model-development.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/Logos/organization_logo/organization_logo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n",
    "</center>\n",
    "\n",
    "# Model Development\n",
    "\n",
    "Estimated time needed: **30** minutes\n",
    "\n",
    "## Objectives\n",
    "\n",
    "After completing this lab you will be able to:\n",
    "\n",
    "-   Develop prediction models\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>In this section, we will develop several models that will predict the price of the car using the variables or features. This is just an estimate but should give us an objective idea of how much the car should cost.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some questions we want to ask in this module\n",
    "\n",
    "<ul>\n",
    "    <li>do I know if the dealer is offering fair value for my trade-in?</li>\n",
    "    <li>do I know if I put a fair value on my car?</li>\n",
    "</ul>\n",
    "<p>Data Analytics, we often use <b>Model Development</b> to help us predict future observations from the data we have.</p>\n",
    "\n",
    "<p>A Model will help us understand the exact relationship between different variables and how these variables are used to predict the result.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "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:\n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                9.0       154.0    5000.0       19          26  16500.0   \n",
       "3               10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                8.0       115.0    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# path of data \n",
    "path = 'https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>1. Linear Regression and Multiple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Linear Regression</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>One example of a Data  Model that we will be using is</p>\n",
    "<b>Simple Linear Regression</b>.\n",
    "\n",
    "<br>\n",
    "<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n",
    "<ul>\n",
    "    <li>The predictor/independent variable (X)</li>\n",
    "    <li>The response/dependent variable (that we want to predict)(Y)</li>\n",
    "</ul>\n",
    "\n",
    "<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    " Y: Response \\\\ Variable\\\\\n",
    " X: Predictor \\\\ Variables\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <b>Linear function:</b>\n",
    "$$\n",
    "Yhat = a + b  X\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li>a refers to the <b>intercept</b> of the regression 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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Lets load the modules for linear regression</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Create the linear regression object</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How could Highway-mpg help us predict car price?</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this example, we want to look at how highway-mpg can help us predict car price.\n",
    "Using simple linear regression, we will create a linear function with \"highway-mpg\" as the predictor variable and the \"price\" as the response variable.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[['highway-mpg']]\n",
    "Y = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using highway-mpg.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can output a prediction \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
       "       20345.17153508])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "Yhat[0:5]   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>What is the value of the intercept (a)?</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.3058581574"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>What is the value of the Slope (b)?</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-821.73337832])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What is the final estimated linear model we get?</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, we should get a final linear model with the structure:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b  X\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plugging in the actual values we get:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>price</b> = 38423.31 - 821.73 x  <b>highway-mpg</b>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 a): </h1>\n",
    "\n",
    "<b>Create a linear regression object?</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1 = LinearRegression()\n",
    "lm1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm1 = LinearRegression()\n",
    "lm1 \n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question #1 b): </h1>\n",
    "\n",
    "<b>Train the model using 'engine-size' as the independent variable and 'price' as the dependent variable?</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.fit(df[['engine-size']], df['price'])\n",
    "lm1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm1.fit(df[['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",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Slope</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([166.86001569])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Intercept</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7963.338906281042"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# Slope \n",
    "lm1.coef_\n",
    "# Intercept\n",
    "lm1.intercept_\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 d): </h1>\n",
    "\n",
    "<b>What is the equation of the predicted line. You can use x and yhat or 'engine-size' or 'price'?</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "Yhat=-7963.34 + 166.86*X\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# using X and Y  \n",
    "Yhat=-7963.34 + 166.86*X\n",
    "\n",
    "Price=-7963.34 + 166.86*engine-size\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Multiple Linear Regression</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>What if we want to predict car price using more than one variable?</p>\n",
    "\n",
    "<p>If we want to use more variables in our model to predict car price, we can use <b>Multiple Linear Regression</b>.\n",
    "Multiple Linear Regression is very similar to Simple Linear Regression, but this method is used to explain the relationship between one continuous response (dependent) variable and <b>two or more</b> predictor (independent) variables.\n",
    "Most of the real-world regression models involve multiple predictors. We will illustrate the structure by using four predictor variables, but these results can generalize to any integer:</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Y: Response \\\\ Variable\\\\\n",
    "X_1 :Predictor\\\\ Variable \\\\ 1\\\\\n",
    "X_2: Predictor\\\\ Variable \\\\ 2\\\\\n",
    "X_3: Predictor\\\\ Variable \\\\ 3\\\\\n",
    "X_4: Predictor\\\\ Variable \\\\ 4\\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "a: intercept\\\\\n",
    "b_1 :coefficients \\\\ of\\\\ Variable \\\\ 1\\\\\n",
    "b_2: coefficients \\\\ of\\\\ Variable \\\\ 2\\\\\n",
    "b_3: coefficients \\\\ of\\\\ Variable \\\\ 3\\\\\n",
    "b_4: coefficients \\\\ of\\\\ Variable \\\\ 4\\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equation is given by\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From the previous section  we know that other good predictors of price could be:</p>\n",
    "<ul>\n",
    "    <li>Horsepower</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Highway-mpg</li>\n",
    "</ul>\n",
    "Let's develop a model using these variables as the predictor variables.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using the four above-mentioned variables.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(Z, df['price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the value of the intercept(a)?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15806.62462632922"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the values of the coefficients (b1, b2, b3, b4)?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([53.49574423,  4.70770099, 81.53026382, 36.05748882])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " What is the final estimated linear model that we get?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, we should get a final linear function with the structure:\n",
    "\n",
    "$$\n",
    "Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
    "$$\n",
    "\n",
    "What is the linear function we get in this example?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Price</b> = -15678.742628061467 + 52.65851272 x <b>horsepower</b> + 4.69878948 x <b>curb-weight</b> + 81.95906216 x <b>engine-size</b> + 33.58258185 x <b>highway-mpg</b>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #2 a): </h1>\n",
    "Create and train a Multiple Linear Regression model \"lm2\" where the response variable is price, and the predictor variable is 'normalized-losses' and  'highway-mpg'.\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute\n",
    "lm2 = LinearRegression()\n",
    "lm2.fit(df[['normalized-losses','highway-mpg']], df['price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm2 = LinearRegression()\n",
    "lm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  #2 b): </h1>\n",
    "<b>Find the coefficient of the model?</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1.49789586, -820.45434016])"
      ]
     },
     "execution_count": 23,
     "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",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>2)  Model Evaluation using Visualization</h3>\n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "import the visualization package: seaborn\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the visualization package: seaborn\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Regression Plot</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When it comes to simple linear regression, an excellent way to visualize the fit of our model is by using <b>regression plots</b>.</p>\n",
    "\n",
    "<p>This plot will show a combination of a scattered data points (a <b>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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's visualize **highway-mpg** as potential predictor variable of price:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 48263.47145098897)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see from this plot that price is negatively correlated to highway-mpg, since the regression slope is negative.\n",
