model-development.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Module%204/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n",
    "</center>\n",
    "\n",
    "# Model Development\n",
    "\n",
    "Estimated time needed: **30** minutes\n",
    "\n",
    "## Objectives\n",
    "\n",
    "After completing this lab you will be able to:\n",
    "\n",
    "*   Develop prediction models\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>In this section, we will develop several models that will predict the price of the car using the variables or features. This is just an estimate but should give us an objective idea of how much the car should cost.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some questions we want to ask in this module\n",
    "\n",
    "<ul>\n",
    "    <li>Do I know if the dealer is offering fair value for my trade-in?</li>\n",
    "    <li>Do I know if I put a fair value on my car?</li>\n",
    "</ul>\n",
    "<p>In data analytics, we often use <b>Model Development</b> to help us predict future observations from the data we have.</p>\n",
    "\n",
    "<p>A model will help us understand the exact relationship between different variables and how these variables are used to predict the result.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import libraries:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#install specific version of libraries used in lab\n",
    "#! mamba install pandas==1.3.3-y\n",
    "#! mamba install numpy=1.21.2-y\n",
    "#! mamba install sklearn=0.20.1-y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the data and store it in dataframe `df`:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object. Click <a href=\"https://cocl.us/DA101EN_object_storage?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\">HERE</a> for free storage.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                9.0       154.0    5000.0       19          26  16500.0   \n",
       "3               10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                8.0       115.0    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# path of data \n",
    "path = 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>1. Linear Regression and Multiple Linear Regression</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Linear Regression</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>One example of a Data  Model that we will be using is:</p>\n",
    "<b>Simple Linear Regression</b>\n",
    "\n",
    "<br>\n",
    "<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n",
    "<ul>\n",
    "    <li>The predictor/independent variable (X)</li>\n",
    "    <li>The response/dependent variable (that we want to predict)(Y)</li>\n",
    "</ul>\n",
    "\n",
    "<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Y: Response \\ Variable\\\\\\\\\n",
    "X: Predictor \\ Variables\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Linear Function</b>\n",
    "$$\n",
    "Yhat = a + b  X\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li>a refers to the <b>intercept</b> of the regression line, in other words: the value of Y when X is 0</li>\n",
    "    <li>b refers to the <b>slope</b> of the regression line, in other words: the value with which Y changes when X increases by 1 unit</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Let's load the modules for linear regression:</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:35: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:597: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, fit_path=True,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:836: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, fit_path=True,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:862: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, positive=False):\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1097: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  max_n_alphas=1000, n_jobs=None, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1344: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  max_n_alphas=1000, n_jobs=None, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/least_angle.py:1480: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, copy_X=True, positive=False):\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:152: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  precompute=False, eps=np.finfo(np.float).eps,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:320: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=np.finfo(np.float).eps, random_state=None,\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/linear_model/randomized_l1.py:580: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  eps=4 * np.finfo(np.float).eps, n_jobs=None,\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Create the linear regression object:</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 5,
     "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": 6,
   "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": 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.fit(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can output a prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
       "       20345.17153508])"
      ]
     },
     "execution_count": 8,
     "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": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.3058581574"
      ]
     },
     "execution_count": 9,
     "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": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-821.73337832])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What is the final estimated linear model we get?</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, we should get a final linear model with the structure:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b  X\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plugging in the actual values we get:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Price</b> = 38423.31 - 821.73 x <b>highway-mpg</b>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 a): </h1>\n",
    "\n",
    "<b>Create a linear regression object called \"lm1\".</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1 = LinearRegression()\n",
    "lm1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "lm1 = LinearRegression()\n",
    "lm1\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question #1 b): </h1>\n",
    "\n",
    "<b>Train the model using \"engine-size\" as the independent variable and \"price\" as the dependent variable?</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "X = df[['engine-size']]\n",
    "Y = df['price']\n",
    "lm1.fit(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "lm1.fit(df[['engine-size']], df[['price']])\n",
    "lm1\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 c):</h1>\n",
    "\n",
    "<b>Find the slope and intercept of the model.</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Slope</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7963.338906281046"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "#Yhat=lm1.predict(X)\n",
    "lm1.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Intercept</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([166.86001569])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "# Slope \n",
    "lm1.coef_\n",
    "\n",
    "# Intercept\n",
    "lm1.intercept_\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 d): </h1>\n",
    "\n",
    "<b>What is the equation of the predicted line? You can use x and yhat or \"engine-size\" or \"price\".</b>\n",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "# using X and Y  \n",
    "#Yhat=-7963.34 + 166.86*X\n",
    "\n",
    "#Price=-7963.34 + 166.86*engine-size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "# using X and Y  \n",
    "Yhat=-7963.34 + 166.86*X\n",
    "\n",
    "Price=-7963.34 + 166.86*engine-size\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Multiple Linear Regression</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>What if we want to predict car price using more than one variable?</p>\n",
