Lab_04_model-development.ipynb

{
 "cells": [
  {
   "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
   },
   "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
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\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()\n",
    "#df.to_csv(\"lab_04.csv\")"
   ]
  },
  {
   "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
   },
   "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
   },
   "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
   },
   "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
   },
   "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
   },
   "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
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.305858157386"
      ]
     },
     "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,
    "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
   },
   "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",
    "lm_model = LinearRegression()\n",
    "lm_model"
   ]
  },
  {
   "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
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-68402.03332369, -68402.03332369, -86480.16764678, -51145.63237893,\n",
       "       -73332.43359362])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "# we will create a linear function with \"engine-size\" as the predictor variable and the \"price\" as \n",
    "# the response variable.\n",
    "X = df[['engine-size']]\n",
    "Y = df['price']\n",
    "# Fit the liner model\n",
    "lm_model.fit(X,Y)\n",
    "# Prediction from linear model \n",
    "Yhat=lm.predict(X)\n",
    "Yhat[0:5] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm1.fit(df[['engine-size']], 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
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([166.86001569])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm_model.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Intercept</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7963.338906281049"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm_model.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=38423.31-821.733*X\n",
    "\n",
    "Price=38423.31-821.733*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": 14,
   "metadata": {
    "collapsed": true
   },
   "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": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 15,
     "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": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15806.624626329198"
      ]
     },
     "execution_count": 16,
     "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": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([53.49574423,  4.70770099, 81.53026382, 36.05748882])"
      ]
     },
     "execution_count": 17,
     "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": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm2 = LinearRegression()\n",
    "train = df[['normalized-losses', 'highway-mpg']]\n",
    "lm2.fit(train, df['price'])\n",
    "            "
   ]
  },
  {
   "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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1.49789586, -820.45434016])"
      ]
     },
     "execution_count": 21,
     "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": 22,
   "metadata": {
    "collapsed": true
   },
   "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": 23,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/raman/anaconda3/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 48283.60500191853)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+oVFD8aR6+2OKH3UgDAAAADCdpqWbirW2X1KHpIsl1Rpjxloqtkjal/u6R1KrJOV+XiPp0OHjR91nvPEJSaYz2tcfU2QkIcvSFQAAADigkN1Umowxtbmvg5LeIel5SQ9Lujp32RpJv8h9vSn3vXI/f8hmU/ImSatz3VYWSjpN0hZJWyWdluvO4lN2k+emyc4zEk1o30BciVTmZF4mAAAAcNIKeejPHEl35bqeuCT9xFr7S2PMc5LuNcZ8RdJTkm7PXX+7pLuNMbuVrYivliRr7U5jzE8kPScpJemT1tq0JBljPiXpN5Lcku6w1u48mYmOJtPq7Y+pvsKnmqD3ZF8vAAAAMClmpi3ROOf8C+wvHtw87s9DPo8aK33yuDkPCQAAACfHGLPdWrv0RNeROI8STaTU2x/T8GjqxBcDAAAAU0AYP4Z0xio8GFd4KE4LRAAAABQMYfw4huMp9URogQgAAIDCIIyfQCqTbYF4iBaIAAAAyDPC+AT151ogJtO0QAQAAEB+EMYnYTSZVm8kpqF40umpAAAAoAwQxicpY60ODo0qPMjmTgAAAEwNYfwkDY9mWyCyuRMAAAAnizA+Bcl0RvsH4uqPJpyeCgAAAEoQYXyKrLU6NJLQ/oGYUmzuBAAAwCQQxvMklkirtz+maIKTOwEAADAxHqcnUE7SGatXB+KqCXpVX+GTMcbpKaHEdXSGtX5zl7ojUbXWhbR2RZtWtjc7PS0AAJAnVMYLYCCWVG9/TIkUy1Zw8jo6w/rc/Tv0VHdEBwbjeqo7os/dv0MdnWGnpwYAAPKEMF4giVT25E56kuNkfe1Xz6s/mpTNSG5jZDNSfzSpr/3qeaenBgAA8oQwXkD0JMdUvNQXlctILpeRMUYul5HLZMcBAEB5IIxPA3qSAwAA4FgI49OEnuSYrLbGCmVs9hMWK6uMtcrY7DgAACgPhPFpdHhP8jTLVnACX7iyXXUhr4ykVDojI6ku5NUXrmx3emoAACBPCOMOiCXS6olE6UmO41rZ3qxvXH2elsyr05yaoJbMq9M3rj6P1oYAAJQR+ow7hJ7kmIiV7c2EbwAAyhiVcYcNxJLaNxBXMk1PcgAAgJmGMF4ERpNp9UboSQ4AADDTEMaLxOs9yYfoSQ4AADBTEMaLzHA8pZ5ITLEEPckBAADKHWG8CKUyGe0fiKlveFTWUiUHAAAoV4TxIjYQS6q3P6bRFFVyAACAckQYL3KJVEb7+uMaiLK5EwAAoNwQxkuAtVZ9I6N6dSDOyZ0AAABlZMaF8VI+9TKaSKmXzZ0AAABlY8aF8Z5ITP/0iz+ptz/m9FROytjmzkMjCTZ3AgAAlLgZF8Yl6dHdfbp+w1Z9/5Gukq2U90cTnNwJAABQ4mZcGJ9TE1BzlV/JtNU9W7p17R1b9ZudrypTglXmsZM7h0dL8w0FAADATDfjwnhVwKsN1y3Tx94yX36PS4dGEvr6r1/QJ3/8lHbuG3B6epOWsVbhwTgndwIAAJSgGRfGJSngdevaSxboruuW6fIzmiRJL7w6pE/f87S++sDzOjg06vAMJ284nlJvf0zxJJs7AQAASoWZaZsAzzn/AvuLBzcfMfZsz4C+8/Bu7QoPS5ICHpc+fNE8ffDCFvm9biemOSV1IZ/qKnxOTwMAAGDGMsZst9YuPdF1M7IyfrRzWmr03Y9coM+/83TVhbyKpzK649GXdd2Gbdr84sGS61oSiSa0rz/G5k4AAIAiR2X8KCOjKf3w8Vf00yd7lcqtwT6/tUafXHmqFjVXTtc088JljBoqfaoKeJ2eCgAAwIxCZfwkVfg9WnvZIt3xsaW6uK1ekvR094DW/nC7vvXbF9UfTTg8w4nLWKuDQ6MKD7K5EwAAoBgRxsfRUhfSV99/jr7+F+dofn1IGSv9x479uvaOrfrpkz1KldASkOFRNncCAAAUI8L4CSxbUK/vX3uhPnX5IlX6PRoeTenWh/forzdu15aXDjk9vQlLpjPa1x9TZKR0KvsAAADljjXjkzAQTerOP76sXz6zT2OrPi5uq9cnLluk1vpQHmdZWH6vW81VfnndvBcDAAAohImuGSeMn4Q9B4d168N79HR3vyTJ4zJ6/5K5+ugl81Xp9+RjmgXH5s7S0NEZ1vrNXeqORNVaF9LaFW1a2d7s9LQAAMAJEMbHkY8wLknWWj2y+zV9r6NLrw7GJUm1Qa9uuHShrjx7ttwuM+XnmA6Vfo8aKv0lM9+ZpKMzrJs37ZTXbRT0uhVLppVMW61btZhADgBAkaObSoEZY7TitCZtuG6Zbrh0gQJel/pjSf2fB1/UJ370pJ7p6Xd6ihMyPJpSbySmWILNncVm/eYued1GIZ9HxmRvvW6j9Zu7nJ4aAADIE8L4FPk8Ln3kovm667rl+rOzZkmSdoeH9bf37dCXf/mcDuSq5sUslclo/0BMfcOjJXfAUTnrjkQVPOoE2KDXrZ5I1KEZAQCAfCOM50lTlV//8O52feeaJWqfXSVJeviFg1pz51Zt+OPLJdFWcCCWVG9/TIlU6bRtLGetdSHFjvq9iSXTaqkrnc3CAADg+AjjeXbWKdX6zoeX6ItXnqGGCp8SqYw2PvaK1tyxVQ91hou+8pxIZdTbH9NANOn0VGa8tSvalExbRRMpWZu9Taat1q5oc3pqAAAgT9jAWUDRREo/fmKv/m17j5Lp7N/z2adU61NXnKrTZ1VNyxymIuhzq6nSLw8tEB0z1k2lJxJVC91UAAAoGXRTGcd0hvEx+/pjWr+5S4/sek2SZCRdefZs3XDpQtVX+KZ1LpPldhk1VvpVUSItGwEAAIoBYXwcToTxMU/ujejWh/fopddGJEkhn1t/dfF8fWDJXPk8xV19rgx41Fjhl4sWiAAAACeU99aGxpj5xph35L4OGmOKf51FkblgXp1u++iF+szbT1N1wKNoIq3bNnfphru26Y97Xivq9eTD8ZR6+2MlsREVAACgVEwojBtjPi7pfknrc0Mtkn5eqEmVM7fL6H3nn6KN1y/XB5bMlctIvf0x/ePPd+qL//6sXukbcXqK40qmM9rXTwtEAACAfJnQMhVjzNOSlkt6wlq7JDf2rLX2nALPL++cXKZyLC/3jejWh/do+ysRSZLLSFctmas1l8wv6qPqvW6Xmqr8ChzVBxv5NbaBszsSVSsbOAEAKBn5XqYyaq1NHPbgHkmURvNgQUOF/r+/OEdfft9iza0NKmOlf3+yVx+9fYt+8fQ+pTPF+decTGe0fyCuQyMJquQF0tEZ1s2bdio8FFdt0KvwUFw3b9qpjs6w01MDAAB5MtEw/ntjzJckBY0xfybp3yT9R+GmNbMYY/TWUxt1+5qlunFFm0I+twbjKd3yu11ae/d2PbU34vQUj8laq/5oQr39MY2mWEueb+s3d8nrNgr5PDIme+t1G63f3OX01AAAQJ5MNIx/UdJBSc9KWivpAUn/WKhJzVQ+j0url7Vq4/XL9e6zZ8tI6nptRP/j357RP2/aqf0DMaeneEyJVEb7+uOKUCXPq+5IVMGjlgEFvW71RKIOzQgAAOTbRMN4UNId1toPWmuvlnRHbgwFUF/h0+ffdYb+9a8u0NmnVEuSHtn1mj5251bd/oeXFEsUXxXaWqsIVfK8aq0LKXZU95pYMq2WupBDMwIAAPk20TD+Ox0ZvoOSfpv/6eBwp8+q0i2rz9f/fM+Zaqr0K5m2+tETe3XtHVv0X88dUKYIq9BjVfL+aOLEF+O41q5oUzJtFU2kZG32Npm2WruizempAQCAPJloGA9Ya4fHvsl9TXluGhhj9PYzm7Xh+mW69pL58nlc6htJ6Gu/6tSn73lKz+8fdHqKb2Kt1aGRbJU8kco4PZ2StbK9WetWLVZzVUADsaSaqwJat2ox3VQAACgjE21t+KikT1trn8x9f6Gk71hrLynw/PKu2FobTtarg3Hd9vsudbx48PWxd541S3/9toVqrPQ7OLNjM8aoPuRTTah42zQCAADk20RbG040jC+TdK+kfbmhOZI+ZK3dPqVZOqDUw/iYHT39uvWhPdp9MPuBRcDr0l9dNF9XX9gin2fCB6sW3JauQ7p3a7deHYppfn2FPnHZIiq7AACg7OU1jOce0CvpDElGUqe1Njm1KTqjXMK4JKUzVr/606u64w8vqT+W/c8xpyagv7lskS49tUHGGEfnt6XrkG55aJc8LqOA16V4MiNrpa9cdTaBHAAAlLW8HPpjjLkid/sBSe+VdLqk0yS9NzdWctwu43hIzRe3y+jPz52jjdcv1wcvbJHbZbR/IK5/3rRTn7v/GXUdHD7xgxTQvVu75XEZBb1uGeVujfTth3YpmWYtOQAAwInWM1yWu33vMf78eQHnVTAel1FrXVA1QW/ZhPLKgEefWLlIt69Zqovb6iVJT+3t1413b9ctv92lgZgzH2LsH4wp4D3yVyzgdWlff0y9kZhj8wIAACgWnuP90Fr7z8YYl6RfWWt/Mk1zKjiP26WGSr9qgl4NxJIajKfK4rCaefUhffX95+iJl/r03Yf3qDsS0y927NNDL4S15pIFWnXeHHnc07eefE51UH0jo0ccXBNPZjS7OqiMteobHlU0kVJTpX9a5wUAAFAsTpiArLUZSZ+ahrlMu7FQXm6V8osWNuj2NUv1iZWLVOF3ayie0nce3q2P371d214+NG3zWL2sVamMVSyZllX2NpWxWr2s9fVrYom0eiIxDcapkgMAgJlnot1U/klSTNJ9kkbGxq2105fs8mTp0qV227Ztx/xZOmPVH02UTaVckvqjCd356Mv65TP7NfaK3rKoQZ+4bJHm1hX+ENXXu6kMxjS7OqjVy1q1PLeU5mghn0eNlT6q5AAAoOTlu7XhS5LedKG1tuSOAjxeGB9TjqF8d3hYtz68Wzt6BiRl185ffWGLPnLRPFX4j7taaVq5jFFDpU9VAfqSAwCA0pXvMB6UdJOkS5UN5Y9I+p61NjbViU63iYTxMeUWyq212rzrNX3v93t0YHBUklQX8uqvL12od509W64iWqZT4feosdIvt6t45gQAADBR+Q7jP5E0KOlHuaFrJNVaa/9ySrN0wGTC+JhyC+WjybR+sr1H9zyxV/HccfWnz6rUpy4/VWfPrXF4dm9wu4waK/1FVbkHAACYiHyH8R3W2vNONFYKTiaMj0lnbLb7SiypTBmE8oNDo/r+I1367fPh18euaG/WjW9bqObqgIMzO1J10KuGCl/ZbLAFAADlLy+H/hzmKWPMxYc9+EWSHj3ZyZUqt8uovsKn1vqQakO+olrWcTKaqvz60nvO1LdXn68zZlVJkh7qDGvNnVu18bGXFU+mnZ1gzmAsqd7+mBIpDgoCAADlZaKV8eclnSFpb25onqTnJWUkWWvtuQWbYZ5NpTJ+tHKqlGes1X/tPKDvP9KlSDTbZrC5yq+/uaxNl53eVBRVaZPb3FnN5k4AAFDk8r1MZf7xfm6tfWUSc3NUPsP4mHIK5SOjKf3oib366ZM9Sqazr+WcuTX61OWLdFqueu40NncCAIBil9cwXk4KEcbHlFMo743E9L3f79Gje/okSUbSe86Zo+svXaC6kM/ZyUnyuFxqrPIp5CvvzZ0dnWGt39yl7khUrXUhrV3RppXtzU5PCwAAnABhfByFDONj0hmrwVhSg/Gk0pnS/vvd9vIh3dqxR6/0RSVJFT63rr1kvq5aMlfeIjicpzLgUWOFX64yrJJ3dIZ186ad8rqNgl63Ysm0kmmrdasWE8gBAChyhPFxTEcYH5PJWA3FUxqIJZXKlO7mw3TGatOOfdrwx5c1FE9Jklrqgrpp5SJd3Nbg8OzKt0p+zW2PKzwUP+J1RRMpNVcFdM+NFx/nnvlDZR4AgJOT724qOAkul1FNyKvW+qAaq/xFUUk+GW6X0fuXzNXG65frfeefIpeReiIxfelnf9IX//1Z7c1VzZ2SymT06kBc4aF4yX8ScbjuSFRBr/uIsaDXrZ7I9Px9j1Xmw0Nx1Qa9Cg/FdfOmneroDJ/4zgAAYEJKMx2WGGOMqgNetdaH1FwdkM9Tmn/tNUGvPvP20/T9a5fqgnm1kqQtLx3SDRu36bsduzWcq5o7ZTieUm8kppFRZ+eRL611IcWOai8ZS6bVUhealudfv7lLXrdRyOdQjrShAAAgAElEQVSRMdlbr9to/eauaXl+AABmgtJMhSWs0u9RS11Is2sCChxV9SwVCxsr9I2rz9WX37dYc2oCSmes7t/eq4/esUW/fGafo9XpVCajA4NxhQdLv0q+dkWbkmmraCJ78ms0kVIybbV2Rdu0PL/TlXkAAGYCwrhDQj6PTqkN6pTaYEmudTbG6K2nNurOjy3Tx9+2UEGvWwOxpL754C79zQ+3a0d3v6PzGx5NqScS1VA86eg8pmJle7PWrVqs5qqABmJJNVcFpnXzptOVeQAAZgI2cBaJ0VRaA9Gkhkt0iUXf8Kh+8IeX9JudB14fu+z0Jq1d0abZNQEHZ5Z949NQ6SvZNftO6egM6/P379BQPKVUJiOPy6WqgEffuPo8NnECAHACbOAsMX6PW83VAbXWh1QV8BbFiZeT0VDp1xeubNd3P7JEZ83JHg70+xcP6mMbtuqOR196U4V1OkUT2bXkA7HSrZI7xUqSyX4SIpP7HgAA5A2V8SKVSmc0GE+V5AFC1lr9LtcSr284IUlqrPTpxhVtent7s6NvNII+t5oq/fJQJT+hYmitCABAqaIyXuI8bpfqK3yaVx9SfYWvpI5+N8boHWfO0sbrluuvLp4nr9voteGEvvpApz59z9PqfHXQsbnFEmn1RGIluxxoOrGBEwCAwiOMFzmXy6g2lA3lDZV+eVyl858s6HPr+rcu1F3XLdeK0xslSc/tH9RNP3pKX/91p/qGRx2ZV8ZahXMdVzIl3nGlkNjACQBA4ZVOspvhjDGqCWYPEGoqsQOEZtcE9L/eu1jf/Mvz1NZUIUn6zc4DuvaOrbpny14lUs6cTprtuBJTLOHcevZi5nRrRQAAZgLWjJewkdGU+mNJjTq4OXKy0hmrB57dr9v/8JIGc4cEzakJ6KaVi/SWRQ2OrSevCXpVX+F70/PP9OPgx15/TySqlhn4+gEAOFkTXTNOGC8DsURa/bFESVV4h+JJbXzsFf386TcOCbpwXq1uuvxULWyscGROPo9LTVV++T3ZddJjx8F73UZBr1uxZFrJtJ3WXt8AAKA0sYFzBgn63JpTkz1AqMJfGgcIVQW8+uTlp+oH116oZQvqJEnb9/br4xu36du/26VBB9oQJlIZ7euPqz+a7QDDcfAAAKDQCONlJOB1a1Z1QC11IVUGPCXRq3x+Q4W+9oFz9NX3n62WuqAyVvr50/t07R1b9POneqf9SHtrrQ6NJLSvP6a9h0boJgIAAAqqNMqomBSfx6XmqoBSoYz6Y0kNxbMb8IqVMUYXtzXowvl1+tlTvbr7sVc0GE/p2w/t1qYd+/Spy0/VBfPrpnVO8WRaTVUBDUQTqgx4Xx+nm8jkzPQ19wAAnAiV8TLmcbvUWOnXvPqQakM+uYq8Uu51u/SXS1t11/XL9Z5zZstIerkvqs/d/4z+6Rd/Um9/bFrns3ppq+KpjAZjCWUyGbqJTNLYmvvwUFy1Qa/CQ3HdvGmnOjrDTk8NAICiwQbOGSSTsRqMJzUYSymVcaad4GS8eGBItz68W8/2Zg8J8rqNrr6wRR+5aN4Rp0IW0pauQ7p3a7cODMbUWl+hm1YuorI7Qdfc9rhe7hvWYCylRDojn9ul6qBHCxoqOcETAFD26KYyjpkcxsdYazU0mtJANKlkurhDubVWHS8c1PrNXQoPZQ8Jqq/w6eNvW6g/O2vWtFf7q4NeNRyjBSLebOlXHtRANCmXy8gYydrsG8KakFfb/vHPnJ4eAAAFRTcVjMsYo+qAV631ITVXB+TzFO+vgTFGl7c3a8N1y7Tmkvnye1w6NJLQ13/9gj7546f03L7BaZ3PYCyp3v6YRlOl00bSKYlURjKSyxgZmewbJyPHDnkCAKAYFW8Kw7So9HvUUhfS7JqAAkd1DikmAa9ba96yQBuuW6bLz2iSJL3w6pA+dc9T+uoDz+tgrmo+HcZaIA5Ep7/9YinxurOfHmQyVtZaZXKdcXxuPlUAAGAMYRySpJDPo1Nqs73Kp2s99smYVR3QP/35WfqXD52n05orJUm/fT6sNXds0Q8ff2XaTiO11qpvZFT7B2JKFflSH6ecPqtaDRU+edxGaWvlcRs1VPh02qxqp6cGAEDRIIzjCAGvW7NrAppbF1RlER8gdG5Lrb77kQv0+XeerrqQV/FURnc8+rKu27BNm188OG2tHGOJtHr7YxoeTU3L85WStSva5PNkf5/OmFWl2TUB+TxuutEAAHAYNnDiuJLpjPqjSQ2PFm+v8pHRlH74+Cv66ZO9SuWWQpzfWqNPrjxVi3LV8+lQGfCoscIvl4tlGGPG+oz3RKJqoc84AGAGoZvKOAjjJyeVzmggd4BQpkh/Z3oiUf1rR5ce6+qTJLmM9N/OnaPr3rJAtSHftMzB43Kpudpf1OvvAQBA4RHGx0EYn5p0xmowltRgPDntR9VP1NaXD+m7D+/RK4eyx9ZX+N1ac8kCXXX+KfK4p2dlVk3Qq3paIAIAMGMRxsdBGM+PTMZqKJ7SQCxZlAcIpdIZbdqxTxv++Mrr67nn1Yd008pFWr6wflrm4PO41FxV3K0jAQBAYTjeZ9wY02qMedgY87wxZqcx5jO58XpjzIPGmF2527rcuDHGfNsYs9sY84wx5oLDHmtN7vpdxpg1h41faIx5NnefbxvKkNPG5TKqCXnVWh9UY5Vf3mmqOE+Ux+3SBy5o0d3XL9eq806Ry0h7D0X1xX9/Vl/62bPqzlXNCymRyqi3P0YLRAAAMK6CVcaNMXMkzbHWPmmMqZK0XdJVkj4m6ZC19mvGmC9KqrPWfsEY8x5Jn5b0HkkXSbrFWnuRMaZe0jZJSyXZ3ONcaK2NGGO2SPqMpMclPSDp29baXx1vXlTGC2d4NKX+aKIoD3XZc3BYtz68R09390uS3C6jDyyZq49eMn9ausYEfW41VfqnbZkMAABwluOVcWvtfmvtk7mvhyQ9L2mupPdJuit32V3KBnTlxjfarMcl1eYC/bskPWitPWStjUh6UNKVuZ9VW2sfs9l3FBsPeyw4oJgPEFrUVKn/88Fz9b9WnaXZ1QGlM1b/tr1H196+Rb98Zn/B17/HEmn1RGiBCAAAjjQtZTpjzAJJSyQ9IWmWtXa/lA3sksb6nM2V1H3Y3XpyY8cb7znGOBxWrAcIGWO04rQmbbhumf760oUKeF3qjyX1zQdf1Cd++KR29PQX9Pkz1io8GFd4MF60m18BAMD0KnhSMsZUSvqppL+11g4eZ1n3sX5gT2L8WHO4UdKNkjRv3rwTTRl5kj1AyK3RVFoDuV7lxcDncenDF83TOxfP0g8eeUn/9dwB7T44rL+7b4dWnt6ktZe1aVZ1QJK0peuQ7t3arf2DMc2pDmr1slYtb5vaBtDh0ZTiyYwaq3xF9WYFAABMv4JWxo0xXmWD+I+stf+eGz6QW2Iytq48nBvvkdR62N1bJO07wXjLMcbfxFp7m7V2qbV2aVNT09ReFCbN73GruTqg1vqQqgLeomn311jp1xff3a5bP7xE7bOrJEkdLx7Umju3asMfX9YfXnxNtzy0S30jo6oOeNQ3MqpbHtqlLV2HpvzcqUxGrw7EFR6KK0OVHACAGauQ3VSMpNslPW+t/eZhP9okaawjyhpJvzhs/NpcV5WLJQ3klrH8RtI7jTF1uc4r75T0m9zPhowxF+ee69rDHgtFyOt2qanKr9a6oKqDxRPKz5xTre98eIm++O52NVT4lEhltPGxV/TlB55TIpVWwOOSkVHQ65bHZXTv1u4TP+gEDcdT6onEFE0Ux6cGAABgehXyM/K3SvqopGeNMU/nxr4k6WuSfmKMuUHSXkkfzP3sAWU7qeyWFJV0nSRZaw8ZY74saWvuunXW2rHS5CckbZAUlPSr3B8UOY/bpcZKv2qDXg3EkhqMp+R0v3uXMXrnWbP0tlMb9eMte/WTbd1Kpq36RpIaSaTVXJk9VTPgdenVwVhen3usSl4V8KqhwieXqzjepAAAgMLj0B84Lp2x6o8miiKUj9nXH9Mnf/yUBmJv9AivDnhU6feouSqgb37ovII8rzf3RiXoK65uNAAAYHIcb20ITJTbZdRQWVzLV06pDeofrmxXfYVXXnd2PoPxlPYPxHVKbUDJdGF6qSfTGe0fiOm14dGieWMCAAAKhzCOojG2fKW1LlgUGz2Xt9Xr79/ZrrNmV6s64JHbZWQlPfCnV3XDXdv02J6+ggXmwVhSPZGY4sl0QR4fAAAUB5apoGgl0xlFogmNjKaLoko8GEtq42Ov6OdP92qsAcqyBXW6aeUizW+oKMhzbuk6pPuf7NH+gZjm1Vdo7Yo2rWxvPvEdAQCAoya6TIUwjqI3FsqH45PvOFKIPuEv943ouw/v0bZXIpIkl5GuWjJXay6Zr6qAd0qPfbgtXYd0y0O75HFlO7kkMxmlM9K6VYsJ5AAAFDnC+DgI46UrkcqoPzbxUH54mA14XYonM0plrD5zxWlTDuTWWj3W1ad/7ehSb3+2u0p1wKPr3rpQf37uHLnz0BHls/ftUG//iIZH00qmM/K6XaoOeLSwsVL3rr1kyo8PAAAKhw2cKDs+j0vNVQG11IVU6feccE35vVu7X68q57tPuDFGb1nUqNvXLNWNK9oU8rk1GE/plt/t0tq7t+vJvZEpP8crh0YUGUkqlbFyuYxSGau+4YReODCk0RRryQEAKAeEcZQcn8eVPdGzLqiaoFeucUL5/sGYAt4jf8Xz3Sfc53Fp9bJWbbx+ud599mwZSV2vjehz//aMbv7FTu3rP/nnSqQyksn2QDcy2ddpsuP7+uOKjCSKYi09AAA4eYU89AcoKI/bpYZKv+pCPg3FUxqMJ49oOTinOqi+kVEFvW/07I4nM5pdHcz7XOorfPr8u87QqvNO0Xce3q2d+wb1h92v6YmX+vSXS1v14eXzJt073Os2Gk1JmYyVMdJY7va5jay1ikQTiibTaqr0y+c59vvqjs6w1m/uUnckqta6EBtAAQAoMlTGUfJcLqOakFet9SHNqg4okAvfq5e1KpWxiiXTssrepjJWq5e1FmwuZ8yu0rdXn6//+Z52NVX6lUxb/eiJvbr2ji36r+cOKDOJSvaChkrVBr3yuI0y1srjNqoNejW/ofL1a0aTafX2xzQQTb7p/h2dYd28aafCQ3HVBr0KD8V186ad6ugM5+W1AgCAqSOMo6xU+D06pTaoU2qDuuLMZl151iwdGkloz8ERHRpJ6MqzZk158+aJGGP09jNnacP1y3TtxfPl87jUN5LQ137VqU/f85Se3z84ocdZvaxVXo9bjZV+LWysUGOlX16P+01vJqy16hsZ1f6BmFKHfTKwfnOXvG6jkC+7vj7k88jrNlq/uSuvrxcAAJw8wjjKUsDr1nP7BvXbzrCaqvxa1FSp+gqffv3cAW3pOjQtcwh63frYWxdow3XLtPL0JknS8/uH9MkfP6Wv/apTrw2PHvf+y9vqJ/VmIpbIVsmHR7PdZroj0SOW6IzNqScSzcOrA8pfR2dY19z2uC79+kO65rbH+VQJQEEQxlG21m/uks/jUlXAK3/u1uvOTzeVyZhdHdDN7z1L3/rQeTq1KbvE5L+eO6Br79iiHz+xN7tR8xi2dB3Sr587oPoKnxY1VUzozUQ6YxUejCs8FFdLbVCxo07wjCXTaqkLTXjuhBHMVCzzAjBdCOMoW4dXho0xcruMqvweHRyKy+Oanl/9LV2H9Nn7duia7z+uux59Rde/dYE++2enqzboVTyZ0Q/+8JKu27BVj+x67U2dUabSmnE4ntJfXNCigWhCuw4M6fn9A9p1YEiDsaTWrmib0NwJI5jJWOYFYLoQxlG2WutCb6oMx1MZzWuoUGt9UI1VfnndhfsnMHboUN/IqKoDHvWNjOr/PrxbzZV+bbx+uT54YYvcLqP9A3H986ad+tz9z6jr4PDr959qa8Z0xiptJatcyDfSZBohEkYwk7HMC8B0IYyjbK1d0aZk2iqaSMna7G0ybbV2RZuMMaoOeNVSV7hQfrzKdmXAo0+sXKTb1yzVRQuza8Cf2tuvG+/ern/57S4NxJKaUx1UPHnkEpbJtGa8d2u3Kv0eza+v0KKmKi1qqlRN0DvhME0YwUx2rDfzk13mBQATQRhH2VrZ3qx1qxaruSqggVhSzVUBrVu1+Ig+24eH8qY8h/KJVLbn1Yf0/37gHH31/WertS6ojJU27dina+/Yotb6oJLpzEm3Zjz8+a21SqYz8rldEw7ThBHnsWbfOcd7Mw8A+cShPyhrK9ubJ3TIjTFGVQGvqgJeDY+m1B9NjLuxcqImc+jQxW0NunB+nX7+9D5tfOxlDcVT+o9n9qu5yi+f26WheEqzq4Navax1wq0Z3/T8VhpOpNRU5VcqnZHnBG881q5o082bdiqaSCnodSuWTBNGptHYmn1vrr/82Jr9dRIHN02Dle3NWqfscq2eSFQtHJoFoEAI48BRKv0eVfo9iiZSikSTGj2qOjxRq5e16paHdimWTCvgdSmezBy3su11u/TBC1v0jjObdeejL+s/n9mv8NCowkOj8ntcqgv58vL8f3lhq3r7Y2qs9KvCP/7/BBBGnHX4mn1JCvmyv5PrN3fx32CaTPTNPABMhTm6g0O5W7p0qd22bZvT00AJiSXSikQTip9EKN/SdUj3bu3Wq4OxSVe2f/5kr763eY8S6Tf+jVb43Pr8O8/QijOa8vL8lX6PGir9crvM5F5YiejoDGv95i51R6JqLbE3E5d+/SHVBr0y5o3/NtZaDcSSeuQLVzg4MwDARBhjtltrl57oOirjwAkEfW4FfcGTCuXL2+pP+sTPzbteU3OVX+mMdHB4VKmM1Ugira888Lz+LpnWuxbPksscP0Sf6PmHR1OKJzNqrPK9XoEtF6W+zKO1LqTwUPyI/y6s2QeA8sMGTpS1fG6AC/rcOqU2qFNqgwr63Ce+wxTtH4wp6HOrKuDRgoaQGip8MpJSGatv/OYF3fSjJ/Wn3oEpP08qk9GrA9mDgjKZ8vmkrNRbM7KBEABmBsI4ylahDq0JeN2aU1P4UH54a0OXMWqo8Gl2TUB1Ia8k6cUDw/rv9z6t/+c/n9fBodEpP99wPKWeSEzRRGrKj1UMSr0140S6AQEASl95fS4NHKbQG+DGQnk8mVZ/NJn3EHusDZiS9IV3tSvkd+vWh/fohQND+l1nWH/Y/ZquWd6qDy1tld978m8QxqrklQGPGiv8cpXwWvJyWObBBkIAKH9UxlG2pqsyGvC6NbsmoFNqg8ftTjJZy9vqdeVZs3RoJKE9B0d0aCShK8+apeVt9Tp7bo1u/cgS/f27zlBdyKvRVEYb/viK1ty5VR0vHNRUN2aXQ5WcZR4AgFJAGEfZmu5DawJet2ZVBzS3LqjKPITyLV2H9OvnDqi+wqdFTRWqr/Dp188d0JauQ5KyS1euPHu27r5huVYva5XXbRQeGtW6Xz6nv71vh3YdGJrS849VyQ8OjZbkWnKWeQAASgGtDVG2Du+mcfihNdMVyBKpjPpjCY2Mpk+qUv3Z+3aoJzKikURayXRGXrdLFT63Wuoq9M0Pnfem63sjMX3v93v06J4+SZKR9J5z5uj6SxdMukf50Twul5qq/NOycRUAgHJAa0PMeE4fWuPzuNRcFVAqlNFALKnBeGpSofzlvmENj6ZkZOQyRqm0VX8sqXRm+JjXz60L6stXna1tLx/SrR179EpfVP/57H51vBDWtZfM11VL5sp7glM3x5PKZLR/IKaqgFcNFb5pW0teyn3CAQCYCCrjwDRJZ6wGY0kNxpNKT2DZx3v/7x80mkrL7XojQKczGfk9bv3Hpy894XNt2rFPG/74sobi2XXfLXVB3bRykS5ua5jS6/C6XWqsnFiVfCph2ulPNooBb0YAoHRNtDLOmnFgmrhdRnUVPrXWhVRf4TvhqZc+j0uyUsZaWVllrJVsbnwCz/X+JXO18frluur8U+QyUk8kpi/97E/64k+f0d6+k9/Emkxnq+QnWks+1daSpd4nfKoK1ZoTAFBcCONAAR3r0CGXy6g25NO8+pAaKvzyuI79z3B+fYXqKrzyuIwyGSuPy6iuwqv59RUTfv6aoFf//e2n6fvXLtUF82olSVtejuiGjdt068O7NRw/+W4pQ/HkcTuuTDVMl3qf8Kma6W9GAGCmIIwDBdLRGdan73lST7zUp55ITE+81KdP3/Pk65VNY4xqQl611gfVUPnmUL56Was8brcaK/1a2Fihxkq/PG63Vi9rnfRcFjZW6BtXn6t1qxZrTk1A6YzVT5/s1Ufv2KJfPrNvQstmjuXw0zuPfoyphunp7oZTbGb6mxEAmCkI40CB/OPPntHQaFpjGTVjpaHRtP7xZ88ccZ0xRjXBbChvrHojlC9vq9dnrjhNDRV+DcVTaqjw6zNXnKblbfUTnsOWrkP67H07dM33H9f/+Mkz8rlduvNjy/TXly5U0OvWQCypbz64S3/zw+3a0d1/3Pt/9r4dr7dVPFq2L3lUw6NvVMlb60LqGxlV18Fhdb46qK6Dw+obGZ1wmJ7pfcJn+psRAJgpCONAgfQOHPuI+vHGjTGqDmRDeX2FTy5jtLytXt/80Hn68ccv1jc/dN6kg/gtD+1S38ioqgMe9Y2M6paHdunpvf368EXzdNf1y/SuxbMkSXsOjujvfrJD//s/ntOrA/Hj3n+8QJ7OWIUH43p1IK5UOqNL2uoVHkookc7IZaREOqPwUEKXTPA1rGxv1tUXzNXBoVE9/+qQDg6N6uoL5s6YDYwz/c0IAMwUhHGgQMZb+HGiBSHGZNeUt9aHVBP0ypiTayN479ZueVzZTiRG2VuPy+jerd2SpMZKv75wZbtu/fASnTWnSpL0+xcP6mMbturOR1/Sj57Ye9z7jyeayJ7e+ciu19RU6ZPP7VLGSj63S02VPj02Tpg/WkdnWPc/2aumKr/OnF2lpiq/7n+yd8ZsYOTQIgCYGegzDhSI0bGD90Sjtdtl1FDpV3XQq0g0MenNlvsHY6oOHPlPPOB16dXB2BFjZ86p1revWaKHcm30+oYTuvvxvXIZqanKr4DH9fobgmPd/1gy1mpvJKqagFcNlX65cve31k54zfPhGxglKeTzKJpIaf3mrhkTSFe2N8+Y1woAMxWVcaBA5tb4JzU+Hq87e3jQ3LqgKv0Tf/88pzqoeDJzxFg8mdHs6uCbrnUZo3ecOUsbr1uuj1w0T163UcZKBwZH1d0fUzy3dnm8+4/3/Nne4Bml0hlZaye15pkNjACAmYAwDhTIV95/rqr8bo21E3cZqcrv1lfef+5JPZ7f41ZzdUCt9SFVBU68fGX1slalMtkAbJW9TWXscbuxBH1u3XDpQm24bpnOOaVaUjaA743E1Nsf02gqM+FuLq8/fyKtVCajwXhSiVRmwmue2cAIAJgJCONAgaxsb9bH39amSr9HbpdRpd+jj79t6icoet0uNVX51VoXVPVx1pRPpRvLnJqgbrlmiT5+6UIFvNn/mRhJpNUfS2rPa8NKpDIneITs81951iwdGkloz8ER9Q0n9I72Zp3bWquJnPzLBkYAwExgJvJ/iuVk6dKldtu2bU5PAzPAdB3nns5YDcSSGoonT7pf+Ike/4Fn9+v2P7ykwdy69VNqA/rEZYv0lkUN474ZGOvG4nEZBbwuxZMZpTJWn7niNL31tMbsevSjlqEcbew4+J5IVC0cBw8AKCHGmO3W2qUnvI4wDhTGNbc9rpdeG9ZQPKVEOiOf26WqgEcLGyt1z40X5/35MhmroXhKA7GkUpkTV64nayie1MbHXtHPn37jkKAL59XqpstP1cLGN58K+tn7dqhvZPSIdd+xZFoNFX5980PnSZJqQz7VhU6+YwwAAMVqomGcZSpAgbx4YFAHh0cVTaRzyy3SOjg8ql0HBgvyfC7XGyd6NlcH5PPk9593VcCrT15+qn5w7YVatqBOkrR9b78+vnGbvv27/5+9Ow+Pq7wS/P9971KrqrRZsmxLXmQbzOoAtlnieCF0QtIPSaeHJDgJS0gCSaCTXtKTnp5fkwk93b8w3Z1pMiEEhyVAFkjoTEIWkg4xxhAwXgADBoNteZFXbSWp9uXeO3+USpZslVVySVUl6Xyex4/sS711r4xVde6p856zm/54etjjj/bHB0tcck7uxtIbS3EodGKDqBBCCDHdSGtDIU4jVybRHorRMsYyiXjKxhqSoHYAy4ZYavyz1kMpla1Pr3IbxFMWvfEU8dT4Bbvz6v18488v4KV9PXxn414OheL8/NUjbNjVwU1XzOeapbPRNcWsoPeUzPhI3VjSls2R3rhkyYUQQkxLkhkXIo9czXdHOEGN16QjnOCOJ3cWPHQmaY0cdOc7PhG8Lp1Z1V5m13gH+3WPB6UUl7XW88CNy/j86lb8Lp3+RIZvbdjD5x7ZxvYDIa5b3kIkmWF/d5S9nRH2d0eJJDN5u7FIllwIIcR0JMG4EHkMHTqjVParqSvu29RW0Ho7z36MfMcnksfUaaoee6/y0Zi6xseWtfDIZ1bwwQuaUMD+7hh/+8RrPLL5QLa2XIFSFDTtKJcl744kC+q4IoQQQkx2EowLkUexQ2f0PMFnvuOlkOtV3lzro8ozfkF5rc/FV953Nt/91MVcMKcagDeP9tOfyOB3Gcyv8zO/zk+V2+Cxre2jPl9fPC1ZciGEENOCBONC5FHs0JlFDVVonEgIK7I/cIsaqgq+ho27Oli3fjMr79rAuvWbCy6RGY3LyE71bKkb36B88cwA//7xpfzDn54zOOwoFEuzrydGXzyN21DDNnCeTi5L3hlOYk9Ay0YhhBCiEkgwLkQexQ6d+bsPnENdlQu3qWHqCrepUVfl4u8+cE5B64utWS+EqWeD8vHMlCulWLukkfNnVRP0GCiyvcqPh5Mc7IkTcJtjer5wIpsljyYz43J9QgghRCWRYFyIPNYsaeTOD51HY8BDXzxNY8AzpoE9a5Y08q/XLj1eK+IAACAASURBVOWillqagh4uaqnlX69dWvD6YmvWxyKXKW+u9Y1bTfknLp2LrikM7cSnAynLYXdnhH/+zVt0hpMFP1fGtjnen+B4f4JMCTfACiGEEBNNWhsKcRprljQWNfGxmPXtoRg13uFZ5LHUrJ8Jl6HRGPRQk7HpjaWIjEM2WmkKnexGTscGy4Gn3+rg+d1dfOLSuXz0kmbco0zizIkmM8RTFrV+F9XesWXYhRBCiEokwbgQE6iYPuUttT46wolhLQnHUrNejPEIyh/b2k6V26Chyj14LJbKoJQikswQiqV58I/7+c3rx7h1dSurFs8oqMe47Th0R5JEkhlmVLlwG4UF8kIIIUQlkjIVISZIsTXfxdasj4dcUD6n1ot/jOUrI03g9Lp00pbNIzev4OPLmjE0xbH+BF//5Zv8zU93sLcjUvDzJ9MWR3oT0gZRCCHEpCbBuBATpNia72Jr1seT29CZOcagfFbQSyI9vL47N4HT7za4dfVCHrxpGZe31gPwansft/5gO//76XfojaUKOofjOINtEGMp2eAphBBi8lHTLaO0bNkyZ9u2beW+DDENrLxrAzXe4ePdc8Hjc1+9soxXVrxUxqY3niKSyB8Ab2nr4e4NuzE0hcfUSKRtMrbDl69czIrWumGP3bq/h+88s5cDPdl6+Cq3wY1XzOPDS2dj6IXnDKrcBvVVbnStjM3chRBCCEAptd1xnGWjPU4y40JMkGL7lFeyoX3KAx5zxFrvFa11fPnKxdT73YQTGer97hEDcYDl8+v43g2XcPvahVS5DSLJDPc8s5fPPrKdLft6Cr6uSDLDoVCM/kS6qO9PCCGEKBXJjAsxQTbu6uArT+wgksxg2Q66pqhyG2NqbzhZZCyb3niacCJTdP12XyzNQy/s51evHSE36+ey1jq+sHohLXWF38h4TJ0ZVW5chuQchBBClF6hmXHppiKmtGK6mYwHBeBky1NwFFO1eMLQNWZUuanxmkUH5dU+k7+8ajHXLJ3FPc/s4dX2Pja39bBtf4iPXDSH6y+fV1Av9ETa4nBvnGqvSa1v5Oy9EEIIUW6SGRdTVq6biakrvKZOPG2RtpySbYJct37zKa0JY6kMjQEPP77lsgk/fzllLJtQLE0kWVym3HEcntvTxXc3tnGsPwFArc/kMysX8P7zmgquDTcHbha8LmmDKIQQojSkZlxMe6WcYDmS9lAM70nDbCZ6aE+lMHSNhoCb5lovVZ4z/wBOKcWqxQ18/9PL+czK+XhMjVAszb/+5zt84Ycv89qh3oKeJ23ZHO2L0xFOYNnTKwEhhBCiskkwLqascgfDU3kDZ6FMPbvRs7nWV1BpST4uQ+OTl87jkZtX8L5zZwKwpyPCXz6+g3/81ZscH8iajyaSkA2eQgghKosE42LKKncwXAlDeypFbnhQc62PKo9xxvXbM6rc/N0HlnDPJy5iSVMAgGfe7uSmh7by/Rf2kzjp//dILNuhK5zkSG+cVMYe9fFCCCHERJKacTFllbtmPHcN921q41AoRnMZNpBWqrRl01tkTbntODz9Vgff29RGdzQ7JKgx4OaWVa2sPbsBpRRb2np4bGs7R/vjzAp6uW55y7DWikoparwmNbLBUwghxDgrtGZcgnExpU32YLjc3WAm2ni0RIynLH605SA/2dZO2so+x/mzg6w5q5H/eOVQQUOHZIPn1DTVf36EEJVNgvE8JBgXk0UlZPZLZTyC8iO9ce7b1MZzu7sGj/ldOjODbgwtW5EXT1vU+9188+NLR3yOKrdBnd81pqmfojJNp58fIURlkm4qQoyDjbs6WLd+Myvv2sC69ZvZuKujZOcudzeYUsr1KW+p9RL0nlnJyOwaL1//0Hn860cvZMEMPwDRlMX+7hg9sRSO4+AxNY71x/M+R3aCZ5y+WLro4UWivKbTz48QYnKTYFyIPHKZtY5wghqvSUc4wR1P7ixZQF7ubjDlMB5B+cVza1l//SU013jRFNgOdEVS7O+JEYqmmRnwnHa97Th0R5McCsWJp0bfECoq03T8+RFCTE4ygVNMacXUjA7NrAH4XAaxVIb7NrWV5GPullof+7sj9MczpCwbl64R9BrMr6+a8HPnlKvmduhEz55YikgiM6b1uqa4fe0i/vfT7xBNZYgksyUKXdEUtX4XB7qjzKv3n/Y5cr3JpXRlcmqp9Z0ydGu6tRYVQkwO8u4ipqxiM9vlzqxd3lpHRzhFyrLRFKQsm45wistP2nw4Ucbjk4Fiy3yMIX3K/WPsU76itY6/uuosFjUEmOE3CQys390R4TMPb+Pbz+whXEC/cSldmZyktagQYrKQzLiYsorNbI9HZq2YzPKLbT00VLkIJ05kxgMegxfbevhSwVdw5or9+xu6gW5oMH8njDm77jI0ZgY9JNIWoViq4PKRFa11g51THMfhhb3d3PvsXo70JvjZy4d5+s3j3LxyAX96wSx0LX9JTK50pT+RpiHgxmNK15VKt2ZJI3fCpO6mJISYHiQYF1NWeyhGjdccdmwsme1bV7Vyx5M7iaUyw7oxFJpZKzYYbQ/FmFHlpmFIjbPjOCXLzBf79zcRZT4eU2dWtZd4yqInliJZwJCfHKUU7140g+Xz6/jZK4f5weYD9Ccy/PvTu3lyxxFuW7OQi+bWnvY50pbNkd7Sla5Ia77irFnSKH9fQoiKJ2UqYsoqdgLnmiWN3Pmh82gMeOiLp2kMeMbUFq3Ybg7lniBa7PknsszH69KZU+NlZtCDyxjby5jL0LhueQuP3LyCD5zfhALaOqP8zU9f4388uZOjffm7reSUonSl3BuIhRBClIYE42LKGo+a0TVLGvnxLZfx3Fev5Me3XDamLFuxwWi5a16LPX8pbib8boPmWh+NQQ/mGLPUdX4Xf/v+s/nOJy/mvNlBADbt7uKmh7bywPP7Ri2FyZWuHO6NkxhDhr5Q0ppPCCGmBwnGxZRVbGa7WC21PrqjSdo6I+w61k9bZ4TuaLJkmfliFXv+W1e10hVJ8sbhPl4/3Mcbh/voiiQn5Gaiym3QUuejIeAec1B+dlOAb133Lv77B5fQUOUmbTn88KWD3PDQFn7/5nHsUTLfqUy2dKUznMSyxy9LXu4NxEIIIUpDasbFlFbOmtHLW+vYsr8HTTGsG8q65YV3Qyl3zWsx53/tUC/98eEtCfvjGV471Dth31PAY1LlNogkM/TG0qQtu6B1Sinee85Mrlg0g8e3tPPYtna6Iyn+/6d28fNXD3P72kWcMyt42ucIJ9LEUhnq/C4CHvO0jy2EtOYTQojpQTLjQkyQF9t6CLh1LNshmXGwbIeAW+fFtp5yX1pJ3P/8Pgxd4TF1vKaOx9QxdMX9z++b0PMqpQh4TJprvcwYY6bca+rc9O75fP/Ty1lzVgMAbx0Nc9uPXuEbT+2iK5I87XrLdugMJznSGyeVKexGIJ9ylykJIYQoDQnGhZgg7xzvJ5qyMDUNj6FhahrRlMXu4/3lvrSSiKYsTu4WqKns8VJQShEcEpQbWuEvd01BD3dccy7//vGlLGrMDln6zzePc8ODW/jRSwdHDbQTaYvDvXG6I0nsMyxdKXeZkhBCiNKQMhUhJkjacrBtBwsHxwGlQAEpa3oMjvG7su0ghwbktpM9Xkq5oDzgNggnM/RG02TswrLWFzbXcO8nL+a3bxzjgef30RtPc//z+/j160f5/OqFrFxUj1Ij9yd3HIe+eJpo0qLWb55R6Uq5y5SEEEJMPMmMCzGBLAdy+/8cJ/vn6eKzKxdgO5CxbWzHHviaPV4OuaC8pc5Lvd992iE/Q+ma4k8vnMUjn1nBRy9pRtcUR/sSfO3JnXzliddo64ycdn3GtgdLV5KZ0nwqIIQQYvKQYFyICaQpcDjxq8D4b0r40lVn8eUrF+E1dTJ2th77y1cu4ktXnVXW61JKUe0zmVvno87vKjgor3IbfGHNQh64cRmXDUz1fOVgL7c8up27n95NXzx92vWJtMWR3kRRpStCCCGmHjVRAysq1bJly5xt27aV+zLENHD+154ikjy1HCLg1nj96x8owxWJkdh2tpykL54+pY3hlrYeHtvaztH+OLOCXq5b3sKKgUD8pX3dfOeZvbSHskOCAh6DGy+fz4eWzhp1MqeuKWr9LoLj0HVFCCFEZVJKbXccZ9loj5PMuBATRFPaYFtDBSd+r+THrpJoA4FxS52Paq85WAO+pa2HuzfspjuaJOgx6I4muXvDbrYMdMO5dEE9D9y4jC+uWYjfrRNOZPj2M3v43KPb2bb/9B1zLNuhKzxxA4OEEEJMHhIVCDFBXIaGrhSmruE2NUw9++exjm+fzDbu6mDd+s2svGsD69ZvruhR7rqmqK9y01zrxe82eGxrO4am8Jo6iuxXQ1M8trV9cI2ha1x7STOP3ryCay6chQIOdMf4r//xOv/9/77B4YGseT7JtMWR3jgd4cS4DgwSQggxeUyfqECIElvcGGBGwIWhKSzbwdAUMwIuFjcGyn1pJbFxVwd3PLmTjnCCGq9JRzjBHU/urOiAHMDUNWYGPXRGEqdMwPSYGsf6Tw2wa3wu/upPzuK+6y9haXM1AC+2dfPp729l/aY2osnMKWuGiiQytPfE6IulmW6lg0IIMd1JMC7EBLl1VSumrtNU7eHsmQGaqj2Yuj5thrbct6kNU1f4XAZKZb+auuK+TW3lvrSCzK3zYzkOhq4Nlq4k0jZNQW/eNYsaq/jmx5bytWvOZWbQTcZ2eGxrOzc8uIWn3jh2Sk36ULbj0B1NcigUJ5Y6ffAuhBBi6pBgXIjTKKbMYs2SRq69eA6d4SRvHQvTGU5y7cVzpk3f6PZQjIxl09YZYdexfto6I2Qsm0OhWLkvrSC5CZjJjIWhQcqyydgO1y1vOe06pRSrz2rg+zct59Pvno/H0AjF0vzL797miz98mTcO9512fdqyOdaX4Ghf8VM8hRBCVD4JxoXIo9gyi427Onji5cM0BNyc0xSgIeDmiZcPV3yZxngJuA0O9ybI2A66psjYDod7E1S5J8essaETMPsTGWZVe/nHDxc+AdNt6lx/2TwevnkFV52TXfPO8QhfeuxV/unXb9EZTp52fTxlcSgUoyuSlHpyIYSYwibHu6IQZXDfpjZSGYvuSIaUZePSNQIeg/s2tRUUkA0t0wDwuQxiqUzB6ye7wdrnXBzpnHR8Esg3ATOazNATTZG2Rs9cNwTc/P0Hz+FDS2dzzzN7eft4mD/s6uCPe7pYt2IuH1vWjNvMP5W0P54mkshQ63MR9Bp5J34KIYSYnCQYFyKPd47305/IoKHQlSJjOXRHU2Ss/oLWt4di1HiH95H2mvqkKdMoViRlMafGQ1ckNXgz01TlJpoqvJXfxl0d3LepjfZQjJZaH7euaq2IGxm/28Dn0gnFsv3JC7nBOH9ONfd88iJ+t/M49z/XRiiW5qEX9vPr14/y+dULWX3WjLyBdq6evD+RZkaVG68rf/AuhBBicpFgXIg80gOz67WBCY1KZQfEpAqcad9S66MjnBjMjAPE0xbNtb7xv9gKlPv+WxuqBo/FUhkaA56C1ufKhExdDSsTuhMKDsgnMphXSlHndxHwGHRHUgVtutSU4gPnN7Fq8Qx++NJB/uPlQ3SEk9z5qze5YE41t69dyOKZ+bvtpC2bo31xqtwGdX7XqMOFhBBCVD55JRciD5ehgZPNSjo42U4YDgX3Cc9tAIylMjhO9mvacqZNN5Viv/9iu7GUqrWiqWs0VXuYGfRgFhgc+90Gt6xq5cEbl/PuhfUAvH64j8//4GX+7T/fIRRLnXZ9JJnhUChObyw1qcp+hBBCnEqCcSHyKLZP+NANgH3xNI0BD3d+qPANgJNdsd9/eyh2Sp/vsZT5lLq1ot9t0FzrpdbnKriue06tl3/8s/P5X//lAubV+3CAX79+lBse2MJPt7Wftibddhx6oikOheLEx1D6I4QQorJImYoQedy6qpU7ntxJU7WB19SJp60xZ7bzbQCcLor5/ltqfezvjtAfP7GBNug1mF9fNfpiylOzr5Si1u+iymPQE03x3Wf28JPth4inLbymzscuaeb6K+afsm7Z/Druv6GWX7x6hIdf3E84keHeZ9v41WtH+eLahVy6oD7vOXOlKz6XQa3fxG1IPbkQQkwmkhkXIo/pntkut8tb6+gIZzd/airb57sjnOLy1rqC1rfU+uiOJof1Oe+OJktSs2/qGo9vOcjDmw+QzFjoGiQzFg9vPsCjL+wfcY2uKf784jk8cvMKPvyu2WgK2kNx/tvP3uC//ex1Dvac/iYilspwOBSnI5wgU0CXFyGEEJVBMuNCnMZ0z2yX04ttPQQ9On3xDGkHNAXVXoMX23r4UgHrL2+tY8v+HjTFsGB+3fLCgvli3f/8PnQt24kHwFGAbfOT7YdGzI7nVHtNvvzexVxz4Sy+s3EvLx/s5aV9PWw7EOIjF83mhsvmU+XJ/9IdSWSIJi2qvSY1XnNwA7IQQojKJJlxIURF2t0RJpKwMHUNj6lh6hqRhMXujnBB619s66GhyoVL17AdcOkaDVUuXmzrmeArz4qmLDSVLV1RSqHI3hTE04XVd7c2VPEv117IP374PGZVe7Bshye2H+b6B7fwq9eOnHYQkOM49MZStIdi9MUKa70ohBCiPCQzLsRpVGqf6+kglbFBZdsBwkBrSeUUPCK+PRRjRpWbhiGtFB3HKVmfd79LJ5rM4GDhONnrVwPHTV0raGCQUop3L5rB8vl1PLH9ED986SB98TTf/P1ufvHqEW5fu4ilLTV511u29CcXQohKJ5lxIfIoVWs8MTJTzwbhtu3gOA72QCbYpRdWdtFS6zslC13KPu/vXdKA5YCd7YiJ7YDlwFXnNNJc66XOX3jXFZeh8YlL5/LIzct5/3kzAdjbGeWvfrKDr//yTY71JU67PrfJs6Nf6smnk427Oli3fjMr79rAuvWb5bVLiAolwbgQeZS6NZ4Y7qyZQer9LgxdYTkOhq6o97tYPDNY0Ppy93k/1p+i1meQK9nWFNT6DI71p1BKUeNz0VzrHTYU6mRb2nr468d3sO57m/nrx3ewtyPKV69ewnc+eRHnzsq22Hz2nU5ufGgLD/5x36glMJFkhvZQnFBU+pNPdZJMEGLykGBciDyK7XMtinPrqlZchk5TtYezZwZoqvbgMvSCg+lyd8NpD8WYU+PjvNnVXDCnmvNmVzOnxjfs38/QgUGGNvzleEtbD3dv2E13NEnQY9AdTXL3ht1saethSVOQ/7PuIv7+g0uor3KRthx+sPkgNz64haffOn7aQNtxHEKxbH/yaHL0qaFicpJkghCTh9SMC5HHdB9nX25rljRyJ9mg4lAoRvMZ1OyXsxvOWPqk+93ZXvahWIr+RDaT/9jWdgxNDd4Q5nrdP7a1nRWtdSiluOqcmbx74Qx+tOUgP9nWTlckxT//Zhc/f+UIf3HlIs5uyj+gKm3ZHO9P4DF16vwuPKbUk08l5eizL4Q4MxKMC5FHbuhPLJU546E/ojiTubXkWFsrapqivspNwGPSE01xtD9O8KQWhh5T41h/fNgxr0vnMysX8MELmrhvUxub3unizaP9fOGHL3P1eU189j0LqPO78l5nIm1xpDeO321Q53dh6vKB6VQgyQQhJg951RUij3KXOYjyK2YD3Jm2VnQZ2dKVeXV+kid1jkmkbZqC3hHXzar28j+uOY9vfmwprQ1+AH678xjXP7CFH285OGoXmmgyw6FQnK5I8rRtE8XkUO49E0KIwqnptoln2bJlzrZt28p9GUKICpfbAGfqatgnI4XekK28awO6gq5IarBMZUaVC9uB5756ZUHn/8pPXyWcyJCxHXRN4XcbfPX9S1gxyhRSy3b4zetHeeD5ffQnsnXhs2s8fGH1Qq5YWD9qFxdNKaq9JtUyNGhSy7VmPdMyLyFEcZRS2x3HWTba46RMRQghRnDfpjZSGYvuyIma74DH4L5NbQUFNFUunT2dUXSVncKZsRwO9yZYNJC1LohSKE2hHIcCuyACoGuKa5bOZs3ZDTzy4gF+/uoRjvQm+Idf7OSSuTV8ce0iFszIfx32wCbP/kSaaq9J0CNB+WQ0mcu8hJhOpExFCCFG8M7xfrqjKTKWMxhMd0dT7D7eX9D6weyzGvJr6PFR3LepjWqvyeLGAOfMquasmUFqfCaPb2sv+HsIeExuW7uI+2+4hOXzawHYfrCXzz2yjW/9YTf98fRp11u2Q080O8mzNybtEIUQYiJMWDCulHpQKdWhlHpjyLE6pdTvlVK7B77WDhxXSqlvKaX2KKVeU0pdPGTNjQOP362UunHI8UuUUq8PrPmWKvQdTggxaRQ7tKSY9WkrG3hqWnacfS4znLIKC0jDyQw+U5HM2CTSNsmMjc9URApsJzhSa02/y6AznKDGV/jAIIB59X6+8ecX8M8fOZ/mWi+2Az9/9Qg3PLiFn79yeNQa8VxQfrAnRl8sLUG5EEKMo4nMjH8fuPqkY38H/MFxnMXAHwb+DPABYPHAr1uAeyEbvANfAy4FVgBfywXwA4+5Zci6k88lhJjEih1asnFXB3/7xA5eORjiWF+cVw6G+NsndhS83mVo2LZDImORSFskMha27eAyCnzZtG36k8M3TfYnbRy7sAmY+SaIttT5qfO7mF3jwT2GdoRKKS5rreeBG5fx+dWt+F06/YkM39qwh1se3c7LB0KjPodlO3RHk7T3xOmLS1AuhBDjYcKCccdxNgEntw34MPDwwO8fBv5syPFHnKzNQI1SahbwfuD3juP0OI4TAn4PXD3w34KO47zoZN8NHhnyXEKIKaDYoSV3/XYXoVgaBzB0DQcIxdLc9dtdBa1vqHJnfzMwzh7npOOj6IyOXAKS7/jJRuuG4TZ05tR4qfe7x5QlN3WNjy1r4eGbV