    "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 47414.1)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #3:</h1>\n",
    "<b>Given the regression plots above is \"peak-rpm\" or \"highway-mpg\" more strongly correlated with \"price\". Use the method  \".corr()\" to verify your answer.</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>-0.058598</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             peak-rpm  highway-mpg     price\n",
       "peak-rpm     1.000000    -0.058598 -0.101616\n",
       "highway-mpg -0.058598     1.000000 -0.704692\n",
       "price       -0.101616    -0.704692  1.000000"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "\n",
    "#'hightway-mpg' is more correlated to 'price' tham 'peak-rpm'\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",
    "-->\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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.residplot(df['highway-mpg'], df['price'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>What is this plot telling us?</i>\n",
    "\n",
    "<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, which leads us to believe that maybe a non-linear model is more appropriate for this data.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n",
    "\n",
    "<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>: We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First lets make a prediction \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_hat = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EXr16MWvWLGrWrLnX84488kjatm3LQQcdxC233EL37t0BaNy4MS+//DIDBw4kKyuLXr16xTSuLlbmnIvbi5VXjx49XKzN2CIiIiLJaPr06XTu3DnsMiSisPfDzMY553oU9nitHIuIiIiIRCgci4iIiIhEKByLiIiIiEQoHIuIiIiIRCgci4iIiIhEKByLiIiIiEQEGo7N7EYzm2pmU8xsqJntvf2JSGX0+edw112wZUvYlYiISAWUnp5Ot27ddl3mzZvHEUccAcC8efN2zTcGmDhxIp988kmpj3HsscdScATvvffeyx133LHHbRMnTix2tN29997Lww8/XOrjByWwcGxmLYDrgB7OuS5AOjAgqOOJpIwxY+DMM+H//g969YI47uojIiICUL16dSZOnLjr0qZNG/73v/8B8QvHhRk4cCBvvfXWHre9+eabXHDBBXF5/UQIuq0iA6huZhlADWBJwMcTSW6//gr9+kHz5vDGG7B4MfToAW+/HXZlIiJSwdWqVQuA22+/ndGjR9OtWzcefPBB7rnnHt566y26devGW2+9xaZNm/jd735Hz549Ofjgg/nwww8B2LJlCwMGDCArK4vzzz+fLYV8+tmxY0fq1avHjz/+uOu2//73vwwYMIB///vf9OzZk65du3LOOeewefPmvZ6ffzV65cqVtGnTBoDc3FxuvfVWevbsSVZWFs899xwAOTk5HHPMMXTr1o0uXbowevTocn+fMsr9CkVwzi02s4eBBcAWYIRzbkTBx5nZYGAwQOvWrYMqRyR8a9dC796wcyd88gl07AhHHQXnnw/nnQfXXAOPPQYZgf21FBGRBLvhBpg4Mb6v2a0bPP548Y/ZsmUL3bp1A6Bt27a8//77u+574IEHePjhh/noo48AaNq0KWPHjuXpp58G4E9/+hPHH388L774ImvXruXQQw/lxBNP5LnnnqNGjRpMmjSJSZMm7drOuaCBAwfy5ptvcthhhzFmzBgaNmzI/vvvT4MGDbjiiisAuOuuu3jhhRe49tprY/qaX3jhBerWrcvPP//Mtm3bOPLIIzn55JN57733OOWUU7jzzjvJzc0tNHCXVmD/C5tZfeAMoC2wFnjbzH7rnHst/+Occ88Dz4PfPjqoekRCtX07nHMOzJkDI0b4YAzQqhV88w388Y/+X7quXeHyy0MtVUREUl+0raIsRowYwbBhw3b1AW/dupUFCxbw7bffct111wGQlZVFVlZWoc8fMGAARxxxBI888ghvvvkmAwcOBGDKlCncddddrF27lo0bN3LKKaeUqqZJkybxzjvvALBu3Tpmz55Nz549+d3vfseOHTs488wzd/1AUB5BLlGdCPzqnFsBYGbvAUcArxX7LJGK6Npr4auvYMgQOPbYPe+rUgUefRS+/BKefVbhWESkAilphTcZOed499136RhdyMnHzEp8fqtWrWjTpg3ffPMN7777Lj/88AMAl1xyCR988AFdu3bl5ZdfZtSoUXs9NyMjg7y8PMCH8vw1PfXUU4UG6m+//ZaPP/6Yiy66iFtvvZVBgwbF+qUWKsie4wVALzOrYf47eQIwPcDjiSSnnBx4/nm4/noo6i+sGVx1FYwbBwXO/BUREYmn2rVrs2HDhiJ/f8opp/DUU0/hnP9Af8KECQAcc8wxvP7664BfBZ40aVKRxxg4cCA33ngj7dq1o2XLlgBs2LCBZs2asWPHjl2vU1CbNm0YN24cwK5V4mhNzzzzDDt27ABg1qxZbNq0ifnz59OkSROuuOIKLrvsMsaPH1/q70dBgYVj59yPwDvAeGBy5FjPB3U8kaQ1bJi/Hjy4+Mf99rdQs6ZfPRYREQlIVlYWGRkZdO3alccee4zjjjuOadOm7Toh7+6772bHjh1kZWXRpUsX7r77bgCuvvpqNm7cSFZWFg899BCHHnpokcfo378/U6dOZcCA3YPK7r//fg477DBOOukkOnXqVOjzbrnlFp555hmOOOIIVq5cuev2yy+/nAMOOIDu3bvTpUsXrrzySnbu3MmoUaPo1q0bBx98MO+++y7XX399ub8/Fv2pIBn06NHDFZyXJ5LyTj0V5s6FmTP9CnFxBg+G11/3Uyzq1UtIeSIiEl/Tp08vdq6vJFZh74eZjXPO9Sjs8dohTyRI69b5XuMzzyw5GANceSVs3gyvqTVfREQkDArHIkH69FPYscOH41gccgj07OlbK5LoUx0REZHKQuFYJEgffABNm8Jhh8X+nKuugqlT4fvvAytLRESClUxtq5VZWd4HhWORoGzb5jf76NcP0tNjf97550PdujoxT0QkRWVmZrJq1SoF5JA551i1ahWZmZmlep624hIJytdfw4YNsbdURNWs6Ue+PfecH5DZqFEQ1YmISEBatmzJokWLWLFiRdilVHqZmZm7RsnFSuFYJCgffAC1asHxx5f+uVdeCU89BS+9BLfeGvfSREQkOFWqVKFt27ZhlyFlpLYKkSDk5cGHH8Jpp0EpP84B4MAD4dBD4b334l+biIiIFEnhWCQIP/0ES5eWvqUiv5NPhp9/hvXr41aWiIiIFE/hWCQI778PGRnQu3fZX+P44yE3F779Nn51iYiISLEUjkXizTkfjo87rny73B1+uG/J+PLLuJUmIiIixVM4Fom3GTNg9uzytVSAD8ZHHul32BMREZGEUDgWibdRo/z1aaeV/7VOOAEmTQKNAxIREUkIhWOReJswAerXhzZtyv9a0TFwX39d/tcSERGREikci8TbhAnQvTuYlf+1DjkE6tRRa4WIiEiCKByLxNOOHb4N4uCD4/N6GRnwm9/opDwREZEEUTgWiafp02H79viFY/B9x9nZsGBB/F5TRERECqVwLBJPEyb463iG42jfsVorREREAqdwLBJPEyZAjRrQoUP8XrNLF2jcWOFYREQkARSOReJp/Hjo2hXS0+P3mmZ+9fjLL/0GIyIiIhIYhWOReMnLg4kT49tSEXX88bBkCcyaFf/XFhERkV0UjkXiZe5c2LDBj3GLtxNO8NeaWiEiIhIohWOReBk/3l8HsXK8337QurX6jkVERAKmcCwSLxMm+LnEBx4Y/9c286vHX3/t2zdEREQkEArHIvEyYYIPxtWqBfP6Rx8Nq1er71hERCRACsci8eCcb6sIot84qmdPf/3zz8EdQ0REpJJTOBaJhyVLYMWKYPqNozp39jOUx44N7hgiIiKVnMKxSDwEsTNeQenpfmVaK8ciIiKBUTgWiYcJE/xJc127Bnucnj39sXbuDPY4IiIilZTCsUg8jB8P++8PtWsHe5wePWDrVpg6NdjjiIiIVFIKxyLxMGFCsC0VUdGT8tR3LCIiEgiFY5HyWr0a5s9PTDhu1w7q1lXfsYiISEAUjkXKK3oyXpBj3KLS0nxrhVaORUREAqFwLFJeiZhUkV+PHjBpEmzblpjjiYiIVCIKxyLlNWECtGwJjRol5ng9e8KOHT4gi4iISFwpHIuU14wZftvoROnRw1+r71hERCTuFI5FysM5yM72Y9wSpXVraNxYfcciIiIBUDgWKY8VK2D9emjfPnHHNPOrx1o5FhERiTuFY5HyyM7214lcOQbfdzxtGmzalNjjioiIVHAKxyLlMXu2v07kyjH4leO8vN2TMkRERCQuFI5FyiM7G9LToU2bxB43elKe+o5FRETiSuFYpDxmz4Z994WqVRN73GbNoEUL9R2LiIjEmcKxSHlkZye+pSKqZ0+tHIuIiMSZwrFIWYUxxi2/Hj1g1ixYuzac44uIiFRACsciZbVyJaxbF+7KMcD48eEcX0REpAJSOBYpq7DGuEUdcoi/HjcunOOLiIhUQArHImUV1hi3qIYNoWVLmDQpnOOLiIhUQArHImWVnQ1padC2bXg1ZGUpHIuIiMSRwrFIWYU1xi2/rCyYPh22bw+vBhERkQpE4VikrMKcVBHVtSvs2AEzZoRbh4iISAWhcCxSFs75leOw+o2jsrL8tVorRERE4kLhWKQsVq3yY9zCXjnu0MG3dSgci4iIxIXCsUhZhD2pIiojAw48EH75Jdw6REREKgiFY5GyCHvGcX5du2rlWEREJE4UjkXKYvbs8Me4RWVlwdKlsHx52JWIiIikPIVjkbLIzg5/jFtU9KS8yZPDrUNERKQCCCwcm1lHM5uY77LezG4I6ngiCZWdHX6/cVQ0HKvvWEREpNwCC8fOuZnOuW7OuW7AIcBm4P2gjieSMMkyxi2qcWNo1kx9xyIiInGQqLaKE4A5zrn5CTqeSHBWr4a1a5PjZLwobSMtIiISF4kKxwOAoYXdYWaDzWysmY1dsWJFgsoRKYdkGeOWX1YWTJ0KO3eGXYmIiEhKCzwcm1lVoB/wdmH3O+eed871cM71aNy4cdDliJRfMo1xi+raFbZvh5kzw65EREQkpSVi5fg0YLxzblkCjiUSvGQa4xalbaRFRETiIhHheCBFtFSIpKTsbGjdGqpVC7uS3Tp2hCpVFI5FRETKKdBwbGY1gJOA94I8jkhCJdOkiqiqVaFzZ41zExERKadAw7FzbrNzrqFzbl2QxxFJqOzs5Oo3jtI20iIiIuWmHfJESmP1alizBtq1C7uSvWVlweLFsGpV2JWIiIikLIVjkdJYsMBfJ9PJeFHaRlpERKTcFI5FSiMajlu3DreOwmgbaRERkXJTOBYpjWQOx/vsA02aqO9YRESkHBSORUpjwQI/wi1ZN6zRNtIiIiLlonAsUhoLFkCrVmAWdiWF69LFbyOdlxd2JSIiIilJ4VikNBYsSM6WiqguXWDLFvj117ArERERSUkKxyKlkQrhGGDKlHDrEBERSVEKxyKx2rEDlixJ7nB8wAH+WuFYRESkTBSORWK1eDE4l9zhuHZtaNNG4VhERKSMFI5FYpXMY9zy69JF4VhERKSMFI5FYpVK4XjGDNi+PexKREREUo7CsUisouG4Vatw6yhJly6wcyfMnh12JSIiIilH4VgkVgsWQKNGUKNG2JUULzqxYurUcOsQERFJQQrHIrFK9jFuUR07Qnq6+o5FRETKQOFYJFapEo4zM2H//RWORUREykDhWCRWqRKOQRMrREREykjhWCQW69bBhg2pFY6zs/1W0iIiIhIzhWORWKTKGLeoLl38hiXTp4ddiYiISEpROBaJRSqGY1BrhYiISCkpHIvEItXCcbt2UK2awrGIiEgpKRyLxGLBAqhSBZo2DbuS2GRkQOfOCsciIiKlpHAsEosFC/zOeGkp9FdGEytERERKLYX+pxcJUSqNcYvq0gUWLvSTNkRERCQmCscisQgwHP/wA/z97/DBBzBvnh8yERfaRlpERKTUMsIuQCTp7dwJixfHPRxv3Qr33AMPP7xnIK5bF7Ky4Ior4KKLynGA/BMrjjiiXLWKiIhUFlo5FilJTg7k5sY1HE+YAD16wD/+4UPw0qV+BfnZZ+GCC2DtWhg0CB59tBwHad0aatVS37GIiEgpaOVYpCRxHOOWm+tbKO67Dxo3ho8/ht69/X1Nm0KvXv7XO3bAhRfCzTf7Te7uvLMMBzPTSXkiIiKlpHAsUpI4huNHH4W774bzz4d//QsaNCj8cVWqwBtvQGYm3HUXbN4Mf/2rz7ul0qULfPhhuesWERGpLNRWIVKSaDhu1apcL7NwIdx7L/TpA0OHFh2MozIy4OWXYfBg+Nvf/CpyqU/W69IFVqyA5cvLWLWIiEjlopVjkZIsWOCTbK1a5XqZG27w4fapp2JfAU5L833ImZnw2GPQvDncckspDpr/pLzjjy9tySIiIpWOVo5FShKHMW6ffALvvedbKtq0Kd1zzeDxx6FvX/jzn/0KdMwOPNBfq+9YREQkJgrHIiUpZzjesgWuuQY6dfKtEWVhBk8+6Veeb7yxFE9s2hQaNlQ4FhERiZHCsUhJyhmO//Y3+PVXfwJe1aplL6NNG39y3rvvwmefxfgkTawQEREpFYVjkeJs2OCHDpfxZLyZM+Ghh+C3v4Xjjit/OTffDB06+JXorVtjfFI0HMdt6z0REZGKS+FYpDjRBt8yrBw750Ns9ep+F7x4qFYN/vlPmDMHHnwwxid16eJDfqmalUVERConhWOR4pRjxvG4cTBypD+JrmnT+JV04ol+TvLf/+5DconyT6wQERGRYikcixSnHOH45Zf9CLZLL41vSeA3E6la1a9Ml9gtoYkVIiIiMVM4FinOokV+2PA++5TqaVu3+h3uzjoL6tWLf1nNm/stqD/7DL7+uoQH168PLVooHIuIiMRA4VikOIsX+2CcUbr9coYNgzVrglk1jrr6amjcGB55JIYHa2KFiIhITBSORYqzZIlfdS2ll17yAy6C3JQuMxP+8Ae/wcj06SU8uEsX/6Dc3OAKEhERqQAUjkWKs3ix72Eo5VNGjIBBgyA9PaC6In7/ex+SH320hAd26eJ7PebODbYgERGRFKdwLFKcJUtKHY5feQXy8uCSS4IpKb/GjX0If/VVWLasmAdqYoWIiEhMFI5FirJ1K6xaVaq2Cud8S8XRR0P79gHWls+NN8K2bfDMM8U8qHNnv1uewrGIiEixFI5FipKT469LsXL8ww8we3awJ+IV1KkT9OnjNwfZsqWIB9WsCfvtp3AsIiJSAoVjkaIsXuyvS7Fy/NJLPof27x9QTUW4+WZYudK3VxRJEytERERKpHAsUpQlS/x1jCvHmzbBW2/BuedCrVoB1lWI3/wGunf3J+bl5RXxoC5dYNYs34MhIiIihVI4FilKKVeO33sPNmxIbEtFlJlfPZ450492K1SXLrBzpw/IIiIiUiiFY5GiLFni56TFuMXdq6/6tt6jjw62rKL07w8tWxazKYgmVoiIiJRI4VikKIsX+1VjsxIfunkzfPMNnH223206DFWq+LnHo0bBnDmFPKBDB7/Tn8KxiIhIkRSORYpSihnH334L27fDSScFXFMJLrrIZ/lXXinkzqpVoWNHhWMREZFiKByLFCW6chyDESOgWrXwWiqiWraEE07YvRHJXjSxQkREpFgKxyKFca5UK8cjRsAxx0D16gHXFYOLL4Z582D06ELu7NLFbyG9aVOiyxIREUkJCscihVm/3jcSxxCOlyyBqVPDb6mIOussP0puyJBC7oyelDdtWkJrEhERSRUKxyKFKcUYty++8NcnnxxgPaUQ3YTk7bcLWSDWxAoREZFiKRyLFKYUG4CMGAFNm8JBBwVcUylcfDFs3AgffFDgjrZtfe/H5MlhlCUiIpL0Ag3HZlbPzN4xsxlmNt3MDg/yeCJxE+PKcV4ejBwJJ54Y3gi3whx9NLRpU0hrRXo6HHigwrGIiEgRgv7v/AngM+dcJ6ArMD3g44nER4wrx5MmwfLlydNSEZWWBoMG+eC+aFGBO7t29YWLiIjIXgILx2ZWBzgGeAHAObfdObc2qOOJxNXixVC/fonjJ0aM8NfJcjJefoMG+aEbr71W4I6sLJ/oly4NpS4REZFkFuTK8X7ACuAlM5tgZv8xs5oFH2Rmg81srJmNXbFiRYDliJRCjGPcvvjCn+PWrFkCaiqldu3gqKN8a4Vz+e7IyvLXWj0WERHZS5DhOAPoDjzjnDsY2ATcXvBBzrnnnXM9nHM9GjduHGA5IqUQwwYgmzf7WcLJ1lKR36BBMGMGjB2b78bomYMKxyIiInsJMhwvAhY5536M/P4dfFgWSX4xrByPHg3btiVnS0XUeedBZmaBE/MaNvTBX+FYRERkL4GFY+fcUmChmXWM3HQCoJ0HJPnl5kJOTokrx198AVWr+p3xklXdutCnD7z7boHtpLOyFI5FREQKEfS0imuB181sEtAN+FvAxxMpvxUrfEAuYeV4xAg/Mq1GjQTVVUbnnuvPvfvf//LdmJXld8nbsSO0ukRERJJRoOHYOTcx0k+c5Zw70zm3JsjjicRFdMZxMeE4J8ePCk7mloqo3r2hWjV45518N2Zl+WA8c2ZodYmIiCSjJNq2QCRJRGccF9NWMXKkv07mk/GiateGU08t0FqhiRUiIiKFUjgWKSiGleNvv/VjkLt2TVBN5XTuuX4zkJ9+itzQsSNUqaJwLCIiUoDCsUhBS5b4LeaaNi3yIT/+CIcdllxbRhenb1+fhXe1VlSpAgccoHAsIiJSQIr81y6SQEuW+GCckVHo3Rs3wtSpPhynirp1fX/0O+/k2xCka1f45ZdQ6xIREUk2CsciBZWwAcjYsb5399BDE1hTHJx7LsyfD+PGRW7IyvI/CKxcGWpdIiIiyUThWKSgEjYAifbtplo4PuMMvxi+q7UielLe5Mmh1SQiIpJsFI5FCiph5fjHH6FdO2jUKIE1xUGDBnD88flaKzSxQkREZC8KxyL5bdsGq1YVu3IcPRkvFZ17LsyZE8nDTZtCkyYKxyIiIvkoHIvkV8KM48WL/SXVWiqizjzTT9jYo7VC4VhERGQXhWOR/KLhuIiV42i/caquHDduDL/5Dbz9dr7WiilT/HbZIiIionAssocSNgD58Uc/Irhbt8SVFG/nnut3jZ42DR+Ot26F7OywyxIREUkKCsci+ZXQVvHjj348cGZmAmuKs7PO8tfvvYdOyhMRESlA4Vgkv8WLoVo1vzd0Abm5fsZxqrZURDVr5r+GYcOAzp0hPV3hWEREJELhWCS/JUv8qrHZXndNn+53x0v1cAzQr58P+otXZUKnTgrHIiIiEQrHIvktXlxsvzFUnHAM8NFH+NYKbSMtIiICKByL7KmY3fF+/BHq1YP27RNbUhAOPBD22y/SWtGtm99XevXqsMsSEREJncKxSH45Ob4ptxA//eTnG6dVgL81Zn71+MsvYWPnnv7GCRPCLUpERCQJVID/5kXiZONGfykkHG/aBJMnV4yWiqh+/fyGgF+s6eFvGD8+3IJERESSgMKxSNTSpf66kHA8bhzk5aXuzniFOeoo3yby4Ve1oU0b/0WKiIhUcgrHIlE5Of56n332uqsinYwXVaUK9O7tT8rLPbiHVo5FRERQOBbZLRqOC1k5/uknaNvWb79ckZxxBqxaBT807AOzZ8P69WGXJCIiEiqFY5GoYtoqfvyxYq0aR51yil9BHrbmaH/DxImh1iMiIhI2hWORqJwcnxQbNtzr5oULK1a/cVTdunDssTDsl9b+BrVWiIhIJadwLBKVk+P7jQvsjhc9T61nzxBqSoB+/WBmdgYzmxytcCwiIpWewrFIVDQcFxDdWTkrK8H1JEjfvv56WMNLNbFCREQqPYVjkailSwvtN540yZ+MV6dOCDUlwL77+k3yhm06HmbM8EOdRUREKimFY5GoInbHmzSp4q4aR/XrB/9b1JoVeQ12L5WLiIhUQgrHIgA7dsCKFXuF461bYeZMOOigkOpKkL59IS/P+JTT1HcsIiKVmsKxCMCyZf66QM/xtGl+Z7yKvnLcvTs0a+YYXu1chWMREanUFI5FoMgNQCZP9tcVPRynpUGfPsbnO09k+1i1VYiISOWlcCwCRW4AMmkSZGZC+/Yh1JRgffvChtwafDOloe8nERERqYQUjkWgyJXjSZOgSxdITw+hpgQ74QTIrJrL8LzeMGVK2OWIiIiEQuFYBHaH46ZN97h50qSKfzJeVI0acMKR2xhOX9w49R2LiEjlpHAsAj4cN2rkt4+OWLYMli+v+P3G+fU9rzrzaMvUL5eGXYqIiEgoFI5FoNANQCrLyXj59enrt87+6IcGIVciIiISDoVjESh0A5DoXhiVpa0CoEUL6N50EcMXH+JnP4uIiFQyCsciUGQ4btYMGjcOqaaQ9D1qLT+4w1jx3cywSxEREUk4hWMR53xbRYENQCZPrlyrxlF9f1sXRxqfvLoq7FJEREQSTuFYZNUq30KQb+V4506YOrVy9RtHde/XkuZpOQz/umbYpYiIiCScwrFIIRuAzJ4N27ZVznBsaUaflr/w+YLObNsWdjUiIiKJpXAsUsgGINGT8SpjOAboe8w6NubV5JuPN4ZdioiISEIpHIsUEY4zMqBTp5BqCtnxA5uSyRaGD1kddikiIiIJpXAsEg3H+U7ImzwZOnaEatVCqilkNY4+hBP5ko++rY1zYVcjIiKSOArHIkuXQq1a/hIxaVLlbakAoHZt+rYYz7y19Zk6NexiREREEkfhWKTAjON162D+/EoejoE+x/p+4+HD8kKuREREJHEUjkUKhOPKuG10YZqfeACHMJbhb28NuxQREZGEUTgWycnZq98YFI7p1Yu+DGfML9VZvjzsYkRERBJD4Vhk6dK9JlXUqwctWoRXUlLo0IG+tb/BOeOTT8IuRkREJDEUjqVy27QJNmzYKxxnZYFZiHUlg7Q0Dj6iOs0zljF8eNjFiIiIJIbCsVRuBWYcO+fbKg46KMSakogd3os+Oz9kxAin3fJERKRSUDiWyq1AOF682C8kd+kSYk3J5PDD6cswNm40vvkm7GJERESCp3AslVuBDUCmT/e/raw74+3l0EM5gS+pXmWHWitERKRSUDiWym3pUn8dWTmeMcP/tnPnkOpJNvXqUf2A/Tix/niGD0e75YmISIWncCyVW04OVKkCDRsCPhzXqwdNmoRbVlLp1Yu+m95k/nyYMiXsYkRERIKlcCyVW3TGcWQ0xfTpvqWi0k+qyO/ww+mz6U0AtVaIiEiFF2g4NrN5ZjbZzCaa2dggjyVSJgU2AJkxQy0Ve+nVi2YspUfblQrHIiJS4SVi5fg451w351yPBBxLpHTybQCybp3PyjoZr4ADDoA6dejb8Ad+/BHtliciIhWa2iqkcsvJ2etkPIXjAtLS4Igj6LNqCM7Bxx+HXZCIiEhwgg7HDhhhZuPMbHBhDzCzwWY21szGrlixIuByRPLZsQNWrNCkilgcdxwH//ouLZvn8uGHYRcjIiISnKDD8ZHOue7AacAfzOyYgg9wzj3vnOvhnOvRuHHjgMsRyWfZMn+db8ZxlSrQtm2INSWr44/HgDO7zOHzz/2u2yIiIhVRoOHYObckcr0ceB84NMjjiZRKITOO998fMjJCrClZHXww1K3L2VWGs3UrfPZZ2AWJiIgEI7BwbGY1zax29NfAyYCmpEryKLB1tCZVFCM9HX7zG46e8W8aNoT33w+7IBERkWAEuXLcFPjOzH4BfgI+ds5pvUmSR75wvH07ZGfrZLxiHX88GXNmcsYJGxk+HLZvD7sgERGR+AssHDvn5jrnukYuBzrn/i+oY4mUSbStokkT5syB3FyF42IddxwAZzcfw/r18NVXIdcjIiISAI1yk8orJwcaNYKqVTWpIhZdukCjRpyw8i1q14b33gu7IBERkfhTOJbKK9+M4+nT/U0dO4ZYT7JLS4NjjyXzm885/XTHBx/41XYREZGKROFYKq+lS3eNcZsxA1q2hFq1Qq4p2R1/PCxcyNlHLGPFCvj++7ALEhERia8Sw7GZPWRmdcysipl9aWYrzey3iShOJFAFdsdTS0UMIn3Hp/Ep1aqptUJERCqeWFaOT3bOrQf6AIuADsCtgVYlEjTndq0cO+fDsU7Gi0HHjtCsGbX+N4KTT/bh2LmwixIREYmfWMJxlch1b2Coc251gPWIJMaaNX4WWbNmLFkCGzZo5TgmZn71+OuvOfssx8KFMG5c2EWJiIjETyzheJiZzQB6AF+aWWNga7BliQQs34zj6KQKrRzH6PjjYdky+nacRXq6WitERKRiKTYcm1kaMBw4HOjhnNsBbAbOSEBtIsGJzjjeZ59dkyoUjmMU6TtuOGEkxx6rcCwiIhVLseHYOZcHPOKcW+Ocy43ctsk5tzQh1YkEpcDKcd26uwZXSEnatoV994WvvuLss2HmTJg2LeyiRERE4iOWtooRZnaOmVng1YgkSoFw3KmTb6eVGET7jkeN4sx+eZjBf/8bdlEiIiLxEUs4vgl4G9hmZuvNbIOZrQ+4LpFgLV0KNWpArVpMn66WilI7+WRYvZrmC3/k2GPhjTc0tUJERCqGEsOxc662cy7NOVfVOVcn8vs6iShOJDCRGcfrNxhLlmhSRamdeipkZMCwYVxwAcyeDePHh12UiIhI+cW0Q56Z1TezQ83smOgl6MJEApWTA/vsw8yZ/rdaOS6l+vXhmGNg2DDOOQeqVPGrxyIiIqkulh3yLge+BT4H7otc3xtsWSIBW7oUmjXTpIry6NcPpk2j/qpseveGN9+E3NywixIRESmfWFaOrwd6AvOdc8cBBwMrAq1KJGiRtooZM/yq5377hV1QCurXz19HWiuWLIFvvw23JBERkfKKJRxvdc5tBTCzas65GUDHYMsSCdCWLbBuHeyzDzNmQPv2PiBLKbVtCwcdBMOG0acP1Kql1goREUl9sYTjRWZWD/gA+MLMPgSWBFmUSKCiG4A0a8bMmdChQ7jlpLR+/eC776ixZRVnnQXvvAPbtoVdlIiISNnFMq3iLOfcWufcvcDdwAvAmQHXJRKcyIzjvKbNmDNH4bhc+vXzjcaffsoFF8DatfDZZ2EXJSIiUnZFhmMz62lmp+W/zTn3TeSXBwValUiQIivHC2nFtm2w//4h15PKevSAZs1g2DBOOAEaN4ahQ8MuSkREpOyKWzn+BzC9kNunRe4TSU2RlePZm5oDCsflkpYGffvCp59SJW8b550Hw4bBhg1hFyYiIlI2xYXjhs65eQVvdM5lAw0Dq0gkaDk5kJ7OrGV1AYXjcuvXDzZuhFGjGDjQn+/44YdhFyUiIlI2xYXj6sXcVzPehYgkzNKl0KQJs+ekUaMGNG8edkEp7vjj/Vbcw4Zx+OGw776aWiEiIqmruHA80sz+z8ws/41mdh/wVbBliQQoMuN49my/arznn3ApterV4eSTYdgw0swxcCCMGAHLloVdmIiISOkVF45vBvYDss3s3cglGz/j+KaEVCcShMjW0dFwLHFwxhmwaBFMnMgll/gBFi+/HHZRIiIipVdkOHbObXLODQROAl6OXE52zg1wzm1MTHkiAVi6lJ1NWzB3rsJx3Jx+OqSnw3//S8eO8JvfwL//DXl5YRcmIiJSOrHMOZ7rnBseucxNRFEigcnNhWXLmFe9Mzt3KhzHTePGcOqp8OqrkJvL4MEwZw58/XXYhYmIiJROLDvkiVQcK1dCXh6zXXtAG4DE1cUXw+LF8NVXnH02NGgAzz8fdlEiIiKlU9wmIG0TWYhIQkRnHG9rDWjlOK769oV69eDll8nM9Fn5/fdh+fKwCxMREYldcSvH7wCY2ZcJqkUkeNFwvL4Jder4bgCJk8xMGDDAJ+L167niCtixA4YMCbswERGR2BUXjtPM7M9ABzO7qeAlUQWKxFVk6+hZy+pqjFsQLr7Y7wLy9tt07gxHH+1bK3RinoiIpIriwvEAYCuQAdQu5CKSeqIrxwsz1VIRhMMOg44ddy0XDx4M2dkwalS4ZYmIiMQqo6g7nHMzgQfNbJJz7tME1iQSnJwcttdpxPwFafz2orCLqYDM/Orxn/4Ec+ZwzjntuO46v3p8/PFhFyciIlKyWKZV/M/MHjWzsZHLI2ZWN/DKRIKwdClzG/YkL0+TKgJz0UU+JL/yCtWrw6BB8N57sGJF2IWJiIiULJZw/CKwATgvclkPvBRkUSKByclhdq2DAU2qCEzLlnDCCfDKK5CXx+DBOjFPRERSRyzhuJ1z7s+RzUDmOufuw28rLZJ6cnKYld4ZUDgO1CWXwLx5MHo0BxwARx0Fzzzj92ARERFJZrGE4y1mdlT0N2Z2JLAluJJEAuIcLF3K7Lz9aNDAb1IhATnrLKhdG17yHzLdcAPMnevbK0RERJJZLOH4KuCfZjbPzOYBTwNXBlqVSBA2bIDNm5m9uYVWjYNWowZccAG8+SYsX86ZZ/qV+gcf9D+jiIiIJKsSw7Fz7hfnXFcgC8hyzh3snJsUfGkicRaZcTx7TSOdjJcIN94I27fD00+Tng633grjxsFXX4VdmIiISNFiWTkGwDm33jm3PshiRAKVk8MWMlm4qqZWjhOhY0fo1w/++U/YtImLLoJ99vGrxyIiIskq5nAskvJycsimPaCT8RLm1lth9Wp48UUyM33v8Rdf+BVkERGRZKRwLJXH0qXMxqdiheMEOfJIOPxwePRR2LmTq66COnXgoYfCLkxERKRwMYVjMzvCzC4ws0HRS9CFicRdTg6z0zsBCscJdeutfqzbu+9Sty5cdRW88w7MmRN2YSIiInsrMRyb2avAw8BRQM/IpUfAdYnEX04OszOzaNrUr15KgvTr538a+cc/wDluuAEyMuDhh8MuTEREZG+xrBz3AI50zv3eOXdt5HJd0IWJxN3SpcxO66BV40RLT4dbbvGNxqNG0ayZ31L6pZdg2bKwixMREdlTLOF4CrBP0IWIBC4nh1nb2ygch2HQIGjSxK8e4zsttm/3rcgiIiLJJJZw3AiYZmafm9mw6CXowkTibcOSDSzd1kDhOAyZmXDttfDppzBuHB06+D1CnnwSFi4MuzgREZHdYgnH9wJnAn8DHsl3EUkd27eTvbo+oJPxQnPttdCwoW+xcI7/+z+/W95dd4VdmIiIyG6x7JD3DTADqB25TI/cJpI6li3bNcZNu+OFpG5duPdeGDUKPv6YffeF666DV1+FiRNDrk1ERCQilmkV5wE/Af2B84AfzezcoAsTiat8M47btQu5lsrsyiv9Tye33go7d/KnP0H9+v63zoVdnIiISGxtFXcCPZ1zFzvnBgGHAncHW5ZInEV2x2veeDs1a4ZdTCVWpYrfAWTGDPjPf6hXD+65B0aOhM8/D7s4ERGR2MJxmnNueb7fr4rxeSLJIyeHObSj/X5angxdv35wzDHw5z/D+vVcfbVfzb/1VsjNDbs4ERGp7GIJuZ9FJlVcYmaXAB8DnwRblkicLV1KNu1p16lK2JWImd8BZPlyeOghqlaFBx6AKVPg5ZfDLk5ERCq7WE7IuxV4HsgCugLPO+duC7owkXjatGAVOTSnfQd96JEUevb0s9weeQQWLeKcc+Dww+Huu2HTprCLExGRyiympOCce9c5d5Nz7kbn3PtBFyUSb3Pm+Ov27cOtQ/L529/8WXg337xrMTknB+67L+zCRESkMisyHJvZd5HrDWa2Pt9lg5mtT1yJIuU3Z3EmoHCcVPbd1y8V//e/MHw4RxwBV1zhF5PHjg27OBERqayKDMfOuaMi17Wdc3XyXWo75+okrkSR8steURfQGLekc+utcNBBcPXVsG4d//gH7LMP/O53fntpERGRRItlzvGrsdxWzPPTzWyCmX1U2uJE4sI5sjc0oVH1jdStG3YxsoeqVeGFF3w/xe23U7cuPPssTJ4MDz4YdnEiIlIZxdJzfGD+35hZBnBIKY5xPTC9NEWJxNXq1WTn7Uf7JhvCrkQK07Mn3HCDT8WjR9O3LwwYAPffD9OmhV2ciIhUNsX1HN9hZhuArPz9xsAy4MNYXtzMWgKnA/+JS7UiZRGdcdxqW9iVSFH+8hdo2xYuvxy2buWJJ6BOHbjsMs0+FhGRxCqu5/jvQF3glQL9xg2dc3fE+PqPA38E8op6gJkNNrOxZjZ2xYoVpaldJCbbFixjAa1p197CLkWKUrMmPP88zJoF999PkybwxBMwZgw89VTYxYmISGVSbFuFcy4PP9u41MysD7DcOTeuhGM875zr4Zzr0bhx47IcSqRYv07eiCON9gdWC7sUKc6JJ8Ill/hm459/5oILoHdvuPNOv9u0iIhIIsTSczzGzHqW4bWPBPqZ2TzgTeB4M3utDK8jUi7ZM3YC0P7g2iFXIiV67DFo1gwGDcK2buHf/4YaNeD882Hr1rCLExGRyiCWcHwc8IOZzTGzSWY22cwmlfQk59wdzrmWzrk2wADgK+fcb8tZr0ipzfnV/zFvl1Uz5EqkRPXqwUsv+aXiP/2J5s1hyBCYNAluvjns4kREpDLIiOExpwVehUiAspfUoE7aBho10spxSjjxRPjDH+Dxx6FfP3r3Po6bb/abgxx/PJxzTtgFiohIRWbOuZIfZNYVODry29HOuV+CKKZHjx5urLbGkjg7rcGPLN9ej3EbO4ZdisRq0yY4+GC/E8ikSWzPrMNRR/nz9SZOhDZtwi5QRERSmZmNc871KOy+WDYBuR54HWgSubxmZtfGt0SR4MzZ2JT29VeFXYaURs2a8MorsHAh3HgjVavCm2+CczBwIOzYEXaBIiJSUcXSc3wZcJhz7h7n3D1AL+CKYMsSiY+dO+HXHS1ot8+msEuR0urVC26/HV58ET76iP3289PexoyBu+8OuzgREamoYgnHBuQfw58buU0k6S2YuYWdVKF96+1hlyJl8ec/w0EHwZVXwpo1nH8+DB7sp70NGxZ2cSIiUhHFEo5fAn40s3vN7D5gDPBCsGWJxEf22LUAtO8Qyx91STpVq/rpFcuWwU03AX5zkO7dYdAgmDs35PpERKTCKTExOOceBS4FVgOrgEudc48HXJdIXMyZvBmA9l0yQ65EyuyQQ+C22+Dll+HTT8nMhHfegbQ0P7liy5awCxQRkYqkNMtpBjjUUiEpJHtWLtXZTLMDG4RdipTHPffAAQfAFVfAunW0bQuvvuonV1xzTdjFiYhIRRLLtIp7gCFAfaAR8JKZ3RV0YSLxkD0vg3bMwZo3C7sUKY9q1Xx7RU4O3HILAKefDnfd5c/Xe0GNXiIiEiexrBwPBHo65+51zv0ZP63iwmDLEomP7JyatGcONGoUdilSXoce6oPxf/4DI0YAcO+9u/cMGT8+3PJERKRiiCUczwPyN2xWA+YEUo1IHOXlwdw19WlXc6lvUJXUd9990LEjXH01bN1Kejq88QY0buz7j1evDrtAERFJdbEkhm3AVDN72cxeAqYAG83sSTN7MtjyRMpuyRLYmluV9g3XhF2KxEtmJjz9tB9T8cgjgA/Gb78Nixf7CRZ5eSHXKCIiKS2WcPw+8Cfga2AUcCfwKTAuchFJStnZ/rp9s43hFiLxdeKJcPbZ8H//BwsWAH6/kMceg48/hr//PeT6REQkpWWU9ADn3BAzqwp0iNw00zmnzVsl6c2JNP+0b5Nb/AMl9Tz6KHzyie9B/u9/Afj97+H77/3ueYceCiedFHKNIiKSkmKZVnEsMBv4J/AvYJaZHRNsWSLllz0rjypsp1W7qmGXIvG2775wxx2+n+KrrwAw89tLd+4MF1wACxeGXKOIiKSkWNoqHgFOds79xjl3DHAK8FiwZYmUX/a07bTlV9Jb7BN2KRKEW2+FNm3guutgh/8wq1YtePdd2LoV+veH7do1XERESimWcFzFOTcz+hvn3CygSnAlicRH9uw82pMNzTTjuEKqXh0efxymToV//WvXzZ06+dnHP/7o9w4REREpjVjC8Tgze8HMjo1c/o1OxJMk5xzMWVDFh+N9tHJcYfXrB6ec4lPwqlW7bu7fHy6/HB56CL79NsT6REQk5cQSjq8CpgLXAdcD0yK3iSStFStgw5YqtGOOVo4rMjN4+GHYsMGfpJfPY4/BfvvBRRfBunUh1SciIimn2HBsZmnAOOfco865s51zZznnHnPObUtQfSJlsmuMm1aOK74uXeC88+DJJ2Hlyl0316oFr73m5x9fe22I9YmISEopNhw75/KAX8ysdYLqEYmLXeG49nK/cYRUbPfcA5s2+VXkfHr1gjvvhFdf9YMtREREShJLW0Uz/A55X5rZsOgl6MJEymPOHEgjlzYtNJK7UjjgABgwwO+et2LFHnfddZefe3zllX4VWUREpDixhOP7gD7AX/Bj3aIXkaSVnQ2tqy2javNGYZciiXLPPbBlC/zjH3vcXKWKb6/Ytg0uucSfrCkiIlKUIsOxmWWa2Q1Af6AT8L1z7pvoJVEFipRFdja0T5urfuPKpFMnv/vH00/DsmV73LX//r7jYuRIeOWVkOoTEZGUUNzK8RCgBzAZOA2tFksKyc52tN8+XZMqKpu77/ZLxA89tNddV14JRxzhd5zON/VNRERkD8WF4wOcc791zj0HnAscnaCaRMplzRpYvdpolzsTmjcPuxxJpA4d/Oy2f/0LcnL2uCstDZ59FtauhT/+MZzyREQk+RUXjnedyeSc25mAWkTiYs4cf92ebGjRItxiJPHuvtvvG/3EE3vdddBBcNNNfge90aNDqE1ERJJeceG4q5mtj1w2AFnRX5vZ+kQVKFJae8w4VjiufNq1gzPPhH//25+gV8A998C++8JVV/kMLSIikl+R4dg5l+6cqxO51HbOZeT7dZ1EFilSGtGV4/2Yq7aKyuq662D1anjjjb3uqlnTn7M3bRo8ojMpRESkgFhGuYmklOxsaF57AzXYonBcWR1zDGRl+V3zCpnd1qcPnH02/OUvMHduCPWJiEjSUjiWCic7G9rXWgoNGmh3vMrKzK8eT5oE335b6EOeeAIyMvzDREREohSOpcLJzob2Vear37iyu+AC/wPSk08WenfLlv7cvY8/hq++SnBtIiKStBSOpULZtAmWLoX2GuMm1avD4MHwwQcwf36hD7nuOmjd2o92y8tLbHkiIpKcFI6lQomejNdu0yStHAtcfbVvsfjXvwq9OzMT/vpXGDcO3norwbWJiEhSUjiWCmXXGLd14xSOxS8Ln3WWH+u2eXOhD7nwQujaFf70J7+5noiIVG4Kx1KhRMNxOzdbbRXiXXed3zbx9dcLvTstDf7xD5g3r8gFZhERqUQUjqVCmTMHGtXbQV3Wa+VYvKOOgm7d4J//LPIhJ50EJ58M99/vc7SIiFReCsdSoWRnQ/smG/xvtHIs4HuOL78cfvkFJk4s8mEPPghr18IDDySsMhERSUIKx1KhZGdD+7or/G+0cixRAwZAlSowZEiRD+nWDS66yM8/XrAgcaWJiEhyUTiWCmPbNli4ENpnLoL0dGjcOOySJFk0bAh9+/q+4x07inzY/ff767/8JUF1iYhI0lE4lgrj11/9TsHtXDY0a+YDskjUxRfDihXw2WdFPqR1a9+BMWRIkaORRUSkglM4lgpj1xi3bVPVUiF7O+00/2nCyy8X+7DbbvNtyg8+mJiyREQkuSgcS4Wxx4xjnYwnBVWp4ocaDx8Oq1YV+bBWreDSS+GFF2Dx4gTWJyIiSUHhWCqMOXOgbl1ouGyaVo6lcBdf7HuO33yz2IfdcYffTvqhhxJUl4iIJA2FY6kwsrOhXds8bN1arRxL4bp1g6ysYqdWALRp4ydXPP88LF2akMpERCRJKBxLhZGdDe2bbfK/0cqxFOXii+Hnn2HatGIf9qc/wfbt8PDDCapLRESSgsKxVAg7d/rtf9s3XO1vUDiWolx4oZ9kUsLqcfv2cMEF8MwzfsiFiIhUDgrHUiEsWOADcrvqOf4GtVVIUZo29ZMrXnsNcnOLfeidd8KWLfDYYwmqTUREQqdwLBXCrkkVGfP8L7RyLMUZNAiWLIFRo4p9WKdOcN558NRTsHp1YkoTEZFwKRxLhbArHO+YDjVrQu3a4RYkye3006FGDXjnnRIfeuedsHEjPPtsAuoSEZHQKRxLhTBnDlSvDs3WTverxmZhlyTJrEYNH5Dfe6/E1oqDDoJTTvGrx9u2Jag+EREJjcKxVAjZ2dCuHVjOEvUbS2z694fly+Hbb0t86C23+JFub7yRgLpERCRUCsdSIWRn++kCLF6sfmOJTe/e/uOGGForTjjBj0d+5BFwLgG1iYhIaBSOJeXl5cHcudBuP+dPslI4lljUrOkD8rvvlthaYQY33wxTp8LnnyeoPhERCYXCsaS8RYtg61bYv/kmv2uD2iokVv37w7Jl8N13JT50wAD/R+uRRxJQl4iIhEbhWFLe7Nn+ukPdyD6/WjmWWJ1+OmRmxtRaUbUqXHcdjBwJv/ySgNpERCQUCseS8qLheP9qC/0vtHIssapVy28I8u67vj+nBIMH+24MrR6LiFRcgYVjM8s0s5/M7Bczm2pm9wV1LKncZs/251U13zLH36CVYymN/v0hJwe+/77Eh9avD5ddBkOH+nYeERGpeIJcOd4GHO+c6wp0A041s14BHk8qqVmz/KSKtKVL/A3NmoVbkKSWPn2gWrWYWisAbrjBLzI/9VSwZYmISDgCC8fO2xj5bZXIRUOQJO5mz4b998ePcWvc2DeHisSqdm3fWvHOOzG1VrRtC+ecA88953fOExGRiiXQnmMzSzezicBy4Avn3I+FPGawmY01s7ErVqwIshypgHbu9GPc9t8fjXGTsjv3XP/n54cfYnr4DTfAunXw+uvBliUiIokXaDh2zuU657oBLYFDzaxLIY953jnXwznXo3HjxkGWIxXQggWwY0e+lWOdjCdl0bev/8Th3Xdjevjhh8PBB8PTT2tTEBGRiiYh0yqcc2uBUcCpiTieVB67JlVEw7FWjqUs6tTx2+ANGxZT2jWDa66BKVPgm28SUJ+IiCRMkNMqGptZvcivqwMnAjOCOp5UTrvCcZsdsHy5Vo6l7Pr1gzlzYPr0mB4+cCA0aOBXj0VEpOIIcuW4GfC1mU0Cfsb3HH8U4PGkEpo924+q3cfl+Bu0cixl1aePvx42LKaHV68Ol18OH3wACxcGV5aIiCRWkNMqJjnnDnbOZTnnujjn/hLUsaTymj3bj3GznMgYN4VjKauWLeGQQ2IOxwBXX+0HXDz3XIB1iYhIQmmHPElpe4xxA7VVSPn06wdjxsCyZTE9vE0bfy7f88/D1q3BliYiIomhcCwpa8cO+PXXSDiOfq7dqlWoNUmK69fPn5D38ccxP+Waa2DFCnj77QDrEhGRhFE4lpQ1bx7k5kbC8YIFvgm0QYOwy5JU1rWr/wGrFK0VJ54IHTvqxDwRkYpC4VhS1h5j3BYuhNat/YwtkbIy86vHI0bAli0xP+Waa+Cnn/xFRERSm8KxpKw9wvGCBWqpkPjo188H4y+/jPkpgwb5qSlaPRYRSX0Kx5KyZs/2ezc0bszulWOR8vrNb6B27VK1VtSpA5dcAm+95cdti4hI6lI4lpQ1axZ06AC2YzssXaqVY4mPatXg1FNh+HA/py1Gf/gDbN8O//lPgLWJiEjgFI4lZe0xxs05hWOJn379/A9cY8fG/JROnfzJec88Azt3BlibiIgESuFYUtK2bb7NeI8xbmqrkHjp3RvS00vVWgH+xLxFi+DDDwOqS0REAqdwLClp7lz/ibdmHEsgGjSAo44qdTju0wf23Vcn5omIpDKFY0lJe02qAIVjia8+fWDy5N0/fMUgPR1+/3sYNco/VUREUo/CsaSkvWYcN2gANWuGWpNUMKef7q8/+aRUT7vsMsjMhH/+M4CaREQkcArHkpJmz/Z5uEEDNONYgtGpE7RpU+pw3LAhDBwIr74Ka9cGUpmIiARI4VhS0q5JFaAZxxIMM39i3siR/gzQUrjmGti8GV5+OZjSREQkOArHkpL2CsdaOZYg9O7tU+6335bqad27wxFH+NaKUoxKFhGRJKBwLClnyxafh/ffH9i4Edas0cqxBOO44/ymIKVsrQC/epydDZ99FkBdIiISGIVjSTlz5vhrjXGTwNWo4QNyGcLxOefAPvvoxDwRkVSjcCwpZ69JFaBwLMHp3dvvVZ6dXaqnVa0KV14Jn35a6qeKiEiIFI4l5RQ641htFRKUMo50Axg82M8+fuaZONckIiKBUTiWlDNrFjRuDHXr4leOzaB587DLkopqv/2gY8cyhePmzX17xYsvwqZNAdQmIiJxp3AsKWf2bOjQIfKbBQugWTOoUiXUmqSC693bb3tXhoR7zTV+3vHrr8e9KhERCYDCsaScGTP8/gyAZhxLYvTu7Wcdf/11qZ965JHQtSs8/TQ4F0BtIiISVwrHklJWr4blywuEY52MJ0E7+mi/PXkZWivM4NprYfJkGD06gNpERCSuFI4lpcyc6a87dcIvwy1YoJVjCV61anDiiT4cl2H5d+BAqF/frx6LiEhyUziWlDJjhr/u1AlYtQq2btXKsSTG6afD/PkwbVqpn1qjBlx2Gbz3HixeHEBtIiISNwrHklJmzvTn3rVpg2YcS2Kddpq/LkNrBcDVV/utpJ97Lo41iYhI3CkcS0qZMcPPN87IQDOOJbFatoSsrDKH4/3284vPzz3nz+0TEZHkpHAsKWWvSRWglWNJnN694bvvYN26Mj392mv9CaVvvx3nukREJG4UjiVl7NgBc+bkC8cLFvgTpRo3DrUuqUR694adO2HkyDI9/aSToHNneOwxjXUTEUlWCseSMubM8blkj5Xjli0hTX+MJUEOP9xvzVjG1gozuP56GD8evv8+zrWJiEhcKFVIythjUgVoxrEkXkYGnHJKmUe6AVx0kR/r9vjj8S1NRETiQ+FYUkY0HHfsGLlBM44lDKefDkuXwoQJZXp6jRpw5ZXw/vswb158SxMRkfJTOJaUMXMmNGsGderg+yuWLNHKsSTeqaf66zK2VgD84Q++xUKbgoiIJB+FY0kZe0yqyMmB3FyFY0m8Jk2gZ89yheOWLaF/f/jPf2DDhjjWJiIi5aZwLCnBuSLGuKmtQsLQuzeMGQMrV5b5JW64wU+EGzIkfmWJiEj5KRxLSli+HNau1YxjSRK9e/uf2EaMKPNLHHYY9OoFTzzhd84TEZHkoHAsKWGvSRXaHU/C1KOHn69djtYK8KvH2dnlfhkREYkjhWNJCYWOcatTJ3J2nkiCpaX5E/M++8z3vpfR2Wf7/uPHHotjbSIiUi4Kx5ISZs70I7BatozcsGCBWiokXKefDqtWwU8/lfklqlTxW0p/9ZXfGERERMKncCwpYcYM6NAh32Z4v/4KbduGWpNUcief7P9AlrMn4sor/Qcg//hHnOoSEZFyUTiWlLDHpArnfDjeb79Qa5JKrn59OOKIcofjunXhqqvgv/+FuXPjVJuIiJSZwrEkvS1b/E5iu8LxqlV+OKxWjiVsvXv7foicnHK9zPXXQ3o6PPponOoSEZEyUziWpDd7tl8s3hWOo8trWjmWsPXu7a8/+6xcL9O8OVx0Ebz4IqxYEYe6RESkzBSOJentNani11/9tcKxhC0rC1q0iMsstltv9Z+SaEtpEZFwKRxL0psxA8xg//0jN0RXjtu0CaskEc/Mrx6PGAE7dpTrpTp1gjPO8OF406Y41SciIqWmcCxJb+ZM2HdfP8oN8OG4SROoVSvUukQAH47Xr4fvvy/3S912G6xeDS+8EIe6RESkTBSOJenNmAEdO+a7QZMqJJmccIIfWByH1orDD4ejjoJHHin3QrSIiJSRwrEktby8AmPcwK8ca1KFJIvateGYY+K2B/Rtt/k9bt5+Oy4vJyIipaRwLElt8WLYvDlfON650ycHrRxLMundG6ZOhfnz4/JSBx4If/ub/+FQREQSS+FYktpekyoWLoTcXK0cS3KJjnT79NNyv1RaGtx5p8/a771X7pcTEZFSUjiWpBYNx7t6jjXjWJJRx47+B7Y4tVacd57/gfD++7V6LCKSaArHktSmTIEGDWCffSI3KBxLMjKD00+HL7+ErVvL/XLp6XDXXTBpEnz4YRzqExGRmCkcS1KbMgW6dPHZA/CTKjIyoGXLUOsS2Uvv3r5B/ptv4vJyAwZAhw7wl7/4HSJFRCQxFI4laTm3OxzvMneuH3qcnh5aXSKFOvZYyMyMW2tFerrvPZ44EYYNi8tLiohIDBSOJWktXOj3VjjooHw3zp2rlgpJTtWrw/HHw8cfx+0lL7gA2reH++7T6rGISKIoHEvSmjLFX++xcvzrr5pUIcnr9NNhzpzdZ5KWU0aGXz2eMCGumVtERIoRWDg2s1Zm9rWZTTezqWZ2fVDHkopp8mR/vSscr18PK1dq5ViSV9++/jqOfRC//a3/I6/VYxGRxAhy5XgncLNzrjPQC/iDmR0Q4PGkgpkyxZ93V69e5IZff/XXCseSrFq1gu7d4zpiIrp6PHZs3NqZRUSkGIGFY+dcjnNufOTXG4DpQIugjicVz+TJhbRUgNoqJLn16wc//ADLlsXtJS+6CNq18yFZc49FRIKVkJ5jM2sDHAz8WMh9g81srJmNXbFiRSLKkRSwcydMn17IyXiglWNJbmec4fsf4tgkXKWK3xDkl1/gzTfj9rIiIlKIwMOxmdUC3gVucM6tL3i/c+5551wP51yPxo0bB12OpIjsbNi+vZAxbnXqQP36odUlUqKuXaF167jv3nH++dCtG9x9t/+7ISIiwQg0HJtZFXwwft05916Qx5KKZa+T8cC3Vey3X74dQUSSkJlvrfjiC78pSJykpcHf/+5/Rvz3v+P2siIiUkCQ0yoMeAGY7px7NKjjSMU0ZYoPA50757tRM44lVZxxBmzZAiNHxvVlTzkFfvMb32KxcWNcX1pERCKCXDk+ErgION7MJkYuvQM8nlQgkyf7zQ+qV4/ckJenGceSOo45xrcAxbm1wgweeMCf6/f443F9aRERicgI6oWdc98B+vxbymTKFMjKynfD0qWwbZtWjiU1VK0KvXvD8OGQmxvX7c579YIzz4R//AOuugoaNYrbS4uICNohT5LQli3+hLy9TsYDhWNJHWecAStWwI97Dekpt//7P99W8fe/x/2lRUQqPYVjSTrTpvlJWIWGY7VVSKo49VS/g0ecWysADjgALr4Ynn4a5s+P+8uLiFRqCseSdKZM8dd7zDj+9VffcLnvvqHUJFJq9erBsccGEo7Bbyedng633RbIy4uIVFoKx5J0Jk+GatX8jmC7zJ0LLVpAZmZodYmU2hlnwMyZ/hJnrVrBH/8Ib70F330X95cXEam0FI4l6UyZ4ke4ZeQ/XXTuXLVUSOrp189ff/BBIC9/663+Z8YbbtC20iIi8aJwLElnypQCLRWwewMQkVTSujX07Alvvx3Iy9esCQ8+COPGwSuvBHIIEZFKR+FYksqaNbB4cYGT8bZu9TcqHEsq6t/fp9foSaVxNnAgHHYY3HGHNgYREYkHhWNJKoWejJed7a/3aEIWSRHnnuuv33knkJdPS/MbgixdqtFuIiLxoHAsSWXyZH+9x8rxjBn+eo+9pEVSRNu20KNHYK0V4DcGufBCeOQRmDcvsMOIiFQKCseSVKZMgbp1oWXLfDdGz/Tv0CGUmkTKrX9/GDvW984H5IEH/CryH/8Y2CFERCoFhWNJKlOm+FVjy7/x+IwZfm5VrVqh1SVSLv37++uAWivA/0B5++1+gXrkyMAOIyJS4SkcS9JwzrdV7NFSAT4cd+wYSk0icdG2LRxySKCtFeBXjdu1gz/8AbZtC/RQIiIVlsKxJI0lS2Dt2gLh2Dkfjjt1Cqsskfjo3x9+/jnQ/Z4zM/2W0rNmwcMPB3YYEZEKTeFYksaECf66a9d8Ny5Z4udTKRxLqgt4akXUqafCOefAX/8aaIuziEiFpXAsSWPcON9rfPDB+W6MTqpQOJZU166d/8MdcGsFwGOPQXo6XH994IcSEalwFI4laYwb51uL9zjvTuFYKpL+/eHHH2HBgkAP06oV3HsvDB8Ow4YFeigRkQpH4ViSxrhx/pylPcyc6dNy8+ah1CQSVwmYWhF1/fVw4IFw3XWweXPghxMRqTAUjiUp5OT49uK9wnH0ZLw9ZruJpKj27aFbN3jrrcAPVaUK/Otf/vy/++8P/HAiIhWGwrEkhXHj/HWPHgXu0Bg3qWguvBB++mn35jYBOuYYuPhiP7li0qTADyciUiEoHEtSKPRkvI0bYeFC9RtLxXLhhX4ru1dfTcjhHnkE6teHyy+H3NyEHFJEJKUpHEtSKPRkvFmz/LXCsVQkzZrBySf7cJyXF/jhGjaEJ57wI5afeirww4mIpDyFY0kKhZ6Mp0kVUlENGuQnVnz7bUION2AA9O4Nd90F8+Yl5JAiIilL4VhCt3RpESfjzZzpP35u3z6UukQCc8YZULs2vPJKQg5nBs8843991VV+40kRESmcwrGELnoyXqErx23b+j1xRSqSGjX8WLe3307YnLXWreFvf4PPP4c33kjIIUVEUpLCsYSu0JPxYPcYN5GKaNAgf9LpBx8k7JB/+AMcdhjccAOsXJmww4qIpBSFYwld9GS82rXz3Zib60/I0xg3qaiOPhr23TdhrRXgt5T+979h7VptLS0iUhSFYwnd2LGFtFQsWABbt2rlWCqutDS46CL44gvfdJ8gBx3kT8x7442ELlqLiKQMhWMJVZEn42lShVQGF13kx7kluAn4jjuga1d/ct7q1Qk9tIhI0lM4llAVezIeKBxLxdahAxx+OAwZktARElWrwssvw6pVvv9YRER2UziWUBV5Mt7MmdCgATRqFEpdIgkzaBBMmbL7J8UE6dbNryC/+ioMH57QQ4uIJDWFYwlVoSfjwe5JFWah1CWSMAMHQs2auwcRJ9Bdd/ke5CuvhDVrEn54EZGkpHAsoSp0ZzzQGDepPOrWhd/+1vcdJzihVq0KL70Ey5fDTTcl9NAiIklL4VhCs2wZLF5cSDhes8bfqTFuUllcfbWfzvLyywk/9CGHwG23+UOrvUJEROFYQlTkyXgzZ/prrRxLZdG1Kxx5pG+tyMtL+OHvuQeysuCKK7Q5iIiIwrGEptid8UDhWCqX3/8eZs+GkSMTfuhq1fxeJKtX+zISODhDRCTpKBxLaMaO9ZOs9joZb/Jk/7/1fvuFUpdIKM45Bxo3hn/9K5TDd+0K994Lb78Nb70VSgkiIklB4VhC4VwxJ+NNmOBPoc/ISHhdIqGpVg0uv9w3/i5YEEoJf/wj9OrlV48TuGmfiEhSUTiWUMyf70/GO/zwAnc4BxMnFtJrIVIJXHmlv37++VAOn5Hh9yPZutXndLVXiEhlpHAsoRg92l8ffXSBOxYs8NMqFI6lMtp3X+jTB/79b9i+PZQSOnSABx+ETz+F//wnlBJEREKlcCyh+O47P961S5cCd0yY4K8VjqWy+v3v/eDhd98NrYQ//AGOPx5uvBHmzAmtDBGRUCgcSyhGj/aTq9LTC9wxYYIfYXHQQaHUJRK6k07yy7f/+EdofQ1paX7ucZUqfn+SnTtDKUNEJBQKx5JwK1fC9OmFtFSA7zfu2NFvpytSGaWl+TPjJkyAESNCK6NVK3j2WRgzBv72t9DKEBFJOIVjSbjvvvPXhYbjCRPUUiFy0UXQogX8/e+hlnH++X7l+C9/8SFZRKQyUDiWhBs92k+t6tGjwB2rVsHChdCtWxhliSSPqlXhllvgm2/gf/8LtZSnn/Y5/be/hY0bQy1FRCQhFI4l4UaPhsMO8wF5DxMn+mutHIv4vZwbNgx99bhuXXj1VZg715+gJyJS0SkcS0Jt3Ajjx8NRRxVypyZViOxWsyZcdx189JHfNTJExxwDt9/uR7t98EGopYiIBE7hWBJqzBjIzS2m37hlS2jUKOF1iSSla66BWrXggQfCroR77/U7Wl52GSxaFHY1IiLBUTiWhBo92p+Mf8QRhdw5YYL6jUXya9AArroK3nzT9zWEqGpVeOMN2LbN9x/n5oZajohIYBSOJaFGj4auXaFOnQJ3bN4MM2eqpUKkoBtv9Ps6P/RQ2JXQoQP885/+PMGQW6FFRAKjcCwJs2OHb6sotKVi8mTIy1M4FimoeXO49FJ48UX49dewq2HQILjgAt9m8f33YVcjIhJ/CseSMOPHw5YtxfQbg8KxSGHuvtuvHt95Z9iVYAbPPAOtW/uQvHZt2BWJiMSXwrEkzOjR/rrIcFyvHuy7byJLEkkNLVrATTfB0KEwdmzY1VCnji9lyRIYPDi0Xa5FRAKhcCwJM3o07L8/NG1ayJ0TJ/qT8cwSXJVIivjjH/0kl1tvTYo0ethh8Ne/wttvw/PPh12NiEj8KBxLQuTl+W2jC1013rkTJk1SS4VIcerUgT//GUaNgk8/DbsawOf0U06B66/f3RklIpLqFI4lIaZPh9Wri9j8Y+ZM2LpV4VikJIMHQ7t2fhU5CWappaX53fMaNYL+/WHdurArEhEpv8DCsZm9aGbLzWxKUMeQ1FFivzFoxrFISapW9TPUpk6FIUPCrgaAxo3hrbdg3jy/QUgSdHyIiJRLkCvHLwOnBvj6kkK+/Rb22ccveu1l4kSoVg06dUp0WSKp59xz4dBD/QSLzZvDrgaAI4/0m/i9+y489VTY1YiIlE9g4dg59y2wOqjXl9SRmwuffw4nn1zE+XYTJsBBB0GVKgmvTSTlmMHDD/tREX/9a9jV7HLzzdC3L9xyC/z4Y9jViIiUXeg9x2Y22MzGmtnYFStWhF2OBODHH32/ce/ehdy5cyf89BP07JnwukRS1tFHw8UXwz/+4TfQSQJmvtOjRQs47zxYuTLsikREyib0cOyce94518M516Nx48ZhlyMB+PhjSE/3Z7Xv5ZdfYOPGIpqRRaRIDz/sZ4NfcUVSnJwHUL++H+22bBkMGOB/9hURSTWhh2Op+D75xPck1qtXyJ3ffuuvFY5FSqdRI3jsMf/RzLPPhl3NLj16+B30vvwS7rgj7GpEREpP4VgCtXixP9/u9NOLeMDo0bDfftCyZSLLEqkYLrwQTjrJp9DFi8OuZpdLL4U//MEvbr/5ZtjViIiUTpCj3IYCPwAdzWyRmV0W1LEkeX3yib8utN/YOR+OtWosUjZmfpl2xw649tqwq9nDo4/6uea/+53vnhIRSRVBTqsY6Jxr5pyr4pxr6Zx7IahjSfL6+GNo3RoOPLCQO2fM8GftHHNMwusSqTDatYN774X33/eXJFG1qu8/rl8fzjoLVq0KuyIRkdiorUICs20bjBzpWyoKHeGmfmOR+LjpJr+JzpVXQk5O2NXsss8+fvbx4sX+BL0dO8KuSESkZArHEphvv4VNm4rpN47uDNK+fULrEqlwqlSBN97wk18uugjy8sKuaJdevXznx8iRcN112kFPRJKfwrEE5uOPITMTjjuukDud8+H4mGOKWFYWkVLp3BmefNKPiXjoobCr2cPvfgd//KMfqvHEE2FXIyJSPIVjCcwnn/hgXKNGIXfOnw+LFqmlQiSeLrvM78Bx110wZkzY1ezh73+Hs8/2HSDDh4ddjYhI0RSOJRCzZ/tLsSPcQCfjicSTGTz3nB+NOHAgrFsXdkW7pKXBq69C9+6+tIkTw65IRKRwCscSiI8/9teFjnAD31JRrx506ZKokkQqh3r1YOhQWLgQBg9OqibfGjVg2DA/waJvX1iyJOyKRET2pnAsgfj4Y98C2bZtEQ8YPdoPQU3TH0GRuDv8cPjrX+G//026/uPmzeGjj2DNGv/DcxItbouIAArHEoCNG+Gbb4ppqVi2DGbOVEuFSJBuu83PT7vjDvjgg7Cr2UPXrvDeezBtGvTrB1u3hl2RiMhuCscSd1984eeZlthvrJPxRIJjBi++CD17+m2mk6zJ9+STYcgQ/8/BwIGwc2fYFYmIeArHEndDh0LjxnDkkUU8YPRo33zYvXtC6xKpdKpX96vGDRr4Jt8k2iAEfCh+4glf4lVXJVV7tIhUYgrHEldr1sCHH8IFF/h9CQr17bd+Z4CqVRNam0il1KyZn522Zg2ceSZs2RJ2RXu49lq4+2544QW4886wqxERUTiWOPvvf2H7dhg0qIgHrFsHv/yifmORROrWDV5/HX7+Gfr3939Jk8h99/mdr//+d38REQmTwrHE1ZAhfjrbwQcX8YCRI/1np8cem8iyROSMM/wWdR9/nHRNvmbwz3/6T5z+9Cd48MGwKxKRyiwj7AKk4pg9G374wU+OKnJH6A8+gIYNi2lIFpHADB7s2ypuuMF/vPPqq5CeHnZVgC9jyBDIy4Pbb/e/v+WWsKsSkcpI4Vji5pVX/NjiCy8s4gE7dvgBp2eeCRn6oycSiuuv9wH5jjsgMxP+85+kmTeekeHzel4e3HqrL+umm8KuKkG2bPEbtyxZ4ttenNt9hmKtWtCqlR8SXeTJHCISL0ooEhd5ef4/tZNO8v9+F+qbb2DtWh+ORSQ8t9/uw9hf/uLD1r/+lTQryBkZvj3aObj5Zv8p1I03hl1VHG3Z4sfq/fyzv0yZ4kPxqlUlP9fMn2DZtq0/qfnII/2lSZPAyxapTBSOJS6+/Rbmzy/hZJoPPvCjpU46KVFliUhR7r3Xf5rz97/7YPbaa34lOQlEA3Jenl853rgR7rqrmHatZJabC2PHwiefwGefwfjxu/u9mzXzJ0v26uVXhlu2hBYt/Ptgtvuybp0P0NHLrFnw9NPwyCP+dTp08NsNXnAB9OiRot8okeShcCxx8corULu2P+enUM75cHzqqX7GsYiEywz+9jdo1Mgv0a5c6f+O1qsXdmWAX9AeOhQuuwzuuceX99hjSdMBUrzt2+Hzz/34ns8+88WnpcFhh8Ef/+g3ZunZ0wfhstq2zQft777zn8r961/w+OPQvr3fGfGii3xoFpFSM5dEU9d79Ojhxo4dG3YZUkqbNsE++8D55/v2xUKNHev/MxgypJg5byISiqFD4eKLoVMnH+aK7I1KvLw8n90ff9yfz/DSS0nadpuX5z9Ce+MNeOcdP1e6QQO/otu7t98SsGHD4I6/dq3fk/uNN+Drr309ffv6b94xx2g1WaQAMxvnnOtR2H1aOZZy++AD/7FnsZn3/fd9T2OfPokqS0RiNXCgX0E++2w4/HD/l7rIeYyJlZYGjz7qd928806fOd9+O4k+gFq0yG/T/cILsGAB1Kzpz6u44ALfQpaoJF+vHvzud/6SkwPPP+9bL4491rda3HILnHtu0vSWiySzVPiASpLckCHQpg0cdVQxD/rgA/jNb/xKiogkn5NOglGjfI/sEUf4JdokYebnHz/7LHz6KZxwAixbFmJBubkwbJj/YX/ffeHPf/YtDEOHwvLlvn+7d+/wlribNfM1LVjgv2nr1vlWi27d/MSgJPrEWCQZKRxLucyf7/f1GDSomF7AWbNg2jRNqRBJdocc4vtYjzjCr0BeeSVs3Rp2VbtceaXvWPjlFzj0UJg0KcEFrFrlB7m3a+dPsBg/3k/+mDMHvvjCB9CkWdLGnwB95ZUwYwa8+aZ/L/v29W0W//tf2NWJJC2FYymXhx/2n9JddlkxD/rwQ39d5Nl6IpI0mjTxJ5Pdfrv/aP7oo+HXX8Ouapezz4bRo/3AhyOPhOHDE3DQX36Byy/30yRuu81/VPbOO35l9v/+D/bbLwFFlENamj8pZNo0f+Le7Nn+m9e/v59+ISJ7UDiWMlu2zJ+AN2gQtG5dzAPff9+vSBX7IBFJGhkZfsTbBx/4T34OOsjv75yXF3ZlgP/n5Oef/fmDZ5wB//hHAJ0CO3b4aRPHHOPbEd54w/9jN2mSbz8555zU28yoShW4+mrIzob77vMtFp07+9Xw7dvDrk4kaSgcS5k99pj/9/S224p5UE4OjBmjlgqRVHTGGTB5sl9lvOYaOP54H6ySQPPmfoJZ//5+Otpvf+tPDC63JUvg/vv9Rhvnn+9PuHv4YVi8GJ57zv+gkOpq1fLz8aZN8+/pbbf5HwBGjQq7MpGkoHAsZbJmjf90rn//EkZpDh/ul3QUjkVSU+vWfrzbCy/4nd2ysnxY3LYt7MqoUcO30v71r/66R48y9iHn5cGIEX41uHVrHxwPOMCfdDd7th+HVr9+3OsPXdu2/mscNszv3Hfccf6njKVLw65MJFQKx1ImTz0FGzb4M8iL9dJL/rPPAw9MSF0iEgAzf4Le1Kl+VMStt/qP4998M/RWCzM/4u2rr2D9er/Pxr//HWObxYoVvqVg//3hlFP8nOKbbvKBeMQIf/JaZRh91revf2/vusvPyevYEZ58cvdOfiKVjMKxlNrGjfDEE/7f06ysYh44dqxvqbj6ag2gF6kIWrTwq4yffea3xBw40KfRr78OuzJ+8xu/sH300TB4sF8AXbeukAc650PwBRfsPsGuZUvfU7xokQ/L7dsnuvzw1ajh20kmT/bbWV9/vd+4acyYsCsTSTiFYym1556D1atjWDX+5z/9QPyLL05IXSKSAGZ+lXX8eD/kfNky37faq5ef87tjR2ilNWnic3u0zaJLF/97wPfX3nWXD76/+Y0fmHz11X7F9JtvfNCvVi202pNGhw7+m/b2235l/fDD/U8bq1eHXZlIwmj7aCmVrVv91KLOneHLL4t54MqVfjXmd7/zzckiUjFt3erH1jz5pG9HaN4cfv97P99xn31CK+unHx2XXrCNaXMzubT+Bzy65hLqpW2AE0/0+1Cfe25yzSRORhs2wL33+o8K69f3veaDBumTQKkQits+WivHUiovv+wHUNx5ZwkPfOEFf8LOH/6QiLJEJCyZmX6SxYwZ8PHHfrn2rrt8SD76aB+sEjVLd906P57s97/n0P77Mm5uPe7gb7yypg8H1l3ERy+v9DOcBw1SMI5F7drwyCP+U4L994dLLvGj7caPD7sykUBp5VhitmmTP4G7WTP44YdiFg9yc/3ycrt2/iwZEalcZsyAt96Cd9/1PawA3bv7kXC9evlL27blW4HcutWPlZswAb7/3l+mTvU9xTVr+u2wTz8devdm7JLmXHopTJnib3rkEX/OmZRCXp4/wfqOO/wng5dd5jdAadIk7MpEyqS4lWOFY4nZzTfDo4/6c1mOPrqYB374oR/d9u67fjsrEam8Zs2C997zfaxjx/qfsgEaNfKrka1a+fFprVpBw4Z+o4oqVaBqVf+4tWt9v+vq1X775jlzfPieN2/3pIzatX1v7JFH7r5kZu5RxvbtvvPj/vth82a49lo/sa1evUR9IyqItWv9N/HJJ/3q+z33+E8O1K8tKUbhWMpt7Fh/UvoVV8Czz5bw4JNO8v95/fpr6u0gJSLB2bnTr+6OGeO3uPv1V99ysWBBbHOT69b1Wzd37OhHRHbs6Ns4Djww5pFry5bB3Xf7NumGDX22u/xyqF69fF9apTNzJtx4oz+xsXVr+POffbuK/s2XFKFwLOWyc6ef6LNsGUyf7v9/KtL06b734v/+L4ZxFiIi+FaIFSv8quSOHX6Zd8cOf3v9+tCggV/ijWPwmjjRZ7tRo6BpU7jlFrjqKr95nJTCyJH+3/roft733+8/MUzTKU2S3HRCnpTLY4/5/0iefrqEYAx+MkXVqn4pRkQkFma+d7VDB78KfPDBcOih/uOqDh18C0acVyS7dfOnRIwa5XeEvvVW2Hdfn+1WrozroSq2E0+EH3/0rTNpaX7b1Kwsf/b29u1hVydSJgrHUqy5c/2nZWeeGUP7cE6OP2Hj/PN1koaIJD0zP/L4iy98p8eRR/o2ixYt/D9jX3wR+gaAqcEMzjrL79392ms+JF96qT/p8qGHitiNRSR5KRxLkZyDK6/058Y8/XQMT7j9dv9R6D33BF6biEg8HXaY3/xvyhQ/pnnkSDj5ZD905y9/8bcnURdickpP9zOkf/nFn4DZubPfgbB5cx+Wv/tO30RJCQrHUqSXX/b/QTzwgF9JKdYPP8Arr/iRFpVx61URqRAOPNC3ki1Z4nfZ239//+nZQQf5cwH/8Af45BPYsiXsSpNYdBfFkSNh3DgfmN95x4856tzZrybPnx92lSJF0gl5UqgffoDjjvPjSL/6qoRzK/Ly/LLLkiX+DGad0SIiFciSJT4Qf/SRb7XYvNl/ota1qz9ZuWdP3yLdsaOGNRRp40a/JfULL/iZ1ACHHALnnOMvHTqEW59UOppWIaUyZ44PxfXq+ZDcqFEJT3jxRT8Q/rXX/AqBiEgFtXUrfPONXzT4+Wc/5nLDBn9fRoYf19y27e5L48b+39LopU4dH6wzMnwXQkaGX2jduXP3JTd3z98XdcnN9c/PyNj9mpmZ/hjRS/XqSbjbc3a2P4Hv3Xfhp5/8bR07+jGgJ58Mxx7rZ1eLBEjhWGK2ejUccYSfqjRmjP9IsVhr1/qf+Pff3/eTJd2/wiIiwcnL8x+Y/fyzv/71192XZcvCrs4H8EaN/M6mzZvvvt5vP//P9v77+wAf2j/dCxfu3iTmm298v0pGhv808ogj/ErN4Yf7wkXiSOFYYrJtm/+hfcwY+PJLOOqoGJ50003w+ON++aR796BLFBFJGVu2wJo1fg0helm3bu/V4by83SvARV2iq8z5L2lpu19nxw5/vWWLX8lev95f1q3zix05Of6yZAksX77nFI46dfzCbVaWH3HXrZv/dZ06Cf6GbdvmWy6++MLP2Bs/fvc4uNatfUiOhuVu3bQrn5SLwrGUyDm/udFrr8Ebb8DAgTE8adIk3zN26aXw/POB1ygiIuW3Y4c/H27WLJg9219mzPDz7Fet2v24/ff34+2OOspfd+yY4BXmbdtgwgTf3zdmjL9euNDfV62ab/o++GAflA8+2J81WaNGAguUVKZwLMXavh2uvtq3Dv/1r3DnnTE8afly/7HXtm1+bE/jxoHXKSIiwXHOryxPnOgvP/3kF3KjgblRI9/pEA3LhxwSwuLt4sV+05EffvCTMCZM8Evy4JfSO3bcHZajwbnEE2ekMlI4liKtWuVPFP7mG7j7brjvvhhWBrZtgxNO8P8wffutP1VbREQqHOd8L/X33/vTSr77zp9PBz4Y9+zpN1I59lgfnBO+cOucXwafONEH5eh1dIUZoGXL3YE5et2mjc6RqeQUjqVQM2dCnz6wYIFfNY5p0IRzcMklfqbxW2/BeecFXaaIiCSRZct8WP7+exg92rcG5+b6iRmHHebHgB57rG8Nrl49pCJXrvSfauYPzDNm7G62rlt3z3aMLl38kOuaNUMqWBJN4Vj28uWXcO65/h+z99/3H5HF5MEH/U54992nnfBERIT1631QHjUKvv7af6iYlwdVq/rz54491q8uH3ZYyNlzyxaYPHnPwDxp0u4dXcz8GI9oWD7oIH/Zf38NsK6AFI5ll/Xr/W5PTz3lW7M++sjP4ozJO+/4leLzz/dn7ekjKRERKWD9et9+EQ3L48f7sJye7hdroyf59erlOx5C/a8kNxfmzvX7g0+e7C9TpvizFaOrzFWr+p398ofmAw7wEzSK3SFLkpnCseCc74K46SZYuhSuvNJvC123boxPfughuOMO/6P/V1+F+FmZiIikknXr/Plz333nV5h//HH3Ym2TJtCjh+9d7tHD587WrZNg7WXrVpg+fc/QPHmyPyEwqkYNH5o7d/ZhOXq9335aaU4BCseV3PTpcO21vpWie3d45hm/1WlMNm/2u9+9+aZfNX7xRfVkiYhIme3Y4TsaojsMjh0L06btXqitVctnzC5dfN5s187nzbZtQ5i9XNCaNT4wT5/ui45eL1q0+zFVq/rNsQqG5g4dNJs5iSgcV0LO+Y+zHn/ct07UqQP/939w1VX+o62YLFgAZ57pe7P+7/98r3HoP86LiEhFs3GjP39uyhSYOtVfpkzxU0Pza9jQryw3a+Yv++zjrxs02HPb7PyXKlUS8AWsX+9P+MsfmKdP9y0b0ZyVluaTfv7A3LkzdOrkfyKQhFI4rkS2bIGhQ30onjzZj3e8+mq45hr/8VVMtm2D556Dv/zF/4j/xhtw+ulBli0iIrKX1av9Vtxz5/rrOXP8Im1Ojm8RXLZsz93+CpOZ6UNy7dq+I7C0lxo1fAtivXr+Ur++v65VK4b1oi1bfP9ywdA8a5bf0jCqdeu9Q/MBB/iDSSAUjiu41avh44/91InPP/edEAcdBDfcABdc4P9hiEluLrz+up9CMX8+HH88/POf/qdaERGRJJOb66e2rV27e8vsoi4bNvisGssllmiUlrY7MNer5xejoivZ+a+jv65dO1+Y3rHDJ/1p0/YMzjNm+H7nqKZNfUguGJybNtUnueWkcFzBbNzoe7W+/963Tnzzjf8Honlz3wXRv78fmxPz35uVK+Hdd+Hpp/3nWN27+7P1TjxRf/lERKRScc7vHBsNyps2+ZMK167d+7Jmze7rlSt3r2jv2LH361av7kNyy5a7Ly1a7Pn7po1ySV80f++e5unTfcKPql9/71Xmzp2hVStN0IiRwnEKW7Fi9w+WU6b47eV/+cWHYfAnLPTt60Nxjx6l+DuxYgUMH+5HWHz5pX/Bzp3h3nv9AGT95RIRESk153xYjgbl6PXSpX577sWLfWvIokU+hOeXnu4XuvIH5pYtoUVzR8vMlbTcNJPmyydSZWa+kwJXrtz9AjVr+k978682d+rkQ3PCty9MbqGFYzM7FXgCSAf+45x7oLjHV7ZwvG2bz6jLl/u/PPPn+3Pg5s/3l1mzdu9pD/4jmZ49/RadRxzhZ0SW2I6Um+tffM4cf0rwzz/DTz/55i3wp/+ef76/dO2qlWIREZEEcM7n2mhQLuqyefOezzPzXRUtWvhziRrX3kpjW0Hj7YtpsmEujVdOp/HiiTReMZUmLKcmmzDwgaFg6o4uX0fPamzQwC9xV4IsEEo4NrN0YBZwErAI+BkY6JybVtRzwgjHW7f6jz9yc0u+7Ny55+937NizR2nz5sJ/vX69/9gl/8cyy5f73xdUpYr/AW/fff1JrQceuPsHwBYtYvzz+vzzfvRaNG0XbPo/9FCfso87zi83V4K/BCIiIqnGOZ8VCgvNixfvXmBbsWLPVuX8MtLzqFN1G3UyNlHHNlA3bw11tq+izvYV1GE9dVhPLTZSnS1kspXMjFwya6aTWbsKmXWqklm3Gpn1MqlWqwpValQhvXpV0jKrkl69Kuk1qu2+rlGNtHQjPc2Rns6uS5o5qmQ4Mqs5f/bktm2+2OjlkEP8JcGKC8dBTqk+FMh2zs2NFPEmcAZQZDgOQ+/evm83CGlp/gewOnV2n+nasKGf19ikyZ6Xffbxgbhp0zh0NKxb5//wHXaYXxHed19o08bvIR/zyAoREREJk9nuE/66dCn6cc753ugVK3ZfoqF57do01q+vHrk0Yv36tixdD7PW5bF+rWPdeti6Pd+M153AusglTg5kClM4qPA777svlHBcnCBXjs8FTnXOXR75/UXAYc65awo8bjAwOPLbjsBMoBGwEkk2el+Sj96T5KT3JTnpfUlOel+SU0V/X/Z1zjUu7I4gV44L+6x+ryTunHseeH6PJ5qNLWqpW8Kj9yX56D1JTnpfkpPel+Sk9yU5Veb3JciRBIuAVvl+3xJYEuDxRERERETKJchw/DOwv5m1NbOqwABgWIDHExEREREpl8DaKpxzO83sGuBz/Ci3F51zU2N8+vMlP0RCoPcl+eg9SU56X5KT3pfkpPclOVXa9yWpNgEREREREQmTtkETEREREYlQOBYRERERiUhIODaz/mY21czyzKxHgfvuMLNsM5tpZqfku/0QM5scue9JM7+Nm5lVM7O3Irf/aGZt8j3nYjObHblcnIivrTIws1Mj70+2md0edj0VkZm9aGbLzWxKvtsamNkXkT/PX5hZ/Xz3xe3vjRTOzFqZ2ddmNj3y79f1kdv1voTIzDLN7Ccz+yXyvtwXuV3vSxIws3Qzm2BmH0V+r/clZGY2L/L9nGhmYyO36X0pjnMu8AvQGb/BxyigR77bDwB+AaoBbYE5QHrkvp+Aw/Hzkj8FTovc/nvg2civBwBvRX7dAJgbua4f+XX9RHx9FfmCP5lyDrAfUDXyfh0Qdl0V7QIcA3QHpuS77SHg9sivbwcejPw6bn9vdCn2PWkGdI/8ujYwK/K91/sS7vtiQK3Ir6sAPwK99L4kxwW4CXgD+Cjye70v4b8n84BGBW7T+1LMJSErx8656c65mYXcdQbwpnNum3PuVyAbONTMmgF1nHM/OP/dfgU4M99zhkR+/Q5wQuSnl1OAL5xzq51za4AvgFOD+6oqjV3bgDvntgPRbcAljpxz3wKrC9yc/8/6EPb8OxCvvzdSBOdcjnNufOTXG4DpQAv0voTKeRsjv60SuTj0voTOzFoCpwP/yXez3pfkpPelGGH3HLcAFub7/aLIbS0ivy54+x7Pcc5FdwBvWMxrSfno+xqeps65HPBBDWgSuT2ef28kBpGPCQ/Gr1LqfQlZ5KP7icBy/KKI3pfk8DjwRyAv3216X8LngBFmNs7MBkdu0/tSjLjNOTazkcA+hdx1p3Puw6KeVshtrpjby/ocKTt9X5NPPP/eSAnMrBbwLnCDc259MQsiel8SxDmXC3Qzs3rA+2bWpZiH631JADPrAyx3zo0zs2NjeUoht+l9CcaRzrklZtYE+MLMZhTzWL0vxDEcO+dOLMPTitpielHk1wVvz/+cRWaWAdTFfxy9CDi2wHNGlaEm2ZO2AQ/PMjNr5pzLiXyktTxyezz/3kgxzKwKPhi/7px7L3Kz3pck4Zxba2aj8C10el/CdSTQz8x6A5lAHTN7Db0voXPOLYlcLzez9/HtknpfihF2W8UwYEDkTMe2wP7AT5El/g1m1ivStzII+DDfc6KTKM4Fvor0v3wOnGxm9SNnXZ4cuU3KR9uAhyf/n/WL2fPvQLz+3kgRIt/DF4DpzrlH892l9yVEZtY4smKMmVUHTgRmoPclVM65O5xzLZ1zbfD/T3zlnPstel9CZWY1zax29Nf4bDQFvS/FS8RZf8BZ+J8stgHLgM/z3Xcn/mzImUTOfIzc3gP/Bs4Bnmb3bn6ZwNv4JvGfgP3yPed3kduzgUsT8bVVhgvQG3+m/hx8m0zoNVW0CzAUyAF2RP6uXIbv2foSmB25bpDv8XH7e6NLke/JUfiPBicBEyOX3npfQn9fsoAJkfdlCnBP5Ha9L0lywX+KG51Wofcl3PdiP/z0iV+AqdH/w/W+FH/R9tEiIiIiIhFht1WIiIiIiCQNhWMRERERkQiFYxERERGRCIVjEREREZEIhWMRERERkQiFYxGREphZrplNNLMpZva2mdUo4nH/i9PxzjSzeyK/vsrMBpXjtV42s3NLeMwoM+sR+fU8M2tU1uPle81rzOzS8r6OiEiiKRyLiJRsi3Oum3OuC7AduCr/nWaWDuCcOyJOx/sj8K/Iaz7rnHslTq8bd9GvvRAvAtclshYRkXhQOBYRKZ3RQHszO9bMvjazN4DJAGa2MfogM/ujmU02s1/M7IHIbe3M7DMzG2dmo82sU8EXN7MOwDbn3MrI7+81s1sivx5lZg+a2U9mNsvMji7k+WZmT5vZNDP7GGiS774TzGxCpK4XzaxacV+omX0QqXWqmQ3Od/tGM/uLmf0IHG5mD0SON8nMHgZwzm0G5pnZobF/a0VEwpcRdgEiIqnCzDKA04DPIjcdCnRxzv1a4HGnAWcChznnNptZg8hdzwNXOedmm9lh+NXh4wsc5khgfDFlZDjnDjWz3sCf8dsn53cW0BE4CGgKTANeNLNM4GXgBOfcLDN7BbgaeLyYY/3OObc6sk3zz2b2rnNuFVATmOKcuyfytb0AdHLOuejWzhFjgaPxu2aJiKQErRyLiJSsuplNxIe9BfgwCPBTwWAccSLwUmT1lEjArAUcAbwdea3ngGaFPLcZsKKYWt6LXI8D2hRy/zHAUOdcrnNuCfBV5PaOwK/OuVmR3w+JPLY415nZL8AYoBWwf+T2XODdyK/XA1uB/5jZ2cDmfM9fDjQv4RgiIklFK8ciIiXb4pzrlv8GMwPYVMTjDXAFbksD1hZ8ncKOBdQt5v5tketciv43vOCxozXFzMyOxYf8wyOr36OAzMjdW51zuQDOuZ2R1okTgAHANexeDc/Efz0iIilDK8ciIvE3AvhddKqFmTVwzq0HfjWz/pHbzMy6FvLc6UD7chz7W2CAmaWbWTPguMjtM4A2ZhZ97YuAb4p5nbrAmkgw7gT0KuxBkRXxus65T4AbgG757u4ATCnrFyIiEgaFYxGROHPOfQYMA8ZGWihuidx1IXBZpFVhKnBGIU//FjjYIkvTZfA+MBt/kuAzRAKwc24rcCm+rWMykAc8W8zrfAZkmNkk4H58a0VhagMfRR73DXBjvvuOBEaW8esQEQmFOVfYp28iIhIWM3sCGO6cS9lgaWYHAzc55y4KuxYRkdLQyrGISPL5G1DoRiMppBFwd9hFiIiUllaORUREREQitHIsIiIiIhKhcCwiIiIiEqFwLCIiIiISoXAsIiIiIhKhcCwiIiIiEvH/4LQ1juoJB68AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(width, height))\n",
    "\n",
    "\n",
    "ax1 = sns.distplot(df['price'], hist=False, color=\"r\", label=\"Actual Value\")\n",
    "sns.distplot(Y_hat, hist=False, color=\"b\", label=\"Fitted Values\" , ax=ax1)\n",
    "\n",
    "\n",
    "plt.title('Actual vs Fitted Values for Price')\n",
    "plt.xlabel('Price (in dollars)')\n",
    "plt.ylabel('Proportion of Cars')\n",
    "\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see that the fitted values are reasonably close to the actual values, since the two distributions overlap a bit. However, there is definitely some room for improvement.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 3: Polynomial Regression and Pipelines</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Polynomial regression</b> is a particular case of the general linear regression model or multiple linear regression models.</p> \n",
    "<p>We get non-linear relationships by squaring or setting higher-order terms of the predictor variables.</p>\n",
    "\n",
    "<p>There are different orders of polynomial regression:</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><b>Quadratic - 2nd order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X +b_2 X^2 \n",
    "$$\n",
    "\n",
    "<center><b>Cubic - 3rd order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X +b_2 X^2 +b_3 X^3\\\\\n",
    "$$\n",
    "\n",
    "<center><b>Higher order</b>:</center>\n",
    "$$\n",
    "Y = a + b_1 X +b_2 X^2 +b_3 X^3 ....\\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We saw earlier that a linear model did not provide the best fit while using highway-mpg as the predictor variable. Let's see if we can try fitting a polynomial model to the data instead.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We will use the following function to plot the data:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PlotPolly(model, independent_variable, dependent_variabble, Name):\n",
