFClEiUD/ooFrtVlLicyQlgicRANq399ssMeSpd+8ODRr43RwREdmTAnWRQrRqFbRtC40b12q3khI49FAvny2yh6FDYfJkH6ScRo0aefrLnDlpPayISEFQoC5SiFaurHXaSwiegtyvX0xtkvw2bJiPNp48Oe2H7tMH5s5N+2FFRPKeAnWRQrRiBRx8cK12WbMG1q+H/v1japPkt5NP9u7vGNJf+vSBRYtg+/a0H1pEJK8pUBcpNCHAsmXQuXOtdksU9DjqqPQ3SQpAs2YwaFBsgfquXZr4SERkbwrURQrN5s2wdWutA/WZM32p1Bep0tCh8Pbbfusljfr08aXSX0RE9qRAXaTQLF/uyy5darXbrFk+qK9Fi/Q3SQrEsGG+nDQprYft1Qvq1VOgLiKyNwXqIoUmEain0KOutBepVv/+0KpV2tNfmjTxMo0K1EVE9qRAXaTQpBCov/++76aBpFKt+vVhyBCf+CiEtB5alV9ERD5LgbpIoVm+HJo2hTZtkt5FA0klacOGwXvvpX3kZ58+fsgdO9J6WBGRvKZAXaTQJCq+mCW9iwJ1SVoiTz3N6S99+sDOnV6mUUREnAJ1kUKzfHlK+ekdO/pkpiLV6tYNunb19Jc06tvXl5qhVERkNwXqIoVm+fKUKr4oP12SNmwYvPSSd4GnySGH+E0g5amLiOymQF2kkHz0EWzcWKse9W3bYMECpb1ILQwbBh9+CNOmpe2QzZp5R70CdRGR3RSoixSSFSt8WYtAvaTEC3ioR12SNniwd3+nOf1FlV9ERPakQF2kkKRQmjExI6l61CVp++8PRx8dy4DSBQvSmlEjIpLXFKiLFJJly3xZi0B91iyv5NixYzxNkgI1bBhMnQpbt6btkH36QFkZLFmStkOKiOQ1BeoihWT5cmjQAA48MOldZs3y3vRaVHMUgaFDvev75ZfTdsg+fXyp9BcREadAXaSQLF8OnTr5DJJJ2L4d3nlHaS+SgkGDfGKtNOap9+7tSwXqIiJOgbpIIallaca33/aZII89Nr4mSYFq3Bg+9zl47rm0HbJFC//4lpSk7ZAiInkt1kDdzEaY2QIzW2RmN1TyupnZ7dHrJWbWv6Z9zay1mT1vZgujZasKr90Ybb/AzIZH65qZ2Xgzm29mc8zs1jjfs0hW1XKyo0R1PQXqkpIRI3z059KlaTtkv34we3baDiciktdiC9TNrD7wJ2Ak0Ac4z8z67LXZSKBn9LgcuCuJfW8AJoUQegKTop+JXh8D9AVGAH+OjgPw2xBCb+AoYJCZjUz/OxbJsrIyWL261oH6AQdoIKmkaGT0q3TixLQdsl8/ePddnxJARKTYxdmjfiywKISwJIRQBowFRu+1zWjgweCmAi3N7MAa9h0NPBA9fwA4q8L6sSGE7SGEpcAi4NgQwschhJcAomPNBBSWSOF57z0viF7LQP3YYzWQVFLUs6fPUvTss2k7ZL9+/jEuLU3bIUVE8lacgXoH4L0KP6+M1iWzTXX7tg8hrAGIlu2SPZ+ZtQTOxHviP8PMLjezGWY2Y8OGDdW+OZGcU8sa6ps3e9aC0l4kZWbeq/7iiz4yOQ0SA5tnzUrL4URE8lqcgXplfXQhyW2S2bdW5zOzBsAjwO0hhEqr9IYQ7gkhDAghDGjbtm0NpxPJMbUM1GfM8OVxx8XUHikOI0d6nsprr6XlcJ06QatWylMXEYF4A/WVQKcKP3cEVie5TXX7rovSY4iW65M83z3AwhDCH2v9TkTywfLl3sPZqVPN27J7IOmAATG2SQrf4MHQqFHa8tTNvFddPeoiIvEG6tOBnmbW1cwa4QM9x+21zTjgwqj6y/HAliidpbp9xwEXRc8vAp6usH6MmTU2s674ANVpAGb2c2A/4No43qhITli+HA46yIOmJEybBoccAi1bxtwuKWz77ONlGtM8oLS01OdTEhEpZrEF6iGEncC3gOeAecBjIYQ5ZnaFmV0RbTYBWIIP/PwrcGV1+0b73AoMM7OFwLDoZ6LXHwPmAs8CV4UQys2sI3ATXj1mppnNNrOvxfW+RbJm2bKk015CgDffVH66pMmIETBv3u70qzrq1w8+/dSrv4iIFLMGcR48hDABD8Yrrru7wvMAXJXsvtH6TcCpVezzC+AXe61bSeX56yKFZflyOP74pDZdtQrWrlWgLmkyciRcf71Xf/nGN+p8uIoDSvvsXdRXRKSIaGZSkUJQXu7lGZPsUddER5JWvXv7Zy9N6S+HHOITn2pAqYgUOwXqIoVgzRpP6K1FoN6wIRx5ZMztkuKQKNM4aZJPvFVHDRvCYYcpUBcRUaAuUghqWZpx2jTPA27cOMY2SXEZORK2bYPJk9NyuETll1BTYV4RkQKmQF2kECQC9S5daty0vNxrqCvtRdJqyBDvCk/TLKX9+sGmTT6eQkSkWClQFykEy5b58uCDa9x0/nzYuhWOOSbeJkmRad4cTj4Zxo9Py+E0Q6mIiAJ1kcKwfDm0aeM1rWvw+uu+HDQo5jZJ8TnzTJg7FxYtqvOhDj/cU9+Vpy4ixUyBukghWL486fz0yZOhfXvo3j3mNknxGT3al+P2ntuu9lq0gB49FKiLSHFToC5SCBYvhm7dktr0tdfgpJO8t1Ikrbp0gSOOgKefrnHTZPTvD9Onp+VQIiJ5SYG6SL7bsQOWLoWePWvcdOVKT2c/8cT4myVFatQov22zaVOdD3X88T49wOrVaWiXiEgeUqAuku+WLfNSLkkE6onKeQrUJTajR8OuXWkZVDpwoC+nTq3zoURE8pICdZF8t3ChL3v0qHHTyZO9OIcmOpLYHH00HHRQWtJf+vWDRo1gypQ0tEtEJA8pUBfJd4kKG0n2qA8cCA0axNwmKV5mnv7y3HPw6ad1OlTjxh73q0ddRIqVAnWRfLdwoZfIaNeu2s02b4aSEqW9SAaMHg0ffQQvvljnQx1/vE/QVVaWhnaXHlSVAAAgAElEQVSJiOQZBeoi+W7hQu9Nr6GMy5QpPh27AnWJ3eDBnmOVhvSXgQO9Y76kJA3tEhHJMwrURfJdIlCvwWuvecrLccdloE1S3Bo3hhEj4JlnfGBpHRx/vC+Vpy4ixUiBukg+Kyvzqi9J5qf375/U5KUidTd6NKxZ43krddCpE3TooDx1ESlOCtRF8tnSpd5jWUOgvn07TJumtBfJoNNOg/r10zJL6fHHq0ddRIqTAnWRfJYozVhDoD5jhgfrJ52UgTaJALRu7R+4J5+s86EGDvTvpOvWpaFdIiJ5RIG6SD5LMlB/5RVfDhoUc3tEKjrnHJg7F+bMqdNhEnnqb76ZhjaJiOQRBeoi+WzhQmjZEvbfv9rNnn/eJzlq2zZD7RIBD9Tr1YNHH63TYfr3h4YNlf4iIsVHgbpIPlu0qMbSjB99BK+/DsOGZbBdIgDt28Mpp3igHkLKh2na1Gcp1YBSESk2CtRF8tnChdCjR7WbvPoq7NihQF2y5Nxz4d13YfbsOh1m4EAfEL1jR5raJSKSBxSoi+Sr7dthxYoa89NfeMHLWmsgqWTF2Wd79Zc6pr+cdBJ8/HGdqz2KiOQVBeoi+WrJkqRKMz7/vA8ibdo0Q+0SqahNGxg6tM7pL4MH+3LSpDS1S0QkDyhQF8lXSVR8WbsWSkuV9iJZNmaMT8w1fXrKh9h/f89TV6AuIsVEgbpIvkoiUH/hBV8qUJesOussaNSozukvp54Kb7wBn3ySpnaJiOQ4Beoi+WrhQp9UpnXrKjd5/nnviTzqqAy2S2RvLVvC8OHw2GOerpWiU0+FsjKvYiQiUgwUqIvkq4ULq+1ND8F71E891UtZi2TVuefCypV1KoZ+0knQoAG8+GIa2yUiksP051skXyVqqFdh3jxYvVppL5IjRo2CJk3qlP7SvDkcd5zy1EWkeChQF8lHn34K771XbaD+/PO+HDo0Q20SqU6LFnDaaZ7+Uodi6EOGeInGzZvT2DYRkRylQF0kHy1e7Lkt1QTqEyf6y126ZK5ZItW66CJYt84/nCk69VRPc3/11TS2S0QkRylQF8lHNVR8+fBDz+MdNSqDbRKpyciR0L493Hdfyoc4/nifE0DpLyJSDBSoi+SjRKDeo0elL0+c6NkFZ52VwTaJ1KRhQ+9V/89/vMh/Cho3hhNP1IBSESkOCtRF8tHChT7jY8uWlb789NPQti0MHJjhdonU5JJLoLwcHnoo5UMMGQLvvONZNCIihUyBukg+qqY0Y1kZjB8PZ54J9etnuF0iNendG044wdNfQkjpEIlKRs8+m8Z2iYjkIAXqIvlo3jwPeCrx8sueo660F8lZl14K8+fD1Kkp7d6/P3To4HeOREQKmQJ1kXyzfr3f8z/88EpffvppaNZMZRklh335y7DPPvC3v6W0u5kPlH7uOa9UKiJSqBSoi+Sb0lJfVhKo79rlgfrw4V4ZQyQntWjhwfqjj8K2bSkdYtQo+PhjVX8RkcKmQF0k31QTqL/1FqxapbQXyQOXXupB+uOPp7T74MEe7yv9RUQKmQJ1kXxTWgrt2nk96r08/bQPID399Cy0S6Q2Bg2CXr1STn9p3BhGjIBnnvE7SSIihUiBuki+KS2ttDc9BHjiCTjpJNh//yy0S6Q2zOBrX4PJk2H27JQOMWqUl2OfPj3NbRMRyREK1EXyya5dMGdOpYH6rFleDGbMmCy0SyQVX/uaj3y+7baUdj/tNL+DNG5cmtslIpIjFKiL5JMlS3wEXSWB+oMPQqNGPkZPJC+0agUXXwz//GdKsxe1bu13kJSnLiKFSoG6SD4pKfHlXoH6jh3wyCM+yVGrVllol0iqrr7aZ+m6666Udh892m8yLV6c5naJiOQABeoi+aS01HN7+/bdY/V//+vl1b/61Sy1SyRVhxzio5/vuiulouijRvnyySfT3C4RkRygQF0kn5SWQo8entdbwUMP+QDSkSOz1C6Rurj2Wv+mOXZsrXft1g2OOcazZ0RECo0CdZF8UknFly1b4KmnfBBpo0ZZapdIXZx6Khx2GPzhD16+qJYuuMAHU8+ZE0PbRESySIG6SL745BNYtOgzgfrjj8P27XDhhVlql0hdmXmvekkJvPxyrXc/91yv/vLww+lvmohINilQF8kXc+d6eca9AvWHHvJ5Y445JkvtEkmH88+HNm28V72W2reHz3/eA3VNfiQihUSBuki+qKTiy8KF8MorPojULEvtEkmHpk3hyit9qtHS0lrvfsEFsGKFz58kIlIoFKiL5IvSUg9munf/36o774SGDX3eGJG8d8010KIF3HJLrXcdPRr22Qf+8Y8Y2iUikiUK1EXyRWmpl2WsXx+ADz+Ev//d83MPOCDLbRNJh9atPVf93/+G2bNrtes++8DZZ8Njj6VU5VFEJCcpUBfJF3tVfPn732HrVu+EFCkY3/kO7LdfSr3qF1zgVZAmTIihXSIiWaBAXSQfbNjgU6xHgXp5OdxxB5xwAgwYkOW2iaRTq1YerD/1FMycWatdhwzxu0v33x9P00REMk2Bukg+SAyuiwL1iRN9yvSrr85im0Ticu210LIl3HxzrXZr0AAuvRTGj/eBpSIi+S7WQN3MRpjZAjNbZGY3VPK6mdnt0eslZta/pn3NrLWZPW9mC6Nlqwqv3Rhtv8DMhldY/wsze8/MtsX5fkVis1egfttt0KGD5+SKFJz99oPrr/cKMNOn12rXyy/35T33xNAuEZEMiy1QN7P6wJ+AkUAf4Dwz67PXZiOBntHjcuCuJPa9AZgUQugJTIp+Jnp9DNAXGAH8OToOwDPAsTG8TZHMKCmBdu2gfXveeQdeeAGuusorvogUpKuv9sGlP/lJrXbr3BnOOAP++lcoK4upbSIiGRJnj/qxwKIQwpIQQhkwFhi91zajgQeDmwq0NLMDa9h3NPBA9PwB4KwK68eGELaHEJYCi6LjEEKYGkJYE8/bFMmACgNJb7nFK9gleg5FCtK++8L3vud5Xi++WKtdr7wS1q+HJ56IqW0iIhkSZ6DeAXivws8ro3XJbFPdvu0TQXe0bFeL81XLzC43sxlmNmPDhg212VUkPmVl3qN+1FHMmgWPP+5j7fbfP9sNE4nZNddAly7eu75zZ9K7DRvm0w38+c/xNU1EJBPiDNQrmycxJLlNMvumcr5qhRDuCSEMCCEMaNu2bW12FYnPrFmwfTsMHMiPfuRFMa67LtuNEsmApk3h97+HOXPgrruS3q1ePfjmN+G111Ka5FREJGfEGaivBDpV+LkjsDrJbarbd12UHkO0XF+L84nknylTfNHwZMaPh+9/38faiRSFs86CoUPhxz+GjRuT3u3ii6FJk1rF9yIiOSfOQH060NPMuppZI3yg57i9thkHXBhVfzke2BKls1S37zjgouj5RcDTFdaPMbPGZtYVH6A6La43J5IxU6ZA58788I9taNcOvv3tbDdIJIPMvMzR1q3wwx8mvdv++8N558EDD8CmTTG2T0QkRrEF6iGEncC3gOeAecBjIYQ5ZnaFmV0RbTYBWIIP/PwrcGV1+0b73AoMM7OFwLDoZ6LXHwPmAs8CV4UQygHM7DdmthJoZmYrzezmuN63SNq98QYvdvsaL74I/+//+VTpIkWlTx//hnrPPZ4KlqTrr4ePP4Y//SnGtomIxMhCqFUad9EYMGBAmDFjRrabIcVu5Up2dOpK/wPX8GHDNixY4LfzRYrO5s3Qqxcccgi8+qr3tCfhzDP9ptTy5fqSKyK5yczeCiFUOs+4ZiYVyWVTpvB