/DBC5pQwL6uKF954jXu+MVOjvTGR32OjG3THUlyKBSnP1HY9yOEEGJkpa4Zn+k4zlGAga+5nSVzgKGFkIcGjp3u+KERjo9IKXWLUmqbUmpbZ2dn0d+EEGLiFTsBta0rOtDjW6FQaEqhqezxQjiOg1IKl67hMTRcuoZSquBs8MltCUc7frJCW2tW+0yaa714XWMb2lPnd/GV953NvZ+6mAvmBAF4fk8Xn/7+Vu5/ro1YavRymrRl0xVO0t4TK7j8RgghxHCV0k1lpLSOcwbHR+Q4znpgPWRbG57JBQohSms8hpbYjkMmY+E4oAaG7+gFZpEjKYs5NZ5hrQmbqtxEU9boi8meL3fenJP/PJpCu2GYusasai998TShaAp7DOUjZ80M8O8ffxcb3+7kvk1tdIST/GhLO7/deZzPvWcBf3LuTLRRLjpt2XT0JwjpGrV+F1XuSnlrEUKIylfqV8zjSqlZjuMcHSg1yRVvHgJahjyuGTgycHzNScc3DhxvHuHxQogp4tZVrfztEzs4HIqTsW0MLdta8B/+9NyC1jf4TQ71JQf/7DhgO9AUME+z6oTczUBrw4nx9bFUhsaAp6D1c4JuDvUlOTkunhMsrMzlTFR7TXwuna5IknjKYktbD49tbedof5xZQS/XLW8ZsUe5Uoq1Sxq5fGE9P9nWzo+3tNMTTXHXb9/m568e4S/WLuLc2cFRzz80KK/xmVS5jTGV0AghxHRU6jKVJ4FcR5QbgV8MOX7DQFeVy4C+gTKW3wHvU0rVDmzcfB/wu4H/FlZKXTbQReWGIc8lhJgiHAA10A5QnebjrxEEvC40TmSilcq+4AW8+UfDD1XsBMP/+ZELCbh1cu25NQUBt87//MiFY/guxi6XJd91tJ+7N+ymO5ok6DHojia5e8NutpxmAqjH1Lnh8vk8/OnlXDmQkX/7WJjbf/wK//ybt+gMJ/OuHSpt2XSGT9SUy0bP8ii2G5EQojQmbAKnUurHZLPaM4DjZLui/Bz4CTAXOAh81HGcnoGA+ttkO6LEgE87jrNt4HluBv5+4Gn/yXGchwaOLyPbscULPAX8hVPANyMTOIWYHNat33xKmUouM/3jWy4bdX2xEzCh+AmG5ZyAuG79Zo73x3EZOvZA68J42qLe7+abH19a0HO8fqiPbz+zh90dEQA8hsa6S+fysUuax9TJxdA0qn0mQY9kykul2AmyQojilX0Cp+M46/L8p/eO8FgHuC3P8zwIPDjC8W3A+cVcoxCicrWHYugK2jojw4LpQjdwttT6ePtYP/G0he2AZVuEExnObhq93OJkZ5qyKOcExPZQjBqviVIKSzlkbBuPqXGsf/RuKTkXNFdz76cu5ndvHOP+5/cRiqV56I/7+c3rR/n86oWsWjyjoOA6132lLzYw0dMrQflEG9qNCMDnMoilMgVPkBVClI7sshGiguUyq+2hGC0lzqyWW8BtsLsjgq4pdE2RsbPj5Bc3Vo2+GGgKunix7UTbPduBnliapmBhZSpDM4tD+5zfCZPi/0FLrY99XRHCiQwpy8bUFH63wZyawjfAQrYbzQcumMWqsxr4weYD/MfLhznen+Trv3yTd7VUc9uaRSws8P9JxrbpjibpjaeyQbnHHBymJMZX7mZsqLF0IxJClE6pa8aFEAUqdujNZDdYdeYM+TX0+Cj+sKtzoLVhtv1S7vd/2FVYe9Ni+5yPh2Jqfi9vraNzoERHU5C2HXpiad6zuB5TH/tLv99tcOvqhTx40zIub60H4NX2Pm79wXb+99Pv0BtLFfxcuYme7aEYvbHUYBmNGD/5hkaNpRuREKI0JBgXokJVQjBYTrnWgoausBwHQ1fMqfEU3FowmrIwdYXb0PGYOm5Dx9RVweuL7XNerGJvxl5s66Ex4MKla9gOuHSNxoCLbQd6mVPjpdpbWFeZkzXX+vinj5zPXf/lAubV+bAd+OWOo9zw4Fae2H6IjFVYH3UYHpSHohKUj6diNyALIUpHgnEhKlS5g8Fya6n1YegarQ1VLGkK0tpQhaFrBWf2/C6dVMYhnrYGf6UyDv4C4p0RiQAAIABJREFUh+OUO7NY7M1YeyhGxrIHN+7F0xYZy+ZQKIamKeqr3Myu8Y5pI+ZQy+fX8b0bLuH2tQupchtEkhm+s3Evn31kO1v25e/YMhLLdgjFUhzskaB8vBQ6NEoIUX5SMy5EhRqPoTeT2a2rWrnjyZ3EUplh3SAKzeydNyvAi/tCw445A8dLcX4orua/2A2sOA6dkeE1852RNM01J4Jvj6kzp+bMhgUBGLrGn1/czHuXzOTBF/bx69eOcrAnxt/97HUua63jC6sX0lI3tiFNoViKvniaoNek2muiS035GSvnBmIhROEkMy5EhZruHzMXm9nbeTR8ygucNnC8FOffuKuDrzyxg1faQxzvT/BKe4ivPLGj4DKTKpfO4d4EGctBV4qMld3AWmhmvyeaDcTVkF9Djw9V7TVprvWe8eTMap/JX111FvddfwnvaqkGYHNbD595eBv3btxLJJkZ0/PZjkNvLEV7T4weyZQLIaY4yYwLUaHWLGnkTihbn+pKUExmL5qyMA2Fpk6E5LZjF1wzXuz5v/HUW/TG0uhKoSuFY0NvLM03nnqroOccbP03NJJ2KLglYNKyMTWwnOz0UaXAUNnjIzF0jcagh0DKoiuSJD2G2u+chQ1V/NtHl/Lcni6+u7GNY/0Jfrr9EL9/8zifWbmAq89vGlOmOxeU98ezLRGrvdJ9RQgx9UgwLkQFk4+Zz5zfpRNNZXAcazAYVQr8rtK87O3rjmU7uAwEj0qBYzvs6y6szCSczDCnxjNsaFFT0F1wltnvypbWuId0TsnYNv5RasS9Lp3mWi+9sTS98bFPz1RKsWpxA5ctqOen29v54UsH6Y2n+bffv8Mvdhzh9rULubC5ZkzPmStf6U+kpSWiEGLKkTIVIcSU9N4lDVh2tlbagYHBP9njpZKxhm8gzViFB7bFbmD97MoFZCyHxMC5EwPn/+zKBaOuVUpR63cxp8aLt8CymJO5DI1PXjqPhz+9gqvOyd5Q7umI8JeP7+Aff/Umx/sTY37Ood1X+mJpKV8RQkwJEowLIaakY/0pfObwlzifqXGsv/B+2MUIeAxOLvSwB44Xotg9Axc21xD0Dj9X0GuMKSvtMjRmVXtpCLjPeCNlQ8DN33/wHL697iKWNGU3zz7zdic3PbSV77+wn0S68LKhHMt26I4mpSWiEGJKkGBcCDElvXO8n7Tt4NY1PIaGW9dI2w67j/eX5PzRPOUk+Y6frNgNpPdtasPn0vG59IEWidnfn0mf+oDHpLnWR8BzZr3JAc6dHeTbn7iIv7v6bOr9LpIZm0dePMBND21lw66OMZfDwPCWiD3RFJYE5UKISUhqxoUQU1J6oCRkaM22bTukxlAqUoyU5WBoA2UyAzXrmmJM5y9mz8DujnA2awzgQMbOlqqkz/D71zVFQ8BNwGPQGT6zDZ6aUrzvvCZWLp7Bj146yE+3H6IjnOR//votfvHqYW5bu4izZp5oPbmlrYfHtrZztD/OrKCX65a3sKK17pTnzW307IunCXgMarwmxhlMGRVCiHKQVyshxJTkMjRwsoGag5Ptoe0MHC8Bv0vn5ESt7VBwa8JixZLWYCcVh+xXy8keL0auN3kxWXKfy+Cz72nloZuWs3LRDABeP9zPF37wMv/6n2/TE02xpa2HuzfspjuaJOgx6I4muXvDbra05R8o5DgO/fE07aE4XZHkmKaBCiFEuUgwLoSYkhY3BpgRcGFoCst2MDTFjICLxY2FDf0p1nuXNGA7wzeQ2k7pNpDmq8U+kxrtk2kDWfKZQU9RQ3lm13i588Pn8a8fvZDWGX4c4DevH+PGB7fwrQ270VV26qxC4TV1DE3x2Nb2UZ9XgnIhxGQiZSpCiIpVzATLW1e18uXHXyGWsnCAjGVh6KpkQ5OO9aeo85n0xtPYTrZEpcZrlmwDab5ilPEs0vG7DdyGRlckRSw1tsE+Q108t5b7rr+EX712lIf+uI/+RIZoykLXFLpKYtkOLkOj1mdyrD9e8PPmgvJwIiPlK9NQMa8fQpSSBONCiIq0cVcHdzy5E1NX1HhNOsIJ7nhyJ3dCQW+orx3qpT8+PEDsj2d47VBvSd6Q20MxAh6DZMYe7BMe8BiFj7OnuGCiFME4ZIcFNVVnN5n2RFPDNmIWWvMN2Zr0D79rNmvPbuCRFw/ws1cOY9kOFtl6+7Rlc7w/ybx6/5ivUYLy6afY1w8hSklejYQQFem+TW0DXUAMlMp+NXVVcDeQ+5/fh6ErPKaO19TxmDqGrrj/+X0TfOVZxY6z37irg688sYNX2kMc70/wSnuIrzyxg427Ogpan694ZKJG5VR7TebUeAdr8s+k5hsg6DW5/cpFNFd7Bo85DmTsbM27VUTJiZSvTB/3bWojbVkc60vw9vEwx/oSpC1rTN2ENu7qYN36zay8awPr1m8u+GdPiLGSYFwIUZHaQzG8J02L9Jp6wZnlaMoCxyGZyXYRSWayf46miq+ZLsQp4+zVScdH8Y2n3qI3lsaxQVcKx4beWJpvPPVWQevzJX4nMiHsMjTm1Hip9po8trUdQ1NnVPMNEM1T234wFOfJHUeKamMoQfnUt7sjTFc4RcZ20DVFxnboCqfY3REuaH2xN8NCjIWUqQghKlJLrY+OcALfkPH18bRV8ARKt64RS1uDmWDHgbTDKYOATqeYMpFix9nv646hqeGtGR3bYV93YTcjixsDvH0sjKNOtFZUDhO+gVUpRX2Vm45IAr9r+FuMx9QKrvlOZWwMDXRNw3GcbFbcdnCAf396N0++eoTb1i7korm1eZ/j0Rf285Pth4inLbymzscuaeb6K+YP/veh5StVboMan4kp5StTQipjg8q204SB1qbKyR4vQO5mWFfqlJthKXMR401edYQQFanYCZR1/mzrPWfIr6HHR5OrOe0IJ4bVnBaaGSt2nH2xvnr1EuqrXLh1DUPL3pzUV7n46tVLSnL+eXV+LNsevJkASKRtmoLegtabusJ2GKi5d7BsBwW4dIUC2rqi/M1PX+NrT+7kaN+pAf6jL+zn4c0HSGYsdA2SGYuHNx/g0Rf2n/JYx3EIJ9K098To6E+MS8cZUV6mnv13Z9sOjuMMTml16YV9MjX0ZlgphaYpNEXBN8NCjIUE40KIilTsBEqUoqHKJBcLagoaqsyCy0SKrVm/dVUr/fE0u4+HeetoH7uPh+mPpwu+mWid4R9oh3iiT7rtZI8XYs2SRv7l2qVcNLeWWdVeLppby79cu7RkWb1bV7WSsbMbL3VNEU9bZGyH65a3FLS+zudipKGczTVevvPJizlvdhCA53Z3cdNDW3ng+X3Eh5Qg/WT7ITSVzaxrShv4mj1+OpFkhiO9cY70xguelioqz1kzg9T7XRi6wnIcDF1R73exeGaw3JcmxCmkTEUIUbGKmUCZK3Npqj6RiY6lMjQGPKdZdUJ7KEaNd3gWfSw16zCQjVcDdeJqbJ1Mvnr1Ev72iR2EExkylo2hZVv7jSWzXczfX7HWLGnkTrI3NYdCMWbXePnYJc1cNC9/WckwKpsBH/p3pgaOn90U4FvXvYsNuzpZv6mNzkiSH750kN++cYzPrWrlqnMaiactNLLlCs7AWl1lS50KkUhn9xqYuka1zyTgNgq+kRPld+uqVu54cidN1QZeUyc+MH12LDfDuzsiKMfJlogNzAlY3DD2bj5CjEaCcSHElJR7M46lMmf0Zlxszfp9m9qo9prMqj5RlhFLZbhvU1tBAXIus50LZpvPoE/yt55+h/uf30c0ZeF36Xx25QK+dNVZBa8v1sk3A47j0BdPE4qlh7VAHEkoluLk6l574Dhkb3Dee04jVyyq5/Et7Ty2rZ3uaIpvPLWLX7x6GENTpKwT53CAjAOeMU5gTVs2XeEkvdE01V6TgMcYVnojKtPJN4Nj/fkZj5thIQolwbgQYkoq9s242GB+PDLrxWS2v/X0O9y9YQ+aAkPL3kjcvWEPQEkD8qGUUtT4XHhdOl2RFMnTZKnjebrenHzca+rc9O75XH1BE+ufbWPjO528dTR/x4xq75m97WVsm+5oklAsRdBrUu01i5o+KiZeMT8/43EzLEShJBgXQkxZxb4ZX3uo95TMcqHPV2xmvVjZfuoOlp3NCCuV/XX/8/vKFoznuA2d2QODgvJlyZN5ul7kO94U9HDHNefy4UO93LNhL3s6I6c8ptZXfKmJ7Tj0xlL0xdMyQGiKK2eZ13iQCaSTh7yCCCHECDbu6uCJlw/TEHBzTlOAhoCbJ14+XHA3lWI3cBYrksxg2dlaVwZqXi2bglsrTrRclnx2jQe3eeogpDOdILq0uYZ7P3UxLTVehiauTU2hKY2ZBe4ZGM3QXuWd4SRp6VUuKkix3aBEaUkwLoQQIyi2mwoUt4GzWMOGDg35WmmbEN2GzpwaL3V+17hdm64pblu7iIaAmyp39pOJtO3QHU0RSWVoGyFrfqZybREPSVAuKsh4vH6J0pEyFSFExSrnx6zF1nwXu4GzWF5TEUk6p7QH9JmVFYzn1Phc+FwGnZEkyYFhTSPdvBR69Sta67jgrSAb3u4cdnxvZ5RbHt3ONUtnc9MV86n2FtZ3fjS5oDySlAFCovzGY8+KKB15pRBCVKRyf8zaUus7pQ3eWGq+20MxvCeVX5TyzfCCObXUeI1hfdZrvAbnzymwtWAZuAyNOTVe6v3uMy5TyXn0hf08vasT+6QF1R4D24FfvHqEGx7cws9ePkxmHLPZJ2fKC534KMR4Kvb1S5SWBONCiIpU7o9Zi50AWu43w1tXtRL0ulgww8/5s4MsmOEn6HWVrGa9GNW+4rPVD794YMTj/YkMX1izEL9bJ5zI8O1n9vC5R7ezbX9P0ecc6kRQnp3qmczIVE9ROsW+fonSkmBcCFGRyp1ZLnYCaLnfDNcsaeTai+fQGU7y1rEwneEk1148Z9J0Uyi2mCZfPtoBPnpJM4/evIJrLpyFAg50x/iv//E6/9/P3+BwKF7kmU8VSWY4HIpztC+et2VjJdq4q4N16zez8q4NrFu/WTb/TSJFTzAWJSU140KIilTu1oBQfGvEYvqcF2toN5i5A33Sn3j5MBc210yKN2RDg/QIEbUxTiXvNT4Xf/UnZ3HN0tnc88wedhzq44W93WzZ18O1lzTzyUvn4neP71tkPGURT8Vxmzq1PnPYv+1KkysTM3U1rEzsTpgU/37E5G/NWKzJ1NpRMuNCiIpU7szyeFizpJEf33IZz331Sn58y2UlfSMod5lPsYJ5NlYGPOMbwC5qrOKbH1vK1645l5lBNxnb4bGt7dzw4BaeeuMY9iiTQs9EMm1xrC/BoVCsYlpNnmyy//sR01u59xyNlQTjQoiKJB+zFqfcZT7FOmtmkKagG79Lx9QVfpdOU9DNopkBtAJaIOZ7xEjHlVKsPquB79+0nE+/ez4eQyMUS/Mvv3ubL/7wZd443FfU95JPKmPT0Z+gvSdGOJGekHOcqfZQjIxl09YZYdexfto6I2Qse9L8+xHT22S7mazcz8iEENPedP+YtRiVUOZTjFtXtXLHkztpqjbwDpTZpC2H29YsYnaNl45w4rSdSs6kG4vb1Ln+snlcfV4T33uujaff6uCd4xG+9NirXLmkkVves4DG4PgMDRoqbdl0hpP0xtJU+0wC7uInhRYr4DbY3RFB1xS6psjYDod7EyxurCrrdQlRiMnW2lEy40IIMQVN9jKf030ykmuBWONzTci5GwJu/v6D5/Ct697F2TMDAGzY1cGND23lkRf3k0hPzCbMtGXTFU7S3hOnL57GmYASmUINntsZ8mvocSEqWLm7WY2VZMaFEGIKKvcG0vFwuk9GlFLU+V34XPqETb48f04193zyIn638zj3P9dGKJbm+y8c4DevH+Pzq1tZfVbDhGSwM7ZNdyRJXyxNtdck6C19pjySsphT46ErkiJl2bh0jaYqN9FJ1A1GTF+5T9ZiqcywT9YqNRkhwbgQQkxR06HMx2PqzKnx0hVNEkmM/2ZITSk+cH4TqxbP4IcvHeQ/Xj5ERzjJnb96iwvmHOH2tQtZPJA9H28Z26Y7mqQ3nsoG5R4TTStNUJ4rc2ptOFGWEktlaAyMf5mOEONtsiUj1HT7yGnZsmXOtm3byn0ZQgghxlkkmaE7ksSyHa78t2fzPm7D36w+43McDsX57rN7+ePebiC7IfSDF8zi5pXzqZ2gspkcXVMEPSZBr4k+wUH50NaGQzOLsolaiMIppbY7jrNstMdJzbgQQogpocptMKfGi89lUJOnBWK+44WaU+vlH//sfP7Xf7mAefU+HODXrx/lhge28NNt7RNSLpNj2Q6hWIr2nhg90RSWPXHJNOlmJETpSGZcCCHElPPUa0f5y8dfJjmkxNmtw9c/dAErWuvG5RyW7fDLHUd46IX9hAdKZJprvXxxzUIua60fl3OcjlKKoMeg2mti6JJbE6LSFJoZl2BcCCHElLThzePcs3Evh3tjNAW9XLe8ZdwC8aH64mm+/8J+frnjCLlk9YoFdXxx9ULm1p9594ZHX9jPT7YfIp628Jo6H7ukmeuvmH/K45RSBDwGNRKUC1FRJBjPQ4JxIYSYHMZrnHU0maE7kiJjT1wJCUBbZ4R7Nu7llYO9QLbG+yMXzeaGy+ZTNcbymEdf2M/Dmw+gKVAKHAdsB268bN6IATlkg/Iqt0GtT4JyISqBBON5SDAuhBCVb7w3EFq2Q/cEdVwZynEc/rinm3uf3cvRvgQA1V6Tz6yczwfOn1Xwxstr/s/zxFPWYItvNfDL69L55V+sPO3aXFC+oz3EA8/vL/pmRghxZmQDpxBCiElrvMdZ65qiMeChqdqDoRX21relrYe/fnwH6763mb9+fAdb2npGXaOUYuXiGTx003I+u3IBHlOjL57mm7/fzed/sJ0d7b0FnTuWsrA5MTHUAeyB46NxHIc/vHmcf/jFTo70xan2GHSEE9zx5E427uoo6PxCiNKRYFwIIfLYuKuDdes3s/KuDaxbv1kCmRJqD8XwmvqwY+MxztrnMmiu9RLwmKd93Ja2Hu7esJvuaJKgx6A7muTuDbsLCsgBXIbGJy6dy6M3r+D9580EYG9nlL/6yQ6+/ss3OdafOO36fDN+Cp3989jWdgxN4dY10paDqWsYGmd8MyOEmDgy9EcIIUYwtEyixmsOZhbvBPmov0DF1Hznhs74XCfepsZrnLWmKRoCbqrcBl2Rkad35oLZ3A1BrlTmsa3tY9oEWl/l5qtXL+HD75rNtzfs4c2jYZ59p5MX27r5+LJmrlsx95SbDgCvoRFNn3pdXqOwHNrR/jjBIXXqtu2ga4r93VESaQvPCOcUopKM156RyUAy40IIMYLxLpOYbnI3Mx3hxLCbmUI/Xbh1VStpyyGWyuA42a/jPc7a69JprvVS7T01S360P47HHP4W6TE1jvXHz+hcS5qC/J91F/H3H1zCjCoXqYzNo5sPcuODW/jDW8c5ef/W4plBgh6dXCJcAUGPzuKZwYLONyvoJXFSMJ9I28wMeDjSG+doX5y4jLYXFarY14/JRoJxIYQYwUSVSUwXxd7MlGrojFKK+io3s2u8mEM6kOQLZpuC3qLOddU5M3n40yv41GVzMXVFVyTFP/1mF1967FXePhYefOx1y1vwu02aa70sbvTTXOvF7za5bnlLQee6bnkLGdshnrZwyH7N2M7g+njK4mhfnMO9cWKpid3UKsRYTbdkiJSpCCHECCayTGI6aA/FqDkp4zzWm5k1SxpL9rG0x9SZU+OlM5Ikmsxw3fIW7t6wm3jawmNqJNL2sGC2GF6Xzs3vXsAHz5/FdzftZdM7Xew80s8Xf/gy7z+vic++ZwErWuv4Mot5bGs7x/rjY+6TXuj6ZNriWJ+Fy9Co8bmocktYIMpvPF4/JhP5qRNCiBHcuqqVO57cSSyVGdZabzzLJKayyXgzo2mKmUEPfbE0ly6s58twxsFwIZqqPfyPa87j1fZevv3MHto6o/x25zE27e7kU5fO5c8vbi7qfCta6wpen8rYdPQnCOkaNT5z1A2uQkykyfj6UQzpMy6EEHnkNhAdCsVonuIbiMbbePcJL7VE2qIzPPLmzolg2Q6/ef0oDzy/j/6BXuizazx8YfVCrlhYjyq0jco4MXWNap9JwG2U/NxCTPbXjxwZ+pOHBONCCFEak/1mxradwbKVUgkn0jzy4gF+/uoRLDv7/nzJ3Bq+uHYRC2b4S3YdOYaWDcqDHgnKRWlN9tcPkGA8LwnGhRBCjEVfPE1PNHVKx5OJdKA7ync27mXr/hAAmoIPLZ3NTVfMJzhC95eJZmga1V6ToFeCciEKJcF4HhKMCyGEGKtUxqYjnCCVKU3ZCmQnab60r4fvbNzLoVC2pWLQY3DTFfO5ZulsdK30QbGuqWxQ7jHRynB+ISYTCcbzkGBcCCHEmXAch55oir54uqTnTVs2P3v5MD/YfIDoQG/w+fU+bl+7iIvn1Zb0WnJ0TRH0mAS9ZlluCoSYDCQYz0OCcSGEEMUo9ebOnJ5oigf/uI+nXj9G7p373Yvq+fzqhcypOfP+58XQlCLoNamWoFyIU0gwnocE40IIIYpl2w5d0SSRROkH5rxzPMw9z+zh9cP9AJi64tpLmvnkpXOHtYIrJaUUQY9BtdfE0GWeoBAgwXheEowLIYQYL5Fkhu5IcrDzSak4jsPGtzu5b1MbHeEkAHV+F597zwL+5NyZaGXaZKmUIjAQlJsSlItpToLxPCQYF0IIMZ4s26E7kiRSwhaIOYm0xWNb23l8azvJgc2lZzcF+Iu1izh3drDk15OjlMLv1qn1uSQoF9OWBON5SDAuhBBiIpQrSw5wvD/B+k1tPPN25+Cxq85p5HPvaaUh4C759QxV5Tao8blwGRKUi+lFgvE8JBgXQggxUSzboavEg4KGeu1QL99+Zi97OiIAeAyNT1w6l49e0ozb1MtyTTl+t0GNz8RtlPc6hCgVCcbzkGBcCCHERCtnltyyHX638xgPPL+PUCzbhrEp6OHzq1t5z+IZZR/a43Nlg3JPmW8OhJhoEoznIcG4EEKIUih3ljySzPDoiwf4v68cJjNwU/CulmpuW7uIhQ1VZbmmobyubE25BOViqpJgPA8JxoUQQpRSObPkAO09Me59di+b23oA0BT86YWzuPmKBVT7zLJc01AeU6fGZ5atLaMQE0WC8TwkGBdCCFFqGcumO5oqW5YcYMu+Hr6zcS8He2JAdmPljVfM48NLZ1dEb3CXoVHjc1HllqBcTA0SjOchwbgQQohyCSfS9ERTZcuSZyybJ3cc4fsvHBhsxTi3zsdtaxeyfH5dWa7pZKauUe0zCbiNste3C1EMCcbzkGBcCCFEOVVClrwvluahF/bzq9eOkLsvuKy1ji+sXkhLna9s1zWUoWlUe02CXgnKxeQkwXgeEowLIYSoBOXOkgPs7YxwzzN7ebW9FwBDU3zkojlcf/m8iikXkaBcTFYSjOchwbgQQohKkbFsuiIpYqnyZckdx+G5PV18d2Mbx/oTANR4TT6zcgFXn9+ErlVGAKxrihqvS4JyMWlIMJ6HBONCCCEqTSVkyVMZm59ub+eHLx0kkbYBWNRYxe1rF3Jhc03ZrutkEpSLyUKC8TwkGBdCCFGJKiFLDtAZTnL/8/v4/ZvHB4+tPbuBW1a1MjPoKeOVDadrKlu+4jHRKiR7L8RQEoznIcG4EEKIShZOpOmOpLDL/P785pF+vv3MHnYdCwPgNjQ+vryF65a3VNSgHl1TBD0mQa9ZMSU1QoAE43lJMC6EEKLSVUqW3HYcnn7zON97bh/d0RQAjQE3t6xqZe3ZDRVVJqIpRdBrUi1BuagQEoznIcG4EEKIyaJSsuSxVIYfvXSQn24/RNrKXsv5s4PcfuUizpoZKOu1nUwpRdBjUONzSVAuykqC8TwkGBdCCDGZVEqWHOBIb5zvPtvG83u6AFDAB85v4uaVC6jzu8p7cSfJBeXVXrMiJoyK6UeC8TwkGBdCCDEZVUqWHODlAyHu2biXfV1RAHwunesvm8efXzwHs8ICX6UUAY9BjQTlosQkGM9DgnEhhBCTVSVlyS3b4VevHeGhP+6nP5G9nuZaL19YvZDLWusqqp4cJCgXpSfBeB4SjAshhJjsKilL3h9P8/CLB/jFq4fJtUlfPr+WL65ZyLx6f3kvbgRKKfxunRqvC5chQbmYOBKM5yHBuBBCiKmgkrLkAPu6onxn4162HwgBoCn4s4vmcOPl8wh4zDJf3cj8boMan4nbqJxWjWLqkGA8DwnGhRBCTCX9iTQ9FZIldxyHF/Z2c++zeznSmwAg6DG4eeUC/vSCWRXb3cTnygblldQ/XUx+EoznIcG4EEKIqSZt2XSGkyTSVrkvBYBUxuZnrxzmB5sPEEtlr6m1wc9taxZy0dzaMl9dfh5Tp8Zn4nMZ5b4UMQVIMJ6HBONCCCGmqt5YilAsTaW8t/dEUzzw/D5++8Yxcle0avEMbl3dyqxqb1mv7XRchkaNz0WVW4JyceYkGM9DgnEhhBBTWTJj0dGfJG3Z5b6UQe8cD/PtDXt440g/AKau+NiyFj6xYi5eV+WWhpi6RrXPJOA2Kq47jKh8EoznIcG4EEKIqc5xHLqjKfrj6XJfyiDHcdiwq5P1m9rojCQBqK9ycct7WnnvOY1oFRzsGlo2KA96JCgXhZNgPA8JxoUQQkwXsVSGznASy66c9/p42uLxLe08tq2dVCabvT93VoDb1i7inFnBMl/d6emaosbrIuAx0Cp0M6qoHBKM5yHBuBBCiOkkY9l0RpLEU5WxuTPnWH+C+55t49l3OgePve/cmXz2PQuYUeUu45WNTtcU1V6ToMeUoFzkJcF4HhKMCyGEmI4qbXNnzo5DvdyzYS97OiMAeEyNT106j2svaa74oTyaUgS9JtVes2LbNorykWA8DwnGhRBCTFeJtEVnuLI2dwJYtsNTbxzjwef30TtQ5z6Y/bCtAAANe0lEQVSr2sPnVy9k5aL6iq/T1pQi4DGo8bkkKBeDJBjPQ4JxIYQQ05ltO3RFkkSSlTG5c6hIIsOjmw/ws1cOD9a5XzS3htvWLKS1oarMVzc6lQvKvSaGXtlZfTHxJBjPQ4JxIYQQIju5szuSqriyFYCDPTHu3biXl/b1AKApuObC2dz07vlUe80yX93olFJUubNTPU0JyqctCcbzkGBcCCGEyEplbI73JyqubCVnc1s3927cS3soDkDAY3Dj5fP50NJZkyLzrJTC79ap8boqvv5djD8JxvOQYFwIIYQ4wXEcuiIpwonK6Uk+VNqy+fmrR3jkxf1Ek9mOMPPqfXxxzUKWz68r78WNQZXboNpn4jYqd8iRGF//r717D7arLO84/v2d+zm5h1wmkxgTQhxukwaNqQgaAS+gHS9TClIValFKaSqdSr3UThGnzrQzbWE6UEQQEhVBqqZFtCgDuSAoISEhEEDMzRiS4ZjkJCbnJOe2n/6x1ulsT/YOe2dzsvZKfp+ZPWevd6+113OeeZP32e9591ouxstwMW5mZnakg70D7D7QS6FO64Kunj7ueWIbP9qwi6EI3z7nFP5y0RymT2jPNLZqjEqXr7goP/G5GC/DxbiZmVlp/YMFOg/00ttfX9ckL7ap8yC3Lt/Ehh37AWhqEJe+ZQYf+8OZjGptyji6ynW0JEV5W7OL8hOVi/EyXIybmZmVFxHs7e5j/6H6XLYCSYwrX97N11ZupvNALwATOpr51DtO5X1nTaWhzi+FWKy9JVlT3t7iovxE42K8DBfjZmZmr+1QX3JN8oFCfX65E6C3f5AH1uzgO6u30zuQxPmmqaNZfMFpnD19XMbRVaetuZHxHc10tORndt+OzsV4GS7GzczMKjNYCPbU6TXJi3X+7jB3Pr6VR1/q/P+2i06fwjXvPJXJY1ozjKx6rc2NjG9vztWSGyvNxXgZLsbNzMyqcyC9Jnm9frlzyPOv7OfW5Zt4+dWDALQ1NXDFwplctmAGrTlbm93S1MD4jhZGuyjPLRfjZbgYNzMzq17/YIHfHujlcB1/uROgEMFPNr7KXY9voasnWfc+ZUwr1y6aw6I3TUI5Wk8O0NzYwPiOZsa01f/Njuz3uRgvw8W4mZnZsevq7mPfof66vHNnse7eAe59ajvff2YH/YNJrPNmjGPxBadx2pTRGUdXvebGBsZ1NDOmtSl3HyhOVi7Gy3AxbmZmVpvD/cmXO+v1zp3FXuk6xNdWbuaJzXsAEPCBedP45HmzmNDRkm1wx6CpISnKx7a5KK93LsbLcDFuZmZWuzxcArHYmm17uW3FZn69pweAUS2NXHnuG/nwOdNpbszfreqbGhoY197M2HYX5fWq0mI8f71vGEkXS/qlpE2SvpB1PGZmZicDSZwyupVp49ppaqj/cmLBrIncdeUC/vrC0xjT1kR33yC3r9zC1UvX8Iste7IOr2oDhQJ7unvZvreHfT19FAon1+TqiSTXM+OSGoGXgfcAO4CngSsi4oVyx3hm3MzM7PVVKAS7u3s5eLi+L4E4ZP+hfpY+uY0Hn93JUA27cPZErls0h5mndGQb3DFqbBBj25oZ295MY4NnyuvByTIzvhDYFBFbIqIPuB/4UMYxmZmZnVQaGsSUMW1MGduWi7tfjmtv5jMXzeXOKxdwzszxAKzeuperv7mG/1yxKTcfKooNFoKunj5+s7eHvd19DHqmPDfyXoxPB35TtL0jbTMzM7PjbHRrE9MntOfmmt6zJ43iXy+dx1c+eBbTxrUxWAi+t/YVPnH3ah7asDOXBW0hgn09fWzf28Oeg70M5OBLtie7vF9JvtTH7yP+5Ui6Brgm3Two6ZfHcK5JwO5jOM4Szl9tnL/aOH+1cf5q4/zVJpP8XZ8+TgDuf7U71hy+sZKd8l6M7wDeULQ9A9g5fKeI+Drw9VpOJGlNJet+rDTnrzbOX22cv9o4f7Vx/mrj/NXG+avdSOcw78tUngbmSpotqQX4KPBgxjGZmZmZmVUk1zPjETEgaTHwE6ARuDsiNmYclpmZmZlZRXJdjANExI+BHx+HU9W0zMWcvxo5f7Vx/mrj/NXG+auN81cb5692I5rDXF9n3MzMzMwsz/K+ZtzMzMzMLLdcjJcg6W5JnZKeL2r7sqRXJK1PH+/PMsZ6JukNkpZLelHSRknXp+0TJT0i6VfpzwlZx1qPjpI/98EKSGqTtFrSs2n+bkrbZ0t6Ku1/302/9G3DHCV/SyRtLep/87OOtZ5JapS0TtJD6bb7XxVK5M/9r0KStkl6Ls3TmrTN42+FyuRvRMdfF+OlLQEuLtF+c0TMTx/HY516Xg0An42IM4C3AX8l6UzgC8CjETEXeDTdtiOVyx+4D1aiF7gwIv4AmA9cLOltwL+Q5G8u0AVcnWGM9axc/gD+rqj/rc8uxFy4HnixaNv9rzrD8wfuf9W4IM3T0OX4PP5WZ3j+YATHXxfjJUTEKmBv1nHkVUTsiohn0ucHSP5DnQ58CFia7rYU+HA2Eda3o+TPKhCJg+lmc/oI4ELge2m7+18ZR8mfVUjSDOADwF3ptnD/q9jw/NnrwuNvHXMxXp3Fkjaky1j8J54KSJoFnAM8BUyNiF2QFJzAlOwiy4dh+QP3wYqkf+JeD3QCjwCbgX0RMZDusgN/wClreP4iYqj/fTXtfzdLas0wxHp3C/A5YOg+5Kfg/leN4fkb4v5XmQB+Kmltegdy8PhbjVL5gxEcf12MV+52YA7Jn213Af+WbTj1T9Jo4PvA30TE77KOJ29K5M99sEIRMRgR80nuyrsQOKPUbsc3qvwYnj9JZwNfBE4H3gpMBD6fYYh1S9IfAZ0Rsba4ucSu7n8llMkfuP9V47yIeDNwCckyx3dmHVDOlMrfiI6/LsYrFBGvpgNUAbiTZIC3MiQ1kxSS90bED9LmVyVNS1+fRjLrZiWUyp/7YPUiYh+wgmTt/XhJQ/dWmAHszCquvCjK38Xp8qmIiF7gHtz/yjkP+KCkbcD9JMtTbsH9r1JH5E/St93/KhcRO9OfncAyklx5/K1QqfyN9PjrYrxCQ5049RHg+XL7nuzS9ZHfAF6MiH8veulB4Kr0+VXA/xzv2PKgXP7cBysjabKk8enzduDdJOvulwOXpru5/5VRJn8vFQ3kIllv6v5XQkR8MSJmRMQs4KPAYxHxMdz/KlImfx93/6uMpFGSxgw9B95LkiuPvxUol7+RHn9zfwfOkSDpPuBdwCRJO4AbgXell1IKYBvwF5kFWP/OAz4BPJeuOwX4e+CfgQckXQ1sB/4ko/jqXbn8XeE+WJFpwFJJjSQTDg9ExEOSXgDul/RPwDqSDzx2pHL5e0zSZJIlF+uBa7MMMoc+j/tfLe51/6vIVGBZ8pmFJuA7EfGwpKfx+FuJcvn71kiOv74Dp5mZmZlZRrxMxczMzMwsIy7GzczMzMwy4mLczMzMzCwjLsbNzMzMzDLiYtzMzMzMLCMuxs3M6pikWZKOuKatpK9IevdrHPtlSTeMXHRmZlYrX2fczCyHIuIfs47BzMxq55lxM7P61yjpTkkbJf1UUrukJZIuBZD0fkkvSfqZpP+Q9FDRsWdKWiFpi6TPpPt/ruj5zZIeS59fJOnb6fPbJa1Jz3lT0evLht5Y0nsk/WB4sJL+TNJ/S/qhpK2SFkv6W0nrJP1C0sR0vxWSbpH0pKTnJS1M2ydLekTSM5LukPRrSZNGJLNmZhlzMW5mVv/mArdFxFnAPuCPh16Q1AbcAVwSEecDk4cdezrwPmAhcKOkZmAV8I709QXA6LT9fODxtP1LEbEAmAcskjQPeAw4I70TIsAngXvKxHw28Kfpeb8K9ETEOcDPgSuL9hsVEW8HrgPuTttuJLkN+puBZcDM18iPmVluuRg3M6t/WyNiffp8LTCr6LXTgS0RsTXdvm/YsT+KiN6I2A10ktzueS3wFkljgF6SAnkBSYE+VIxfJukZklu3nwWcGcktm78FfFzSeOBc4H/LxLw8Ig5ExG+B/cAP0/bnhsV/H0BErALGpu97PnB/2v4w0HWU3JiZ5ZrXjJuZ1b/eoueDQHvRtqo8tiki+iVtI5nZfhLYAFwAzAFelDQbuAF4a0R0SVoCtKXvcQ9JYX0Y+K+IGJD0EZLZbIBPlThvoWi7wO+PPTEs3qjgdzIzO2F4ZtzMLN9eAk6VNCvdvrzC41aRFNyrSGbDrwXWp7PfY4FuYL+kqcAlQwdFxE5gJ/APwJK0bVlEzE8fa6qM/3IASecD+yNiP/Az4LK0/b3AhCrf08wsNzwzbmaWYxFxSNJ1wMOSdgOrKzz0ceBLwM8jolvS4bSNiHhW0jpgI7AFeGLYsfcCkyPihdfhV+iS9CTJB4A/T9tuAu6TdDmwEtgFHHgdzmVmVneUTIKYmVleSRodEQclCbgN+FVE3DyC57sVWBcR36jxfVYANwyfTZfUCgymS2DOBW6PiPm1nMvMrF55ZtzMLP8+LekqoIXkC5d3jNSJJK0lWcLy2ZE6B8nVUx6Q1AD0AZ8ewXOZmWXKM+NmZmZmZhnxFzjNzMzMzDLiYtzMzMzMLCMuxs3MzMzMMuJi3MzMzMwsIy7GzczMzMwy4mLczMzMzCwj/wdsW7HS7pzS7QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see from this plot that price is negatively correlated to highway-mpg, since the regression slope is negative.\n",
    "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": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 47422.919330307624)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing the regression plot of \"peak-rpm\" and \"highway-mpg\" we see that the points for \"highway-mpg\" are much closer to the generated line and on 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": 25,
   "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": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df[[\"peak-rpm\", \"highway-mpg\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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": 