    "\n",
    "<p>If we want to use more variables in our model to predict car price, we can use <b>Multiple Linear Regression</b>.\n",
    "Multiple Linear Regression is very similar to Simple Linear Regression, but this method is used to explain the relationship between one continuous response (dependent) variable and <b>two or more</b> predictor (independent) variables.\n",
    "Most of the real-world regression models involve multiple predictors. We will illustrate the structure by using four predictor variables, but these results can generalize to any integer:</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Y: Response \\ Variable\\\\\\\\\n",
    "X\\_1 :Predictor\\ Variable \\ 1\\\\\\\\\n",
    "X\\_2: Predictor\\ Variable \\ 2\\\\\\\\\n",
    "X\\_3: Predictor\\ Variable \\ 3\\\\\\\\\n",
    "X\\_4: Predictor\\ Variable \\ 4\\\\\\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "a: intercept\\\\\\\\\n",
    "b\\_1 :coefficients \\ of\\ Variable \\ 1\\\\\\\\\n",
    "b\\_2: coefficients \\ of\\ Variable \\ 2\\\\\\\\\n",
    "b\\_3: coefficients \\ of\\ Variable \\ 3\\\\\\\\\n",
    "b\\_4: coefficients \\ of\\ Variable \\ 4\\\\\\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equation is given by:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b\\_1 X\\_1 + b\\_2 X\\_2 + b\\_3 X\\_3 + b\\_4 X\\_4\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From the previous section  we know that other good predictors of price could be:</p>\n",
    "<ul>\n",
    "    <li>Horsepower</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Highway-mpg</li>\n",
    "</ul>\n",
    "Let's develop a model using these variables as the predictor variables.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 21,
     "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": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15806.624626329194"
      ]
     },
     "execution_count": 22,
     "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": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([53.49574423,  4.70770099, 81.53026382, 36.05748882])"
      ]
     },
     "execution_count": 23,
     "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": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 24,
     "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": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "lm2 = LinearRegression()\n",
    "lm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n",
    "\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  #2 b): </h1>\n",
    "<b>Find the coefficient of the model.</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1.49789586, -820.45434016])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm2.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "lm2.coef_\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>2. Model Evaluation Using Visualization</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've developed some models, how do we evaluate our models and choose the best one? One way to do this is by using a visualization.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the visualization package, seaborn:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the visualization package: seaborn\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Regression Plot</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When it comes to simple linear regression, an excellent way to visualize the fit of our model is by using <b>regression plots</b>.</p>\n",
    "\n",
    "<p>This plot will show a combination of a scattered data points (a <b>scatterplot</b>), as well as the fitted <b>linear regression</b> line going through the data. This will give us a reasonable estimate of the relationship between the two variables, the strength of the correlation, as well as the direction (positive or negative correlation).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize **highway-mpg** as potential predictor variable of price:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 48249.05196220048)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see from this plot that price is negatively correlated to highway-mpg since the regression slope is negative.\n",
    "\n",
    "One thing to keep in mind when looking at a regression plot is to pay attention to how scattered the data points are around the regression line. This will give you a good indication of the variance of the data and whether a linear model would be the best fit or not. If the data is too far off from the line, this linear model might not be the best model for this data.\n",
    "\n",
    "Let's compare this plot to the regression plot of \"peak-rpm\".</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 47414.1)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing the regression plot of \"peak-rpm\" and \"highway-mpg\", we see that the points for \"highway-mpg\" are much closer to the generated line and, on average, decrease. The points for \"peak-rpm\" have more spread around the predicted line and it is much harder to determine if the points are decreasing or increasing as the \"peak-rpm\" increases.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #3:</h1>\n",
    "<b>Given the regression plots above, is \"peak-rpm\" or \"highway-mpg\" more strongly correlated with \"price\"? Use the method  \".corr()\" to verify your answer.</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "# The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692  compared to \"peak-rpm\" which is approximate -0.101616. You can verify it using the following command:\n",
    "\n",
    "df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Residual Plot</h3>\n",
    "\n",
    "<p>A good way to visualize the variance of the data is to use a residual plot.</p>\n",
    "\n",
    "<p>What is a <b>residual</b>?</p>\n",
    "\n",
    "<p>The difference between the observed value (y) and the predicted value (Yhat) is called the residual (e). When we look at a regression plot, the residual is the distance from the data point to the fitted regression line.</p>\n",
    "\n",
    "<p>So what is a <b>residual plot</b>?</p>\n",
    "\n",
    "<p>A residual plot is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n",
    "\n",
    "<p>What do we pay attention to when looking at a residual plot?</p>\n",
    "\n",
    "<p>We look at the spread of the residuals:</p>\n",
    "\n",
    "<p>- If the points in a residual plot are <b>randomly spread out around the x-axis</b>, then a <b>linear model is appropriate</b> for the data.\n",
    "\n",
    "Why is that? Randomly spread out residuals means that the variance is constant, and thus the linear model is a good fit for this data.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "sns.residplot(df['highway-mpg'], df['price'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>What is this plot telling us?</i>\n",
    "\n",
    "<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, leading us to believe that maybe a non-linear model is more appropriate for this data.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n",
    "\n",