7ruOdNW24804F6VLEWraEW2+FyZPhL39Jercf/MBTX+67L8a2iYjERIG6SA5b+uwCbuEnfGH0Ls48M9utEcmySy7x2ovf/S4sWZLULieeCIMGwe9+Bzt2xNw+EZE0U6AukqNCgG89MZj69eH2O/VfVQQz+NvfoH59uPRS2LUrqd1+8ANPfXnssZjbJyKSZvrrL5Kj/j12BxM2D+KnJ0+iY8dst0YkR3TqBH/8I7zyCtxxR1K7nH66j0f99a/9C7CISL5QoC6Sg1atgm9eCUcxk29fWZ7t5ojklosvhjPOgBtvhHffrXHzevW8V720FJ56Kv7miYikiwJ1kRyzcyecfz588nHgn5xPgxOPz3aTRHKLmQ8obdLEg/adO2vc5fzzvWjMj3+cdMaMiEjWKVAXyTE//alXn7vryL/Qu8t2OOCAbDdJJPccdJAXSJ8yJamJkBo0gJtvhnfeUa66iOQPBeoiOWTSJPj5z72T8Kurfw0DB2a7SSK567zz4PLLPfk8iZyWc8+Fww7zgD2JTngRkaxToC6SI5Yu9dvzhxwCd96w0hPVFaiLVO+222DAALjoIli4sNpN69WDW26BBQvg4Ycz1D4RkTpQoC6SAzZtghEjvM7zE0/APm+/4S8oUBepXpMm8Pjjntty9tnw0UfVbv6FL8BRR3mKmeqqi0iuU6AukmWffAKjRnmd53Hj4NBD8bzbpk3hyCOz3TyR3Ne5MzzyCMyZA9/4RrU1GM3gZz/z+ZLuvTeDbRQRSYECdZEsKi+HCy7wuPwf//BZFAFfMWAANGyY1faJ5I3Pf97zWh5+GH71q2o3Pe00OPlkz1X/8MPMNE9EJBUK1EWyZMcOD9KfeAJ+/3s455zohS1b4K23KkTtIpKUm26Cr3zFl/ffX+VmZvDb38L69fCb32SueSIitaVAXSQLysq8AsXYsR4oXHtthRdfeMFLUowcmbX2ieSlevXgvvtg6FD42tfg2Wer3PSYY7xozO9+BytXZrCNIiK1YEHzKVdqwIABYcaMGdluhhSgTz/13vPx4+H22+Hb395rg0svhSefhA0bfICciNTOhx/C5z7nVWBeesmj8kosW+ZVls47r9oOeElWWRm8955/89m+3ccKJGKMdu18LEHr1n5LQ0T+x8zeCiEMqOw1RQEiGbRhA4we7Snof/mLl4Dew65dMHEiDB+uIF0kVfvu6/+PBg6E00/3GcR69/7MZl26wDXXeBrMNdd4NRhJ0urV/otsyhSYNs1H565eXe1AXgCaN/eA/eij4ZRTYPBg/4cQkUqpR70K6lGXdJs3z2OGNWvgoYcq5KRXNHOm/wF74AG48MKMt1GkoLz7ro8aDcFnEzvssM9ssnkz9OgBffvCyy+rs7dKO3bAK6/4xFLjx/vtCIDGjaF/f+jVywPwzp3h4IO9apWZP0KAtWu9tNXy5R7UT5kCGzf6MTp3hrPO8pne+vXL1jsUyRr1qItk2fPPw5e+5CWfX3kFjj22ig3Hj/c/bCNGZLR9IgWpVy//DzdkiPfevvDCZwLBli3hF7+AK66ARx+FMWOy09ScVF7uv7weesh/N23Z4gH4sGF+C2LgQL+ejRvX/ti7dsHcuf7t6IUX4K67fPKqfv2iqZm/6mkyIkVOPepVUI+6pMOuXXDrrfCjH0GfPvCf/3jnUZUGDvSd3nwzY20UKXiLFnmwvm0b/Pe/Xvq0gvJy//K8bh3Mn+/ZGUVtwQJP2n/wQU9nad3ac/bOOssH6jZrlv5zvv++18K//36YMcP/Ea66Cq67zvPbRQpYdT3qqvoiEpPNm30WxJtu8govU6fWEKRv3OgB+mmnZayNIkWhRw/PU2/ZEk491QeYVlC/PtxxB6xaBb/8ZZbamG3l5T6IfcgQz+f/v//zlJbHH/d8vfvu85nZ4gjSwb8MXHUVTJ8Os2fDGWd4SawuXTxYX7s2nvOK5DgF6iIxmD7dU80nTPDKLg8/DPvsU8NOzz7ruZynn56RNooUlS5dPA2mY0efHOmvf93j5RNO8GEhv/2tF4spGh984AFx9+5w9tl+9+GXv/TqLc88A1/8IjRqlNk2HXmk967Pm+c5g7ffDj17eju3b89sW0SyTIG6SBrt2uV/6E84wUuhv/KKl19MaoDahAl+i7d//9jbKVKUOnWCN97w9I3LL/ee2vLy/73861/7OJKrr665eEneW7ECvvMdvyY/+AF07Qr//rcP9LzxRjjwwGy30GtnPvCAB+xDhng7+/aFceOK4B9IxClQF0mTtWu9M/x73/M7xLNne8CelPJy71EfOdInbRGReOy3n/cUX301/OEPnnu9ZQsABxwAP/uZ/1f817+y3M64vP22T4ncrZvn+3zhC/7L6qWXvEc9F8vC9uwJTz/t/zCNGvm/2emn+5cNkQKniEAkDZ5+Gg4/3AsY/OlPntbZqlUtDjB1qt+CVtqLSPwaNPAKI3fd5cHfkUfC668D8K1vedraNdf4OJOCkChPOXy4V1V5+mn/orJkiVd0OfLIbLcwOcOH+xeNP/zBxxz07Qt33+23MkUKlAJ1kTrYtg2+/nUvhtCpk5dBv/LKFGoxT5jgI9qGDYulnSJSiSuugMmT/f/eySfDT35C/bCTe+6B9es9AySvlZX5AJkBAzzdp6TE889XrIDf/97rneebhg3h2muhtBSOOw6++U1Pi1m0KNstE4mFAnWRFE2d6p1Tf/sb3HCD/3zooSkebMIEOPFEr0ohIplz/PGe+vHVr8JPfwonnUT/ZvO55hrvrH3jjWw3MAUbN3pA3rWrp7l8/DHce69PUnTjjbW83Zejunb1Gu/33guzZsERR/iXjwpjDkQKgQJ1kVrauRNuvtnj6p07Pd3lV7+qQ2GEefM8UBg1Ko2tFJGktWjh9bvHjvVC6ocfzk93/j86ddzF5ZfnUaGROXN8kGynTl4X9vDDYeJEX3/ZZalNTJTLzPx9zZ3rZTevvx4GDfKfRQqEAnWRWigt9Q64W26B88/3dMmTT67jQf/2N8+ZveCCtLRRRFJ07rnw7rtw8cU0v/NW7tp2IXPmwM9+msMVRnbt8mD885+Hww7znPMLL/Tg/NlnfZbjQh+g3qGDV4J5+GFPgTnqKJ9udseObLdMpM4K/H+vSHrs2AE//7kPMluxwitCPPigF5Cok7IyLz82erRm3xPJBW3beo31N9/k9EMWcRH3c+svy5lxy/jcCvyWLfMeg+7dfZK0OXM83WXlSvjLX3wq5GJi5r0nc+f6oKEf/tBz2EtKst0ykTpRoC5Sg5IS/33/ox/53B9z5sA556Tp4OPGeT7p176WpgOKSFoccwy88QZ//Gtz2jfYxMU3d2Z7t0O9WsyHH2anTRs2+B