    "    x_new = np.linspace(15, 55, 100)\n",
    "    y_new = model(x_new)\n",
    "\n",
    "    plt.plot(independent_variable, dependent_variabble, '.', x_new, y_new, '-')\n",
    "    plt.title('Polynomial Fit with Matplotlib for Price ~ Length')\n",
    "    ax = plt.gca()\n",
    "    ax.set_facecolor((0.898, 0.898, 0.898))\n",
    "    fig = plt.gcf()\n",
    "    plt.xlabel(Name)\n",
    "    plt.ylabel('Price of Cars')\n",
    "\n",
    "    plt.show()\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "lets get the variables\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df['highway-mpg']\n",
    "y = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's fit the polynomial using the function <b>polyfit</b>, then use the function <b>poly1d</b> to display the polynomial function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        3         2\n",
      "-1.557 x + 204.8 x - 8965 x + 1.379e+05\n"
     ]
    }
   ],
   "source": [
    "# Here we use a polynomial of the 3rd order (cubic) \n",
    "f = np.polyfit(x, y, 3)\n",
    "p = np.poly1d(f)\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's plot the function \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "PlotPolly(p, x, y, 'highway-mpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.polyfit(x, y, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can already see from plotting that this polynomial model performs better than the linear model. This is because the generated polynomial function  \"hits\" more of the data points.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  #4:</h1>\n",
    "<b>Create 11 order polynomial model with the variables x and y from above?</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            11             10             9           8         7\n",
      "-1.243e-08 x  + 4.722e-06 x  - 0.0008028 x + 0.08056 x - 5.297 x\n",
      "          6        5             4             3             2\n",
      " + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n"
     ]
    },
    {
     "data": {
      "image/png": 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jiaGG4Z8krWY9G8tX0RxQggrNAWVFRW2ii2aMMXFjgSaG9o04C0WYpm+R5hNSBNJ8wsSy3EQXzRhj4saazmIomD2Q5kETGF75Cndf9BVWVNQysSzXms2MMX2KBZoYaxjxSfLfvJMJObsYd/zQ9jMYY0wvY01nMbZv+CcByFr3QoJLYowxiWGBJsYCeWU0lk6l37sPIvt2J7o4xhgTdxZo4qDmxNlIUx15y36b6KIYY0zcWaCJA3/RkdSP/izZ7z1BalW0p1UbY0zvY4EmTmonX0cwI5/8N27rUfOf2YwGxpiuskATJ//dlcpLA64kY+syssqfT3RxOmTl1nquf2YtD7y5leufWWvBxhhzSCzQxEHogv2N8oms0FHkvXIz6VuWJLpY7VpRUWszGhhjuizhgUZEfCKyQkSed8tFIrJARNa634Vh284WkXIR+UBEzglLnyQiK926u0VEXHqGiDzh0t8SkeFxf4McuGD7NYX/1/QtdqUPpuiFa0jbviIRxemwiWW5NqOBMabLEh5ogBuA98KWbwJeVtVRwMtuGREZDcwExgDTgXtFxOfy3AdcDYxyP9Nd+lXAblUdCfwauCO2byWy8At2rS+fVaf8nmB2f4rnf5W0nasTUaQOGVeSw90XjeLqqSU2Eagx5pAlNNCISBlwHvDHsOQLgTnu9RxgRlj646raqKrrgXJgioiUAHmqulhVFXi4VZ7Qvp4CzgzVduKp9QX7qBGHUXX+nwmm51L8/BVkbHwl3kXqsHElOVxx/GALMsaYQ5boGs1vgO8CwbC0Qaq6FcD9HujSS4FNYdtVuLRS97p1eos8quoHaoDi1oUQkatFZJmILKuqquriW4qs9QU70G8IlRc8ij/vMIpe/Do5Kx/uUaPRjDGmoxIWaETkfGCHqi7vaJYIaRolPVqelgmqD6jqZFWdXFx8UByKmWC/wVRd8Bf2HXY6+Yt/Rv7rP4FgIG7HN8aYeEhkjeZk4AIR2QA8DpwhIn8BtrvmMNzvHW77CiB8VsoyYItLL4uQ3iKPiKQC+cCuWLyZQ6Vp2ez+5N3UHXslOWv+SuHL34JAU6KLZYwx3SZhgUZVZ6tqmaoOx+vkX6iqXwDmAbPcZrOA59zrecBMN5JsBF6n/xLXvFYrIlNd/8sVrfKE9nWJO0bytU9JCnumfoeaqd8ja/2LFM//KtJUl+hSGWNMt0h0H00ktwOfFJG1wCfdMqq6GpgLrAFeAK5V1VA70zV4AwrKgY+A+S79QaBYRMqB/8GNYEtW9cd+id2n30H61mUU/+NKpMlukDTG9HySjF/wE2n8+PE6f/789jeMoYwNCylacD2NpVPZdc694EtPaHmMMaY9paWly1V1cqR1yVij6fMah59B9ak/JrPidQpe+QFosP1MUSTrfGXJWi5jTPeyJ2wmqYajLsa3dyd5S39DMHsAe6Z+55D2E5r+pjmgpPm2Jc2Nl8laLmNM97MaTRKrm3A19aM/R7///onMdS8e0j6Sdb6yZC2XMab7WaBJEhGbkUSoOekmmgaOp+CVH+Dbs7HT+03W+cqStVzGmO5ngwFaScRggJbNSHJQM5KvdjMDnv4M/twyKi987KDBASu31rOiopaJZbkRm5/aW58oyVouY0znRRsMYH00SSBSM1L4hfedugLqhnybz6y/mby3fsGek76/f11H+jrGleQk5YU8WctljOle1nSWBKI1I4UCyXfeP4I5wen0W/UI6ZsX719vfR3GmGRngSYJRJuOPzyQ3N48k10ZZRS8egvSvBewvg5jTPKzprMk0VYz0sSyXHwp29CA4k/JoHzSD5nyxtXkLrubPSfetD9I9cS+DuujMaZvsEDTI+j+37uLj6P+mMvJWfkwDYdPp3nQhB7Z12H30RjTd1jTWZJbUVFLIOiFmkDQW95zwrcJ5gyi4NWbe+xMz9a3ZEzfYYEmyUXqg9H0flR/4oek7S4nZ9UjiS7iIbG+JWP6Dms6S3Jt9cE0HnY6+4ZNI/fte2kYeT7BnEEJLmnnjCvJ4YZTy1hUXs20kQXWbGZML2Y1mh6g9WOgQ2pOmo0E/QQX3d7jJqdcubWeu16tYNmmWu56taJHld0Y0zkWaHqwQN4w1h1+BUM2v8CKtxZy/TNre8wF2/pojOk7LND0cM9kf4bN2p9bUx8iGPD3mAu2N2xbEMCXYn00xvRmFmh6uHHDBvCz4Bc5JmUTX0hd2MMu2NrqtzGmN7JA08ONK8nh0xd+jo/7TWR25tMcW+Tv1v3H6uFkkYZtG2N6p4QFGhHJFJElIvKuiKwWkR+59CIRWSAia93vwrA8s0WkXEQ+EJFzwtInichKt+5uERGXniEiT7j0t0RkeNzfaByMG9KPrHNuIc1fS+7y33XbfkM3VT7w5tZu7/+x4c3G9B2JrNE0Ameo6nhgAjBdRKYCNwEvq+oo4GW3jIiMBmYCY4DpwL0i4nP7ug+4Ghjlfqa79KuA3ao6Evg1cEcc3ldC+IuPYu/Rl5Kz+q+kVq/rln3GssM+2vxuxpjeJWGBRj11bjHN/ShwITDHpc8BZrjXFwKPq2qjqq4HyoEpIlIC5KnqYvUervNwqzyhfT0FnBmq7fRGtZO/gaZmkrf49m7ZX6xrHW0N2zbG9C4J7aMREZ+IvAPsABao6lvAIFXdCuB+D3SblwKbwrJXuLRS97p1eos8quoHaoDiCOW4WkSWiciyqqqqbnp38RfMKqZ20tfJ3PQfMja+0uX9Wa3DGNMdEhpoVDWgqhOAMrzaydgom0eqiWiU9Gh5WpfjAVWdrKqTi4sPikM9Sv2Yz+PPH07+4tu7ZR40q3UYY7oqKUadqWo1sAivb2W7aw7D/d7hNqsAhoZlKwO2uPSyCOkt8ohIKpAP7IrFe0gavnRqTryJ1JoN5Kx+LNGlMcaYhI46GyAiBe51FnAW8D4wD5jlNpsFPOdezwNmupFkI/A6/Ze45rVaEZnq+l+uaJUntK9LgIWuH6dXaxx2GvuGnkLu8t+Rsrcy0cVp07OrKrnx2XKeXZW8ZTTGdF0iJ9UsAea4kWMpwFxVfV5EFgNzReQqYCNwKYCqrhaRucAawA9cq6oBt69rgIeALGC++wF4EHhERMrxajIz4/LOkkDNibMZ+OQF5C67i5pTf5Lo4hzk2VWV3LnQ63JbstEbzTZjbP9EFskYEyMJCzSq+l9gYoT0KuDMNvLcBtwWIX0ZcFD/jqruwwWqviZQMIL6sV8gZ+Uc9h4zk+YBYxJdpBYWlVcftGyBxpjeqVNNZyJSKCLHxqowpnvVTvo6waxi8l/7EQQD7WeIo2kjC6IuG2N6j3YDjYgsEpE8ESkC3gX+LCK/in3RTFdpei57Tvwe6TtXkv3+k4kuTgszxvbnu2cMZcqwXL57xlCrzRjTi3WkRpOvqnuAi4E/q+okvI570wM0HHEejUOmkrfk16Q0JNc9QjPG9uc3M0ZakDGml+tIoEl1w4wvA56PcXlMdxOh5hM3I/4G8t78eaJLY4zpgzoSaH4EvAiUq+pSETkcWBvbYpnu5C84nLpjryR77XOkb1mS6OLsF6uZoY0xySVqoHFDj4eq6rGq+nUAVV2nqp+JS+lMt6k77qv484ZR8MoPkObEX9hjOTO0MSa5RA007j6VC+JUFhNDmppF9Wm34autIO+txI/lWFFRS5PfzQztt0c5G9ObdaTp7A0RuUdEThGR40I/MS+Z6XZNJZOpH/tFctY8RvrmNxNalrys1P2TzgXdsjGmd+rIf/dJ7vePw9IUOKP7i2NiYeXWelZU1DKxLJdjp9xI5qZXKHjlf9l5yTw0PTGTZe5p8CMcmBV1T0P3PhnUGJM82g00qnp6PApiYiPUF9IcUNJ827j7olEcd9rP6D/v8+S//mOqp90OCXhEz8SyXNJTt7ly2RM2jenNOtReISLn4T3ZMjOUpqo/bjuHSRaRnpI57viJ1E66lrzl99A0eBJ7j7ks7uUKPesmVNOyxxAY03u1G2hE5H4gGzgd+CPeLMjJM0bWROU9JfPgmkPdcdeQvn0F+W/cRvOAMTT3j/9caONKcizAGNMHdGQwwEmqegWwW1V/BJxIy+fCmCTW5lMyJYXq0+8kmFlE4YIbkcaauJetK/fR2D04xvQcHWk6a3C/94rIEKAKGBG7Ipnu1lbNIZhVxK6zfkX/eVdQ9K8bqZr+e/Clx6VMkfqOOlq7Wbm1nuueXos/oKT6tnHPxfaYaWOSWUdqNM+7B5T9HHgb2AA8HsMymThqHjSR6tN+QsbmNyn89/fiNstzpL6jjpr/3i6aA4ri5Z3/Xu9+aKoxPV1HRp2Fnpr1NxF5HshU1fi3s5iYaThyBikNu8h/6+cEMwupOfnmDo9ECx863ZlaRVt9Rx3T+iGpvf6hqcb0aG0GGhH5AiCq+kgoTVUbReQKEalXVXsgfS9SP/5KfA1V9PvvnwimZVM75VvtBpuuNH91ZdTZuccU84/3qvAHINXnLbf27KpKFpVXM21kgc0ObUyCRavRfAs4NUL648AioEuBRkSGAg8Dg/FuDn9AVe9yz715AhiO10x3marudnlmA1cBAeB6VX3RpU/iwKOc/wncoKoqIhnuGJPw+pYuV9UNXSl3b7bnhG8jzfXkvvsgvr07qT71J1H7bCIOne5EwDjUUWfjSnK45+Ij2wxS9phoY5JLtD4an6oe1HDu0tK64dh+4FuqegwwFbhWREYDNwEvq+oo4GW3jFs3E+9+nunAvW7ST4D7gKuBUe5nuku/Cm+03Ejg18Ad3VDu3kuEmk/cwp7JN5C9dh7FL3wVaWq778Rr/hJShLjfdDmuJIcrjh8cMVBFeky0MSZxogWaNBE56L9YRHKBLg9NUtWtqvq2e10LvAeUAhcCc9xmc4AZ7vWFwOOq2qiq64FyYIp7Vk6eqi5WVcWrwYTnCe3rKeBMkQTcBt+TiFB33NfYPe1npG9ZxoCnLyF92/KIm44ryeGGU8uYPDSXG04tS5qRX/aYaGOSS7SmsweBp0TkmlBzk4gMB37n1nUbt9+JwFvAIFXdCl4wEpGBbrNSIHwmyAqX1uxet04P5dnk9uUXkRqgGKjszvL3Rg1HziCQW0bBotkUz/si9eNmsef4GyB1/+QQrNxaz12vVtAcUN7dUscRxVlJEWxCzWTWR2NMcmgz0KjqL0SkDnhFRPrhDe2pB25X1fu6qwBu338DblTVPVEqHJFWaJT0aHlal+FqvKY3SktLD8rQVzWVTGbRJx6jcOkvmbTyITLXvUjdhKvYe9QlkJrR5T6aQx2x1hEzxva3AGNMkog6vFlV7wfud8FAIvXZdIWIpOEFmUdV9WmXvF1ESlxtpgTY4dIraDkjQRmwxaWXRUgPz1MhIqlAPnDQTReq+gDwAMD48eNtrKyzcms91/99M82Byzk59VjuTn+Owtd/Su7b91M/5vOcXHAqf/bJIQ1Rbu+my1gGIWNMfHXkhk1UtS4GQUbwmuDeU9XwJ3HNA2a517OA58LSZ4pIhoiMwOv0X+Ka2WpFZKrb5xWt8oT2dQmw0PXjmA4IfzjZ683H8PvDfkPl+XPwF40kb9ldnPLvz7Cs8Ac8Oux5Hp+6iQn9qqGDpzfaTZcdefqmTUETP3auTVcl8mlTJwNfBFaKyDsu7fvA7cBcEbkK2AhcCqCqq0VkLrAGb8Tate4JoADXcGB483z3A14ge0REyvFqMjNj/J56lYMeTpadRtOQKVQNmUJK3Vay1i8gc/1LTN3+BLL9MVgGwbR+BPoNJpAziCoK2dKYQWFhEQOKCtHULDQ1E03LpmR3LceKsodsdmoBu/Y27T9uKMApB56+2bq2c6j37yRaT6up9eRzbZJHtBs2L1XVJ0VkhBvl1a1U9TUi96EAnNlGntuA2yKkLwPGRkjfhwtUpvPCH0bW+uFkwX4l1I+7gvpxV4B/H2m7PiStcjWpuz/CV7+dpuotpOx+j6NpIHdnw0H7/h5AxoHlfVuzSH1iEP784ZztH8KOlDze0ZGs05KDnr7Z1b6h9sQqGPTEi3asz7XpG6LVaGYDT+L1odijm/ug8Au8EuVxy6mZNA88luaBx+5PenjpNh7YvpWggk+CXHd8Pp89Ng9pbkCa9/L6B5t5fsUG8tjLAKnmvGF+jszcQ2r1OsZXv8Zx6V5Qq9Q8KtdMJCvtbPYddgaaWdDF6Wuii2Uw6IkX7Viea9N3RAs0VSLyb2CEiMxrvVJVL4hdsUwy6MrjlieW5eJL2YYGlJQUH6MPKyGYfeCi+syb6bwaPDB1zPuSx+2fPAKAVZtr+M1z/2G8fsBU3/ucve99sl55BZVUGktPYMqoC/jtBafw9tbGNmsd0Wol0dbFMhiEnxNfSs+4aNsD6kx3iBZozsOryTwC/DI+xTHJpKuPW/a7zn5/4OABApX1/jaXx5bmc/6pU1lUfjRDR85i95hi6ipXk7nuRbLWvUDhv7/HtPQCcgs/RVPx54AjWuwr2oi29ka7xf4bvLb6nfzsAXWmq6LdR9MEvCkiJ6nqTjcjgKpqXfyKZxKpK99m73t9c4tL6n2vb+beS47cv/78McWs2b63xXJI5BtBx9I8YCy1U77JlpX/ZvcbD3HGtr8S2PYE24dfSPpJXyeQ690DFRrRBgdGtIXKHm1dV99ze1ZU1BIIeucjEKRHNJ0Z0x06MupskIi8BBThjUreCcxS1VWxLZpJBu19m22rGerj3ftabNd6Odrd+1GbrySFfzWO4YHm/6FEd/L1tHnM3DiPlE1/Z+/Rl1A76Tp27W1ucayWy+0/YiBW3+Ctv8P0VR0JNA8A/6Oq/wYQkWku7aTYFcv0BNE6zn0pLQcUtl4GOKI4iz0Nfo4ozmqR3t4FObR+a2AAP9avUHbmN5m85S9kvzeXrPLn+Uzu5bzJKTS5uV+Lsg98zDvyiIFYsf4O01d1JNDkhIIMgKouijTZpul7otU8UlpNJdR6OVqQau+C3Hr9qJIcag6/hfoxXyDvzTu4cNMfGZv+D37gv5LFwTEcOTC7Rd5ojxiINevvMH1RRwLNOhG5GW9QAMAXgG6/r8b0PNFqHhNK+/HSB7tbLIdrb3RXexfkSOv9hUew69wH+Pvf/8b0zXfz1/TbeCpwKiu2fgPCmubsYm9MfHVkCporgQHA0+6nP/DlWBbKJI9o04+EahZXTy056H6T7LSWH63Wy7F8ls17OcdzdtOd/M5/ARemvM7sj79C5roXum3/xpjOabdG455ueX0cymKSTEduXmy7dtC6T6blcuhZNqHBAN1Zwwj1w/zCP5N/6kk8VjCHon99k4bDX6Tm5JsJZhVFzd/TponpDn3xPZv4SeRcZybJtTfnGLR9gTr3mCLX6a6k+oRzjyk6KN+vX6nAH1BWbO78s2yiXRjHleTwzdOGuiB2MvWjz0PefZDc5b8jfcsSak79MfuGR5zlqEdOE9NVffE9m/jq0OzNpm86aFLNVlPQRJtleVxJDpdNGEBpfjqXTRhw0IUr2uzN7WlvdufQfTjLNtVy16sVrNzeSN3Er7Lz4qcI5gyi6KXrKFj0faTp4FvCIvUddadknAk51u/ZGAs0pk2hKWgg8hQ00S5Qz66q5NHlO6ioaeLR5Tt4dlXrh5q2fz9LW9q7MIY/3qDJf2C9v+hIds54nNqJXyVr7XMMeOoC0rcsaZE3ln1HHXn8QSLE8j0bAx0INCJypIi8LCKr3PKxIvKD2BfNJJo3BY13AUpPbet+lsgXqLkrdrTYtvXyuccUk+bzAlhaJ+9nae/CWNsUaDErQW1T4MBKXzq1x99I5QWPQkoaxc9/ibzFd4C/EYg+wAG6ViNJ1ppDe+/ZmK7qSB/NH4DvAL8HUNX/ishjwE9jWTCTeB25n6WtDv19/mCLbVsvd+V+lvbKtbbVYwlaLwM0D5rAzs88Q96bd9Jv5UNkVLxG9bTbaR4wps0BDl3ty0jmmQFsyLeJpY4EmmxVXSItb7jr+DS+pkeLdgHyOvQ34Q/Ais21LTr0B+ems632wNQvg3PTO7XvrpSroFVfUuvlFgMJTrmVfYedQcGrN9P/2cupm/hVFpd8kbe37DsoiHV1ZmebGcD0VR3po6kUkSNwjegicgmwNaalMj3C/PeqaA7gOvS95ZDhRZkttm29HEvVrfqSwpdDszf/fvFWrnva6ydpHHYqOy6dR8MRnyL37Xspe34mr735xv71IR3py3h2VSU3PlseoU/KM64khyuOH2xBxvQpHQk01+I1mx0tIpuBG/EenWz6vLbvlelKH0xXTRtZ0OZyW6PdNCOf6jPu5MHBtzCAap5Nv5lvyaP8a/WW/Xnb68t4dlUldy7cxJKNtdy5cFObwcYckIyj8Ez368gNm+uAs9z8Zimq2m09mCLyJ+B8YIeqjnVpRcATwHBgA3CZu2kUEZkNXAUEgOtV9UWXPgl4CMgC/gncoKoqIhnAw8AkoAq4XFU3dFf5+7ojB2a1uZzIOcWizQwdfWZnWNnvJO5qLGV26l/5WurzVG5cjmz8IY3DprV73OdXVx20HH5ssBsjw9n9O31HR0ad/Z+IFKhqvarWikihiHTXQICHgOmt0m4CXlbVUcDLbhkRGQ3MBMa4PPeKiM/luQ+4GhjlfkL7vArYraojgV8Dd3RTuQ3tD39OZDPRjLH9+c2MkQdd6MNnco60fO4xxdSn9GO2///xueYfkJmRTvEL11D0wtf4aO17XPf0h67Z7cODvoWn+yTqcqRmu74sWUfhme7Xkaazc1W1OrTgahef6o6Dq+qrQOs79S4E5rjXc4AZYemPq2qjqq4HyoEpIlIC5KnqYlVVvBrMjAj7ego4U1qNajCHrr3hz8kofCbnSMvA/lt63gqO5o1pj1NzwndI37qUE/99Od+XORRTc1CfFEB9kz/qclduUu2N7P6dvqMjo858IpKhqo0AIpIFZMSwTINUdSuAqm4VkYEuvRR4M2y7CpfW7F63Tg/l2eT25ReRGqAYaNF4LiJX49WIKC0txXRMV0dRJaIZKbzWFakW9ujy7YSePB1Q+MuKXYw9/0oaRp3P+0/fxhfrF3C5bxF/CkxnTd1MYNj+vDvrWu6r9XJ7N6k+u6oyYnNfbxXL+e5MculIoPkL8LKI/BnvP+NKDtQS4ilSTUSjpEfL0zJB9QG8h7kxfvz4nvMw9yRwqEOUE9U+H37z5kE3cwIf7twbcTmYPZA/FdzAj3afwzdTn+K61Odo3P4C/tcuom7cLAL5wxlelMk7Ww40h7UeaXfuMcX8fXUVAQWftBwgERpIALBko9eE1NuDTeRHdscp2ASbSatcQ/qOlfjqtuCr3UJKQyWkpKK+DDQtm+aiUTQPGEfTgLFoZmF8ytVLdWQwwJ0ishI4E+/C/ZNQJ3yMbBeRElebKQFCt5RXAEPDtisDtrj0sgjp4XkqRCQVyOfgpjqTAF29J+VQtXczZ1Mg2OZyUXYqr2oJ1zd/g7v9F/GTAQuZ+v7fyF7zBI2lJ3Jd8Rl8Y8vhNOAFmLOPbjmR6EdVDS1qSx9VNex/z5FmUujtgSben4GUvTvIXLeAzI3/Jn3bClL83pcI9WXg7zeEYPYACPpJaaojpWYDmeteRNz30saSKew9+hIaRnwSUuM3VL+36NDszao6H5gf47KEzANmAbe738+FpT8mIr8ChuB1+i9R1YCI1IrIVOAt4Argt632tRi4BFjo+nFMgiXqLvlpIwv21xhCy+EyfCl4gxrDlz3hj4H+OKWMPaf9lO353ydnzRNkrX2Wszb/lKUZmSwKTuDfgQm8tWZqi2CxqLy6xbEWlVfvX9/eTApdlYyj3eLxGZDmvWSue4HsD58jfetSBKW54AgajpxB45DjaRo0kWD2QIjQdStNdV6tZ+tSstfOo/Df3yX/9Tzqxl1B/bFfRtMi9O+ZiNoMNCLymqp+QkRqadncJICqal5XDy4ifwWmAf1FpAK4BS/AzBWRq4CNwKV4B1wtInOBNXgzE1yrqqErwjUcGN4cHhQfBB4RkXK8mszMrpbZdI9E3SU/Y2x/Ntc08kp5NadF6AsZlJvG1rAZDQblprUoc+sh20FyqJ18HbWTvs4P/jCXTwZe5UzfCs73vQnV99M89wiaB4ylacA4PjdgIJs2CtspJEhKiyCXmtLyQtd6GYBAEymNNe5nD9JYQ0pTLdJUx45du9m5q4Yh/YQBWYAGQFJAfOzcG2TNBw3s0ywWLM2h+OTRDBs6jEDOIDQ9L+JFNh5i+RlI3fWh+wIwj5TmOvz5w6k77hoaDp+Ov2gU4PrEFlQzbaTvoM/Bgf6yw5kxaQp1x11D+tZl5Kz6C3nL7yHn/SfZc/yNNIy6wDvPJiqxL/gtjR8/XufPj1flzcRby74hOahv6JqnPuTdsH6W8UNyuO+SI1vkb+vCOOux91hbuQ9QxsjHXJy7ms8P3kzazlX4Gg6MP2lSHzsoJDOngNz8IjQtm9c/rqM5KAhKOs1kp/iZOMiHNNXtDyYp/oPnbAsXVKGJVFLT0knxpYIqqB9/czPpNEfOk56Hv2A4qxoHsbhuMJll4/jUaaegmQWdOKtJIugnc8NCclY/SsbWJagvnYYR57D3mMtoGjypRUAN7xMD+O4ZQ/cHm2jrANK3LSdv8e2k71xF45AT2H36HQRzBsXhDXaCBsn8+N809R9NsF9JXA5ZWlq6XFUnR1oXtelMRFKA/4ZupjSmp2uvX6Cm1Si0mgjT13gPc9vGPRe3DFIleRku0AirdTjF/cdz7vTDQZWU+m384Z+v0bDzY4bJDgZINYf5GxmnAVL27mCo1BMUr7lsH2mQkk4wLR/NKSGY3g9N70cwo4BgZj7B9Dw0I59gRh7B9Fzmrmng/uU11GsGKSJcfVwJVxw/eH+5PvfIGip215PLXvJkL8fm7uVHp2Thq99O6p6NbPv4A0rqlnOt7IKPgYfBnzeMpkETaBp0HE2Dj8NfODJhNZ/2pOytJPv9J8l5by6++m34+w1hz5RvUX/0Z9rsxI/WjBltHUDT4ElUzniC7A/+Rt4btzPwqQupPu2n7Bt+VofKG+tmTF/NxxS8ejMZW5cSTMtmz5T/Ye/ozya05hU10KhqUETeFZFhqroxXoUyJlYmluXiS9mGBhRfysH9AsMKM9mwu7HFckjoPhg4cB9Mhy4UIgT7lVA8+vSW35RPGcoQdwH7wbPlLfqOpgzL5TfnjezQezpyRD3+d9aS0kZfR11TAD+p7CaP3ZpHfSCVfUeM279+1kerqWhsooBaxqRs4BNZG/lS0XYyKl4ne+08AAKZRTSVHE/jkCk0lU7Fnz8isYFHg6RvfpPsD/5G1voFSLCZfaUnUXPyD9g3bBqk+KJmj9ZX114/HgCSwt6jL6Vx8GQKF36Hope+Qd3YL7Jn6nchpe3LakxHW6qSs+oRcpf8Gnxp1Jz0fTI2vkrB6z8lq/yfVJ9xJ4HcxNy+0ZHBACXAahFZAuxvU1DVC2JWKmNiSlv9PuDzkwbx+oYaAkHwpXjLB+eLvNzerAPRpsbZUtPYYtvWy9G019exe68/6vLeZq+rs5pcXg+O4z2dwIVnHwuq+Go3kb51ORlb3iJ9yxKy1nsDTgPZA2kccgKNpVNpGnJCzC5gLe4tGlNM6u61ZK17gawPnyO1bgvBjHzqR8+kfvRnCRSM6PB+o/0toq1rLVAwgsoLHyPvrV/Qb9UjpFavY/eZv0IzIndhx3KkXc7Kh8h/8072DTud6lNuJZgzkPoxXyBr7XPkv/YTgq/cycODZidkQEhHAs2PYl4KY+JkRUUtgaAXIgJBDvpHH1eSw72fiTxHW/ios9QIE4W2tx68i1ikC9fowTlU1DS1WO6MaPczidAiJrauiOzaG4i8LEIgbxgNecNoOOqi/YEnY/Ob3k/F62SX/x0Af78hNA2eRNPg42gaNBF/4RFRv9l3xLOrKrlr4UdMSvkQtqwia8U7FDZsRBGaSk+gdsr/0DD8LEg9tPvH2/pbtLfuIL509pz0ffxFR5L/nx/R/9mZ7Jp+H4H8ww7aNFYj7TI3/Iu8N39Ow+HT2X3mLw80k4nQcOQM6tYtoejj+Ty0/nP82ZcR93nloo06ywS+BowEVgIPqqo9h8b0aB35R2/rot3eRKFdmUj08FY3d7Ze7oozRhXy0ge7WyyHaxWHIt7l7K3wAs/evGHsPeYyUCV1d7lX29m6lIzNi/cHHvVl0Fx0JM3FR/NuwwBery5g2PBRnDbucIIZBeALez6RKtK8l5SGSnx7d5K6+yPSdn3I6Wvf4aqMtWRIM35N4X3/WOQTX2Lf8LO8e16SzN6jL8GfN4zCBTfQ/7nPsmv6/TQPPLbFNrEYaZdWuZqChd+lecA4dk/7WcS+mDfSpnK5PMNJsopFgePidt9aSLSvHHPwpnf5D3AuMBq4IR6FMiZWYj2s+lBnSphYlktG6qF/043WwfyZYwew4IPd+6fR+MyxLS/SaT4InyAhrVX3Rpv7FsFfNAp/0Sjqx37B1XgqSN/+DmlV75FWuYaU8pc4yV/DSQDvuh8g6MsESUGDAVSDpGrLUXHBtBwKMkcwp+Fs3giOZmnwaK49+UhmjE7um1ibhkyhcsZfKf7n1RQ//yV2n/Wrg2b+7s6nmabUb6foha8TzCxg1zn3sHJngBUV2w76WxUefSq15Vmc61vK6zop7vPKRQs0o1V1HICIPAgsiU+RjImtZJw2pysBsL1yraioRcQb7SxycHPhtJEtazzTRhZ2eN8tiBDIG0pD3lAaRn0agK888QEV23dwmOxgqOxgdF4TV4zLJKVxDzvrmlhYXo0/KOyRfkyfdBRDSkrxF4wg0G+IF8hWVbK3vJpre9D8b4H84VRe+BhFL3yNohevo+aUW9h79KXdfhzxN1D04rVIcx1VFzzGuzXZbf6txpYWUFs2jfO3vU7+9BGMTaI+mv1fMdyElHEojjHJK9ZTphxqAGyvXO01F956znAA3tywh6nD8/Yvd2Tf7emfk8Ya+rFS+7FSD6euKJ+LJx4OwBNLt/FA81aCCikCASnhiqGDW+TvVF9JEglm96fq03Mo/Nc3KXj1h/hqN1M7+YbuG6mnSsGi75NWuYZd5/wOf/FRrFi6LerfKnP0uWRtns9xrKGJE7unHB0ULdCMF5E97rUAWW6522YGMKYnSdS0Oe1pr1wdqS2FB5fO7Ls90UbxJev57C6alsOuc35H/ms/IXfF7/HVbqb6tNta9k8don5v30vWuheoOeHbNB52OtD++Wwc+gmCvkyy1i+gqTS+gcZmBmjFZgYw0STjnGEQ23J1dd/R8ifr+exWqvR75w/kLf01jYMnsfvMXxHMGdh+vjZkr36Mgtd/wt4jZ1B92v+1qCW1dz4LX7qe9B3vsP3zi7r9Bs5oMwNYoGnFAo0xJhYyP/onBa/8AE3LZvcZv6CpdGqn99HvnT+Qt+RX7Bt2Ors++ZtO146yyp+ncOF32HnhYzQPmtjp40cTLdDYbHDGGBMH+474FJUXzSWYUUDxP68id9nd4N/Xscyq5C75FXlLfsXekeez6+y7DqkJbt+w09CUNLLW/6vTebvCAo0xxsSJv3AklRc9QcPI88l9+z4GPXEuWR8+C9r2YyHSt71N/3mfI/edP1B/zOVUT7sdUtLa3D4aTc+lufgoUnd9cIjv4NB07dZdY4wxnaJpOVSffgd7j76EvDd/TuGi2eSu+D37hp5CU8nxNBeOxFe/jdTaCjI2vkrWhn8RyB7A7lN/SsNRF3d55Jo/bxjpO1Z207vpGAs0xhiTAE0lx1M543GyPppP9gd/I/u9J+m36pEW2wTTctgz+Xrqx83qtgetBfKG4lv3IgSbD7lm1FkWaIwxJlEkhYaR59Ew8jwINJG+cyW+mo0E+pUQyC0j0G9wl+eMa82fNwzRAL7aLRHnY4sFCzTGGJMMfOneA9oGT4rpYQJ5wwBI3bMpboHGBgMYY0wf4neBxrcnfo8Y6xOBRkSmi8gHIlIuIjclujzGGJMowewBBH2ZpFqg6T4i4gN+x4EZqD8rIqMTWypjjEkQN/mpb8+m9rftJr0+0ABTgHJVXaeqTcDjwIUJLpMxxiSMP38YqXs+jtvx+kKgKQXCQ3eFS9tPRK4WkWUisqyqqiquhTPGmHgL5A0jdU9F1BtFu1NfCDSR7m5qMcGbqj6gqpNVdXJx8cGP3zXGmN7EnzcMCTSSUr8jLsfrC4GmAhgatlwGbElQWYwxJuECed4lMV4DAvpCoFkKjBKRESKSDswE5iW4TMYYkzD+PO/+mXgFml5/w6Z7Ouh1wIuAD/iTqq5OcLGMMSZhAv0Go5Iat5FnvT7QAKjqP4F/JrocxhiTFFJSCeQOsaYzY4wxsePPPyxuswNYoDHGmD4okDuU1D2bIA5PWbZAY4wxfZA/fxgpTbWkNFbH/FgWaIwxpg+K5+SaFmiMMaYP2v+4gBoLNMYYY2LAn1uGIlajMcYYEyOpGQRyBsdliLMFGmOM6aOC/Qbji8N8ZxZojDGmjwpmFNioM2OMMbETzCwgZV91zI9jgcYYY/qoYGYBYoHGGGNMrAQzCkgJ7AP/vpgexwKNMcb0UcGMfABSGmtiehwLNMYY00cFMwsAYt5PY4HGGGP6qP2BJsYjzyzQGGNMHxXMKACsRmOMMSZGrOnMGGNMTPXqwQAicqmIrBaRoIhMbrVutoiUi8gHInJOWPokEVnp1t0tIuLSM0TkCZf+logMD8szS0TWup9ZcXuDxhjTE6RmEvRl9to+mlXAxcCr4YkiMhqYCYwBpgP3iojPrb4PuBoY5X6mu/SrgN2qOhL4NXCH21cRcAtwAjAFuEVECmP4nowxpsfROMwOkJBAo6rvqeoHEVZdCDyuqo2quh4oB6aISAmQp6qLVVWBh4EZYXnmuNdPAWe62s45wAJV3aWqu4EFHAhOxhhjiM80NMnWR1MKbApbrnBppe516/QWeVTVD9QAxVH2dRARuVpElonIsqqqqm54G8YY0zPEY2LNmAUaEfmXiKyK8HNhtGwR0jRK+qHmaZmo+oCqTlbVycXFxVGKZ4wxvUs85jtLjdWOVfWsQ8hWAQwNWy4Dtrj0sgjp4XkqRCQVyAd2ufRprfIsOoQyGWNMrxXMyO+do86imAfMdCPJRuB1+i9R1a1ArYhMdf0vVwDPheUJjSi7BFjo+nFeBM4WkUI3COBsl2aMMcbxms5qQCM2+HSLmNVoohGRi4DfAgOAf4jIO6p6jqquFpG5wBrAD1yrqgGX7RrgISALmO9+AB4EHhGRcryazEwAVd0lIj8Blrrtfqyqu2L/7owxpucIZhYgGkCaatGMvJgcIyGBRlWfAZ5pY91twG0R0pcBYyOk7wMubWNffwL+1KXCGmNMLxY+31kgRoEm2ZrOjDHGxNH+2QFiOCDAAo0xxvRhB2o0sRsQYIHGGGP6sHjM4GyBxhhj+jCNwzNpLNAYY0wfFkzPQxGr0RhjjImRFB+akWeBxhhjTOwEM/IRazozxhgTK8HMAht1ZowxJnaCGfnWdGaMMSZ2Yv2oAAs0xhjTx8X64WcWaIwxpo8LZhaQ0lwPgaaY7N8CjTHG9HH7ZweI0YAACzTGGNPHxXq+Mws0xhjTx2mMZ3C2QGOMMX1cMMbznVmgMcaYPi7WMzhboDHGmD5uf42mNwUaEfm5iLwvIv8VkWdEpCBs3WwRKReRD0TknLD0SSKy0q27W0TEpWeIyBMu/S0RGR6WZ5aIrHU/s+L5Ho0xpqfQ1Gw0JS1m850lqkazABirqscCHwKzAURkNDATGANMB+4VEZ/Lcx9wNTDK/Ux36VcBu1V1JPBr4A63ryLgFuAEYApwi4gUxv6tGWNMDyPiTUPTm0adqepLqup3i28CZe71hcDjqtqoquuBcmCKiJQAeaq6WFUVeBiYEZZnjnv9FHCmq+2cAyxQ1V2quhsvuIWCkzHGmDCxnB0gGfporgTmu9elwKawdRUurdS9bp3eIo8LXjVAcZR9HURErhaRZSKyrKqqqktvxhhjeiJvBufqmOw7NSZ7BUTkX8DgCKv+V1Wfc9v8L+AHHg1li7C9Rkk/1DwtE1UfAB4AGD9+fMRtjDGmN2ssPRnxN8Rk3zELNKp6VrT1rnP+fOBM1xwGXq1jaNhmZcAWl14WIT08T4WIpAL5wC6XPq1VnkWH8FaMMabXqzvuazHbd6JGnU0HvgdcoKp7w1bNA2a6kWQj8Dr9l6jqVqBWRKa6/pcrgOfC8oRGlF0CLHSB60XgbBEpdIMAznZpxhhj4ihmNZp23ANkAAvcKOU3VfVrqrpaROYCa/Ca1K5V1YDLcw3wEJCF16cT6td5EHhERMrxajIzAVR1l4j8BFjqtvuxqu6K+TszxhjTghxotTLg9dHMnz+//Q2NMcbsV1paulxVJ0dalwyjzowxxvRiFmiMMcbElAUaY4wxMWWBxhhjTExZoDHGGBNTNuqsFRHZCXzchV30Byq7qTjdycrVOVauzrFydU5vLNdhqjog0goLNN1MRJa1NcQvkaxcnWPl6hwrV+f0tXJZ05kxxpiYskBjjDEmpizQdL8HEl2ANli5OsfK1TlWrs7pU+WyPhpjjDExZTUaY4wxMWWBxhhjTExZoDlEIvInEdkhIqvC0m4Vkc0i8o77+VQCyjVURP4tIu+JyGoRucGlF4nIAhFZ634XJkm5EnrORCRTRJaIyLuuXD9y6Yk+X22VK+GfMVcOn4isEJHn3XJCz1eUciX8fInIBhFZ6Y6/zKUl/Hy1Ua6YnC/rozlEInIqUAc8rKpjXdqtQJ2q/iKB5SoBSlT1bRHJBZYDM4AvAbtU9XYRuQkoVNXvJUG5LiOB58w9SC9HVetEJA14DbgBuJjEnq+2yjWdBH/GXPn+B5gM5Knq+SJyJwk8X1HKdSuJ/5/cAExW1cqwtISfrzbKdSsxOF9WozlEqvoq3oPWkoqqblXVt93rWuA9oBS4EJjjNpuDd5FPhnIllHrq3GKa+1ESf77aKlfCiUgZcB7wx7DkhJ4vaLNcySrh5yueLNB0v+tE5L+uaS0hzQchIjIcmAi8BQxyj8TG/R6YJOWCBJ8z19zyDrADWKCqSXG+2igXJP4z9hvgu0AwLC3h56uNckHiz5cCL4nIchG52qUlw/mKVC6IwfmyQNO97gOOACYAW4FfJqogItIP+Btwo6ruSVQ5WotQroSfM1UNqOoEoAyYIiJj412GSNooV0LPl4icD+xQ1eXxPG57opQr4Z8v4GRVPQ44F7jWNbsng0jlisn5skDTjVR1u7s4BIE/AFMSUQ7Xpv834FFVfdolb3f9JKH+kh3JUK5kOWeuLNXAIrx+kISfr0jlSoLzdTJwgWvffxw4Q0T+QuLPV8RyJcH5QlW3uN87gGdcGRJ9viKWK1bnywJNNwp9cJyLgFVtbRvDMgjwIPCeqv4qbNU8YJZ7PQt4LhnKlehzJiIDRKTAvc4CzgLeJ/HnK2K5En2+VHW2qpap6nBgJrBQVb9Ags9XW+VK9PkSkRw3+AURyQHOdmVI9OcrYrlidb5Su2MnfZGI/BWYBvQXkQrgFmCaiEzAa/vcAHw1AUU7GfgisNK17wN8H7gdmCsiVwEbgUuTpFyfTfA5KwHmiIgP74vXXFV9XkQWk9jz1Va5HkmCz1gkif58teXOBJ+vQcAz3vcsUoHHVPUFEVlKYs9XW+WKyefLhjcbY4yJKWs6M8YYE1MWaIwxxsSUBRpjjDExZYHGGGNMTFmgMcYYE1MWaIzpABGpa7X8JRG5x73+mohc0U7+/dvHk4g8JCJ7Q/dMuLS7RERFpL9bDog3U+8qEXlSRLJd+iAReUxE1rlpShaLyEXxfg+m57NAY0wXqer9qvpwossRRTneJI6ISApwOrA5bH2Dqk5ws5A3AV9zN9g+C7yqqoer6iS8GyHL4lpy0ytYoDGmi8R7hse33evj3YSEi0Xk5xL2vCJgiIi8IN4zSO50218mIr9yr28QkXXu9REi8pp7/UMRWepqHA+I5wgReTusDKNEpK35x/4KXO5eTwNeB/xtbPsfYCRwBtCkqveHVqjqx6r6206dHGOwQGNMR2XJgYdBvQP8uI3t/gx8TVVPBAKt1k3Au+CPAy4XkaHAq8Apbv0pQJWIlAKfwLvoA9yjqse7GkcWcL6qfgTUuLu4Ab4MPNRGmdYCA8SbifezeHOBHUREUvEmWFwJjAHejrSdMZ1lgcaYjgk1L01wMyr/sPUGbm6yXFV9wyU91mqTl1W1RlX3AWuAw1R1G9DP9aEMdXlOxQs6oUBzuoi8JSIr8WoaY1z6H4Evu2lqLo9wvHBP4zV9nRC235AsFzyX4U2H8mCE9/Y78Z72uTTKMYyJyOY6M6b7SDvrG8NeBzjw/7cYr0byAV4QuBI4EfiWiGQC9+I9CXGTeE9AzHT5/oY3x95CYLmqVkU59uN4NZQ5qhp0c1yFNLjgeeCNiKwGPhNaVtVr3eCBZe28R2MOYjUaY7qJqu4GakVkqkua2cGsrwLfdr9X4HXWN6pqDQeCSqV4z/K5JOx4+4AX8Z4h8ud2yrYR+F+8oNURC4FMEbkmLC27g3mNacECjTHd6yrgATf7swA1HcjzH7xms1dVNQBsAl6D/c+i+QNev8mzQOumq0dxT0ps7yCq+nvXt9Mu9WbbnQGcJiLrRWQJ3iOH4/pce9M72OzNxnQjEemnqnXu9U1AiareEMPjfRvIV9WbY3UMY7rK+miM6V7nichsvP+tj4EvxepAIvIM3mN3z4jVMYzpDlajMcYYE1PWR2OMMSamLNAYY4yJKQs0xhhjYsoCjTHGmJiyQGOMMSam/j+ymo3RhSkTmgAAAABJRU5ErkJggg==\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",
    "f1 = np.polyfit(x, y, 11)\n",
    "p1 = np.poly1d(f1)\n",
    "print(p1)\n",
    "PlotPolly(p1,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 11rd order (cubic) \n",
    "f1 = np.polyfit(x, y, 11)\n",
    "p1 = np.poly1d(f1)\n",
    "print(p1)\n",