    "<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>. We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's make a prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_hat = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAscAAAJcCAYAAAAVVwmuAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8/fFQqAAAACXBIWXMAAAsTAAALEwEAmpwYAACCr0lEQVR4nO3dd3iUVfrG8e+TBAi9g1RBkKIYEEGxrr0gYEVBV9RVUXftZdW1rK7721XXrruWXQs2dO1gRVQUXVFp0ktAeui9Q3J+f5wZCCFlksw770xyf65rroFp75MM5c6Z532OOecQERERERFIC7sAEREREZFkoXAsIiIiIhKhcCwiIiIiEqFwLCIiIiISoXAsIiIiIhKhcCwiIiIiEqFwLCIVjpnda2avhXTsjWa2X4CvH8jXZmaXmNl38X7dEo7Z1My+NbMNZvZIIo8dOf6fzOw/iT6uiCQ3hWMRiTszG2Vma8ysWoyPT3gwKy8zm2dmWyJhOHpp7pyr5ZybG3nMy2b210Ked2IA9bQws51m1q6Q+943s4fjfcw4GAysBOo4524u74tF/hzlRt6L9WY20cz6FPV459zfnHOXl/e4IlKxKByLSFyZWRvgaMAB/cKtJnB9I2E4elkSViHOucXAl8BF+W83swZAb2BIGHWVYF9gmivDblRmllHEXT8452oB9YAXgP9GvgexPl9EKjmFYxGJt0HAGOBl4OL8d5hZKzN7z8xWmNkqM3vazDoDzwKHR1b81kYeO8rMLs/33D1Wl83sCTNbGFkhHGdmR8dSnJlNz7+aaGYZZrbSzLqbWaaZvRapba2Z/WxmTUvzxZuZM7P2ZjYYuBD4Y+TrGm5mrwKtgeGR2/4YeU4vM/tf5Ji/mNmx+V6vrZl9E2k9+AJoVMzhh1AgHAMDgKnOuclmdruZzYm81jQzO6uIr6FN5OvIyHdbwffjd5Hv5Roz+9zM9o3cbmb2mJktN7N1ZjbJzLoUcoyX8X8+ot+fE82smpk9bmZLIpfHo58+mNmxZrbIzG4zs6XAS8V8H3DO5QEvAtWB/SLtKO9E3t/1wCVWoEXFzI7K9z4sNLNLIrdXM7OHzWyBmS0zs2fNrHpxxxeR1KVwLCLxNgh4PXI5JRouzSwd+AiYD7QBWgBvOuemA1cRWfFzztWL8Tg/A92ABsAbwNtmlhnD84YCA/P9/hRgpXNuPD6s1QVaAQ0jdW2JsZ49OOeex38PHop8XX2dcxcBC9i94vyQmbUAPgb+GvlabgHeNbPGkZd6AxiHD8X3U+AHjgLeBxqZ2VH5brsIeCXy6zn4Vf26wH3Aa2bWrLRfm5mdCfwJOBtoDIzGf18BTgaOATrgV2/PB1YVfA3n3CXs+f0ZCdwJ9MK/r12BQ4G78j1tH/z3aF98S0ZxNWYAlwMbgdmRm88A3onU9XqBx7cGPgWeinxN3YCJkbsfjHw93YD2+D+79xR3fBFJXUkXjs3sxciKw5Q4vV5upO9sopkNi8drikjhIqFsX+C/zrlx+DB2QeTuQ4HmwK3OuU3Oua3OuTL3GTvnXnPOrXLO7XTOPQJUAzrG8NQ3gH5mViPy+wsitwHswIfi9s65XOfcOOfc+mJe64PIKuNaM/ugjF/Kb4FPnHOfOOfynHNfAGOB3pHA1hO42zm3zTn3LTC8qBdyzm0B3sb/gIKZ7Q8cEv36nHNvO+eWRI7zFj40HlqGmq8E/u6cm+6c2wn8DegWWT3eAdQGOgEWeUxOjK97IfAX59xy59wKfIDPvxKeB/w58r0o6oeWXpFPH5bifwg6yzm3LnLfD865DyJff8HnXwiMdM4Ndc7tiPzZmmhmBlwB3OicW+2c2xD5egfE+DWJSIpJunCM/yj21Di+3hbnXLfIpaL3P4qE7WJghHNuZeT3b7B7pbMVMD8SpsrNzG6OfKy/LhKG6lJ8ywEAzrlsYDrQNxKQ+7E7HL8KfA68GflY/yEzq1LMy53pnKsXuZxZxi9lX6B/vpC9FjgKaIb/YWKNc25TvsfPL+H1hgDnRVbRLwI+c84tBzCzQZGFguhxuhDD96yImp/I9zqrAQNaOOe+Ap4G/gksM7PnzaxOjK/bnD2/vvmR26JWOOe2lvAaYyLvRyPnXK/IinTUwmKe1wr/w1xBjYEawLh8X+9nkdtFpAJKunAcWRlZnf82M2tnZp+Z7yscbWadQipPRIoQ6cE8D/iNmS2N9IXeCHQ1s674YNLaCj8RqrATsjbhQ0nUPvmOdTRwW+R49SOtGOvwAS0W0daKM/AnhGUDRFYM73POHQAcAfQhsgpbRoV9XQVvWwi8mi9k13PO1XTOPQDkAPXNrGa+x7cu9oDOjca3MZyBX5V+BSCyqvtv4BqgYeR7NoXCv2fRMF7o9z9S85UFaq7unPtfpIYnnXOHAAfi2xFuLa7mfJbgg3dU68htu768GF+nKMU9fyGw16QP/DSNLcCB+b7WupGT/kSkAkq6cFyE54FrI//Y3gL8qxTPzTSzsWY2JtInJyLBOBPIBQ7A92Z2Azrj+1EHAT/hw94DZlbT/MlvR0aeuwxoaWZV873eROBsM6thZu2By/LdVxvYCawAMszsHiDW1UmAN/G9sVeze9UYMzvOzA6K9Eevx7cI5JbidQtaBhSceVzwttfwq9inmFl65PtyrJm1dM7Nx7dY3GdmVSNtK31jOO4r+D7Zeuxuw6iJD4crAMzsUvzK8V4iLQ2Lgd9GavodewbHZ4E7zOzAyGvVNbP+kV/3NLPDIivum4CtxP49HArcZWaNzawRvq83UfOqXwdONLPzzJ+k2dDMukVO7Ps38JiZNYFdY/NOSVBdIpJgSR+OzawWfgXnbTObCDyH/7gRMzvbzKYUcvk830u0ds71wPcVPm6FzAAVkbi4GHjJObfAObc0esF/xH4hfoWyL/6EpgXAIvzJWgBfAVOBpWYWbcl4DNiOD5ND2PMEqs/xJ0/Nwn/0vpXiPzLfQ6QH9gf8vy1v5btrH/wJW+vxrRffUL5w9gJwQIGe5L/jA+BaM7vFObcQv8r7J3xwXYhfaY3++3wBcBj+E7U/s/vkuuK8gl91fcs5tw3AOTcNeAT/dS8DDgK+L+Y1rojUsQq/Avy/6B3Ouffx4ftN85MfpgCnRe6ugw+Ta/DvzSog1hnLf8X/MDAJmAyMj9wWOOfcAvzIu5vx3+uJ+JMCwX9KkQ2MiXy9I4mtv11EUpCVYbxk4MzPSf3IOdcl0qs20zlX6jOqC3ndlyOv+055X0tEREREKp6kXzmOnCn+a76P7CzSv1giM6tvu2dkNgKOBKYFVqyIiIiIpLSkC8dmNhT/sV9H8wPfL8N/JHuZmf2C/+j1jBhfrjMwNvK8r4EHIh8tioiIiIjsJSnbKkREREREwpB0K8ciIiIiImEpbN5oaBo1auTatGkTdhkiIiIiUoGNGzdupXOu0M18kioct2nThrFjx4ZdhoiIiIhUYGZW5G6jaqsQEREREYlQOBYRERERiVA4FhERERGJSKqeYxEREZFUt2PHDhYtWsTWrVvDLqXSy8zMpGXLllSpUiXm5ygci4iIiMTRokWLqF27Nm3atMHMwi6n0nLOsWrVKhYtWkTbtm1jfp7aKkRERETiaOvWrTRs2FDBOGRmRsOGDUu9gq9wLCIiIhJnCsbJoSzvg8KxiIiIiEiEwrGIiIhIBfT+++9jZsyYMaPExz7++ONs3ry5zMd6+eWXueaaa/a4bd68ebRs2ZK8vLw9bu/WrRs//fRToa8zb948unTpUuY64kHhWERERKQCGjp0KEcddRRvvvlmiY8tbzguTJs2bWjVqhWjR4/edduMGTPYsGEDhx56aFyPFU8KxyIiIiIVzMaNG/n+++954YUX9gjHubm53HLLLRx00EFkZWXx1FNP8eSTT7JkyRKOO+44jjvuOABq1aq16znvvPMOl1xyCQDDhw/nsMMO4+CDD+bEE09k2bJlxdYxcODAPY7/5ptvMnDgQObNm8fRRx9N9+7d6d69O//73//2em7B1eg+ffowatQoAEaMGMHhhx9O9+7d6d+/Pxs3biz196goGuUmIiIiEpQbboCJE+P7mt26weOPF/uQDz74gFNPPZUOHTrQoEEDxo8fT/fu3Xn++ef59ddfmTBhAhkZGaxevZoGDRrw6KOP8vXXX9OoUaNiX/eoo45izJgxmBn/+c9/eOihh3jkkUeKfPx5553HwQcfzFNPPUVGRgZvvfUWb7/9Nk2aNOGLL74gMzOT2bNnM3DgQMaOHRvTl79y5Ur++te/MnLkSGrWrMmDDz7Io48+yj333BPT80uicCwiIiJSwQwdOpQbbrgBgAEDBjB06FC6d+/OyJEjueqqq8jI8BGwQYMGpXrdRYsWcf7555OTk8P27dtLnB+8zz77cOCBB/Lll1/StGlTqlSpQpcuXVi3bh3XXHMNEydOJD09nVmzZsVcw5gxY5g2bRpHHnkkANu3b+fwww8v1ddRHIVjERERkaCUsMIbhFWrVvHVV18xZcoUzIzc3FzMjIceegjnXEzjzfI/Jv+c4GuvvZabbrqJfv36MWrUKO69994SXyvaWtG0aVMGDhwIwGOPPUbTpk355ZdfyMvLIzMzc6/nZWRk7HEyX7QO5xwnnXQSQ4cOLfHYZaGeYxEREZEK5J133mHQoEHMnz+fefPmsXDhQtq2bct3333HySefzLPPPsvOnTsBWL16NQC1a9dmw4YNu16jadOmTJ8+nby8PN5///1dt69bt44WLVoAMGTIkJjqOeecc/jkk0946623GDBgwK7XadasGWlpabz66qvk5ubu9bw2bdowceJE8vLyWLhw4a4JF7169eL7778nOzsbgM2bN5dq5bkkCsciIiIiFcjQoUM566yz9rjtnHPO4Y033uDyyy+ndevWZGVl0bVrV9544w0ABg8ezGmnnbbrhLwHHniAPn36cPzxx9OsWbNdr3PvvffSv39/jj766BL7k6Pq1atHr169aNq06a42jN///vcMGTKEXr16MWvWLGrWrLnX84488kjatm3LQQcdxC233EL37t0BaNy4MS+//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>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": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def PlotPolly(model, independent_variable, dependent_variabble, Name):\n",
    "    x_new = np.linspace(15, 55, 100)\n",
    "    y_new = model(x_new)\n",
    "\n",
    "    plt.plot(independent_variable, dependent_variabble, '.', x_new, y_new, '-')\n",
    "    plt.title('Polynomial Fit with Matplotlib for Price ~ Length')\n",
    "    ax = plt.gca()\n",
    "    ax.set_facecolor((0.898, 0.898, 0.898))\n",
    "    fig = plt.gcf()\n",
    "    plt.xlabel(Name)\n",
    "    plt.ylabel('Price of Cars')\n",
    "\n",
    "    plt.show()\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's get the variables:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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": 35,
   "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": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEWCAYAAABMoxE0AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8/fFQqAAAACXBIWXMAAAsTAAALEwEAmpwYAABHl0lEQVR4nO3deXxU1d348c83k5VACASQkKAoi7IJCFJc6lrr0lbRumul1pbWatWn9mml/T2P2qe26qO1UqtWSxVXxN3HiktVXFoEQZAIqKAgRAJI2JIAWWa+vz/uGZiE2ZLJZCaZ7/v1mtfMPfeee8/cTO65Z7nniKpijDHGtFVWqhNgjDGmc7OMxBhjTEIsIzHGGJMQy0iMMcYkxDISY4wxCbGMxBhjTEIsI0kTIrJGRL6R6nSEEpE5IjIlzm1bnf7W7L+V+10mIsdFWT9XRH7Y3sdtTyIySERURLLbGH/PdxSRi0Tk1ZB1KiJD4tyPiMgDIrJVRBa0JS2JEJGvi8gnHX3cdCYiN4jII6lORyjLSNqZu6DuEpFaEdno/gm7pzpdbaGqp6rqzET3IyIPikiDOyfB13mh+xeR74vIu4mnGlR1pKrOdftN6J9ORI5zF95nWoSPceFz49xP0v75Y+1bVR9V1W+2cfdHAycB5ao6sY372CMkgwz+DtaIyHWRtlfVd1T14ESP2x7cb6Gyqx+zLSwjSY7vqGp34DDgcOD/pTg96eBWVe0e8noi1Qlqha+AI0WkJCRsCvBpitLTkQ4A1qhqXWsjxihNFbv/kQuA/xaRU1oZ36QRy0iSSFW/BOYAowBE5HRX7bLNVT0MbxlHRPqLyM7Qi5aIjBeRr0QkJ3jnLiK3ueqG1SJyasi2A0TkBRHZIiKrRORHIetuEJEnReQREakRkQoRGSYi00Rkk4isE5FvhmwfWj0yWETeEJFqEdksIo+KSHEi5ye4f3ce7gWOcHep28Jse7yIVIQs/zO0qsWdk8nu8xoR+Ya7OP0aOM/t98OQXR4gIv9y5+FVEekTJakNwHPA+W7/PuBc4NEWabzTncMdIrJIRL7uwsOmw33/P4jIAhHZLiLPi0jvCOcq7N81xncMxg1X2jtNRD53f8v/FZF9rgUichnwN/b+XW504T9yadji0jQgJI6KyBUishJYGeWcAqCq84BlwKjg3beI/EpENgAPtLwjF5GBIvKM+3+oFpG7Qtb9QERWuP+LV0TkgFjHby/u7/O0S9dqEbkqZN0NIjJbRB5yv7dlIjIhZP1hIrLYrXtSRJ4Qkd+JSCHe9WOA7C3BBc91bqT9pYJlJEkkIgOB04DFIjIMeBy4BugLvAT8n4jkhsZR1Q3AXLwLVdDFwCxVbXTLXwM+AfoAtwIzRETcuseBSmAAcDbwexE5MWRf3wEeBnoBi4FX8H4HZcBvgb9G+jrAH9x+hwMDgRviOhExqOoK4CfAPFdaKQ6z2TxgiIj0Ee9OdRRQLiI9RKQAGA+802K/LwO/B55w+x0TsvpC4FKgH5AL/CJGMh8CLnGfT8a7+K1vsc37wFigN/AY8KSI5MdIxyXAD/DOaxMwPcLxw/5dY+w7mjOBCXil5jNcGppR1Rk0/7tcLyIn4P0OzgVKgS+AWS2iTsb7jY6IlgDxHAWMxPstAvTHO38HAFNbbO8DXnTHHIT3m53l1k3Gy1DPwvv/egfvnLVayP9SvNtnAf8HfOjSdCJwjYicHLLZ6S6txcALwF0ubi7wLPAg3vd+HO9vgysFngqsDynJr4+2v1SxjCQ5nnN31e8Cb+H9o58H/ENVX3MZwm1AAXBkmPgz8TKP4D/PBXgX/6AvVPV+VfW7bUuB/VzGdTTwK1XdrapL8O4ovxcS9x1VfUVVm4An8f7pbnZpmgUMkjAlDVVd5dJer6pfAX8Ejm3FOfmFeCWxbSKyuRXxgsffDSwEjsG7AC7FO79HAZOAlapa3YpdPqCqn6rqLmA2XgYQ7fj/BnqLyMF4F/+HwmzziKpWq2qTqt4O5AGx6vcfVtWP3EXjv4Bz3d98jzj/rq11i6puUdW1wJ/wfmPxuAj4u6p+oKr1wDS8EsugkG3+4Pa9K8p+NgNb8L7Hdar6ugsPANe731nL+BPxMtL/VNU6dy6CJa0fu+OucL/t3wNjI5VKRORSEflQvHbMh0XkWBHpJyKXAlfHeS6CDgf6qupvVbVBVT8H7seVYJ13VfUl9z/7MBDM8CcB2cB0VW1U1WeAeDo1RNpfSlgdZHJMVtV/hga4IukXwWVVDYjIOrw7mJaeB+4VkYOAYcB2VQ39cW0I2c9OdwPVHSgBtqhqTci2X+BdeIM2hnzeBWx2P8bgcnBf21qkvx/e3fLXgR54NyFbw6Q9kttUNdG2oreA4/DuzN9yxz8WqHfLrbEh5PNOvO8cy8PAlcDxeHfwF4auFJFrgR/iXewUKMIrNUazLuTzF0BOmDgDiP13ba2Wxx0QacMwafkguKCqtSJSjfc7XhNm35H0cRf8lr5yNw3hDMS7iQoX7wDgThG5PSRMXLq+CLP9t4BTgDq8v+MdeDdkrxK7dBru2AOkeZWsj+Yl5Ja/t3xXsh4AfKnNR8+N5/yF3V+Ec5N0lpF0nPXA6OCCKz4PBL5suaGq7haR2Xh3f4fQvDQS6xi9RaRHyEVn/3DHaIM/4F0cD1XValeV0J7F6XiGoX4LuB1YC9yMl5Hcj5eR/CWB/cbrYWAV8FBIBg543VSBX+FVayxzNwpb8S5m0dIxMOTz/kAj3t16aHisv2tbvuNAvOq54L5aVtNFsh7vwgmAq8cvoflvLJFzHi3uOmD/CBfMdcBNqvpomHjhnKuqAff5Xvdqq3XAalUd2oa4VUCZiEhIZjIQ+Mx97hTDs1vVVseZDXxLRE4UkRzgWrwL4L8jbP8Q8H28utC4uo2q6jq3vz+ISL6IHApcRotG4TbqAdQC20SkDPjPdthnqI14bR65Ubb5N15V0URggaouw7uofQ14O8p+B0mYxuTWUtXVeCWg34RZ3QOvjeMrIFtE/huvRBIrHReLyAgR6YbXRvVUSAkxeNxYf9e2fMf/FJFertrsaiDeXnSPAZeKyFgRycOrQpqvqmtacey2WoB34b1ZRArduTjKrbsXmCYiIwFEpKeInBNpRyGZSKu54+55uXTtEK+TQIGI+ERklIgcHsfu5gF+4EoRyRaRM/B+30EbgRIR6dnW9HYEy0g6iKp+gtfu8We8O87v4HUTboiw/b/w6os/aOU/6QV4DZHr8RrxrlfV19qe8j1uxGuY3Q78A3gm+uat9gbeHfKGSG0orh3hA7w7/uB5m4dX3bEpwn6fdO/VIvJBhG3ipqrvhjR4hnoFr4fNp3hVKbtpXkURKR0P4zW0bgDygasIL9rftS3f8XlgEbAE7+85I55Iri3jv4Cn8S7qg2neFpA0LoP9DjAEr1Raidf2iKo+C9wCzBKRHcBHeA3V7a0Mrwo49HWgS9dYYDXe//ffgJgXf/c7PgvvxmAb3jXiRbybTFT1Y7wG+M9d+2K8VZAdStQmtkpbIvIG8Jiq/i3VaTHtT7yHGR+xv68JJSLzgXtV9YFUpyVeViJJU65YfBjxVzkYYzoh12Osv6vamgIcCryc6nS1hjW2pyERmYnXF//qFj11jDFdz8F4bajd8RrZz1bVqtQmqXWsassYY0xCrGrLGGNMQjKuaqt37946cODA2BsaY4zZY+nSpZtVtW+4dRmXkQwcOJA5c+akOhnGGNOplJWVhRshALCqLWOMMQmyjMQYY0xCLCMxxhiTEMtIjDHGJMQyEmOMMQmxjMQYY0xCLCNpJxVVdTz0/gYqqupSnRRjjOlQSc9I3Nj8i0XkRbd8g4h8KSJL3Ou0kG2nicgqEfkkdL5jERkvIhVu3fTgnMoikiciT7jw+S2m++wwFVV1XPXsSu57r4qrnl1pmYkxJqN0RInkamBFi7A7VHWse70EICIj8OY1GIk3BebdIXNX3wNMBYa61yku/DJgq6oOwZsq85akfpMIFlfW0OhXAgqNfmVxpY2zaIzJHEnNSESkHG9u5HjmWzgDmKWq9W4mulXARBEpBYpUdZ6bivIhvJFxg3Fmus9PAScGSysdaVx5D3J8QpZAjk8YV96jo5NgjDEpk+whUv4E/BJvGtJQV4rIJcBC4FpV3Yo389h7IdtUurBG97llOO59HYCqNonIdrz5o5vNsCciU/FKNJSVldHeRpcWMv3MoSyurGFceQ9Glxa2+zGMMSZdJa1EIiLfBjap6qIWq+7Bm55zLN5UnbcHo4TZjUYJjxaneYDqfao6QVUnlJSUxJH61htdWsglh/e3TMQYk3GSWbV1FHC6iKwBZgEniMgjqrpRVf2qGgDuZ+9E95VA6LC85XjzU1e6zy3Dm8URkWy8OZK3JOfrAP6w06sbY0xGS1pGoqrTVLVcVQfhNaK/oaoXuzaPoDOBj9znF4DzXU+sA/Ea1Re4mcJqRGSSa/+4BHg+JM4U9/lsd4ykzNTVbdmj7Pf4N6BpdzJ2b4wxnVYqhpG/VUTG4lVBrQF+DKCqy0RkNrAcaAKuUFW/i3M58CBQAMxxL4AZwMMisgqvJHJ+shLd1GsIvp1fUfD5y+waNjlZhzHGmE4n46baHTNmjLZpPhJV+s0+jUB+MZvPeLz9E2aMMWmsrKxskapOCLfOnmyPlwh1w88jd+MSsqs/TnVqjDEmbVhG0go7h01GfbkUrngi1Ukxxpi0YRlJK2h+MbsOOpWClS8gDTYMijHGgGUkrVY34jyyGndS8Nk/Up0UY4xJC5aRtFJjv7E09j6YbstnQYZ1VDDGmHAsI2ktEepGnEdu9Qpyvlqa6tQYY0zKWUbSBruGnE4gp5DCZY+lOinGGJNylpG0geYWsmvoGRR8NoesXckbkcUYYzoDy0jaqG7kBUigkW6fPJ3qpBhjTEpZRtJGTb2GUF860Wt0D/hjRzDGmC7KMpIE1I28kOza9eStezvVSWkzm2veGJOoVAza2GXsHnQC/m79KFz2GPUHHJ/q5LRacK75Rr+S49vA9DOH2nwqxphWsxJJIrJyqBt+LvmV7/LZyuWd7s7e5po3xrQHy0gStHP4uQQkm9Wv389971Vx1bMrO01mYnPNG2Pag2UkCQp068vy4uM5U96im+7sVHf2wbnmp04qtWotY0ybWUbSDmpGXUwP2cXZvnc63Z29zTVvjElU0jMSEfGJyGIRedEt9xaR10RkpXvvFbLtNBFZJSKfiMjJIeHjRaTCrZvuptzFTcv7hAufLyKDkv19wjlg+ES29RrNVd1fZ/rkwXZRNsZklI4okVwNrAhZvg54XVWHAq+7ZURkBN5UuSOBU4C7RcTn4twDTMWbx32oWw9wGbBVVYcAdwC3JPerRKbjptC7vpIJTYtTlQRjjEmJpGYkIlIOfAv4W0jwGcBM93kmMDkkfJaq1qvqamAVMFFESoEiVZ2n3rzAD7WIE9zXU8CJwdJKR9t14En4u/WlcNkjqTi8McakTLJLJH8CfgkEQsL2U9UqAPfez4WXAetCtqt0YWXuc8vwZnFUtQnYDpS0TISITBWRhSKysLq6OsGvFIEvl7oR55O/7h2yt32enGMYY0waSlpGIiLfBjap6qJ4o4QJ0yjh0eI0D1C9T1UnqOqEkpJ98pl2s3P4ed5UvBUPJe0YxhiTbpJZIjkKOF1E1gCzgBNE5BFgo6uuwr1vcttXAgND4pcD6114eZjwZnFEJBvoCaRsON5AQQk7h3ybgk+fR3ZvTVUyjDGmQyUtI1HVaaparqqD8BrR31DVi4EXgClusynA8+7zC8D5rifWgXiN6gtc9VeNiExy7R+XtIgT3NfZ7hgpnbawbvQUsvy7KVzxZCqTYYwxHSYVz5HcDJwkIiuBk9wyqroMmA0sB14GrlDV4LC6l+M12K8CPgPmuPAZQImIrAJ+jusBlkpNvYexu+xICpc9Cv6GVCfHGGOSTlJ8A9/hxowZo3PmzIm9YQLy1r5Nycs/Zuvxt7Br6OlJPZYxxnSEsrKyRao6Idw6e7I9CeoHHk1j8WAKK2ZChmXUxpjMYxlJMkgWdaMvIXfzcnKr3k91aowxJqksI0mSnUNPx5/fi+5LH0h1UowxJqksI0mW7HzqRl5E/tq5ZG9dlerUGGNM0lhGkkQ7R15IwJdP4dIHU50UY4xJGstIkiiQ34tdB59Jt5UvkLVzU+wIxhjTCVlGkmS1o6dAoInCjx5NdVI6VEVVXaebetgY0zaWkSSZv+cB7D7wJAqXz0Ia2v+imo4X7IqqOq56dmWnm3rYGNM2lpF0gNoxPyCrYQfdPm7fYVPS9YK9uLKGRr8SUDrV1MPGmLaxjKQDNPYbQ33p4XSvmNmuw6ak6wV7XHkPcnxCltDpph42xrSeZSQdpHbsj/DVbaBg1Yvtts90vWCPLi1k+plDmTqplOlnDrWph43p4rJTnYBMsdA3jrEFQyhceB+7hp4BWb7YkWIIXrAXV9YwrrxHWl2wR5cWplV6jDHJYyWSDlBRVcdVz63idztOpXvdF2xc8lK77Xt0aSGXHN7fLtrGmJSxjKQDBNsyXvJPZI3uR//lM2wwR2NMl2EZSQcItmWo+JgR+A6lOz8h98t5ccdPxy6+xhgTlMw52/NFZIGIfCgiy0TkRhd+g4h8KSJL3Ou0kDjTRGSViHwiIieHhI8XkQq3brqbKRE3m+ITLny+iAxK1vdJRGjj8zHfuRR/t770WHJfXHHTtYuvMcYEJbNEUg+coKpjgLHAKSIyya27Q1XHutdLACIyAm9K3pHAKcDdIhJskb4HmIo3/e5Qtx7gMmCrqg4B7gBuSeL3SUiwLWNkeW9qD/0Beevnk7vhAyB6iSNdu/gaY0xQMudsV1WtdYs57hWtYeAMYJaq1qvqarxpdSeKSClQpKrz3HzsDwGTQ+LMdJ+fAk4MllbS2c7h53pDzC++N2aJI127+BpjTFBS20hExCciS4BNwGuqOt+tulJElorI30WklwsrA9aFRK90YWXuc8vwZnFUtQnYDpSEScdUEVkoIgurq6vb58slQHO6UTf6++Sve4f1ny6MWuKwZzKMMekuqRmJqvpVdSxQjle6GIVXTTUYr7qrCrjdbR6uJKFRwqPFaZmO+1R1gqpOKCnZJ59JibqRFxLILeK07U/ELHFYF19jTDrrkF5bqroNmAucoqobXQYTAO4HJrrNKoGBIdHKgfUuvDxMeLM4IpIN9AS2JOdbtC/N7U7dqIvZb8Ob3Di+ngkDe3D1MeWWWRhjOp1k9trqKyLF7nMB8A3gY9fmEXQm8JH7/AJwvuuJdSBeo/oCVa0CakRkkmv/uAR4PiTOFPf5bOAN147SKdSO+h5Nvm4ULb6XhetquPPtyi7TK8u6LBuTOZI5REopMNP1vMoCZqvqiyLysIiMxauCWgP8GEBVl4nIbGA50ARcoap+t6/LgQeBAmCOewHMAB4WkVV4JZHzk/h92p3mF7Ogz2RO2fA4g6nkM385iytrOn2pJNiBoNGv5Pg2WNuOMV1c0jISVV0KjAsT/r0ocW4CbgoTvhAYFSZ8N3BOYilNrd1jfsCuDc9wVfYz/EKv7hK9ssJ1WbaMxJiuy55sT7FDBpWxcegFfNs3nxnfyOoSF1zrsmxMZrGMJA10O/JHaE4B49c+mOqktAvrsmxMZrGMJA0E8ntRN/Ji8j9/mewtK1OdnHZhXZaNyRyWkaSJukO/j+YU0OODu1OdFGOMaRXLSNJEIL8XdaO+R8HnL5Nd/XGqk5Mw6/5rTOawjCSN1B56KYHcHvRY+OdUJyUhNmKxMZnFMpI0onk9qT30Ugq+eIOcTUv3hHe2u3sbsdiYzGIZSZqpG3UJ/vxe9Fg4Heicd/fW/deYzJLMJ9tNG2huIbVjf0TP924lt+p9FlcO7HQP9wW7/y6urGFceY+0T68xJjFWIklDdSMu8GZRfP9OxpV1t7t7Y0xasxJJOsrOp+awn1L87o1MaFrI9DMP71R39zbWljGZxUokaWrnId+lqWh/ihbcwej+BZ3q4T5rbDcms7QqIxGRXiJyaLISY0Jk5bDj8KvJ2fIpBateTHVqWsUa243JLDEzEhGZKyJFItIb+BB4QET+mPykmd0HnUJDyXCvB5e/ISnHSEbXYhtry5jMEk+JpKeq7gDOAh5Q1fF4k1SZZJMsar52Ldk1X1K4Yna77z6ZXYttrC1jMkc8GUm2m9XwXKBz1bF0AfVlR1I/YBLdP7gbaaht131bW4Yxpj3Ek5HcCLwCrFLV90XkICDmELUiki8iC0TkQxFZJiI3uvDeIvKaiKx0771C4kwTkVUi8omInBwSPl5EKty66W7KXdy0vE+48PkiMqiV3z/9ibDja7/At3sr3Zf8rV13bW0Zxpj2EDUjcdPkDlTVQ1X1pwCq+rmqfjeOfdcDJ6jqGGAscIqITAKuA15X1aHA624ZERmBN1XuSOAU4G53fIB7gKl487gPdesBLgO2quoQ4A7glri+dSfT2HckO4d8m+4VD5JVu6Hd9mttGcaY9hA1I3Fzpp/elh2rJ1gXk+NeCpwBzHThM4HJ7vMZwCxVrVfV1cAqYKKrVitS1XmqqsBDLeIE9/UUcGKwtNLV1Bx+DWiAIjd0SnuxtgxjTKLiqdr6t4jcJSJfF5HDgq94di4iPhFZAmwCXlPV+cB+qloF4N77uc3LgHUh0StdWJn73DK8WRxVbQK2AyVh0jFVRBaKyMLq6up4kp52/D3KvGHmP32uSwwzb4zpOuLJSI7Eq276LXC7e90Wz85V1a+qY4FyvNLFqCibhytJaJTwaHFapuM+VZ2gqhNKSvbJZzqNmnFT0bwiit77X9B9vqYxxqREzCFSVPX4RA+iqttEZC5e28ZGESlV1SpXbbXJbVYJDAyJVg6sd+HlYcJD41SKSDbQE9iSaHrTleb1pOawy+k572by1r1F/f7HpTpJxhgT35PtIvItEfmliPx38BVHnL4iUuw+F+A9e/Ix8AIwxW02BXjefX4BON/1xDoQr1F9gav+qhGRSa7945IWcYL7Oht4w7WjdFl1Iy6gqecgiubdCoHGVCfHGGPierL9XuA84Gd4VUnnAAfEse9S4E0RWQq8j9dG8iJwM3CSiKwETnLLqOoyYDawHHgZuMI19gNcDvwNrwH+M2COC58BlIjIKuDnuB5gXZovl+2TfknO9tUULp+V6tQYYwwS6wZeRJaq6qEh792BZ1T1mx2TxPY1ZswYnTNnTuwN05kqvV/6Ibmbl7HxvDlofq/YcYwxJgFlZWWLVHVCuHXxVG3tcu87RWQA0Agc2F6JM20gwo4jfoU01NBj0V9SnZqwOtv0wMaYtotnPpIXXVvH/wIf4PWKat9HrE2rNfUexs5DzqFw+Sx2Dj+Xpt7DUp2kPSqq6rjymU9p8kO2r4q7zhpmz6kY04XFLJGo6v+o6jZVfRqvbeQQVf2v5CfNxFJz+NVobnd6/vsPadUdeM6Kahr93h1Ho99bNsZ0XREzEhG5WES+FxqmqvXAuSJyYdJTZmIK5Pdix4Sfkbf+PfJXv5rq5IRo+XhPlxxswBjjRCuRXAs8FyZ8lltn0sDO4efR2Ptgit67BWnaFTtCBzh1eG9yfILgDQZ56vDeqU6SMSaJomUkPlXdZ1xxF5aTvCSZVsnKZvtRvyG7toruS+5PdWoAb/yuu84ayo+PKOWus2wwSGO6umiN7TkiUqiqzbrdiEgPIDe5yTKt0VB6ODsHf4vuH85g57DJ+Iv2T3WSGF1aaBmIMRkiWolkBvBU6Bwf7vMst86kkR2Tfolm5dDzX79Lq4Z3Y0zXFzEjUdXb8IYieUtEqkVkM/AW8KKq/m9HJdDEJ1DYj5oJPyN/3Tvkr3kt1ckxxmSQWPOR3KuqB+B1+z1QVQ9Q1Xs6JmmmtepGXkRj74Pp+e8/II32IKAxpmPENWijqtaGa3g3aSYrm21HX4+vbgM9Ft2d6tQYYzJEXBmJ6Twa+4+j7uDvUlgxk+zqT1KdHGNMBoj2QOI57t3G1epkdnztWgJ5RRS/898Q8MeOYIwxCYhWIpnm3p/uiISY9qP5vdhxxDRyNy2lmw01b4xJsmjPkVSLyJvAgSLyQsuVqnp68pJlErVryLcpWPk8Re/fwe5BJxLo3r9Dj19RVcfiyhrGlfew50mM6eKilUi+hVcq2czeudpDX1GJyEAReVNEVojIMhG52oXfICJfisgS9zotJM40EVklIp+IyMkh4eNFpMKtm+5mSsTNpviEC58f+sxLxhNh+9HXQ8BPz3//rkMPXVFVx1XPruS+96q46tmVNpS8MV1ctOdIGlT1PeBIVX0Lbwj5Rar6lluOpQm4VlWHA5OAK0RkhFt3h6qOda+XANy684GReHO73y0iPrf9PcBUvOl3h7r1AJcBW1V1CHAHcEvc3zwD+IsGUjv+CgrWvE7+56902HEXV9bQ6FcCCo1+ZXGldfgzpiuLp9fWfiKyGPgIWC4ii0RkVKxIqlqlqh+4zzXACqAsSpQzgFmqWq+qq/Gm1Z0oIqVAkarOc/OxPwRMDokz031+CjgxWFoxntpDp9DQZwQ9//U/yO6tHXLMceU9yPEJWeIN2jiuvEeHHNcYkxrxZCT3AT93DyPujzfy732tOYirchoHzHdBV4rIUhH5u4gE54ktA9aFRKt0YWXuc8vwZnFUtQnYDpSEOf5UEVkoIgurqzNsboysHLYdexNZu7fTc97NHXLI0aWFXH1MORMG9uDqY8qtjcSYLi6ejKRQVd8MLqjqXCDuK4Ob4/1p4BpV3YFXTTUYGAtUsbe9JVxJQqOER4vTPED1PlWdoKoTSkr2yWe6vKaSQ6gd9yO6rXyBvLXx1EompqKqjjvfrmThuhrufLvS2kiM6eLiyUg+F5H/EpFB7vX/gNXx7FxEcvAykUdV9RkAVd2oqn5VDQD3AxPd5pXAwJDo5cB6F14eJrxZHBHJBnoCW+JJW6apGfcTGnsNofidG5CG5LZZWBuJMZklnozkB0Bf4Bn36gNcGiuSa6uYAaxQ1T+GhJeGbHYmXtsLwAvA+a4n1oF4jeoLVLUKqBGRSW6fl+ANJhmMM8V9Pht4w7WjmJZ8uV4V185NFCW5isvaSIzJLNGeIwFAVbcCV7Vh30cB3wMqRGSJC/s1cIGIjMWrgloD/NgdZ5mIzAaW4/X4ukJVg49lXw48CBQAc9wLvIzqYRFZhVcSOb8N6ezUWvO8RmO/Q6kd8yN6LPkruwd9g/oDjk9KmkaXFjL9zKH2HIkxGUIy7QZ+zJgxOmfOnNgbdgLB5zUa/UqOT5h+ZhyzEfob6PvsOWTt2sKmc15A83tF394YY4CysrJFqjoh3DobtLETa1NbhC+XrcfdTNbubd4kWMYYkyDLSDqxtrZFNPUZTs34n9Lts5fI/+ylJKfSGNPVxcxIRGSYiLwuIh+55UNdzy2TYsG2iKmTSuOr1gpRO/ZHNPQ7lOJ3biSrdkMSU2mM6eriKZHcjzfmViOAqi4lAxu109Xo0kIuObx/6xu0s7LZevytEGii19xpoIHkJNAY0+XFk5F0U9UFLcKakpEY07H8PQ9gx5HTyFv/HoUVM2NHaIWKqjoeen+DPYxoTAaI2f0X2Cwig3FPjIvI2XhPpJsuYOfB3yVv7VyKFtxB/YBJNPUZnvA+m/cm29DqarfgPqz7sDGdQzwlkiuAvwKHiMiXwDV4z3WYrkCE7cf8D4H8Ynq9fi3SuDPhXSb6ZLsNQ29M5xIzI1HVz1X1G3hPtx+iqker6pqkp8x0mEB+L7YefyvZ29dQ9O+bEt5fok+2L66soaHJZURNNsSKMekunl5bvxeRYlWtU9UaEeklIvYAQhfTUDaJ2rFTKfzkGfJX/SOhfSXSmwygqCB7z8ibAbdsjElf8VRtnaqq24ILbsiU0yJvbjqrmglX0LDfWIrfuR7fjnWxI0TR5t5kwI5dTXuGdRa3bIxJX/FkJD4RyQsuiEgBkBdle9NZZeWw9YTbQHz0+ud/sKxyS0p6Xo0r70Futlc1lpttgz4ak+7iqTN4BHhdRB7A67n1A/bOSmi6GH+PMrYd93t6v3olX714Pfc1/qDNPa/aKtagj9ajy5j0Es/ov7eKSAVwIl5Nw/+oasdNAG463O5BJzK/33lcuOkJ3pNDeNF/JIsrazr0oj26tDDs8Sqq6rjymZU0+ZVs3wbuOqvjMjhjTHhxtWKqaujQ7SYDbD/8P1j04hL+kHM/K/2DGFc+LNVJAmDOii00+r2m+Ea/MmfFFstIjEmxiG0kIvKue68RkR0hrxoR2dFxSTSpMKqsJzUn/RHJyefJ4r9waNrMUNxy2oPMmgbBmHQUMSNR1aPdew9VLQp59VDVoo5LokmVYQcdxM6T/0Rh3RcUv/VrSIO5a04dXkKOz6tjzfF5y8aY1Iraa0tEsoKj/raWiAwUkTdFZIWILBORq114bxF5TURWuvdeIXGmicgqEflERE4OCR8vIhVu3XQ35S5uWt4nXPh8ERnUlrSayBrKJrFj4rUUrH6V7h/OSHVyGF1ayF1nDePHR5Ry11nDrFrLmDQQNSNR1QDwoYjs34Z9NwHXqupwYBJwhYiMAK4DXlfVocDrbhm37nxgJHAKcLeI+Ny+7gGm4s3jPtStB7gM2KqqQ4A7gFvakE4TQ92hl7LroFPo8f4d5FX+K9XJSegZFWNM+4vnOZJSYJmbk+SF4CtWJFWtUtUP3OcaYAVQBpzB3u7DM4HJ7vMZwCxVrVfV1cAqYKKIlAJFqjpPvXmBH2oRJ7ivp4ATg6UVk7g9I/hu2Mm2Y39HU/Fger1+Lb7tX6Q6acaYNBJPr60bEz2Iq3IaB8wH9lPVKvAyGxHp5zYrA94LiVbpwhrd55bhwTjr3L6aRGQ7UAJsbnH8qXglGsrKyjCxhRvBd+zJf6Hvs+fQ+5Ur2Dz5cTTXHhQ0xkTvtZUvItcA5wCHAP9S1beCr3gPICLdgaeBa1Q1Wm+vcCUJjRIeLU7zANX7VHWCqk4oKbHG2XiEG8HXXzSQLSfdSfb2L+j1xn9CwJ/qZBpj0kC0qq2ZwASgAjgVuL21OxeRHLxM5FFVfcYFb3TVVbj3TS68EhgYEr0cWO/Cy8OEN4sjItlAT2BLa9Np9hVpBN+GAV9j+1G/Jn/tWxQt+GOKU2mMSQfRqrZGqOpoABGZAbScJTEq11YxA1ihqqFXnBeAKcDN7v35kPDHROSPwAC8RvUFqup3z65MwqsauwT4c4t9zQPOBt5w7SgmTpGGG4k2TMnOEReQs2Ul3Zf+naaeB7Bz+Ln77Pe5jzYzd9U2jhtSzORRfTrkuxhjUiNaRtIY/ODaH1q776OA7wEVIrLEhf0aLwOZLSKXAWvxqs5Q1WUiMhtYjtfj6wpVDdadXA48CBTgPWEffMp+BvCwiKzCK4nYXPKtEGsmw0jDlABsP/LX+Goq6fnub/H3KKO+/Kg96577aDO3vuGNHrxgrTeXiGUmxnRd0TKSMSFPsAtQ4JYF0FgPJarqu4RvwwBv3K5wcW4C9plZSVUXAqPChO/GZUSm9cK1g8TdpTYrm60n/pE+L1xEr9euYfMZj9LU2xtGZe6qbc02nbtq2z4ZiQ28aEzXEe3Jdl+Lp9mz7cn2rmVceQ98WYIAvqzWD9euud3Zcso9aHY+vef8hKy6jQAcN6S42XYtl+OZSndP12ObZjfp7FybRMXzHInp0rTFe/wqqup4YEUW8yf8iayG7ZTM+THSUMPgkgJ87pfly4LBJQXN4sWaStfmbO84dq5Ne7CMJIMtrqzBH/CyEH+AVs2NHnoBuvRNHx8cdivZWz+j96s/Y+na6j3Dcqnuu99YU+mGq3LrDDrjnX1nPdcmvVhGksEidfGNR8sL0D8bRrLt2N+Rt34+F391GzlZGrHKLNZUuomkK5ZkXew76519Ms+1yRxxzUdiuqbRpYVcfUz5nm66rWn09i5AG1yPL+8CtKv0DLJ2baZ0/m1cnxXgN/4fRIybm908bst0RZshsa1i9VJLREIdF1IoWefaZBbLSDJYRVUdd75dSaNf+XB9LYNLCuK+kES6ANWNuYzlq7/kwk2Ps0W780f/eftcVOO5eEXretxWybzYh8tYO4tknGuTWSwjyWCJXlgjXYB2TPw5jz+/kSuzn6eGQsaV/zzuuMmUzIu93dmbTGYZSQZL1oX1sy27ua3xB3RnJ9OyH+Ptj/aD0qntsm+I/QxKW57WN8a0nWUkGSzRC2ukYVDmrtpGgCz+o/Gn5NHIN1ffwbYVxWGHUmmtWO0ciTytn8x0GdOVWa+tDNfWSaKCw6AsWFvDrW+s47mP9o7cH3wAsYlsrmy8ii+KJ9HznRso+OTZPdvE6j0VaX2sZ1BirU8W60ZrMpmVSEybzF68aZ/lYKkk+B4sreQcci/1r/yU4rd+AyIs6HFSm0sVsZ5BibU+WTpzY7sxibKMxCTF5FF9mlV3bT35Lnq9ciXFc3+Nf/9qGv2HRWzkj9YJIPgMSnCimpbPoMRanyzW/mIymVVtmTY5d1y/qMstaXYBW07+C/UDj+a0tbfxvex/RnwILtpDcuPKe5Dt88YHy44QNzfbi5ub3bElA5tL3mQqK5GYiKL1jhpcUkAWXvVRFvuOpxVWdj5bTvozvf95NTeu/TvH7J9H02GX7bPv2Hf3kccHs5KBMR3PMhITVqxeSI8u2kDAfQ645Zu/PTj2jrPz2HLSdHq9+StO/PweavaDmv4/gxbz3UTqXbW4soYmvxsfzE/YZ1/sATtjOlbSqrZE5O8isklEPgoJu0FEvhSRJe51Wsi6aSKySkQ+EZGTQ8LHi0iFWzfdzbyIiOSJyBMufL6IDErWd8lEsXohrd1aH3U5aq8sXy5bT7iNuoPPoscH91A07w+ggX23CyNVjenGmMiS2UbyIHBKmPA7VHWse70EICIj8GY3HOni3C0iPrf9PcBUvKl3h4bs8zJgq6oOAe4AbknWF8lEsQbz279XXsTluAYwzPKx/ZjfUTt6Ct0/epjiN34J/oaY6QptPO/IxnRjTGRJy0hU9W286W/jcQYwS1XrVXU1sAqYKCKlQJGqznNzsT8ETA6JM9N9fgo4MVhaMYkLtjVMnVQa9uG6i8b3J8ud7SzxloPifqZChB2TfsWOiT+n22f/oOTlHyMNtVHTFVoCUaxEYkw6SEWvrStFZKmr+urlwsqAdSHbVLqwMve5ZXizOKraBGwHSsIdUESmishCEVlYXV3dft+ki4vVC8mXhRsqvnl4q4YmF6F27I/YetwfyF2/kD7/dwlZdZsibh5rCHpjTMfr6IzkHmAwMBaoAm534eFKEholPFqcfQNV71PVCao6oaQkbF6Tsdo6P0doo3eTv/nkVbFKM+HsGjaZLafcjW/HF/R97jyyqz8Ou10qu/caY8Lr0HoBVd0Y/Cwi9wMvusVKYGDIpuXAehdeHiY8NE6liGQDPYm/Ks2Q2PhQoY3e4aqY2tJzqn7g19l8+qOUvPwT+rxwEVtP/CP1+x+7z36te68x6aVDSySuzSPoTCDYo+sF4HzXE+tAvEb1BapaBdSIyCTX/nEJ8HxInCnu89nAG64dxcQpkfGhQquYsmi/KqamkkP4avITNBUdQO9Xfkrh0gehxZ/VHvwzJr0ks/vv48A84GARqRSRy4BbXVfepcDxwH8AqOoyYDawHHgZuEJV/W5XlwN/w2uA/wyY48JnACUisgr4OXBdsr5LV5XINKuhVUw5YaqYEpnSNlC4H9WnP8zuA06g53u3UDx3GjTVx44Yh844r3qiMvE7m44lmXYTP2bMGJ0zZ07sDTNEtKfX2zrvR/MqM2n7kOoaoPsH91C06C4a+h7Klm9OJ1C4X+v3097p6kQy8Tub5CgrK1ukqhPCrbOxtkxY8TwLEqmKqT2Gcq+oquOhhZuYN+D7bDlpOtlbV9H36bPI/fK9hDoIZNpQ75n4nU3Hs074GSxaY3s80/BGKpEk+vT5vuk6knFnzqbXa1dR8o/LqPCfx31N3ybHl9WqO+xkD/UeqwSXCja8vekIlpFksGiZRawLUEVVHVc+s5Imv5Lt28BdZ+29oCc6lHvYdB0+mM2TZ7PtuV/wi22PM46P+WXTj1s1z3wye3yl6wyJ1svNdATLSDJYtMwi1gVozootNPq9ckejX5mzYkuzTCg3u+13wZHSpbmFrD36f5n93F+4zvcI/8idxtr8m4H+0XcYIlkDOsZTgksVG8TSJJtlJBksVmYR7QK0ZWdDxOVE74Kjxf9sy24eaPomC/zD+HPOdCbMu5y63VOpGf9TyMpp1XHak1UhmUxmGUmGa/vdasuBBeIbBj7RdM1dtQ2AZTqI7zTcxF+KH+W4xfeSV/kuW4+/FX/xgW0+ZiKsCslkMuu1ZdqoZbfxjulGftyQ4j2f6yhg+WE3suUbd+LbUUnfp8+i8KNH4h6SPpxEnrmwByVNprISiWmT3t1yoy4ny+CSAnxZ4A94g0UOLilgd+k3aeg/luK3/h89/30T+atfYdsxv8Pf84BW7TtdG8yNSXdWIjERRbs7P3V4b7LdOPLZWcKpw3t3SJoWV9YQcAUODewdLDLQrR9bTvkrW4/9PTnVn9D3qckULn0AAvH3GLNnLoxpG8tITFhe995P+eu8Kq585tOwmYmIIu69o0R9RkWEXQefydvHzuazwsPo+d6t9H32XHI2VezZJFrmmMiQMcZkMqvaMmHNWVFNoxvtrNHvLYdW8yyurMEfcHOnB8LPnZ4MsZ5Rqaiq46o522j0X8Fp2V/jtrpH6PPceewccQHvDfwhV/1jY8SqK2swN6ZtrERiIojeKytVd++x5iPZOzyL8FLj4dw97AHqRl5EtxWzOOL1MzlLXwcNRBy6JVaD+XMfbeaa51bx3Eebk/L9jOmMrERiwjp1eG9eXF5NU0DDtoGk6u491nFbVn3ld+/JjlG/Yech36Xp1ev5Q9PfuND3T25qupiigoH77D+a5z7azK1veBN5LljrZUKTR/VJ9CsZ0+lZRmIiitUGkqonpqMd99NNu8IuN5UcwkOD/0TVgqf5Zc4sZuX+jpUfvUF2+W9oKj4oruMGn2EJXbaMJLp0HH/MtD+r2jJhhWsD6RwiP98ybmARL2cdzTcabud2/3kcuPND+j75HXq+9Rt8teuJZWjfgqjLNu9Hc/GMIG26BiuRmLA665Afpw4v4R8rqmnyQ7bPWw4KrRYbVf6fbC7+Gd0X30fh8sfptvL/qBtxPgtLL+S9zflh76Dr6gMRl+0ZlH2l8/hjpn0lc4bEv4vIJhH5KCSst4i8JiIr3XuvkHXTRGSViHwiIieHhI93syquEpHpbspd3LS8T7jw+SIyKFnfJRMFL7pTJ5V2qovi6NJC7jprGD8+opS7zhoWdvywYGN6oKCEHUdOY9P5L7Nz6Ol0W/YYR7x6OgPe/z2/e2ZemDvoyKWd9piDpaux7tSZI5lVWw8Cp7QIuw54XVWHAq+7ZURkBHA+MNLFuVtEfC7OPcBUvHnch4bs8zJgq6oOAe4AbknaN8lQXXHIj3C9rvzdB7D92N9x0/4zeMZ/NBf43uD17GsonjuN7K2r9mw3rF+3ZvsKXU50DpauqLPejJjWS9qvXVXfDlNKOAM4zn2eCcwFfuXCZ6lqPbDazcM+UUTWAEWqOg9ARB4CJuPN234GcIPb11PAXSIimmlzB5tmolUxxep1tbKxLzOafsRdTZP5YfZLXFg7l7wnX2P3/sdSO+oSXl3RvOfaqx9X74mf6BwsXZUNYZ8ZOrqxfT9VrQJw7/1ceBmwLmS7ShdW5j63DG8WR1WbgO1ACWGIyFQRWSgiC6urq9vpq5h0FK2KKVyvq1C9u3n3VV/SlxubpvDbQQ+zY/yV5GyqoM9Ll3H71qu40Pc63dgNwPodjXvixnq+BTKzMT4Tv3MmSpfyd8un32DvzV248Ghx9g1UvQ+4D2DMmDFWYunColUxDe1bsKckElwOderwEv5vefWeASGPGXUQtaWjqR3zQwo+n0PBezP4PTOYlv0Yz/uPZNv+5+yJG+v5lkxsjM/E75ypOrpEslFESgHc+yYXXgmEPh1WDqx34eVhwpvFEZFsoCewJWkpN62SqjvRSM+RAKzbWt9sXctlgCzx7lCyQm9TsvPYNWwyfO8F/nrgnbzrm8h5Oe9w5ec/oc/TZ1H40cNk7d4aNV2hJaWGDGmMt0EwM0dHZyQvAFPc5ynA8yHh57ueWAfiNaovcNVfNSIyyfXWuqRFnOC+zgbesPaR9JDa5wci96z6qq6x2ZqWyzGfnRHhOyd9kzE/vJfN33uL7Uf+BkTo+e/f0+/hY8h5fiobFjzFdc9W7POdQ0tKSmY0xluvrcyRtF+ziDyO17DeR0QqgeuBm4HZInIZsBY4B0BVl4nIbGA50ARcoapuyEAux+sBVoDXyD7Hhc8AHnYN81vwen2ZNJDK5weiPUcysDiPFRt3NlsOFc+zM899tJm5q7Zx3JBiJo+6mLpRF5Nd/Qmr33mM4Rv/yQk5H7BT81j7ztcoOOx0du9/LJrbnffW7Gi2n/fW7OjyT8XbIJiZI5m9ti6IsOrECNvfBNwUJnwhMCpM+G5cRmTSSyofZgw+RxLu4rWtRU+qlsuxLnyRen01lRzMoiE/4/y1p3O4fMJ3fPM4q+4DCt94G83KoX7A15i0ZTifyygqtS8Am1uUhroq67WVGbp++dp0uFTfiUa6eMVqbI8WF2D24k37LId2/4UsFuhwFjYN58uR0/jh/hvIX/0a+Wvn8tPd7/LTPFgVGMA7gdH4en4daShHc+0iazo/y0hMUqTjnWhdvT/qciK87r8hpbCBPWnoP4CG/oex44hf8cDL8wh89gZfz6rgfN+bFKx9BZ15PY19R1JfejgNpRNo6DcWzS9u0/FtcESTSpaRmC4n8kU1+hwrsRx1UE/WLNrUbDlodGkhVx9Tvqf9pOXFfO6Wnqz0n8YM/2nk0cAZxav5r+EbyF3/Pt0rHkI+nAFAY/FgGvuNoaHfKBr7jqax9zDw5UbNKLzZLFfS5FeyfRu46yzrZmsZa8eyjMR0KdGeXSjMa95JseVyLNFKNBVVddzx1jqa/LD4yxoGlxQ0u4B9Vbu3PaaeXF7dPYJrDvf6h0jTLnI2VZC7cTG5Gz4gb+2bdPv0GQA0K4ea7gdSt60//sBAZi8cSN7JX2fYgQeCN+wcc1ZsodHv9Qlr9CtzVmzJ6ItnPBlr804TXbvTQ0ewjMR0KdF6jC2urG2xbe0+8aPfyUYu0cSamnhQ73yWrK9rthyk2QU0DJhIw4CJLkDx1XxJzlcV5FSv4KvPPuQoWcpZ2W976/95M4Gc7jQVD6Kp5yCO2dgTySpirfZjnfZja13zzg2ZdtGMlbHaBGXtzzIS06VE6zHWpzCn2bYtl2M9iT2sX/PG+ebL0avNLj+qjJ88+eme4RouP6