24IUM8R/uWW3zW1Uce2Z1/vv/+2WlbrmjXDh591GvCr1rlA2lvucU7RUTykAVNGlCpAQMGhBkzZmS7GZJFO3Z47vnPf+5jr+66y8sMp9WIEd4DtHSpV54QkZwzcULgtNONGzs9xC/fu9Bzvc88E847z3uzmzSJ58QheAnF8ePhiSfgtdc81aV7d7joIn/kY+WWTNm0yctQ/vOfPtj0nnu810Ukx5jZWyGEAZW+pkC9cgrUi9uUKV716+23/W7qbbdBmzZpPsny5d4r9uMf++hUEclZl13m400n3zOXgW/f7b2269fDvvt66cMTT/THUUelPmnQ9u2wYAG8+aZPa/zyy94rDF4z/Oyz/XHkkSnUgC1i48Z53dzVq335i1+kIW9RJH0UqKdAgXpx2rTJSy3ee6+PT7rzTk93jMVPfuLTIC5dCp07x3QSEUmHLVs8Bg/BizTtt89On83z0Ud9uWSJb7jPPl6ntUuX3Y9WrbwsVMOGvvzkE/9ls3GjP5Yu9Zy6RYt2T97Tvj2ccgp87nNe0aRXr+y88UKxdavnL95xh1/bP/4RvvQlfeGRnKBAPQUK1ItLWZmPv7rlFp+N8NprPY5u0SKmE5aX+x/wvn29MoOI5LypU73T/Mtf9gIje8R4q1b57KaTJ3uv+LJlftesptqOzZp5OcW+fX0AaN++/o2gVy8FkXGYMcNLWM6aBSed5LOcHn10tlslRU6BegoUqBeHEDz184YbvDNryBDvaDn88JhPPHGi57b+619pHJkqInH7xS+8oMj993uKeLV27YJ163zwaVmZD3wpK/Oc9jZtfOBn06aZaLZUtHOnD8r90Y/8jsaFF/o/bIcO2W6ZFCkF6ilQoF7Yyss9QP/lL/02dt++8JvfwMiRGerE+uIX4dVXvRcu5ZmSRCTTyss9JX36dJg5UxkpeW3LFv8j8Mc/eq35K66A738fDjww2y2TIlNdoK7yjFJUtm71gf+HHea3rz/+2HvGZs/2Du6MBOlLlvjgpgsvVJAukmfq1/c5hZo08XGd27Zlu0WSsv32g1//2meHPvdcz1/v2tUrxSQG8YpkmQJ1KXghwLRp3lly0EHwjW/4H9lHH/XKiBddlHqRhpT88Ic+qOz66zN4UhFJl44dYexYj+8uucR/x0ge69bNe2wWLICvfAX+/GcP2M8/38cd6B9YskiBuhSk7du9stm113pBleOO8wlAv/hFL704c6b3qGe8dPlbb/nkJN/5jn9rEJG8NHQo3HorPP44/N//Zbs1khbdu3vu+sKFXsZxwgQfPdy/v9+K3bw52y2UIqQc9SooRz1/hODlcWfN8jj4lVc8GP/0U5+XZPhwv0U9ejS0bJnlhg4b5nk2ixerjq9IngsBxozxYH3iRPj857PdIkmrjz7y8j5/+pNPUd2okedInncenHGGV+wRSQMNJk2BAvXc89FHXpll0SLv8Fi40J/Pm+cza4PnmPfr5+WHTzkFBg+OscRibf33v/6t4Q9/8K5+Ecl7H30EAwd6JcZXX/W5iKTAhLD7bujYsd4ztM8+flvltNP80bFjtlspeUyBegoUqGdHCLBmjQff8+fvfsyb99mxPe3bQ8+eXnWhXz8vPXzkkTkUmFe0a5fX6t282d9Q48bZbpGIpMnKlR6s79rld/MOPjjbLZLYlJfDa695ad3x4/0bGsARR3jv0Ekn+aN9+6w2U/KLAvUUKFDPjI0b/XfetGk+a/Zbb3nJ4YQWLaB3b5/or1cvD8x79PDHvvtmr9219o9/wFe/6suvfCXbrRGRNHvnHU9nPuggn/Oodetst0hiF4JXJBg/3ieumzrVZ50F/2OVCNpPOskHrGoCK6mCAvUUKFCPR3m5/xGbMAFeeMHzykPwqiv9+sExx3jpxN69/XHggQXwu23bNn9TrVv7rHj1NIZbpBC9/LJntw0Y4HFbTt7dk/iUlXmlgtde88fkyfDBB/7agQfCscf6H7kBA/yx//7Zba/kDAXqKVCgnj7l5TBpkt8pfPppzydv2NBvFQ8d6rOBHn20l0wsOCF4D/rYsfDSS/C5z2W7RSISo3//2weYJoJ1jRkvYrt2eY97ImifMQPefXf361277g7cjznGq8vk1a1iSRcF6ilQoF538+Z5adp//MPH3jRv7gPlzz4bRowokt6mO++Eb38bfv5zuOmmbLdGRDLgySd9/px+/eC556BVq2y3SHLGli2e4zljhk9vO2MGLFvmr5nBIYfsDtwHDPAPkarLFDwF6ilQoJ6anTt90s077vDbwPXrw8iRcPHFcPrpBdprXpUpU7wHffhwv5WglBeRovHMM3DOOdC3r6cwa1Z6qdKGDR68JwL36dO9qgL4H9G+fT1o79/fA/cjj/SeLykYCtRToEC9djZuhHvvhbvughUrvOrBlVd6gF6Ug9/Xr/dfqo0b+y9edamJFJ1nn/VgvWVLD9yPOirbLZK8sXr17sA9Ebxv2uSvmXlFhUS5s379/HHAAQUwqKs4KVBPgQL15Mya5b3njzziEwwNHuyZHmee6QNEi1JZmd9GeOMN71Xv1y/bLRKRLJk9G0aN8hjroYc89U+k1kLwGsWzZvmHavZsf7506e5t2rXbM3A/4ggvl1a0f4zzhwL1FChQr9qOHfDEEx6gv/66p8999avwrW95cZOitnmz/yV+6SX4+9/9loKIFLW1a+Gss7wE7Xe+A7/8ZZGlAUp8Nm/2WVMTgfvs2TBnjv+hBp9N9dBD4fDD93x06KDe9xyiQD0FCtQ/67334K9/9RSXNWu8LOxVV8EllyizA/Ccn5EjfcrUv/9d9dJF5H8+/RSuu87TA/v29d51pcJILMrKvNpMaemej4qzBrZs6T1rFYP3ww7z9ZJxCtRToEDd7drlM9/fdRf85z9+923kSPjmN31Zv362W5gjZs3y0bIff+wlHwYPznaLRCQHTZwIl17qqTDf/S7ceGORVMCS7Hv/fZ+Zq7R097K0dM9ZBjt12jNwP/xwn9REs2nHSoF6Coo9UF+1yssq/uUvngLXrh1cdhl8/ete+lUi27fD7bfDLbf45BUTJnh3mYhIFTZtgmuv9d+x7drBz37mwbtSiSXjQvDb5RV73t95x+srJ9JnGjTwXPe902c6d1Y1szRRoJ6CYgzUN22Cp56Chx/20ooheHXBK67wtOtGjbLdwhwSgtehvP56WLzYC8T/5S8+f7iISBKmTfNfIZMnexGPa67xYS2qvCdZt2OHT860d/pMouY7+Ae1b9/PBvBt2mSt2flKgXoKiiFQD8H/H06Y4GW+J0/2WUR79PD06vPP9y/RUkFZmddcu/12n261Tx/4wx/g85/PdstEJA+F4B0kv/61Dzbdbz8f93