26,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+DfTlCOgAACAyFjbNkKRsukPFclXDoxOhzDSssAMAACBWotY0g8AOAACAWIla0wwCOwAAAGIlak0zCOwAAACIlag1zWDTKQAAAGInSk0zCOwAANygkfG8hkcnNFkoqqc7q6H+3sgEAADRQUkMAAA3IGp9nAFEF4EdAIAbsLCPs1n9MpU0DY9OBD01AG2GwA4AwA2IWh9nANFFYAcA4AZErY8zgOgisAMAcAOi1scZQHQR2AEAuAFR6+MMILpo69gGaCsGAMGIUh9nANHFCnvE0VYMAACgvbHCHnEL24pJUjbdoWK5quHRiaZXfVihBwAACC9W2CPOb1sxVugBAADCjcAecX7binHwBwAAQLgR2CPOb1sxDv4AAAAINwJ7xPltK8bBHwAAAOHGptM24Ket2FB/r3YeGFOxXFUmlVSp4nHwBwAAQIiwwh5zHPwBAAAQbqywg4M/AAAAQowVdgAAACDECOwAAABAiBHYAQAAgBAjsAMAAAAhRmAHAAAAQozADgAAAIQYgR0AAAAIMfqwQyPjeQ2PTmiyUFRPd1ZD/b30ZQcAAAgJVthjbmQ8r50HxpSfntX6TEr56VntPDCmkfF80FMDAACAWGGPveHRCaWSpmy6/qOQTXeoWK5qeHQiNqvsvMMAAADCjMAec5OFotZnUovGMqmkpgrFgGbUWnPvMKSStugdhl1SZEI7LzgAAGhvlMTEXE93VqWKt2isVPG0qTsb0Ixaa+E7DGb1y1TSNDw6EfTUmjIyntcj+4/qR5MFvXV+Vj+aLOiR/UcpaQIAtL2R8bx27D2kbbsPasfeQ239fx+BPeaG+ntV8ZyK5aqcq19WPKeh/t6gp9YSk4WiMqnkorEovcPwuadf1tliRa4mJc3katLZYkWfe/rloKcGAMCKidsePAJ7zA305bRr+xblujp1rlRRrqtTu7ZviU1JRdTfYTh+uqiESYmEycyUSJgSVh8HAKBdRf0d8qWihh0a6MvFJqBfbqi/VzsPjKlYriqTSqpU8WL1DgMAAFEUtz14ga6wm9kTZpY3s58uGLvJzJ41s9cal92NcTOzPWZ2zMxeMrP3LbjPRxq3f83MPrJg/NfN7CeN++wxM2vtM0TYRf0dht5bVqvmpJpzcnKqOaeaq48DANCuov4O+VIFXRLzFUkPXDb2CUnfc85tlvS9xnVJ+pCkzY2PQUlfkuoBX9KnJf2mpHskfXou5DduM7jgfpc/FqCBvpyeHLxX/8+fv19PDt4bmbAuSX/+QJ+6symZpKpXk0nqzqb05w/0BT01AABWTNz24AUa2J1zo5LOXDb8YUlfbfz5q5J+b8H411zdIUnrzew2SR+U9Kxz7oxzriDpWUkPND631jn3gnPOSfragq8FtIWBvpz+6sH36tfe0a3b1mX0a+/o1l89+N5IvegAAGCpov4O+VKFsYb9Vufcm5LknHvTzOa+87dLmlxwu6nG2NuNT11lHGgrcd6DAACIrzj9/xd0ScxSXK3+3N3A+JVf2GzQzA6b2eGTJ0/6mCIAAACwvMK4wv6Wmd3WWF2/TdJcQ80pST0LbrdJ0i8a4wOXjY80xjdd5fZXcM7tlbRXkrZu3XrVUA8AANBOOCk7OsK4wn5A0lynl49I+rsF43/Y6BZzr6RzjdKZZyR9wMy6G5tNPyDpmcbnps3s3kZ3mD9c8LUAAABiK24HD0Vd0G0dn5T0gqR3mdmUmX1U0uck/Y6ZvSbpdxrXJekpSROSjkn6G0kfkyTn3BlJfynpB42PXY0xSfojSfsa9/kvkp5uxfMCAAAIs7gdPBR1gZbEOOd2XONTv32V2zpJf3yNr/OEpCeuMn5Y0j/xM0cAAIB2E7eDh6IujCUxAAAAWEFxO3go6gjs8G1kPK8dew9p2+6D2rH3EPVvAACEXNwOHoo6Ajt8YdMKAADRE7eDh6IujG0dESELN61IUjbdoWK5quHRCX7pAQAIsTgdPBR1rLDDl8lCUZlUctEYm1YAAACWD4EdvrBpBQAAYGUR2OELm1YAAABWFoEdvrBpBQAAYGWx6RS+sWkFAABg5bDCDgAAAIQYgR0AAAAIMQI7AAAAEGIEdgAAACDECOwAAABAiBHYAQAAgBAjsAMAAAAhRmAHAAAAQozADgAAAIQYgR0AAAAIMQI7AAAAEGIEdgAAACDECOwAAABAiBHYAQAAgBAjsAMAAAAhRmAHAAAAQozADgAAAIRYR9ATAAAAiKI9z72qfc8f14Wyp9XppB7adqcevv+uoKeFNkRgBwAAWKI9z72qxw8eU8KkjoRUqnh6/OAxSSK0Y9lREgMAALBE+54/3gjrCSUs0bisjwPLjcAOAACwRBfKnhK2eCxh9XFguRHYAQAAlmh1OqmaWzxWc/VxYLlRww5E3Mh4XsOjE5osFNXTndVQf68G+nJBTwsA2tpD2+7U4wePqVqrKWH1sF5z9XFgubHCDkTYyHheOw+MKT89q/WZlPLTs9p5YEwj4/mgpwYAbe3h++/Sn77/V5RJJVWtSZlUUn/6/l9hwylWBCvsQIQNj04olTRl0/Vf5Wy6Q8VyVcOjE6yyA8AKe/j+uwjoaAlW2IEImywUlUktrpfMpJKaKhQDmhEAAFhuBHYgwnq6sypVFnckKFU8berOBjQjAACw3AjsQIQN9feq4jkVy1U5V7+seE5D/b1BTw0AQm9kPK8dew9p2+6D2rH3EPt/EFoEdiDCBvpy2rV9i3JdnTpXqijX1ald27dQvw4A18GmfUQJm06BiBvoyxHQAWCJ2LSPKCGwAwCA2JksFJU0aeLkjMpeTelkQresSbNpH6FESQwAAIidrlUdeuPsrKo1p2TCVK05vXF2VmtWsZaJ8OGnEgAAxI5zrvEHLbqcHwdChBV2AAAQOzNlT7ev71RH0uQ5p46k6fb1nbpQ9q5/Z6DFWGEHAACx09OdVX56Vr0b1syPFctV5bo6A5wVcHWssAMAEFNx7kPOORaIEgI7AAAxFPc+5JxjgSihJAYAgBiiDznnWCA6COxAxI2M5zU8OqHJQlE93VkN9ffyHxCA65osFLU+k1o0lkkl6UMOhBCBHYiwube0U0lb9Jb2LonQHhO8YPMnzt+/uU2XcyvsklSqeNrUnQ1wVgCupukadjP7ZTO7v/HnjJl1rdy0ADRj4VvaZvXLVNI0PDoR9NTQAnGvQfYr7t8/Nl0C0dFUYDez/1HSfknDjaFNkv7PlZoUgOZMForKpJKLxnhLOz54weZP3L9/bLoEoqPZkpg/lnSPpBclyTn3mpnxGw0EjLe0440aZH/4/rHpEoiKZktiLjrnynNXzKxDlw7zBRAQ3tKOt57urEqVxacy8oKteXz/AERFs4H9/zazv5CUMbPfkfQtSd9ZuWkBaAZvaccbL9j84fsHICrMuesvlJtZQtJHJX1Akkl6RtI+18ydI2br1q3u8OHDQU8DAJoy1+VkqlDUpph1OVkOfP8ABMnMjjjntl73dk0G9tWSZp1zXuN6UtIq51zbFfoR2IGliXNbPAAA/Gg2sDdbEvM9SZkF1zOSnruRiQFoH3FviwcAQCs0G9g7nXMzc1caf2ZXDhBzcW+LBwBAKzQb2C+Y2fvmrpjZr0sqrcyUAEQFfeABAFh5zfZh/zNJ3zKzXzSu3ybpv1uZKQGICvrAAwCw8ppaYXfO/UBSn6Q/kvQxSe92zh1ZyYkBCD/a4gEAsPLedoXdzN7vnDtoZv/NZZ/abGZyzv3nFZwbgJAb6Mtpl0RbPAAAVtD1SmJ+S9JBSf/iKp9zkgjsACRx9DEAACvlbQO7c+7TjUOTnnbOfbNFcwIQEXNtHVNJW9TWcZfEKjsAAMvkuptOnXM1M/sTSQR2AIssbOsoSdl0h4rlqoZHJ5oO7By8BADA22u2S8yzZvaIpL+VdGFu0Dl3ZkVmBSASJgtFrc+kFo0tpa0jK/T+8YIHANpfs4H9f1C9RPVjl43TCgKIMb9tHYdHJ1TxPJ2eqars1ZROJrQ207GkFfo44wUP/OIFHxANzR6cdLekv5Z0VNKPJf0HSVtWalIAosFvW8fX8tM6NV1WteaUTJiqNadT02W9lp9e4Zm3B06ahR9zL/jy07OLXvCNjOeDnhqAyzQb2L8q6d2S9qge1t/dGAMQYwN9Oe3avkW5rk6dK1WU6+rUru1bml6hK1drkkkJM5lMCTPJGuO4Lk6ahR+84AOio9mSmHc559674Po/mNnRlZgQgGgZ6Mvd8FvoqaSpVJFqNSczyTV6Q6aTtowzbF+cNAs//O5BAdA6za6w/8jM7p27Yma/Ken/XZkpAYiLu25dq5tXp9WRNHnOqSNpunl1WptvXRv01CKBk2bhR093VqWKt2iMF3xAODUb2H9T0vfN7HUze13SC5J+y8x+YmYvrdjsALS1of5epTuS2riuU++6tUsb13Uq3ZEkcDbJb0kS4o0XfEB0mHPXP5/QzH757T7vnPvZss0oYFu3bnWHDx8OehpAbMx1qZgqFLWJLhVAS/H7BwTLzI4457Ze93bNBPY4IbADAACgFZoN7M2WxAAAAAAIQGgDe6Ne/idm9mMzO9wYu8nMnjWz1xqX3Y1xM7M9ZnbMzF4ys/ct+Dofadz+NTP7SFDPBwAAALgRoQ3sDf/MOferC94q+ISk7znnNkv6XuO6JH1I0ubGx6CkL0n1gC/p06pvmr1H0qfnQj4AAAAQBWEP7Jf7sC4d2PRVSb+3YPxrru6QpPVmdpukD0p61jl3xjlXkPSspAdaPWkAAADgRoU5sDtJ3zWzI2Y22Bi71Tn3piQ1Lue2st8uaXLBfacaY9caX8TMBs3ssJkdPnny5DI/DQAAAODGNXvSaRD+qXPuF2aWk/SsmY2/zW2vdiyie5vxxQPO7ZW0V6p3ibmRyQIAAAArIbSB3Tn3i8Zl3sy+rXoN+ltmdptz7s1GyUu+cfMpST0L7r5J0i8a4wOXjY+s8NSBlprrozxZKKqHPsoAALSdUJbEmNlqM+ua+7OkD0j6qaQDkuY6vXxE0t81/nxA0h82usXcK+lco2TmGUkfMLPuxmbTDzTGgLYwMp7XzgNjyk/Pan0mpfz0rHYeGNPIeP76dwYAAJEQ1hX2WyV928yk+hz/d+fc35vZDyR908w+Kunnkv5l4/ZPSfpdScckFSX9a0lyzp0xs7+U9IPG7XY558607mkAK2t4dEKppCmbrv8qZ9MdKparGh6dYJUdAIA2EcrA7pybkPTeq4yflvTbVxl3kv74Gl/rCUlPLPccgTCYLBS1PpNaNJZJJTVVKAY0IwAAsNxCWRIDoDk93VmVKt6isVLF06bubEAzAgAAy43ADkTYUH+vKp5TsVyVc/XLiuc01N8b9NQAAMAyIbADETbQl9Ou7VuU6+rUuVJFua5O7dq+hfp1AADaSChr2AE0b6AvR0AHAKCNscIOAAAAhBiBHQAAAAgxAjsAAAAQYgR2AAAAIMQI7AAAAECIEdgBAACAEKOtI4BYGxnPa3h0QpOFonq6sxrq76VNJgAgVFhhBxBbI+N57Twwpvz0rNZnUspPz2rngTGNjOeDnhoAAPMI7ABia3h0QqmkKZvukFn9MpU0DY9OBD01AADmEdgBxNZkoahMKrloLJNKaqpQDGhGAABcicAOILZ6urMqVbxFY6WKp03d2YBmBADAlQjsAGJrqL9XFc+pWK7KufplxXMa6u8NemoAAMwjsAOIrYG+nHZt36JcV6fOlSrKdXVq1/YtdIkBAIQKbR0BxNpAX46ADtwg2qICrcEKOwAAWDLaogKtQ2AHAABLRltUoHUI7AAAYMloiwq0DjXsAABgyXq6s3r99IzOl6oqezWlkwmtzXTojpvXBD01oO2wwg4AAJbsvt6blJ8uq+zVlDCp7NWUny7rvt6bgp4a0HYI7AAAYMlemDijDWvSSicTqjkpnUxow5q0Xpg4E/TUgLZDSQwAAFiyyUJRt6xZpQ1dnfNjzjlq2IEVwAo7AABYsp7urEoVb9FYqeJpU3c2oBkB7YvADgAAlmyov1cVz6lYrsq5+mXFcxrq7w16akDbIbADAIAlG+jLadf2Lcp1depcqaJcV6d2bd/CSafACqCGHQAA3JCBvhwBHWgBVtgBAACAECOwAwAAACFGYAfgFlWGAAAgAElEQVQAAABCjMAOAAAAhBiBHQAAAAgxAjsAAAAQYgR2AAAAIMToww4g0kbG8xoendBkoaie7qyG+nvpCw0AaCussAOIrJHxvHYeGFN+elbrMynlp2e188CYRsbzQU8NAIBlQ2AHEFnDoxNKJU3ZdIfM6peppGl4dCLoqQEAsGwI7AAia7JQVCaVXDSWSSU1VSgGNCMAAJYfgR1AZPV0Z1WqeIvGShVPm7qzAc0IAIDlR2AH4MvIeF479h7Stt0HtWPvoZbWjw/196riORXLVTlXv6x4TkP9vS2bAwAAK40uMYBPce5SMrfpM5W0RZs+d0kt+R4M9OW0S/Va9qlCUZti9v0HAMQDgR2Bi3LgDTqwBm3hpk9JyqY7VCxXNTw60bLnP9CXi8X3+lqi/PsDAGgOJTEIVNTb8sW9S0kYNn0GWZITtKj//gAAmkNgR6CiHnjDEFiDFPSmz7gH1qj//gAAmkNgR6CiHniDDqxBC3rTZ9wDa9R/fwAAzSGwI1BRD7xBB9agDfTltGv7FuW6OnWuVFGuq1O7tm9pWQ113ANr1H9/AADNYdMpAjXU36udB8ZULFeVSSVVqniRCrx0KQl202dPd1b56dn5Ta9SvAJr1H9/AADNIbAjUO0QeKPepSTKXUbiHljb4fcHAHB95pwLeg6hsnXrVnf48OGgpwG0xMK2lAsDbyvLWvyae8FBYAWWLsov2IF2YGZHnHNbr3c7VtiBGAtDH3W/gSHq73AAQYn7ORJAlLDpFIixoDdtxr0tIxCkuHdZAqKEwA7EWNBdRggMQHCCfsEOoHkEdiDGgm5LSWAAghP0C3YAzSOwAxE3Mp7Xjr2HtG33Qe3Ye2hJ5SRB91EnMADBCfoFO4Dm0SXmMnSJQZREvcvLyHhej+4/qunZqqq1mjoSCXV1duivHnxvJOYPRB1dloBg0SUGiIHh0QlVPE+nZ6oqezWlkwmtzXQsqctL0G3dnCSZZGaSNa4DaAm6LAHRQGAHIuy1/LTOFStKJEzJhKlaczo1XVbFm27q/kG3dRsendC6TEq3rcvMj7W6rSQAAGFHDTsQYeVqTTIpYSaTKdFYpS5Xa03dP+guLWw6BQDg+gjsQISlkiZJqtWcnHOq1eoFJenG+PUEHZjZdAoAwPUR2IEIu+vWtbp5dVodSZPnnDqSpptXp7X51rVN3T/owEyXCsCfPc+9qvc89oze+RdP6T2PPaM9z70a9JQArAACOxBhQ/29SncktXFdp951a5c2rutUuiPZdOANOjAH3VYSiLI9z72qxw8eU6niqSNRf7H9+MFjhHagDdHW8TK0dUTU+G3LRls3IJre89gzjbB+ae2tWqspk0rqpcc+GODMADSLto5ATPhty0ZbNyCaLpQ9JeR0serJOclMSlp9HEB7IbADCFTQfeCBqFqVTKhY8TS3xdw5qeKkbIpqV6DdENiBiIty4A26DzwQZTetTql41rvisLGbVqcCmQ+AlcPLcCDC5gJvfnp2UeAdGc8HPbWmBN0HHog0M21Yk1KiscSeMGnDmlT91GAAbYUVdiDCFgZeScqmOyJ1Uuhkoaj1mcWrgRychFba89yr2vf8cV0oe1qdTuqhbXfq4fvvCnpaTenpzio/PauN6y61YS2Wq8p1dQY4KwArgRV2IMKCPvjIr6D7wCPeot4WMei2rABah8AORFgYAu/IeF479h7Stt0HtWPvoSWV4xA4EKR9zx9XwqSOREIJSzQu6+NRwDkGQHxQEgNE2FB/r3YeGFOxXFUmlVSp4rU08PrdNDrQl9MuiT7wuGF+Nl1fKNdX1hdKRKwtIm1ZgXggsAM+BdmlJejAuxw19EEHjih32Yk7vy8YV6eTunCxKqdLfcxN0upV/NcIIFz4VwnwIQxtCYMMvMuxaTTIwByGvz/cOL8vGH+7b4O+/eM356/PHfz9230bVmS+AHCj2r6G3cweMLNXzOyYmX0i6PmgvcS9LaHfGvqg21LG/e8v6vxuuj5xvqzubMeitojd2Q6dOF9e7qkCgC9tHdjNLCnpryV9SNLdknaY2d3BzgrtJOpdWvzyu2k06MAc97+/qOvpzur0hYuaODmj8RPnNXFyRqcvXGz6BeNkoajb12e15ZfW6b+6fZ22/NI63b4+y98/gNBp68Au6R5Jx5xzE865sqRvSPpwwHNCGwlDl5Yg+e1SEXRgjvvfX9Td13uT8tNllb2aEiaVvZry02Xd13tTU/fn7x9AVLR7YL9d0uSC61ONsWv62c9+pu985zuSpGq1qsHBQT311FOSpNnZWQ0ODuq73/2uJGlmZkaDg4M6ePCgJOns2bMaHBzU6OioJOnUqVMaHBzU97//fUnSiRMnNDg4qBdffLE+makpDQ4O6siRI5Kk119/XYODgzp69Kgk6dixYxocHNTY2Jgk6ZVXXtHg4KBeeeUVSdLY2JgGBwd17NgxSdLRo0c1ODio119/XZJ05MgRDQ4OampqSpL04osvanBwUCdOnJAkff/739fg4KBOnTolSRodHdXg4KDOnj0rSTp48KAGBwc1MzMjSfrud7+rwcFBzc7OSpKeeuopDQ4OqlqtSpK+853vaHBwcP57+e1vf1sf+9jH5q9/61vf0sMPPzx//cknn9THP/7x+etf//rX9eijj85f/8pXvqJPfvKT89f37dunT33qU/PXv/zlL+szn/nM/PUvfvGL+uxnPzt//Qtf+IJ27949f/3zn/+8Pv/5z89f3717t77whS/MX//sZz+rL37xi/PXP/OZz+jLX/7y/PVPfepT2rdv3/z1T37yk9p89vD8CvOZf3hChaPPza8wf/zjH9eTTz45f/uHH35Y3/rWt+avf+xjH9O3v/3t+euDg4OR/Nkb6MvpE7+Z0bv/yzf0bz6wUQN9uaZ/9m5bVVWp4ml28qc6/ff/QbXZGZUqntaffbUlP3tz7xAUjj6nM//wxPw7BJvPHg79z95XvvKV+euPPvqovv71r89fj8vP3gsTZ3TLxTe15gdPSDOnlE4mdEtpSt96fGdT/+4N9feqNDmm/NN75JWmVSxXVfrZS/JGh/l3r4GfPf7PncPP3sr97DWj3QP71c5ndlfcyGzQzA6b2eFKpdKCaaFd9ObWzK8wV7ya1qzqaHkf5JHxvAa/dlg/mjyrv3rmlZbVfy+Hf3XvO1TxnC5WPTlJxUZbyg/cfWtLHn/uHYI1qzpU8Wrz7xD05ta05PHhz2ShqFRy8T/zqaTpYrXW1P0H+nL67+95h9LJhM7P1k8I3fEbPVqfTV3/zgDQQubcFfm1bZjZfZIec859sHH9k5LknPs317rP1q1b3eHDh1s0Q8CfhV1OFvZhj9LhKXNdYujDjqX60BdG9Vp+RsmEyaze5cWrOW3OrdHTf9Yf9PQA4LrM7Ihzbuv1btfubR1/IGmzmd0p6Q1Jvy/pD4KdErB8lqMPetCC7sOO6JpfcJpbd3KXjQNAm2jrwO6cq5rZn0h6RlJS0hPOubGApwUsm+Xogx40Di7CjZope7p9fadOzdQ3nqaTCW1cs2pJJ5Xy8wcgCto6sEuSc+4pSU8FPQ9gJfR0Z5Wfnp1fYZei1eWCg4vgx9zPf++GS3sOiuV6LXozRsbzemT/Uc1crMqrOZ2auahH9h/Vv33wvfz8AQiVdt90CrQ1v33QgxZ0H3ZE21B/r86VKnotP63xE+f1Wn5a50qVpn/+P/f0yzo1U9ZspaaK5zRbqenUTFmfe/rlFZ45ACxN26+wA2Hn5y35gb6cdkm+Nm0GWRLQDiU9CJZJkmvUrTu7amuwaxl/a2ZJ4wAQFAI7EKDlKAnxs2kz6JKUqJf0hEGca7CHRye0NpPSxnWZ+bGobboGgGZQEgMEaDlKQkbG89qx95C27T6oHXsPLakPe9AlKVEv6ZH8ff+X47F3HhhTfnp20QuuKPXi92OyUFTVq2ni5IzGT5zXxMkZVb0a79AAaDsEdiBAk4WiMqnkorGllIT4DWx+H9+vuYOLcl2dOleqzB9cFJXV0aADc9AvuILWtapDU4WSihVPVc+pWPE0VShpzSrePAbQXvhXDQiQ35KQ4dEJlaueTs9U59vadXV2NF0SEIaSlCj3YQ+6D37c9wBMl8ryFrZcd5LXGG9G16qEpi9eeSpq1yrWsgCEC/8qAQHyWxLy6lvndfpCWVXPKWmmqud0+kJZr711viWPH3fL8Q6Fn5Kanu6sSpXFPcfjtAfg5IXKFZtMrTHejPXZVUsaB4CgENiBAPktCak0lhcTCZOZKZGox5ey19xJj1EvSQma38A8Mp7Xo/uP6kc/L+jEuZJ+9POCHt1/tOnQvhwvuIKswffLq9V0+U+6a4w348S52SWNA0BQKIkBAuanJCTdkVCp7KnmnMwk5yS5+ngrHj/uhvp7tfPAmIrlqjKppEoVb0mBefffj6tQrCiZMHUkE3JOKhQr2v334039nfht6xl0l6C5Odxol5tkIqHqVcJ5MtHcz3/VXf2F7bXGASAorLADEbY516VbutLqSJi8mlNHwnRLV1qbc11BTy0W/L5DMXHqghImJcxkMiXMlLD6+FLdSMQMetOq3027tdrVn/W1xq9wrZst4ZsZ5XcoAEQHK+xAhM2t8G5c13FDK7zwL8h3KPyukAe9adXvpt1EwmQ1tyhfW2O8Kaarh/Mm7x6GdygAxAMr7ECEUYMebXfenFXN1VeEnXOq1Zxqrj7eDL8r5EFvWvW7aXdNOnHVGvY16eb+a7tW5UuzFTFBv0MBID5YYQcijhr06PrEh96t/+nJH+pC2VPNSQmTVqeT+sSH3t3U/f2ukA/19+qR/Uf1xtmSvJpTMmFas6pDn/rndy/5udwIv21FZ8pX31x6rfHlFvQ7FADigxV2AAhQZyqpdDKhjoSUTibUedmK89tZjhVykyQnOeck13Q1yLLw2+XmYvXqwfxa45e7VuVMsxU1Qb9DASA+COwAEJDh0QmtzaS0+dYuvfu2ddp8a5fWZlJNl1T4Dbx+H98vvyVdZpcu5z4Wjl/PXbk1V+3jflduTVP35xwDAK1CSQxiz09bOcAPvyUVfts6hqGkw09J1+1rV2nq3MUras5vX9vcwUef+NC79cj+o5q5WF1UEtRsSZLf7z8ANIvAjlijywOC5LeGW/IXeJfj8YP03/7GO/TvnnvtquPNGOjL6d8++F5fgZs9JABagcCOWPPbVg7wY6i/V4/uP6o3CiVVazV1JBLq6mzdps+h/l49/OQPNbNg0+uadLJlj+/XCxNntHHtKk3PVlX2akon69+/FybO6OEmvwaBG0AUENgRa2EoCUC8OUkyycwku7EDkG7US1Nn58O6JNWcNFP29NLU2UiE2MlCUbesWaUNXZ3zY845fn8BtB02nSLW6PKAIA2PTmhdJqXNuS71bVyrzbkurWvhps99zx9XMmHKpJLzH8mEad/zx1vy+H7x+wsgLgjsiDW6PCBIfg8O8utC2buihWHC6uNRwO8vgLggsCPWOCkUQQp6hXh1OjlfDjOn5urjUcDvL4C4oIYdscemMwRlqL9XOw+MqViuKpNKqlTxWrpC/NC2O/X4wWOq1mpKWD2s11x9PCr4/QUQB6ywA0BABvpyevB9t+vk9EW9fGJaJ6cv6sH33d6yAPrw/XfpT9//K8qkkqrW6uU4f/r+X9HD99/VkscHADSHFXbEHgcnISgj43nt/+Eb2tC1Su9orLDv/+Ebes+m9S0N7QR0AAg3AjtiLQwHJ8X9BUOcn38YzgGI8/cfAKKCkhjE2sLAZFa/TCWtZW31RsbzemT/Uf1osqC3zs/qR5MFPbL/qEbG8y15/KDNvWDKT88uesEUl+cfdJeYuH//ASAqCOyItaAD0+eefllnixW5mpQ0k6tJZ4sVfe7pl1vy+EEL+gVT0Hq6szo1c1ETJ2c0fuK8Jk7O6NTMxZZ1iRkenVDF83Ti3KxeeWtaJ87NquJ5sfn+A0BUENgRa0G31Tt+uqhazemiV9NstaaLXk21mtPx0/E4qTHoF0xBu6/3Jr11/qIulOvdYS6UPb11/qLu672pJY//Wn5ap6bLqtackglTteZ0arqs1/LTLXl8AEBzCOyItaAPXqlUa6pdNlZrjMdB0C+YpHpZyI69h7Rt90Ht2HuopeUg3zoypcvaoMs1xpvlZ/7lak0151TxarpYqani1a+XY/LzBwBRQWBHrAV+8IotcbzNBP2CKega7qlCSZJkdulj4fj1+J1/zdXkNXqvO9UvPSc5R2AHgDChSwxij4NXgjPQl9Mu1WuppwpFbWpxl5Kgu7Rcvrp+vfHL+Z2/d41czgI7AIQLgR0I0JpVHbpwsSonybnGKquk1avi86sZ5AumyUJR6zOpRWOtrKHPpBIqVWpy7srxZvidf7V29ZcG1xoHAASDkhggQA9tu1MyUzJhSnfUL2UWqaPh/drz3Kt6z2PP6J1/8ZTe89gz2vPcqy177KBr6P/ot94p06UKqLk//9FvvbOp+/vuMuN3iR8A0BIEdiBAcT8afs9zr+rxg8dUqnjqSNTD8uMHj7UstAddQ//w/Xfp4/dvVldnh5IJU1dnhz5+/+am//7v671JJ2fKKns1JUwqezWdnCk33WUmlbz6fwHXGg+jIDcNA0CrxOd9dyCk4nw0/L7njythUkeiHhATJlVrNe17/nhLvicDfTk9OHVW+54/rgtlT6vTST207c4llej4PSnUz9//CxNnlOtK63ypqrJXUzqZ0NpMh16YOKOHm7h/InH1pfTkNcbDJgwnFQNAKxDYgYiL8tHyF8r1lfWFElYfb4WR8bz2//ANbehapXekkipVPO3/4Rt6z6b1TX0Pgw6Mk4Wibl69Sres6Zwfc841XcOesIQSVmvc71KXGrNorLAHvWkYAFolGv8qA23Mz1v6Qbcl9Gt1OqnL9zfWXH28FfyetBr0Sa1+a/DTHQklzZRKJrQqlVAqWb+evvxVVEjF/eAtAPERjX+VgTblN3AHHRglfy84Htp2p2quXgZTc7XGpVq26dZv4JssFFX1aos2fVa9WssCo98a/M25Lt3SlVZHwuTVnDoSplu60tqc61rhmS+PoDcNA0CrENiBAPkN3EGvMPp9wRH0plu/gW9NOqk3zs6q6jklzVT1nN44O9uydwj8Hvw11N+rVDKpjes69a5bu7RxXadSyWTLNt36FfSmYQBoFWrYEXtB1oD77aPd051Vfnp2voZXau0K43LUEAe56Xaov1c7D4ypWK4q06hhX0rgs/mib13qzegWjLeAnz72QR9c5VfU5w8AzSKwI9aC3jTY053V8VMzmp691OWjq7NDd96ypqn7+w2cfgV98JBffgPf9MWqbl/fqVON1orpZEIb167SzMXqyk58GUX9pN+ozx8AmkFgR6wF3WXivt6b9OLx0/MbLyuep1LF0x/c846m7h/0CmPQK/yS/3dI/AS+ueffu+HSC6xiuapcV+fb3AsAgKUhsCPWgl4hfvqnJ+arKZwuVVY8/dMTTZeJBLnCGPQKf9DvkAz19+rR/Uf1RqGkaq2mjkT9HZJP/fO7V/yxAQDxwaZTxFrQXSYmTl2QWb3/tUnzf544daElj++X302PfoWhS46TJGvUrVvjOgAAy4gVdsRa0CvENedUrTX2K1r98Jqqk8yiE/uCXOEP+h2S4dEJrcukdNu6zPxY1A7u2fPcq1ec9BrXk3cBIKwI7Ii1oGvAOxKmiufqq7Ju8Xhc+KlBD7qGPugXDH7tee5VPX7wmBImdSTq37vHDx6TJEI7AIQIgR2xF+QKcTad1MVqTc4tqGG31p30GTS/NehB15AvxwuGINuK7nv+eCOs16sjE1Y/xGrf88cJ7AAQItSwAwG669a1ynWtUjadbNRiJ5XrWqXNt64NemotsRw16EHWkPs9uGdkPK9H9h/VjyYLeuv8rH40WdAj+48u6bRYPy6UPck5Xax6mq14ulitX79Q9q5/ZwBAyxDYgQAN9fcq3bH4pMl0R3ROmvTL70mtczXkm3Nd6tu4VptzXVqXSbVs06nfTbefe/plnS1W5GpS0kyuJp0tVvS5p19ueg4j43nt2HtI23Yf1I69h5YU9ld1JFSp1fdOzO2hqNTq4wCA8KAkBghQ0DX0QfNbUhKGGnI/JVXHTxeVMCnR2LNgJrma0/HTzc3fb0nRTZkOFcveFXsobsrwXwMAhAn/KgMBi/NJjX5r0Hu6s3r99IzOly6dFLs206E7bm7upNioGx6dULnq6fTM4pNym+5Sk0how5qUTl+oqObqNew3r07JEqywA0CYENgBBMpPDfp9vTfpH18/U1+lNqns1ZSfLmvHb9y0QrNdXr23rNb4iWmVvUs14yapb2NzLzhefeu8zs9WlZApaaaq53T6QllV73xT9597h2PjukvvaHBSKwCED8soAALjtwb9hYkz2rAmrXQyoZqT0smENqxJ64WJMys880v81JD3bVxzxQsUp+YDe8Wr3zuRMJnZfGlN2WvuZY/fTbMAgNZghR1AYPzWoE8WirplzSptWLAi7JxrWQ273xry742f1FzLfefqNexz481IdyRUKnuqOVevf3eSXH28GWHYQxFkW0sAiAoCO4DA+N10uhx90P2c9LmwLaUkZdMdSzrp9ELZUyppStilgF1ztabbKm7OdV1Zw786taQa/iD3UPh9wQMAcUFJDBAwPyUVUee3JMPv/edO+ixVvEUnfe557tWm7u+3LeXqdFK1y6pXaq75g7OG+nuVSi5uC5pKRqct6HL04QeAOCCwAz75CdxzK4z56dlFK4xxCe1++5j7vf/Ckz4Tlmhc1seb0dOdVamyeDV8KSv8D227UzVXP1205mqNy/p4M/w+/6D5fcEDAHFBSQzgg9+39P2WVLQDvyUZfu5/oVxfWV8oYWq6JGWov1c7D4ypWK4qk0qqVPGWtML/8P136fipGR146YQqnlMyYdr+no1Nl+RI/r9/QdaQL0dJEwDEASvsgA9+39JfjhXGOJfU+OW3JMXvCvfIeF5Hfn5Od9yc1T/5pbW64+asjvz8XMv+DoN+h4cuNQDQHFbYAR/8djnxu8LIpj1/Htp2px4/eEzVWk0Jq4f1pZSkSP5WuIN+hyXoxw9DlxoAiAICO+CD38Dtt6Qi6MAVdctRkuKH3xd8UX98Kd4n/QJAsyiJAXzw+5b+QF9OD77vdp2cvqiXT0zr5PRFPfi+25sOMGza8yfokpSe7qxOzVzUxMkZjZ84r4mTMzo1c7FlNdx+N80CAFqDwA74sBw1zPt/+IY2dK3Suzd2aUPXKu3/4RtNB0YClz9BtxW8r/cmnZwpq+zVS3LKXk0nZ8q6r/emljw+NeQAEA2UxAA+BVnD7LekJu6CLgl5YeKMcl3pxQcfZTr0wsQZPdyCx6eGHACigcAOBMhvYBzoy+nBqbNXnNRJ4GpO0G0FJwtF3bx6lW5Z0zk/5pyjhhwAsAglMUCA/Ja0+C2pibugS0IoaQIANIPADgTIb2AMugY76gb6cvr1d6zT66eL+ukvzuv100X9+jvWtWzFOegXDACAaCCwAwHyu2mVLjH+7HnuVR146YQSJq3qMCVMOvDSCe157tWWPL7fv38AQDxQww4EzE8NcdA12GEwMp7X8OiEJgtF9Sxx0+S+548rYVJHor52kTCpWqtp3/PHW9aLnRpyAMD1sMIORFjcSyrmTnrNT88uOum12Rr+C2VPCVs8lrD6eKuMjOe1Y+8hbdt9UDv2HmL/AQDgCgR2IMLiXlLht4Z/dTqpmls8VnP18Vbw+4IDABAPlMQAERfnkgq/bTEf2nanHj94TNVa/eCimqt/PLTtzpWY7hX89uEHAMQDK+wAIstvW8SH779L9/zyelU8p4tVp4rndM8vr29Z/TqbhgEAzSCwA4gsvzX8e557Vf/4s7NKJU2rOkyppOkff3a2ZV1i6MMOAGhG6AK7mT1mZm+Y2Y8bH7+74HOfNLNjZvaKmX1wwfgDjbFjZvaJBeN3mtmLZvaamf2tmaVb/XwArBy/NfwLu8QkLNG4rI+3Qtw3DQMAmhO6wN7w751zv9r4eEqSzOxuSb8vaYukByT9RzNLmllS0l9L+pCkuyXtaNxWknY3vtZmSQVJH231EwHQGu76N7lC0F1i4r5pGADQnChtOv2wpG845y5KOm5mxyTd0/jcMefchCSZ2TckfdjMXpb0fkl/0LjNVyU9JulLLZ01gBUz12UllbRFXVZ2SU2F3tXppEqVxaG9lV1ipHhvGgYANCesK+x/YmYvmdkTZtbdGLtd0uSC20w1xq41frOks8656mXjVzCzQTM7bGaHT548uZzPA8AK8tvW8aFtd6rm6ocl1Vytcdm6LjESfdgBANcXSGA3s+fM7KdX+fiw6ivg75T0q5LelPT5ubtd5Uu5Gxi/ctC5vc65rc65rRs2bFjy8wEQDL9dVh6+/y5tf89G1Zx0sepUc9L292xsWZcY+rADAJoRSEmMc+7+Zm5nZn8j6f9qXJ2S1LPg05sk/aLx56uNn5K03sw6GqvsC28PoA30dGf1+ukZnS9VVfZqSicTWpvp0B03r2nq/iPjeR35+TndcXNWmVS9POb/b+/+g+w6ywKOf5+9u9tNmrVJadJCk9pGM4ZGsWJkRGqsgFLQKaD8UtEqKGGAUUdRRJwgGTsjzmgRRSbIj3YQKVitBAQUbOOKVDBpizQ0QN1Wk5Z2+bFNtt1sdu/dxz/u2bDZ7iY3Obv3ns39fma29973nHPPu8++0/OcN+95333/d5g9B0baMkzFedglSa2o3JCYiHjirI8vBO4u3u8GXhYR50TEZcAm4PPAfwGbihlh+mk+mLo7MxO4DXhRcfy1wEfa8TtIao+nbzyfkbFJJhvNhY8mG9OMjE3y9I3nt3T8rqFhJusNHjo8wZcfHuOhwxNM1hstD6mBckNanIddktSKKj50+icRcQXN4Sv3A9sBMnN/RO4opIoAABKoSURBVHwY+BJQB16bmQ2AiHgd8M9ADXhvZu4vvusNwE0R8UfAncB72vmLSK3Yc2CEXUPDHBwdZ8OalWzfttHe1RbdPvwt1q7qZ2zi2z3sgwO93D78LX69heO/8vARjkzU6SGoRVBvJN98bJJ640hL5y/70OuGNSsZGZs43sMOzsMuSXq8yiXsmfmLJ9l2HXDdPOUfBz4+T/kw355JRqqcsglftzs4Os4Fq85h7eDA8bLMbLmHeqrRfKylp5gmJgKmp5PJRmuTRJYd0rJ920Z27N7P+GT9+JAc52GXJM1VuSExUjcpO8tJtyu7Umh/bw8kTGeSJNOZkEV5C8oOaXEedklSKyrXwy51k4Oj46xe0XdCmWOYW1e2h3rTusHHP7R6bl/LD60uxpAW52GXJJ2KPexSB5XtIe52ZXuot2/bSF+txkXnDfA9Fw5y0XkD9NVqLSf827dtZKqRjE/WyWy+OqRFkrTY7GGXOsgxzOWV6aG+avM6dtIcmnRodJz1p/nQb9njJUlqRTRnP9SMrVu35t69eztdDXWRt3/6K7z7M/fx2GSDc/tr/OqVl7Vt4R5JktQ5EbEvM7eeaj972KUO2nNghJvveIC1g+dwSdHDfvMdD/CU9avtpW0Tb5gkSVVnwi6VVGYedVe67Ky3f/or/Pmt99IT0NvTfH7gz2+9F6DlpN159CVJS82HTtX1yqxUOTOP+sjYxAnzqLf6HQdHx6k3phn++qMceOgIw19/lHpj2lli2uTdn7mvSNZ76Ime4rVZ3oqyf39Jklphwq6uVjbhKjuP+qr+Gg88MkG9kcdX2nzgkQnO7a+d+mCV9thkg2LNpON6olneCufRlyS1gwm7ulrZhKvswjkRQWYyOT3Nsfo0k9PTZCYRceqDVdq5/TXqjeRYvcHEVINj9Qb1RrZ8w1T27y9JUitM2NXVyiZcZedR//qjx5pvmgtsFv+ZVa4l9azNa2kkTBfxn05oZLO8Fc6jL0lqBxN2dbWyCVfZhXMm69P09AQDfTVW9NUY6KvR0xNM1qdP+3fR6XvoyCRrVvYeHxbTE7BmZS8PHZls6XgXTpIktYMJu7pa2YSr7EqbfbVgOpOJqQZHp5rDMqYz6a85JKYdDo6Oc/HqlWx50nl838XnseVJ53Hx6pUt/wtL2b+/JEmtcFpHdbXFWKmyzEqba1edw+hjUyeU5TRcsOqcM/o+nZ4Na1YyMjZxfFpNOP0hLWX+/pIktcKEXV2vkwlXRNDTE9R6ggjIhMa0D522y/ZtG9mxez/jk3VWFAtXOaRFklQ1DomROmjsWJ2LVw/Q2xM0ppPenuDi1QM8eqze6ap1BYe0SJKWA3vYpQ6aGZKxce2q42Xjk3XWDQ50sFbdxSEtkqSqs4dd6iBnGZEkSadiD7vUQYvx0Gu323NghF1DwxwcHWeD8ZMknYVM2KUOc0jGmdtzYIQdu/fTVwtWr+hjZGyCHbv3sxOMqSTprOGQGEnL1q6hYfpqwcr+XiKar321YNfQcKerJknSorGHXeowh3ScuYOj46xe0XdC2Yq+WssLH0mStByYsKvrdTJhdkhHOYux8JEkSVXnkBh1tZmEeWRs4oSEec+Bkbac3yEd5TjLjiSpG5iwq6t1OmE+ODrOir7aCWUO6WidCx9JkrqBQ2LU1To9BtohHeU5y44k6WxnD7u62oY1Kzk61TihrJ0Js0M6JEnSqZiwq6t1OmF2SIckSToVh8Soq1VhpVGHdEiSpJMxYVfXM2GWJElV5pAYSZIkqcJM2CVJkqQKM2GXJEmSKsyEXZIkSaowE3ZJkiSpwkzYJUmSpApzWkeppD0HRtg1NMzB0XE2dGAed0mSdHYzYZdK2HNghB2799NXC1av6GNkbIIdu/ezE0zau4Q3bJKkpWbCLpWwa2iYyXqDbz5aZ7IxTX+th8GBXnYNDZu0tUknE2Zv2CRJ7eAYdqmErzx8hG8+Nkm9kdQiqDeSbz42yVcfPtLpqnWFmYR5ZGzihIR5z4GRtpx/19AwfbVgZX8vEc3Xvlqwa2i4LeeXJHUHE3aphKlGAtDTE0QEPT0BwGRRrqXV6YT54Og4K/pqJ5St6KtxaHS8LeeXJHUHE3aphP7eHkiYziRJpjMhi3ItuU4nzBvWrOToVOOEsqNTDdavWdmW80uSuoNZhVTCpnWDXDDYT29P0JhOenuCCwb72bRusNNV6wqdTpi3b9vIVCMZn6yT2XydaiTbt21sy/klSd3BhF0qYfu2jfTValx03gDfc+EgF503QF+tZsLWJp1OmK/avI6d12xh3eAAh49OsW5wgJ3XbPGBU0nSoopMx9rOtnXr1ty7d2+nq6FlZGaWkkOj46x3Wr+2M/6SpOUqIvZl5tZT7mfCfiITdkmSJLVDqwm7Q2IkSZKkCjNhlyRJkirMhF2SJEmqMBN2SZIkqcJM2CVJkqQK6+10BaTlbmZawYOj42xwWkFJkrTITNilEvYcGGHH7v301YLVK/oYGZtgx+797IS2Je3eMEiSdHZzSIxUwq6hYfpqwcr+XiKar321YNfQcFvOP3PDMDI2ccINw54DI205vyRJWnom7FIJB0fHWdFXO6FsRV+NQ6PjbTl/p28YJEnS0jNhl0rYsGYlR6caJ5QdnWqwfs3Ktpy/0zcMkiRp6ZmwSyVs37aRqUYyPlkns/k61Ui2b9vYlvN3+oZBkiQtPRN2qYSrNq9j5zVbWDc4wOGjU6wbHGDnNVva9tBnp28YJEnS0nOWGKmkqzav69isLFdtXsdOmmPZD42Os95ZYiRJOuuYsEvLXCdvGCRJ0tJzSIwkSZJUYSbskiRJUoWZsEuSJEkVZsIuSZIkVZgJuyRJklRhJuySJElShZmwS5IkSRVmwi5JkiRVmAm7JEmSVGEm7JIkSVKFmbBLkiRJFWbCLkmSJFWYCbskSZJUYSbskiRJUoV1JGGPiBdHxP6ImI6IrXO2vTEi7o2IL0fEc2aVX12U3RsRvzer/LKI+FxEfDUiPhQR/UX5OcXne4vtl7br95MkSZIWS6d62O8GfgYYml0YEZcDLwO2AFcDfxURtYioAe8AngtcDvxcsS/AW4HrM3MTMAq8sih/JTCamd8NXF/sJ0mSJC0rHUnYM/OezPzyPJueD9yUmccy8z7gXuBpxc+9mTmcmZPATcDzIyKAZwI3F8ffCLxg1nfdWLy/GXhWsb8kSZK0bFRtDPvFwMFZnw8VZQuVPwF4JDPrc8pP+K5i++Fif0mSJGnZ6F2qL46ITwMXzbPpTZn5kYUOm6csmf/GIk+y/8m+6/EnjXgV8CqASy65ZIGqSZIkSe23ZAl7Zj77DA47BGyY9Xk98GDxfr7ybwCrI6K36EWfvf/Mdx2KiF7gPOBbC9T1XcC7ALZu3TpvUi9JkiR1wpIl7GdoN/C3EfFnwJOATcDnafaWb4qIy4AHaD6Y+vOZmRFxG/AimuParwU+Muu7rgVuL7bfmpmnTMb37dv3jYj43zOs/wU0byJ0ZoxfOcavHONXjvErx/iVY/zKMX7llInfd7ayU7SQwy66iHgh8BfAWuAR4K7MfE6x7U3AK4A68JuZ+Ymi/HnA24Aa8N7MvK4o30gzWT8fuBN4eWYei4gB4P3AD9DsWX9ZZg4v8e+1NzO3nnpPzcf4lWP8yjF+5Ri/coxfOcavHONXTjvi15Ee9sy8BbhlgW3XAdfNU/5x4OPzlA/TnEVmbvkE8OLSlZUkSZI6qGqzxEiSJEmaxYR9cb2r0xVY5oxfOcavHONXjvErx/iVY/zKMX7lLHn8OjKGXZIkSVJr7GGXJEmSKsyE/QxExHsjYiQi7p5V9ocR8UBE3FX8PK+TdayyiNgQEbdFxD0RsT8ifqMoPz8iPhURXy1e13S6rlV0kvjZBlsQEQMR8fmI+EIRv7cU5ZdFxOeK9vehiOjvdF2r6CTxuyEi7pvV/q7odF2rLCJqEXFnRHys+Gz7Ow3zxM/216KIuD8ivljEaW9R5vW3RQvEb8mvvybsZ+YG4Op5yq/PzCuKn8fNaKPj6sBvZ+aTgR8GXhsRlwO/B/xrZm4C/rX4rMdbKH5gG2zFMeCZmfn9wBXA1RHxw8BbacZvEzAKvLKDdayyheIH8Duz2t9dnavisvAbwD2zPtv+Ts/c+IHt73T8eBGnmakIvf6enrnxgyW+/pqwn4HMHGKBVVN1apn5tcy8o3g/RvN/uhcDzwduLHa7EXhBZ2pYbSeJn1qQTY8WH/uKnwSeCdxclNv+FnCS+KlFEbEe+Cng3cXnwPbXsrnx06Lw+ltxJuyL63UR8d/FkBn/OakFEXEpzcWtPgdcmJlfg2ZSCqzrXM2WhznxA9tgS4p/Tr8LGAE+BfwP8Ehm1otdDuFN0ILmxi8zZ9rfdUX7uz4izulgFavubcDvAtPF5ydg+zsdc+M3w/bXmgT+JSL2RcSrijKvv62bL36wxNdfE/bF807gu2j+E/HXgD/tbHWqLyJWAX9Pc0XbI52uz3IzT/xsgy3KzEZmXgGsp7nw2pPn2629tVo+5sYvIr4XeCOwGfghmitPv6GDVaysiPhpYCQz980unmdX2988Fogf2P5OxzMy86nAc2kOqdzW6QotM/PFb8mvvybsiyQzHy4uYtPAXzPP6qv6tojoo5lsfiAz/6EofjginlhsfyLN3jvNY7742QZPX2Y+Auyh+SzA6oiYWf15PfBgp+q1XMyK39XFUK3MzGPA+7D9LeQZwDURcT9wE82hMG/D9teqx8UvIv7G9te6zHyweB2huer80/D627L54teO668J+yKZaeiFFwJ3L7RvtyvGa74HuCcz/2zWpt3AtcX7a4GPtLtuy8FC8bMNtiYi1kbE6uL9CuDZNJ8DuA14UbGb7W8BC8TvwKyLfdAc/2r7m0dmvjEz12fmpcDLgFsz8xew/bVkgfi93PbXmog4NyIGZ94DP0kzVl5/W7BQ/Npx/e099S6aKyI+CFwFXBARh4A3A1cV00glcD+wvWMVrL5nAL8IfLEYBwvw+8AfAx+OiFcC/we8uEP1q7qF4vdztsGWPBG4MSJqNDstPpyZH4uILwE3RcQfAXfSvCnS4y0Uv1sjYi3N4R13Aa/uZCWXoTdg+yvjA7a/llwI3NK8r6EX+NvM/GRE/Bdef1uxUPzev9TXX1c6lSRJkirMITGSJElShZmwS5IkSRVmwi5JkiRVmAm7JEmSVGEm7JIkSVKFmbBL0jIXEZdGxOPm/Y2InRHx7FMc+4cR8fqlq50kqSznYZeks1Rm7uh0HSRJ5dnDLklnh1pE/HVE7I+If4mIFRFxQ0S8CCAinhcRByLiMxHx9oj42KxjL4+IPRExHBG/Xuz/u7PeXx8RtxbvnxURf1O8f2dE7C3O+ZZZ22+Z+eKI+ImI+Ie5lY2IX46If4yIj0bEfRHxuoj4rYi4MyL+MyLOL/bbExFvi4jPRsTdEfG0onxtRHwqIu6IiF0R8b8RccGSRFaSOsyEXZLODpuAd2TmFuAR4GdnNkTEALALeG5mXgmsnXPsZuA5wNOAN0dEHzAE/GixfSuwqii/Evj3ovxNmbkVeArwYxHxFOBW4MnFqpMAvwK8b4E6fy/w88V5rwPGM/MHgNuBX5q137mZ+SPAa4D3FmVvprks/VOBW4BLThEfSVq2TNgl6exwX2beVbzfB1w6a9tmYDgz7ys+f3DOsf+Umccy8xvACM3lt/cBPxgRg8Axmkn0VppJ/EzC/pKIuAO4E9gCXJ7N5bPfD7w8IlYDTwc+sUCdb8vMscz8OnAY+GhR/sU59f8gQGYOAd9RfO+VwE1F+SeB0ZPERpKWNcewS9LZ4dis9w1gxazPcZrH9mbmVETcT7OH/LPAfwM/DnwXcE9EXAa8HvihzByNiBuAgeI73kcz+Z4A/i4z6xHxQpq94gC/Os95p2d9nubE61POqW+28DtJ0lnDHnZJOvsdADZGxKXF55e2eNwQzaR8iGav+quBu4pe9O8AHgMOR8SFwHNnDsrMB4EHgT8AbijKbsnMK4qfvadZ/5cCRMSVwOHMPAx8BnhJUf6TwJrT/E5JWjbsYZeks1xmHo2I1wCfjIhvAJ9v8dB/B94E3J6Zj0XERFFGZn4hIu4E9gPDwH/MOfYDwNrM/NIi/AqjEfFZmjcJryjK3gJ8MCJeCvwb8DVgbBHOJUmVE82OEknS2SwiVmXmoxERwDuAr2bm9Ut4vr8E7szM95T8nj3A6+f2ykfEOUCjGG7zdOCdmXlFmXNJUlXZwy5J3eHXIuJaoJ/mQ6K7lupEEbGP5nCZ316qc9CcFebDEdEDTAK/toTnkqSOsoddkiRJqjAfOpUkSZIqzIRdkiRJqjATdkmSJKnCTNglSZKkCjNhlyRJkirMhF2SJEmqsP8H7Cv8sicTl/MAAAAASUVORK5CYII=\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": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Y_hat = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/raman/anaconda3/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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": 29,
   "metadata": {
    "collapsed": 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": 30,
   "metadata": {
    "collapsed": 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": 31,
   "metadata": {
    "collapsed": 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": 32,
   "metadata": {
    "collapsed": 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": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 33,
     "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": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            11             10             9           8         7\n",
      "-1.243e-08 x  + 4.722e-06 x  - 0.0008028 x + 0.08056 x - 5.297 x\n",
      "          6        5             4             3             2\n",
      " + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "f_11 = np.polyfit(x, y, 11)\n",
    "p_11 = np.poly1d(f_11)\n",
    "print(p_11)\n",
    "\n",
    "PlotPolly(p_11, x, y, 'highway-mpg')"
   ]
  },
  {
   "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 3rd order (cubic) \n",
    "f1 = np.polyfit(x, y, 11)\n",
    "p1 = np.poly1d(f1)\n",
    "print(p)\n",
    "PlotPolly(p1,x,y, 'Length')\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": 36,
   "metadata": {
    "collapsed": 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": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": 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": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "after the transformation, there 201 samples and 15 features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 41,
   "metadata": {
    "collapsed": true
   },
   "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": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we input the list as an argument to the pipeline constructor "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False))])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/raman/anaconda3/lib/python3.7/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  return self.partial_fit(X, y)\n",
      "/home/raman/anaconda3/lib/python3.7/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  return self.fit(X, y, **fit_params).transform(X)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False))])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/raman/anaconda3/lib/python3.7/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  Xt = transform.transform(Xt)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #5:</h1>\n",
    "<b>Create a pipeline that Standardizes the data, then perform prediction using a linear regression model using the features Z and targets y</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/raman/anaconda3/lib/python3.7/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  return self.partial_fit(X, y)\n",
      "/home/raman/anaconda3/lib/python3.7/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  return self.fit(X, y, **fit_params).transform(X)\n",
      "/home/raman/anaconda3/lib/python3.7/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  Xt = transform.transform(Xt)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([13699.11161184, 13699.11161184, 19051.65470233, 10620.36193015,\n",
       "       15521.31420211])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \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[0:5]"
   ]
  },
  {
   "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": 47,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.7609686443622008\n"
     ]
    }
   ],
   "source": [
    "#highway_mpg_fit\n",
    "lm.fit(X, Y)\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(X, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\"."
   ]
  },
  {
   "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": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output of the first four predicted value is:  [13728.4631336  13728.4631336  17399.38347881 10224.40280408]\n"
     ]
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "print('The output of the first four predicted value is: ', Yhat[0:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "lets import the function <b>mean_squared_error</b> from the module <b>metrics</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": 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": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value is:  15021126.02517414\n"
     ]
    }
   ],
   "source": [
    "mse = mean_squared_error(df['price'], Yhat)\n",
    "print('The mean square error of price and predicted value is: ', mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 2: Multiple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.8093562806577457\n"
     ]
    }
   ],
   "source": [
    "# fit the model \n",
    "lm.fit(Z, df['price'])\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(Z, df['price']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 80.896 % of the variation of price is explained by this multiple linear regression \"multi_fit\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we produce a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": 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": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value using multifit is:  11980366.87072649\n"
     ]
    }
   ],
   "source": [
    "print('The mean square error of price and predicted value using multifit is: ', \\\n",
    "      mean_squared_error(df['price'], Y_predict_multifit))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 3: Polynomial Fit</h3>"
   ]
  },
  {
   "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": 54,
   "metadata": {
    "collapsed": 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": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square value is:  0.674194666390652\n"
     ]
    }
   ],
   "source": [
    "r_squared = r2_score(y, p(x))\n",
    "print('The R-square value is: ', r_squared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 67.419 % of the variation of price is explained by this polynomial fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>MSE</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the MSE:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20474146.426361218"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 57,
   "metadata": {
    "collapsed": 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": 58,
   "metadata": {
    "collapsed": 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": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X, Y)\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce a prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7796.47889059, -7629.6188749 , -7462.75885921, -7295.89884352,\n",
       "       -7129.03882782])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat=lm.predict(new_input)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot the data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": 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": [
    "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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