qMiETwF5XjLypn9+BTWTXQS1d3/3aG+77k1+MaOMC/Dt+OL8jd8AGTa6s4K3fv8zJNVdnweH/83Uv5orEY34ZcRmsxn1T2ZOG2oUwaPohAfi8CecWQnRc5HZ1W5GeJwCYoSwbLSEyXEq3H2EXj9+Nfa7bvGQLlovH7NYsbfPpc2TtOV2j8aAMznjq8t3t+Rcn27Ts18WfVu5o9kPhZ9a64q5+af6cJFJcWsj1k/VVPfsSWDV+wv2yiXL5iXI/tnLpfA77aKnpsWcoU3xbyxXU3Xu5eTiC7AM3tQSCvB5pbRCCnEHWvQE43NDsfzSlAffmoLw+yc9GsHDQrB3zuXXyQ5UPFB5K156W4YQKQPdVwqHpnQEEIfg6EhAeQ4LIGAO+zaCDMtu69hUuL6glkb8AfAMnKYkpxOXlffLYnnRf23Ulg3WYayKGRbM4cUI6v5kvUl+t93+wCyGr7pTET22csIzFdTqQeY6NLC7n7u+GfMYHYQ8GPK+9Btm/DnswitLTjPb8Sucvzi8uq91luzV1wtF5wlbWwQQfwuQ4A4J/+HI44wXv06roXP+ftz7dRRB19ZAcnDPDz03F5ZO3eRlb9NrJ2b0MaashqqCGrfgdZ9duR2vVkNdYhjbuQpl1IoHM989IbmB76p1vYfP1kYHJoQWyJe4XQrBw0p5uXseZ29zLW3B4E8np6GW9+sVeqy++Fv6A3gYISAgV9+HBrDlc991nGjS9mGYnpcqLdEUa7IMc3FLy2eI9v330Ks6MuJ2JnQyDi8qRBRbz9+XZ20J0d2p2zDx7I7oNaWY0TaET8DYi/AZp2I4FGxN8IgSYvk1E/EvBDoAlQCPi90kazkkMIEYKlFK/UkhUS5n3WYMkG8UoSgtvWt7d0I8HOEi2rFVscW/2IKmjTnnRKoNF9L++74a9H/PVI024v83SZaFZjHdJQS1ZDLVm7qsnetpqsBi/DDaevZPO6r5gNWb2p0t70nD+IbkOH4O9RTlPR/vh7lIEvt3XnvxOwjMR0KYmMOLvPsyAtnsgPNxZXvPu+aHx/3l29g4B6A0JeNL5/a79aRIEWF+rQ5ccWbWy27rFFG1vfHuCqsjSnfe+sO3UVUKDJK8Ht3krWrmqydlXj27WZ6k1fsvTTz+nHFkZnrWH/zYvI2rS3RKcI/h4DaOp5IE3FB9JUPJim3kNp7DUEzStKKEmpPJ+WkZguJZFxvmI9kZ/o0C++LFC/996ehvTJZ8n6nc2Wg6pqGppt23I5VTr9sy9Z2QQKehMo6A29Bu8JzgcKhtfxtvsN5fYvIGvXZnw7viR7x1qyd6zFt/0LsrevptvHH5DVtPfv1lRYSmOf4TSVDKehzwga+40m0K1vXMlJ9ZD9lpGYLiXRi3206qlEhn5JpDQTy+VHlXP5U5/uKe1cftTemRdyfcKugDZbTgdd+dmXlr+hQLd+BLr1o7H/uOYbquKrqyJ7y6fkbFlJdvUn5FR/TP7aua5zgctc+h1KQ//DaOh/GI0lh4TtCJDKgVLBMhLTxSR7nK+2Dv2SzIEsR5cWcs/Z4TsR+APNq71aLqdO9C66GUEEf/cB+LsPoH7/4/YGN+4ku/oTcjd9SM5XFeRuXELB6lcACGR3o6F0PA2lE6kvm0RjyXDI8qV0oFSwjMR0Qek4zleqMrjueT627PQ3W04H0Yb7z3Sa043G/uOalWCyajeQu/ED8qoWkrt+AUXrbgfAn1dMffmRTCw/mntPm8D8r3JS0kYimTYX1JgxY3TOnDmxNzSmE4nU0Br6FDfAL08Y2K4P3yXy1HynbmxPsaydX5G3fj55694lr/Jf+HZtRhEa9xvD7v2PZ9eBJ+EvPrBdj1lWVrZIVSeEW5eSjERE1gA1gB9oUtUJItIbeAIYBKwBzlXVrW77acBlbvurVPUVFz6evZNevQRcHWuWRMtITFfTvKFV9mlojXWxb+sFPZ5MyjKLDqBKTvVy8r6YS/4Xb5K7eRkAjb2Gsuugk9k1+LR2yVSiZSSprNo6XlU3hyxfB7yuqjeLyHVu+VciMgJv9sORwADgnyIyzM2geA8wFXgPLyM5hb0zKBrTaul64YuWrlgNrZNH9YlYWkikt0+shyxT3ZOoq4n4GxChsc9IGvuMpHb8FWTVVlGw+jXyV79Kj0V/oWjRXTT0GcmuId9m15DTCHTr1+5pS6c2kjPwpuYFmAnMBX7lwmepaj2w2k2tO9GVaopUdR6AiDyE99CqZSSmTdL1whcrXYk0tCbS2yfW2GWp7knUlbTmtxnoXkrd6EuoG30JWXWbKPjsJQpWvUjP925BfTnsHHlRu6cvVRmJAq+KiAJ/VdX7gP1UtQpAVatEJJhtluGVOIIqXVij+9wyfB8iMhWv5EJZWZTB8kxGS9cLX6x0JdKQn0gmFGvsslT3JOpK2vrbDBT2o+7Q71N36PfxbVvtPfeSBKnKSI5S1fUus3hNRD6Osm24ju8aJXzfQC+jug+8NpLWJtZkhnS98MWTrrb2VEskE4o1dlmqp1zuStrjt9neje+hUpKRqOp6975JRJ4FJgIbRaTUlUZKgeBUdJXAwJDo5cB6F14eJtyYNknXC1+6PhsTT9x07IrdGaXrbzOowzMSESkEslS1xn3+JvBb4AVgCnCze3/eRXkBeExE/ojX2D4UWKCqfhGpEZFJwHzgEuDPHfttTFeTrhe+dE2X6Tjp/BtIRYlkP+BZ8UbwzAYeU9WXReR9YLaIXAasBc4BUNVlIjIbbxaFJuAK12ML4HL2dv+dgzW0G2NMh+vwjERVPwfGhAmvBk6MEOcm4KYw4QuBUe2dRmOMMfFr53FIjTHGZBrLSIwxxiTEMhJjjDEJsYzEGGNMQjJu9F8R+Qr4oo3R+wCbY27V8SxdrWPpar10TZulq3USSdcBqhp2ysaMy0gSISILI41+mUqWrtaxdLVeuqbN0tU6yUqXVW0ZY4xJiGUkxhhjEmIZSevcl+oERGDpah1LV+ula9osXa2TlHRZG4kxxpiEWInEGGNMQiwjMcYYkxDLSCIQkb+LyCYR+Sgk7AYR+VJElrjXaSlI10AReVNEVojIMhG52oX3FpHXRGSle++VJulK6TkTkXwRWSAiH7p03ejCU32+IqUr5b8xlw6fiCwWkRfdckrPV5R0pfx8icgaEalwx1/owlJ+viKkKynny9pIIhCRY4Ba4CFVHeXCbgBqVfW2FKarFChV1Q9EpAewCG+u+u8DW1T1ZhG5Duilqr9Kg3SdSwrPmXjzFRSqaq2I5ADvAlcDZ5Ha8xUpXaeQ4t+YS9/PgQlAkap+W0RuJYXnK0q6biD1/5NrgAmqujkkLOXnK0K6biAJ58tKJBGo6tvAllSnoyVVrVLVD9znGmAF3lz1ZwAz3WYz8S7i6ZCulFJPrVvMcS8l9ecrUrpSTkTKgW8BfwsJTun5gojpSlcpP18dyTKS1rtSRJa6qq+UFO+DRGQQMA5vhsj9VLUKvIs60C9N0gUpPmeuOmQJ3vTNr6lqWpyvCOmC1P/G/gT8EgiEhKX8fEVIF6T+fCnwqogsEpGpLiwdzle4dEESzpdlJK1zDzAYGAtUAbenKiEi0h14GrhGVXekKh0thUlXys+ZqvpVdSxQDkwUkbSYDC1CulJ6vkTk28AmVV3UkceNJUq6Uv77Ao5S1cOAU4ErXLV4OgiXrqScL8tIWkFVN7p//gBwPzAxFelwdepPA4+q6jMueKNrpwi2V2xKh3SlyzlzadkGzMVrh0j5+QqXrjQ4X0cBp7v69VnACSLyCKk/X2HTlQbnC1Vd7943Ac+6NKT6fIVNV7LOl2UkrRD8YThnAh9F2jaJaRBgBrBCVf8YsuoFYIr7PAV4Ph3SlepzJiJ9RaTYfS4AvgF8TOrPV9h0pfp8qeo0VS1X1UHA+cAbqnoxKT5fkdKV6vMlIoWucwkiUgh806Uh1b+vsOlK1vnq8DnbOwsReRw4DugjIpXA9cBxIjIWr+5xDfDjFCTtKOB7QIWrXwf4NXAzMFtELgPWAuekSbouSPE5KwVmiogP78Zptqq+KCLzSO35ipSuh9PgNxZOqn9fkdya4vO1H/Csdx9FNvCYqr4sIu+T2vMVKV1J+X1Z919jjDEJsaotY4wxCbGMxBhjTEIsIzHGGJMQy0iMMcYkxDISY4wxCbGMxBi8YV0kZKTnkPDfisg3YsS9QUR+kbzUGZPe7DkSY6JQ1f9OdRqMSXdWIjFmL5+I3C/e/CCvikiBiDwoImcDiMhpIvKxiLwrItPFzYnhjBCRuSLyuYhc5bb/ZcjnO0TkDff5RDfsCCJyj4gslOZzkpwoIs8GdywiJ4nIM7TgSkIzXVrXiMhZInKreHNQvOyGrAnOS3GLePOfLBCRIS58sIi8JyLvu5JXbctjGBMPy0iM2Wso8BdVHQlsA74bXCEi+cBfgVNV9Wigb4u4hwAn441ddL27iL8NfN2tnwB0d+FHA++48N+o6gTgUOBYETkUeAMYLiLBY1wKPBAhzYPxhlY/A3gEeFNVRwO7XHjQDlWdCNyFN4ouwJ3Anap6OLA++qkxJjLLSIzZa7WqLnGfFwGDQtYdAnyuqqvd8uMt4v5DVevdJEKb8IaoWASMd2Me1QPz8DKUr7M3IzlXRD4AFgMjgRHqDTfxMHCxG4/rCGBOhDTPUdVGoALwAS+78IoW6X885P0I9/kI4En3+bEI+zcmJmsjMWav+pDPfqAgZFlaGTdbVRvdaLWXAv8GlgLH45UiVojIgcAvgMNVdauIPAjku308APwfsBt4UlWbROQK4EdufXCK1HoAVQ2ISKPuHfMoQPP/b43w2ZiEWYnEmPh8DBwk3qRdAOfFGe9tvMzibbxSyE+AJe6CXwTUAdtFZD+8eSOAPUOArwf+H/CgC/uLqo51r9ZWRZ0X8j7PfX6PvdV357dyf8bsYSUSY+KgqrtE5KfAyyKyGVgQZ9R3gN8A81S1TkR2uzBU9UMRWQwsAz4H/tUi7qNAX1Vd3g5fIU9E5uPdPF7gwq4BHhGRa4F/ANvb4TgmA9nov8bESUS6q2qtm3vlL8BKVb0jice7C1isqjMS3M8aYIJrvwkN7wbsUlUVkfOBC1T1jESOZTKTlUiMid+PRGQKkIvXOP7XZB1IRBbhVXtdm6xjAOOBu1zGuA34QRKPZbowK5EYY4xJiDW2G2OMSYhlJMYYYxJiGYkxxpiEWEZijDEmIZaRGGOMScj/B41kdnX8dWerAAAAAElFTkSuQmCC\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": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 37,
     "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": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            11             10             9           8         7\n",
      "-1.243e-08 x  + 4.722e-06 x  - 0.0008028 x + 0.08056 x - 5.297 x\n",
      "          6        5             4             3             2\n",
      " + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \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')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "# Here we use a polynomial of the 11rd order (cubic) \n",
    "f1 = np.polyfit(x, y, 11)\n",
    "p1 = np.poly1d(f1)\n",
    "print(p1)\n",
    "PlotPolly(p1,x,y, 'Highway MPG')\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2) polynomial with two variables is given by:</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b\\_1 X\\_1 +b\\_2 X\\_2 +b\\_3 X\\_1 X\\_2+b\\_4 X\\_1^2+b\\_5 X\\_2^2\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can perform a polynomial transform on multiple features. First, we import the module:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a <b>PolynomialFeatures</b> object of degree 2:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_pr=pr.fit_transform(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the original data, there are 201 samples and 4 features.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the transformation, there are 201 samples and 15 features.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z_pr.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Pipeline</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Data Pipelines simplify the steps of processing the data. We use the module <b>Pipeline</b> to create a pipeline. We also use <b>StandardScaler</b> as a step in our pipeline.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create the pipeline by creating a list of tuples including the name of the model or estimator and its corresponding constructor.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We input the list as an argument to the pipeline constructor:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(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": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe=Pipeline(Input)\n",
    "pipe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we convert the data type Z to type float to avoid conversion warnings that may appear as a result of StandardScaler taking float inputs.\n",
    "\n",
    "Then, we can normalize the data,  perform a transform and fit the model simultaneously.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(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": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = Z.astype(float)\n",