PeeT7njcb7SU7ZutV73CumzpSW7i4dCV4mcu/0mT59NHFTNRSop6AQA/WdO30w+PTp8Mor8OKLXqoV/P/S6NFemeDoo/XHYQ+7dnkd24cegrFjvWh8u3bwwx/67YaGDbPdQhEpAFOn+vf+J5/0Ds0uXbwO+9ChMGiQetolR4XgpY0qps6UlnrA8emnvk2i9nvFnve+fT19pmnT7LY/B2QtUDezEcBtQH3g3hDCrXu9btHrpwEfAxeHEGZWt6+ZtQYeBboAy4AvhxA+iF67EbgMKAeuDiE8F60/GrgfaApMAK4JNbzxfA7UP/zQc8xXrPA0s7lz/f/LrFnwySe+Tbt2Pt5xyBD/I9CtW3bbnDPKy2HlSpg/3/9qvvGGLz/80AfTjB4NF17oPegK0EUkBh984Hc5H3sMnn/eO1kaNPDJKY8+2iemPOIIn21eRTokZ/D6JdEAAAv7SURBVJWXe2ro3ukzixZ5cJ/Qtq0H7AcfvOejUyd/bf/9fcR1AfcgZiVQN7P6wLvAMGAlMB04L4Qwt8I2pwHfxgP144DbQgjHVbevmf0GeD+EcKuZ3QC0CiH8wMz6AI8AxwIHAS8AvUII5WY2DbgGmIoH6reHECZW1/5sBOpr1vgv6PJyf+zcufv5jh3w0UceL27duudjwwYPzFet8hhz27Y9j9umjd916t/fb6Uec4x/sS3gz3ztPP88/O53sGSJ598lBtCY+bf+E07w7qwzztBfRRHJqG3bvL/g5Zfh1Vfh7bf3/B2/337e896hA7RuveejVSt/NG3q/QxNmnj807Zttt6NCF4dLdGLuGLFno/lyz3Y2VvDhh6w77+/BzWJ582b+we8WTN/JJ4nlonSdImAZ+9lWZn3+n/yiS979IBTTon9EuytukA9zjHmxwKLQghLokaMBUYDcytsMxp4MOrdnmpmLc3sQLy3vKp9RwOnRPs/ALwM/CBaPzaEsB1YamaLgGPNbBmwbwhhSnSsB4GzgGoD9Wy46SYvv10bzZr5Z7VDB09fGT7cn3fs6I/evfVLuUbbt3vZqqOOgi9+0W8vdO/u3Vf77pvt1olIEWve3G/gJYbB7Nrl/QklJd4xuWyZV+Zau9bjng8+gC1bqj7e73/vky6JZE2zZn5r6OijP/taCD6J04oVXo1m40Z/bNrkj8TzBQt8+dFHHviXl6enbZdckpVAvTpxBuodgPcq/LwS7zWvaZsONezbPoSwBiCEsMbM2lU41tRKjrUjer73+s8ws8uBy6Mft5nZgqreXK74+GN/vPdepS+3ATZmtkV5bPr0dB1J1z17dO2zQ9c9O2p93a+7zh9SZ/rMZ0e81/3vf699j2l6dK7qhTgD9coSK/bOs6lqm2T2TfZ8SR8rhHAPcE8N58kbZjajqlspEh9d9+zRtc8OXffs0HXPHl377CjG6x5npfqVQKcKP3cEVie5TXX7rovSY4iW65M4Vsca2iEiIiIiklPiDNSnAz3NrKuZNQLGAOP22mYccKG544EtUVpLdfuOAy6Knl8EPF1h/Rgza2xmXYGewLToeFvN7PioysyFFfYREREREclJsaW+hBB2mtm3gOfwEov3hRDmmNkV0et34xVYTgMW4eUZL6lu3+jQtwKPmdllwArgS9E+c8zsMXzA6U7gqhBCYnTBN9ldnnEiOTiQNCYFk8aTZ3Tds0fXPjt03bND1z17dO2zo+iuuyY8EhERERHJQXGmvoiIiIiISIoUqIuIiIiI5CAF6nnEzL5kZnPMbJeZDdjrtRvNbJGZLTCz4RXWH21mpdFrt0cDaokG3T4arX/TzLpU2OciM1sYPS5CkmZmI6J/g0XRzLlSS2Z2n5mtN7N3KqxrbWbPR5/J582sVYXX0vbZL2Zm1snMXjKzedHvmWui9br2MTKzJmY2zczejq77LdF6XfcMMLP6ZjbLzP4T/azrngFmtiy6ZrPNbEa0Tte+MiEEPfLkARwKHILPxjqgwvo+wNtAY6ArsBioH702DRiI15OfCIyM1l8J3B09HwM8Gj1vDSyJlq2i562y/d7z4YEPfF4MdAMaRf8mfbLdrnx7ACcD/YF3Kqz7DXBD9PwG4NfR87R99ov9ARwI9I+etwDeja6vrn28192A5tHzhsCbwPG67hm7/tcB/wT+E/2s656Z674MaLPXOl37Sh7qUc8jIYR5IYTKZksdDYwNIWwPISzFq+gca15nft8QwpTgn9YHgbMq7PNA9Pxx4NTom+hw4PkQwvshhA+A54ERMb6tQnIssCiEsCSEUAaMxa+z1EII4VXg/b1WV/y8PsCen+N0ffaLWghhTQhhZvR8KzAPn8VZ1z5GwW2LfmwYPQK67rEzs47A6cC9FVbrumePrn0lFKgXhg7AexV+Xhmt6xA933v9HvuEEHYCW4D9qzmW1EzXLj7tg8+JQLRsF61P52dfItFt4qPw3l1d+5hF6Rez8Qn8ng8h6Lpnxh+B7wO7KqzTdc+MAPzXzN4ys8ujdbr2lYitjrqkxsxeAA6o5KWbQghVTdRU2bfEUM36VPeR6unaZV46P/sCmFlz4N/AtSGED6vphNK1T5Pgc370M7OWwJNmdlg1m+u6p4GZnQGsDyG8ZWanJLNLJet03VM3KISw2szaAc+b2fxqti3qa69APceEEIamsNtKoFOFnzsCq6P1HStZX3GflWbWANgPTzdYCZyy1z4vp9CmYlTVv4PU3TozOzCEsCa63bk+Wp/Oz37RM7OGeJD+cAjhiWi1rn2GhBA2m9nLeLqhrnu8BgGjzOw0oAmwr5n9A133jAghrI6W683sSTx1VNe+Ekp9KQzjgDHRKOeuQE9gWnTraKuZHR/lZl0IPF1hn0RFl3OAF6Mcr+eAz5tZq2jE9eejdVKz6UBPM+tqZo3wASzjstymQlHx83oRe36O0/XZL2rRdfobMC+E8PsKL+nax8jM2kY96ZhZU2AoMB9d91iFEG4MIXQMIXTBf1e/GEK4AF332JnZPmbWIvEcjzPeQde+cpkevapH6g/gC/i3xO3AOuC5Cq/dhI+EXkA06jlaPwD/D7AYuJPds9E2Af6FD8qYBnSrsM+l0fpFwCXZft/59ABOw6tlLMbTlbLepnx7AI8Aa4Ad0ef9Mjy3cBKwMFq2rrB92j77xfwATsRvDZcAs6PHabr2sV/3I4BZ0XV/B/hxtF7XPXP/Bqewu+qLrnv817sbXsXlbWBO4m+lrn3lj8QbEhERERGRHKLUFxERERGRHKRAXUREREQkBylQFxERERHJQQrURURERERykAJ1EREREZEcpEBdRCSPmFm5mc02s3fM7F9m1qyK7SYk6nPX8XxHmdm90fNRZnZDHY51s5l9t4Zt7jezc6LnL5vZgFTPV+GYZ5jZLXU9johIpilQFxHJL5+EEPqFEA4DyoArKr5orl4I4bQQwuY0nO//AXcAhBDGhRBuTcMxY2Fm9at4aTw+C2WlX2pERHKVAnURkfz1GtDDzLqY2Twz+zMwE+hkZsvMrA2AmV1oZiVm9raZPRSta2tm/zaz6dFj0N4Hj2YPPCKE8Hb088Vmdmf0/H4zu93M3jCzJYle8EqOcZOZLTCzF4BDKqzvZ2ZTo3Y9Gc2EXCUzu8vMZpjZnIq949H7/LGZTQa+ZGZXm9nc6LhjAYJPGPIycEbSV1ZEJAc0yHYDRESk9sysATASeDZadQg+k/CV0euJ7fris/oNCiFsNLPW0fa3AX8IIUw2s4OB54BD9zpNYta/qhyIz2jaG5+y+/G92ng0Pj37Ufjfm5nAW9HLDwLfDiG8YmY/BX4CXFvNuW4KIbwf9ZpPMrMjQggl0WufhhBOjM65GugaQti+V+rPDOAk4LFqziEiklMUqIuI5JemZjY7ev4a8DfgIGB5CGFqJdsPAR4PIWwECCG8H60fCvRJBPTAvmbWIoSwtcK+BwIbqmnLUyGEXcBcM2tfyesnAU+GED4GMLNx0XI/oGUI4ZVouwfw6b6r82Uzuxz/u3Ug0AdIBOqPVtiuBHjYzJ4Cnqqwfj1+nURE8oYCdRGR/PJJCKFfxRVRsP1RFdsbECpZXw8YGEL4pLpzAU2qeX37XuepTGXnrhUz6wp8FzgmhPCBmd2/V7sqvvfTgZOBUcCPzKxvCGFntH1171VEJOcoR11EpLBNwnuj9weokPryX+BbiY3MrF8l+84DetTh3K8CXzCzplG++5kAIYQtwAdmdlK03VeBV6o4BsC+eDC+Jeq5H1nZRmZWD+gUQngJ+D7QEmgevdyL6tN4RERyjnrURUQKWAhhjpn9AnjFzMqBWcDFwNXAn8ysBP9b8Cp7VZAJIcw3s/0qSYlJ9twzzexRYDawHE/VSbgIuDuqxLIEuKSa47xtZrOAOdG2r1exaX3gH1FqjeE5+InKN4OBG2v7HkREssl8MLyIiMhnmdl3gK0hhHuz3ZZURb3w/wwhnJrttoiI1IZSX0REpDp3sWcuej46GLg+240QEakt9aiLiIiIiOQg9aiLiIiIiOQgBeoiIiIiIjlIgbqIiIiISA5SoC4iIiIikoMUqIuIiIiI5KD/DzS0Jl2EylA8AAAAAElFTkSuQmCC\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(Yhat, 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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 3: Polynomial Regression and Pipelines</h2>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><b>Quadratic - 2nd order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X^2 +b_2 X^2 \n",
    "$$\n",
    "\n",
    "\n",
    "<center><b>Cubic - 3rd order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X^2 +b_2 X^2 +b_3 X^3\\\\\n",
    "$$\n",
    "\n",
    "\n",
    "<center><b>Higher order</b>:</center>\n",
    "$$\n",
    "Y = a + b_1 X^2 +b_2 X^2 +b_3 X^3 ....\\\\\n",
    "$$"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We will use the following function to plot the data:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "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": [
    "lets get the variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "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 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "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": 35,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 35,
     "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  #4:</h1>\n",
    "<b>Create 11 order polynomial model with the variables x and y from above?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# calculate polynomial\n",
    "# Here we use a polynomial of the 11rd order (cubic) \n",
    "f1 = np.polyfit(x, y, 11)\n",
    "p1 = np.poly1d(f1)\n",
    "print(p)\n",
    "PlotPolly(p1,x,y, 'Highway MPG')\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2)polynomial with two variables is given by:</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b_1 X_1 +b_2 X_2 +b_3 X_1 X_2+b_4 X_1^2+b_5 X_2^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can perform a polynomial transform on multiple features. First, we import the module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a <b>PolynomialFeatures</b> object of degree 2: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "Z_pr=pr.fit_transform(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The original data is of 201 samples and 4 features "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "after the transformation, there 201 samples and 15 features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Z_pr.