    "PlotPolly(p1,x,y, 'Highway MPG')\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2)polynomial with two variables is given by:</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b_1 X_1 +b_2 X_2 +b_3 X_1 X_2+b_4 X_1^2+b_5 X_2^2\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can perform a polynomial transform on multiple features. First, we import the module:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a <b>PolynomialFeatures</b> object of degree 2: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_pr=pr.fit_transform(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The original data is of 201 samples and 4 features \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "after the transformation, there 201 samples and 15 features\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z_pr.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Pipeline</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Data Pipelines simplify the steps of processing the data. We use the module <b>Pipeline</b> to create a pipeline. We also use <b>StandardScaler</b> as a step in our pipeline.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create the pipeline, by creating a list of tuples including the name of the model or estimator and its corresponding constructor.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we input the list as an argument to the pipeline constructor \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False))])"
      ]
     },
     "execution_count": 44,
     "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. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.6/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/jupyterlab/conda/envs/python/lib/python3.6/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": 45,
     "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\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.6/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": 46,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.6/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/jupyterlab/conda/envs/python/lib/python3.6/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/jupyterlab/conda/envs/python/lib/python3.6/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, 13869.66673213, 15456.16196732, 15974.00907672,\n",
       "       17612.35917161, 10722.32509097])"
      ]
     },
     "execution_count": 47,
     "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[0:10]"
   ]
  },
  {
   "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",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 4: Measures for In-Sample Evaluation</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n",
    "\n",
    "<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n",
    "<ul>\n",
    "    <li><b>R^2 / R-squared</b></li>\n",
    "    <li><b>Mean Squared Error (MSE)</b></li>\n",
    "</ul>\n",
    "    \n",
    "<b>R-squared</b>\n",
    "\n",
    "<p>R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.</p>\n",
    "    \n",
    "<p>The value of the R-squared is the percentage of variation of the response variable (y) that is explained by a linear model.</p>\n",
    "\n",
    "<b>Mean Squared Error (MSE)</b>\n",
    "\n",
    "<p>The Mean Squared Error measures the average of the squares of errors, that is, the difference between actual value (y) and the estimated value (ŷ).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 1: Simple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.4965911884339176\n"
     ]
    }
   ],
   "source": [
    "#highway_mpg_fit\n",
    "lm.fit(X, Y)\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(X, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\".\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output of the first four predicted value is:  [16236.50464347 16236.50464347 17058.23802179 13771.3045085 ]\n"
     ]
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "print('The output of the first four predicted value is: ', Yhat[0:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "lets import the function <b>mean_squared_error</b> from the module <b>metrics</b>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we compare the predicted results with the actual results \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value is:  31635042.944639888\n"
     ]
    }
   ],
   "source": [
    "mse = mean_squared_error(df['price'], Yhat)\n",
    "print('The mean square error of price and predicted value is: ', mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 2: Multiple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.8093562806577457\n"
     ]
    }
   ],
   "source": [
    "# fit the model \n",
    "lm.fit(Z, df['price'])\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(Z, df['price']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 80.896 % of the variation of price is explained by this multiple linear regression \"multi_fit\".\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we produce a prediction \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_predict_multifit = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we compare the predicted results with the actual results \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value using multifit is:  11980366.87072649\n"
     ]
    }
   ],
   "source": [
    "print('The mean square error of price and predicted value using multifit is: ', \\\n",
    "      mean_squared_error(df['price'], Y_predict_multifit))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 3: Polynomial Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let’s import the function <b>r2_score</b> from the module <b>metrics</b> as we are using a different function\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We apply the function to get the value of r^2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square value is:  0.674194666390652\n"
     ]
    }
   ],
   "source": [
    "r_squared = r2_score(y, p(x))\n",
    "print('The R-square value is: ', r_squared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 67.419 % of the variation of price is explained by this polynomial fit\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>MSE</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the MSE:  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20474146.426361218"
      ]
     },
     "execution_count": 57,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new input \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_input=np.arange(1, 100, 1).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Fit the model \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X, Y)\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce a prediction\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([37601.57247984, 36779.83910151, 35958.10572319, 35136.37234487,\n",
       "       34314.63896655])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat=lm.predict(new_input)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot the data \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(new_input, yhat)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Decision Making: Determining a Good Model Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now that we have visualized the different models, and generated the R-squared and MSE values for the fits, how do we determine a good model fit?\n",
    "<ul>\n",
    "    <li><i>What is a good R-squared value?</i></li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>When comparing models, <b>the model with the higher R-squared value is a better fit</b> for the data.\n",
    "<ul>\n",
    "    <li><i>What is a good MSE?</i></li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>When comparing models, <b>the model with the smallest MSE value is a better fit</b> for the data.</p>\n",
    "\n",
    "<h4>Let's take a look at the values for the different models.</h4>\n",
    "<p>Simple Linear Regression: Using Highway-mpg as a Predictor Variable of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.49659118843391759</li>\n",
    "    <li>MSE: 3.16 x10^7</li>\n",
    "</ul>\n",
    "</p>\n",
    "    \n",
    "<p>Multiple Linear Regression: Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.80896354913783497</li>\n",
    "    <li>MSE: 1.2 x10^7</li>\n",
    "</ul>\n",
    "</p>\n",
    "    \n",
    "<p>Polynomial Fit: Using Highway-mpg as a Predictor Variable of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.6741946663906514</li>\n",
    "    <li>MSE: 2.05 x 10^7</li>\n",
    "</ul>\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Regression model (SLR) vs Multiple Linear Regression model (MLR)</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Usually, the more variables you have, the better your model is at predicting, but this is not always true. Sometimes you may not have enough data, you may run into numerical problems, or many of the variables may not be useful and 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.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Model (SLR) vs Polynomial Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li><b>MSE</b>: We can see that Polynomial Fit brought down the MSE, since this MSE is smaller than the one from the SLR.</li> \n",
    "    <li><b>R-squared</b>: The R-squared for the 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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression (MLR) vs Polynomial Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li><b>MSE</b>: The MSE for the MLR is smaller than the MSE for the Polynomial Fit.</li>\n",
    "    <li><b>R-squared</b>: The R-squared for the MLR is also much larger than for the Polynomial Fit.</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Conclusion:</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing these three models, we conclude that <b>the MLR model is the best model</b> to be able to predict price from our dataset. This result makes sense, since we have 27 variables in total, and we know that more than one of those variables are potential predictors of the final car price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thank you for completing this lab!\n",
    "\n",
    "## Author\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
    "\n",
    "### Other Contributors\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
    "\n",
    "Bahare Talayian\n",
    "\n",
    "Eric Xiao\n",
    "\n",
    "Steven Dong\n",
    "\n",
    "Parizad\n",
    "\n",
    "Hima Vasudevan\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a>\n",
    "\n",
    "<a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "## Change Log\n",
    "\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                            |\n",
    "| ----------------- | ------- | ---------- | --------------------------------------------- |\n",
    "| 2020-09-09        | 2.1     | Lakshmi    | Fixes made in Polynomial Regression Equations |\n",
    "| 2020-08-27        | 2.0     | Lavanya    | Moved lab to course repo in GitLab            |\n",
    "\n",
    "<hr>\n",
    "\n",
    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
   ]
  }
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