    "pipe.fit(Z,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly,  we can normalize the data, perform a transform and produce a prediction  simultaneously.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #5:</h1>\n",
    "<b>Create a pipeline that standardizes the data, then produce a prediction using a linear regression model using the features Z and target y.</b>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13699.11161184, 13699.11161184, 19051.65470233, 10620.36193015,\n",
       "       15521.31420211, 13869.66673213, 15456.16196732, 15974.00907672,\n",
       "       17612.35917161, 10722.32509097])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 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": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python\n",
    "Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
    "\n",
    "pipe=Pipeline(Input)\n",
    "\n",
    "pipe.fit(Z,y)\n",
    "\n",
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:10]\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>4. Measures for In-Sample Evaluation</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n",
    "\n",
    "<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n",
    "<ul>\n",
    "    <li><b>R^2 / R-squared</b></li>\n",
    "    <li><b>Mean Squared Error (MSE)</b></li>\n",
    "</ul>\n",
    "\n",
    "<b>R-squared</b>\n",
    "\n",
    "<p>R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.</p>\n",
    "\n",
    "<p>The value of the R-squared is the percentage of variation of the response variable (y) that is explained by a linear model.</p>\n",
    "\n",
    "<b>Mean Squared Error (MSE)</b>\n",
    "\n",
    "<p>The Mean Squared Error measures the average of the squares of errors. That is, the difference between actual value (y) and the estimated value (ŷ).</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 1: Simple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.7609686443622008\n"
     ]
    }
   ],
   "source": [
    "#highway_mpg_fit\n",
    "lm.fit(X, Y)\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(X, Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that \\~49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\".\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output of the first four predicted value is:  [13728.4631336  13728.4631336  17399.38347881 10224.40280408]\n"
     ]
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "print('The output of the first four predicted value is: ', Yhat[0:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import the function <b>mean_squared_error</b> from the module <b>metrics</b>:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the predicted results with the actual results:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value is:  15021126.025174143\n"
     ]
    }
   ],
   "source": [
    "mse = mean_squared_error(df['price'], Yhat)\n",
    "print('The mean square error of price and predicted value is: ', mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 2: Multiple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.8093562806577457\n"
     ]
    }
   ],
   "source": [
    "# fit the model \n",
    "lm.fit(Z, df['price'])\n",
    "# Find the R^2\n",
    "print('The R-square is: ', lm.score(Z, df['price']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that \\~80.896 % of the variation of price is explained by this multiple linear regression \"multi_fit\".\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We produce a prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_predict_multifit = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We compare the predicted results with the actual results:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value using multifit is:  11980366.87072649\n"
     ]
    }
   ],
   "source": [
    "print('The mean square error of price and predicted value using multifit is: ', \\\n",
    "      mean_squared_error(df['price'], Y_predict_multifit))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 3: Polynomial Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let’s import the function <b>r2\\_score</b> from the module <b>metrics</b> as we are using a different function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We apply the function to get the value of R^2:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square value is:  0.674194666390652\n"
     ]
    }
   ],
   "source": [
    "r_squared = r2_score(y, p(x))\n",
    "print('The R-square value is: ', r_squared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that \\~67.419 % of the variation of price is explained by this polynomial fit.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>MSE</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the MSE:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20474146.426361214"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(df['price'], p(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>5. Prediction and Decision Making</h2>\n",
    "<h3>Prediction</h3>\n",
    "\n",
    "<p>In the previous section, we trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction. Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new input:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_input=np.arange(1, 100, 1).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the model:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X, Y)\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce a prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7796.47889059, -7629.6188749 , -7462.75885921, -7295.89884352,\n",
       "       -7129.03882782])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat=lm.predict(new_input)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the data:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAD4CAYAAADo30HgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8/fFQqAAAACXBIWXMAAAsTAAALEwEAmpwYAAApQ0lEQVR4nO3dd3xW9fn/8dfF3ntFQtgrDBXCUmttQcFRQdFvaR3YWmmtrdZ+q4A4q61orVbr6I9qVVqrUkBBxYlaR1nBkcUKQwh7E1bIuH5/3Id+bzAsc4d7vZ+PRx459+eck1xHYt45474+5u6IiIgcVCXaBYiISGxRMIiIyCEUDCIicggFg4iIHELBICIih6gW7QIqqlmzZt6uXbtolyEiElcWLly4xd2bl7cu7oOhXbt2ZGZmRrsMEZG4YmZfHWmdLiWJiMghFAwiInIIBYOIiBxCwSAiIodQMIiIyCEUDCIicggFg4iIHELBICISZ/YdKOX+NxdRsH1vpXz9uH+Dm4hIMvlP/hbGTc9m9ba9pDauw1UD20b8eygYRETiwM59xdw/axEvLVhDu6Z1eGnMQAZ2aFop30vBICIS497N28jtr2azubCIn57dgZvP7UKt6lUr7fspGEREYtSW3UXcPTOX17PW061Vff56dQa9UxtV+veNyM1nM7vZzHLNLMfMXjSzWmbWxMzeNbNlwefGYduPN7N8M1tiZkPDxvuaWXaw7jEzs0jUJyIST9ydVz4vYMjD/+ad3I3877ldmPmLs05KKEAEgsHMWgM3Ahnu3hOoCowCxgGz3b0zMDt4jZmlB+t7AMOAJ83s4DnRU8AYoHPwMayi9YmIxJN1O/bxo+cWcPPLX9K+WV3euPEsfjm4MzWqnbyHSCN1KakaUNvMioE6wDpgPHBOsP554ENgLDAceMndi4CVZpYP9DezVUADd58DYGaTgRHAmxGqUUQkZpWVOS/MX83EWYsoc7jjonSuOaMdVauc/AsnFQ4Gd19rZg8Bq4F9wDvu/o6ZtXT39cE2682sRbBLa2Bu2JcoCMaKg+XDx7/GzMYQOrMgLS2toocgIhJVK7fsYey0LOav3MZZnZpx/6W9aNOkTtTqqXAwBPcOhgPtgR3Av8zsyqPtUs6YH2X864Puk4BJABkZGeVuIyIS60pKy3j6k5U88u5SalSrwoMje3N5RirRvr0aiUtJQ4CV7r4ZwMymA2cAG80sJThbSAE2BdsXAG3C9k8ldOmpIFg+fFxEJOHkrdvF2GlZZK/dydAeLbl3eE9aNKgV7bKAyDyVtBoYaGZ1gqeIBgOLgJnA6GCb0cCMYHkmMMrMappZe0I3mecHl50KzWxg8HWuDttHRCQhFJWU8sd3lnDx45+wfuc+nryiD3+5sm/MhAJE5h7DPDObCnwGlACfE7rMUw+YYmbXEgqPy4Ptc81sCpAXbH+Du5cGX+564DmgNqGbzrrxLCIJY+FX2xk7LYv8Tbu5tE9r7rgwncZ1a0S7rK8x9/i+RJ+RkeGZmZnRLkNE5Ij2FJXw0DtLeO4/q0hpUIvfX9qLc7q2OPaOlcjMFrp7Rnnr9M5nEZFK9MmyLYybnkXB9n1cPagttw7rRr2asf2rN7arExGJUzv3FvO7WXlMySygQ7O6TPnpIPq3bxLtso6LgkFEJMLeytnAHTNy2LbnAD8/pyM3Du5cqU3vIk3BICISIZsK93P3zFxmZW8gPaUBz17Tj56tG0a7rBOmYBARqSB3Z/pna/nt63nsKy7llqFdGXN2B6pXjc9JMhUMIiIVULB9LxNeyeHfSzfTt21jHhjZm04t6kW7rApRMIiIfANlZc4/5n3FA28uxoF7Lu7BVQPbUiUKTe8iTcEgInKClm/ezbhpWSxYtZ2zuzTn95f0JLVx9JreRZqCQUTkOBWXljHpoxU8OnsZtatX5aHLT2Vkn9ZRb3oXaQoGEZHjkLN2J2OnZZG7bhcX9GrF3Rf3oEX92OlvFEkKBhGRo9hfXMpjs5fx/z5aQeM6NfjLlX0Y1jMl2mVVKgWDiMgRZK7axq3TslixeQ+X903l9gvTaVinerTLqnQKBhGRw+wpKuHBtxYzee5XnNKwNpN/3J+zuzSPdlknjYJBRCTMv5du5rbp2azbuY/Rg9pxy9Cu1I3xpneRllxHKyJyBDv2HuDe1xcx7bMCOjavy79+OoiMdvHR9C7SIvJ+bTNrZGZTzWyxmS0ys0Fm1sTM3jWzZcHnxmHbjzezfDNbYmZDw8b7mll2sO4xS7RnwEQkJr2ZvZ4hD3/Eq1+s5Rff6cQbN34raUMBIhQMwKPAW+7eDTiV0NSe44DZ7t4ZmB28xszSgVFAD2AY8KSZHWw7+BQwhtB0n52D9SIilWLTrv387O8Luf6Fz2jZoCYzf3EmvxnaNa46oVaGCl9KMrMGwNnANQDufgA4YGbDgXOCzZ4HPgTGAsOBl9y9CFhpZvlAfzNbBTRw9znB150MjEDTe4