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Pipeline</h2>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'PolynomialFeatures' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-3-71794ed1efe5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mInput\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'scale'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mStandardScaler\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m'polynomial'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mPolynomialFeatures\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minclude_bias\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m'model'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mLinearRegression\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'PolynomialFeatures' is not defined"
     ]
    }
   ],
   "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 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "pipe=Pipeline(Input)\n",
    "pipe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can normalize the data,  perform a transform and fit the model simultaneously. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "pipe.fit(Z,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Similarly,  we can normalize the data, perform a transform and produce a prediction  simultaneously"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #5:</h1>\n",
    "<b>Create a pipeline that Standardizes the data, then perform prediction using a linear regression model using the features Z and targets y</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "</div>\n",
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
    "\n",
    "pipe=Pipeline(Input)\n",
    "\n",
    "pipe.fit(Z,y)\n",
    "\n",
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:10]\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 4: Measures for In-Sample Evaluation</h2>"
   ]
  },
  {
   "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",
    "\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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 1: Simple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#highway_mpg_fit\n",
    "lm.fit(X, Y)\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(X, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Yhat=lm.predict(X)\n",
    "print('The output of the first four predicted value is: ', Yhat[0:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "lets import the function <b>mean_squared_error</b> from the module <b>metrics</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we compare the predicted results with the actual results "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "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\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we produce a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Y_predict_multifit = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we compare the predicted results with the actual results "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2"
   ]
  },
  {
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We apply the function to get the value of r^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>MSE</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the MSE:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "mean_squared_error(df['price'], p(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 5: Prediction and Decision Making</h2>\n",
    "<h3>Prediction</h3>\n",
    "\n",
    "<p>In the previous section, we trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction. Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "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 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "new_input=np.arange(1, 100, 1).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Fit the model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "lm.fit(X, Y)\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce a prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "yhat=lm.predict(new_input)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot the data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "plt.plot(new_input, yhat)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Decision Making: Determining a Good Model Fit</h3>"
   ]
  },
  {
   "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",
    "\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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Regression model (SLR) vs Multiple Linear Regression model (MLR)</h3>"
   ]
  },
  {
   "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 or even act as noise. As a result, you should always check the MSE and R^2.</p>\n",
    "\n",
    "<p>So to be able 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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Model (SLR) vs Polynomial Fit</h3>"
   ]
  },
  {
   "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 Polyfit 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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression (MLR) vs Polynomial Fit</h3>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Conclusion:</h2>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Thank you for completing this notebook</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "\n",
    "    <p><a href=\"https://cocl.us/corsera_da0101en_notebook_bottom\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/BottomAd.png\" width=\"750\" align=\"center\"></a></p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>About the Authors:</h3>\n",
    "\n",
    "This notebook was written by <a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>, <a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>, Bahare Talayian, Eric Xiao, Steven Dong, Parizad, Hima Vsudevan and <a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a> and <a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "<p><a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a> is a Data Scientist at IBM, and holds a PhD in Electrical Engineering. His research focused on using Machine Learning, Signal Processing, and Computer Vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "<p>Copyright &copy; 2018 IBM Developer Skills Network. This notebook and its source code are released under the terms of the <a href=\"https://cognitiveclass.ai/mit-license/\">MIT License</a>.</p>"
   ]
  }
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