pIhLk7/1pYwH2v57G/pIyxw7px3bfaUy1Om95FWiTuMXQANgPPmtmpwELgJqClu68HcPf1ZnZwHrvWwNyw/QuCseJg+fDxrzGzMYTOLEhLS4vAIYhIslizbS/jp2fzSf4W+rdrwv0je9GxeXw3vYu0SARDNaAP8Et3n2dmjxJcNjqC8u4b+FHGvz7oPgmYBKE5n0+sXBFJRqVlzuQ5q3jwrSVUMbh3eA+uGJAYTe8iLRLBUAAUuPu84PVUQsGw0cxSgrOFFGBT2PZtwvZPBdYF46nljIuIVEj+pkJunZrFZ6t3cE7X5vzukl60blQ72mXFrApfUHP3DcAaM+saDA0G8oCZwOhgbDQwI1ieCYwys5pm1p7QTeb5wWWnQjMbGDyNdHXYPiIiJ6y4tIzH31/GBY9+woote3jk+6fy7DX9FArHEKn3MfwSeMHMagArgB8RCp0pZnYtsBq4HMDdc81sCqHwKAFucPfS4OtcDzwH1CZ001k3nkXkG8ku2MktU79k8YZCLuydwt3f60Hz+jWjXVZcMPf4vkSfkZHhmZmZ0S5DRGLE/uJSHnlvKU9/vJKmdWtw74ieDO3RKtplxRwzW+juGeWt0zufRSRhzFuxlXHTs1m5ZQ+j+rVh/AXdaVg78ZveRZqCQUTiXuH+Yh54azH/mLuaNk1q88JPBnBmp2bRLituKRhEJK59sGQTE6Zns37Xfq49qz3/e14X6tTQr7aK0H89EYlL2/Yc4N7X83jl87V0blGPadefQZ+0xsfeUY5JwSAiccXdeSN7PXfNyGXnvmJu/G4nbvhuJ2pWS+7+RpGkYBCRuLFx135ufzWHd/M20ju1If/4yQC6pzSIdlkJR8EgIjHP3Xl5wRp+N2sRB0rKuO2Cbvz4TDW9qywKBhGJaau37mXc9Cz+s3wrA9o34YGRvWnXrG60y0poCgYRiUmlZc6zn67koXeWUK1KFe4b0ZMf9k9T07uTQMEgIjFn6cZQ07sv1uzgu91a8LtLepLSUP2NThYFg4jEjAMlZTz14XIe/2AZ9WpW49FRp3HxqaegWX5PLgWDiMSEL9fsYOy0LBZvKGT4aadw50XpNK2npnfRoGAQkajad+Bg07sVtKhfi6evzmBIestol5XUFAwiEjVzlm9l/PQsVm3dyw/6pzH+gm40qKWmd9GmYBCRk27X/mImvrmYf85bTVqTOvzzugGc0VFN72JFxN4dYmZVzexzM3s9eN3EzN41s2XB58Zh2443s3wzW2JmQ8PG+5pZdrDuMdMdJ5GEM3vRRs57+CNemr+a677Vnrd/dbZCIcZE8m2DNwGLwl6PA2a7e2dgdvAaM0sHRgE9gGHAk2Z2sMnJU8AYQtN9dg7Wi0gC2Lq7iBtf/Jxrn8+kYe3qTP/5mUy4MJ3aNdTjKNZEJBjMLBW4EHg6bHg48Hyw/DwwImz8JXcvcveVQD7Q38xSgAbuPsdD08pNDttHROKUuzPji7Wc+8hHvJmznpuHdOG1X57FaW0aRbs0OYJI3WP4E3ArUD9srKW7rwdw9/Vm1iIYbw3MDduuIBgrDpYPH/8aMxtD6MyCtLS0CJQvIpVh/c593P5KDrMXb+LUNo14cGRvuraqf+wdJaoqHAxmdhGwyd0Xmtk5x7NLOWN+lPGvD7pPAiZBaM7n46tURE6WsjLnpQVruH/WIorLyrj9wu786Mz2VFU7i7gQiTOGM4GLzewCoBbQwMz+AWw0s5TgbCEF2BRsXwC0Cds/FVgXjKeWMy4icWTVlj2Mm57F3BXbGNShKRNH9qJtUzW9iycVvsfg7uPdPdXd2xG6qfy+u18JzARGB5uNBmYEyzOBUWZW08zaE7rJPD+47FRoZgODp5GuDttHRGJcSWkZkz5aztA/fUTu2l1MvLQX/7xugEIhDlXm+xgmAlPM7FpgNXA5gLvnmtkUIA8oAW5w99Jgn+uB54DawJvBh4jEuEXrdzF2WhZZBTsZ0r0l943oSauGtaJdlnxDFnoAKH5lZGR4ZmZmtMsQSUpFJaU88cFynvwgn4a1q3PP8B5c2CtFTe/igJktdPeM8tbpnc8i8o18tno7Y6dmsWzTbkacdgp3fq8HTerWiHZZEgEKBhE5IXsPlPDHd5byt09X0qpBLZ69ph/f6dbi2DtK3FAwiMhx+zR/C+OmZ7Fm2z6uGJDGuPO7UV9N7xKOgkFEjmnnvmLun7WIlxasoX2zurw8ZiADOjSNdllSSRQMInJU7+Ru4PZXc9i65wA//XYHbh7ShVrV1d8okSkYRKRcW3YXcffMXF7PWk+3VvV5ZnQ/eqU2jHZZchIoGETkEO7Oq1+s5Z7X8thbVMqvz+3Cz77dkRrVItmMWWKZgkFE/mvdjn1MeCWbD5Zspk9aIx4Y2ZvOLdX0LtkoGESEsjLnhfmrmThrEWUOd16Uzugz2qnpXZJSMIgkuRWbdzNuWjbzV23jW52b8ftLetGmSZ1olyVRpGAQSVIlpWU8/clKHnl3KTWrVeHBy3pzed9UtbMQBYNIMspbF2p6l712J0N7tOTe4T1p0UBN7yREwSCSRIpKSnn8/Xye+nA5jepU54kf9uGCXq10liCHUDCIJImFX21j7LRs8jftZmSfVG6/sDuN1fROyqFgEElwe4pK+MPbS3h+zipOaVib537Uj3O6qumdHFmF37FiZm3M7AMzW2RmuWZ2UzDexMzeNbNlwefGYfuMN7N8M1tiZkPDxvuaWXaw7jHT+a1IhXy8bDND//QRz89ZxdUD2/L2zWcrFOSYIvFWxhLgf929OzAQuMHM0oFxwGx37wzMDl4TrBsF9ACGAU+a2cHGK08BYwhN99k5WC8iJ2jn3mJu+deXXPXMfGpUq8KUnw7inuE9qVdTFwnk2Cr8UxLM1bw+WC40s0VAa2A4cE6w2fPAh8DYYPwldy8CVppZPtDfzFYBDdx9DoCZTQZGoOk9RU7IWzkbuGNGDtv2HODn53TkxsGd1fROTkhE/3wws3bA6cA8oGUQGrj7ejM7eP7aGpgbtltBMFYcLB8+Xt73GUPozIK0tLQIHoFI/NpUuJ+7Z+YyK3sD6SkNePaafvRsraZ3cuIiFgxmVg+YBvzK3Xcd5fZAeSv8KONfH3SfBEyC0JzPJ16tSOJwd6Z/tpbfvp7HvuJSbhnalTFnd6B6VTW9k28mIsFgZtUJhcIL7j49GN5oZinB2UIKsCkYLwDahO2eCqwLxlPLGReRIyjYvpfbXsnho6WbyWjbmIkje9OpRb1olyVxLhJPJRnwDLDI3R8OWzUTGB0sjwZmhI2PMrOaZtae0E3m+cFlp0IzGxh8zavD9hGRMGVlzuQ5qxj6yEdkrtrGPRf3YMpPBykUJCIiccZwJnAVkG1mXwRjtwETgSlmdi2wGrgcwN1zzWwKkEfoiaYb3L002O964DmgNqGbzrrxLHKY5Zt3M25aFgtWbVfTO6kU5h7fl+gzMjI8MzMz2mWIVLri0jL++vEK/vTeMmpXr8odF6Uzsk9rtbOQb8TMFrp7Rnnr9FCzSBzIWbuTW6dmkbd+F+f3bMU9w3vQor6a3knlUDCIxLD9xaU8OnsZkz5aQZO6NfjLlX0Y1jMl2mVJglMwiMSoBau2MXZqFiu27OHyvqncfmE6DetUj3ZZkgQUDCIxZndRCX94azGT537FKQ1r8/dr+/Otzs2jXZYkEQWDSAz5cMkmJrySw7qd+xg9qB23DO1KXfU3kpNMP3EiMWD7ngPc+0Ye0z9bS8fmdZn6s0H0bdsk2mVJklIwiESRu/NmzgbunJHDjr3F/OI7nfjl4E7UrKamdxI9CgaRKNm0az93zMjh7dyN9GrdkMk/HkD6KQ2iXZaIgkHkZHN3/rWwgPtez6OopIxx53fjJ2e1p5qa3kmMUDCInERrtu3ltley+XjZFvq3a8LEkb3o0Fz9jSS2KBhEToLSoOndg28toYrBvcN7cMWAtlSponYWEnsUDCKVbNnGQsZOy+Kz1Ts4p2tzfndJL1o3qh3tskSOSMEgUkmKS8v4y4fL+fP7+dSpWZVHvn8qI05T0zuJfQoGkUqQXbCTW6Z+yeINhVzUO4W7L+5Bs3o1o12WyHFRMIhE0P7iUh55byl//WgFzerVZNJVfTmvR6tolyVyQhQMIhEyb8VWxk3PZuWWPYzq14bxF3SnYW01vZP4E3PBYGbDgEeBqsDT7j4xyiWJHFXh/mIeeGsx/5i7mjZNavPCTwZwZqdm0S5L5BuLqWAws6rAE8C5QAGwwMxmuntedCsTKd8Hizdx2yvZbNy1n5+c1Z5fn9eFOjVi6n8rkRMWaz/B/YF8d18BYGYvAcMJzQ8tEjO27TnAva/n8crna+ncoh5PXn8Gp6c1jnZZIhERa8HQGlgT9roAGHD4RmY2BhgDkJaWdnIqEyHUzuKN7PXcNSOXnfuKuWlwZ37+nY5qeicJJdaCobwHvP1rA+6TgEkAGRkZX1svUhk27trP7a/m8G7eRnqnNuSF6wbQrZWa3kniibVgKADahL1OBdZFqRYRIHSW8PKCNfxu1iIOlJRx2wXd+PGZanoniSvWgmEB0NnM2gNrgVHAD6NbkiSz1Vv3Mm56Fv9ZvpUB7ZvwwMjetGtWN9pliVSqmAoGdy8xs18AbxN6XPVv7p4b5bIkCZWWOc9+upKH3llC9SpV+P0lvRjVr42a3klSiKlgAHD3WcCsaNchyWvpxkJunZrFF2t2MLhbC+67pCcpDdX0TpJHzAWDSLQcKCnjqQ+X8/gHy6hfqzqPjjqNi089RU3vJOkoGESAL9fs4NapWSzZWMjFp57CXd9Lp6ma3kmSUjBIUtt3oJSH313CM5+spEX9Wjx9dQZD0ltGuyyRqFIwSNL6z/ItjJ+ezVdb9/KD/mmMv6AbDWqp6Z2IgkGSzq79xdw/azEvzl9N26Z1ePG6gQzq2DTaZYnEDAWDJJX38jYy4dVsNhcWMebsDtw8pAu1a6idhUg4BYMkha27i7jntTxmfrmObq3qM+mqDE5t0yjaZYnEJAWDJDR3Z+aX67h7Zi67i0r49bld+Nm3O1KjmtpZiByJgkES1vqd+7j9lRxmL97EaW0a8eBlvenSsn60yxKJeQoGSThlZc6LC1Zz/6zFlJY5d1yUzjVntKOq2lmIHBcFgySUVVv2MG56FnNXbOPMTk25/5LepDWtE+2yROKKgkESQklpGX/7dCV/fGcpNapVYeKlvfh+vzZqZyHyDSgYJO4t3rCLW6dmkVWwk3PTW3LfiJ60bFAr2mWJxC0Fg8StopJSnvhgOU9+kE/D2tV5/Ienc2GvFJ0liFSQgkHi0mertzN2ahbLNu3mktNbc+dF6TSuWyPaZYkkhAo9zG1mfzCzxWaWZWavmFmjsHXjzSzfzJaY2dCw8b5mlh2se8yCP+/MrKaZvRyMzzOzdhWpTRLT3gMl/Pa1PEY+9R/2FJXw7DX9eOT7pykURCKoou/yeRfo6e69gaXAeAAzSyc0LWcPYBjwpJkd7DvwFDAG6Bx8DAvGrwW2u3sn4BHggQrWJgnm0/wtDP3TR/zt05VcOaAtb998Nt/p1iLaZYkknAoFg7u/4+4lwcu5QGqwPBx4yd2L3H0lkA/0N7MUoIG7z3F3ByYDI8L2eT5YngoMNl0sFmDnvmLGTs3iiqfnUa1KFV4eM5B7R/SkvjqhilSKSN5j+DHwcrDcmlBQHFQQjBUHy4ePH9xnDfx37uedQFNgy+HfyMzGEDrrIC0tLXJHIDHnndwN3P5qDlv3HOBn3+7Ir4Z0plZ1Nb0TqUzHDAYzew9oVc6qCe4+I9hmAlACvHBwt3K296OMH22frw+6TwImAWRkZJS7jcS3zYVF3P1aLm9krad7SgOeGd2PXqkNo12WSFI4ZjC4+5CjrTez0cBFwODg8hCEzgTahG2WCqwLxlPLGQ/fp8DMqgENgW3HcQySQNydV79Yyz2v5bG3qJTfnNeFn367I9WrqumdyMlSoUtJZjYMGAt82933hq2aCfzTzB4GTiF0k3m+u5eaWaGZDQTmAVcDfw7bZzQwB7gMeD8saCQJrN2xjwmvZPPhks30SQs1vevUQk3vRE62it5jeByoCbwb3Cee6+4/c/dcM5sC5BG6xHSDu5cG+1wPPAfUBt4MPgCeAf5uZvmEzhRGVbA2iRNlZc4L81czcdYiHLjre+lcPUhN70SixeL9j/KMjAzPzMyMdhnyDa3YvJtx07KZv2obZ3Vqxv2X9qJNEzW9E6lsZrbQ3TPKW6d3PktUlJSW8dePV/LIe0upVa0KD17Wm8v7pqqdhUgMUDDISZe3bhe3TvuSnLW7GNqjJfcO70kLNb0TiRkKBjlp9heX8vj7+fzl38tpVKcGT13Rh/N7pUS7LBE5jIJBToqFX23j1qlZLN+8h5F9Urnjou40qqP+RiKxSMEglWpPUQl/eHsJz89ZxSkNa/Pcj/pxTlf1NxKJZQoGqTQfLd3M+OnZrN2xj9GD2nLLsG7Uq6kfOZFYp/9LJeJ27i3m3jfymLqwgA7N6/Kvnw2iX7sm0S5LRI6TgkEi6q2c9dwxI5dtew7w83M6cuNgNb0TiTcKBomITYX7uWtGLm/mbCA9pQHPXtOPnq3V9E4kHikYpELcnWmfreXe1/PYV1zKLUO7MubsDmp6JxLHFAzyjRVs38v46dl8vGwLGW0bM3Fkbzq1qBftskSkghQMcsLKypzJc1bx4NtLALjn4h5cNbAtVdT0TiQhKBjkhORv2s24aVlkfrWds7s05/eX9CS1sZreiSQSBYMcl+LSMiZ9tIJH31tG7RpV+ePlp3Jpn9ZqeieSgBQMckw5a3dy69Qs8tbv4sJeKdx9cQ+a168Z7bJEpJJE5NERM/uNmbmZNQsbG29m+Wa2xMyGho33NbPsYN1jFvzJaWY1zezlYHyembWLRG3yze0vLuWBtxYz/IlP2by7iL9c2ZcnruijUBBJcBU+YzCzNsC5wOqwsXRCM7D1IDS153tm1iWYxe0pYAwwF5gFDCM0i9u1wHZ372Rmo4AHgO9XtD75Zhas2sbYqVms2LKH/8lIZcIF6TSsUz3aZYnISRCJM4ZHgFuB8KnghgMvuXuRu68E8oH+ZpYCNHD3OcF8zpOBEWH7PB8sTwUGmy5gn3S7i0q4c0YOl/9lDgdKy/jHtQN48LJTFQoiSaRCZwxmdjGw1t2/POx3eGtCZwQHFQRjxcHy4eMH91kD4O4lZrYTaApsKef7jiF01kFaWlpFDkHCfLhkE7dNz2b9rv386Mx2/Oa8rtRV0zuRpHPM/+vN7D2gVTmrJgC3AeeVt1s5Y36U8aPt8/VB90nAJAjN+VzeNnL8tu85wL2v5zH987V0alGPqT87g75tG0e7LBGJkmMGg7sPKW/czHoB7YGDZwupwGdm1p/QmUCbsM1TgXXBeGo544TtU2Bm1YCGwLYTORg5Me7OrOwN3DUzhx17i7nxu5244budqFlNTe9Ektk3vk7g7tnAf2dcMbNVQIa7bzGzmcA/zexhQjefOwPz3b3UzArNbCAwD7ga+HPwJWYCo4E5wGXA+8F9CKkEm3bt544ZObydu5FerRvy92sH0D2lQbTLEpEYUCkXkN0918ymAHlACXBD8EQSwPXAc0BtQk8jvRmMPwP83czyCZ0pjKqM2pKdu/OvhQXc93oeRSVljD+/G9ee1Z5qanonIgGL9z/KMzIyPDMzM9plxIU120JN7z7J30L/9k14YGRv2jerG+2yRCQKzGyhu2eUt06PnCSB0oNN795aQtUqxr0jenJF/zQ1vRORcikYEtyyjYWMnZbFZ6t3cE7X5vz+kl6c0qh2tMsSkRimYEhQxaVl/OXD5fz5/Xzq1qzKI98/lRGnqemdiBybgiEBZRXs4NapWSzeUMj3Tj2Fu76XTrN66m8kIsdHwZBA9heX8si7S/nrxytoXr8mk67qy3k9yntvoojIkSkYEsTcFVsZNy2LVVv38oP+bRh3fnca1lZ/IxE5cQqGOFe4v5iJby7mhXmrSWtSh3/+ZABndGp27B1FRI5AwRDH3l+8kQmv5LBx135+clZ7fn1eF+rU0D+piFSMfovEoW17DvDb13J59Yt1dG5RjyeuP4M+aWp6JyKRoWCII+7Oa1nruXtmLrv2FXPT4M78/Dsd1fRORCJKwRAnNuzcz+2vZvPeok2cmtqQB64bQLdWanonIpGnYIhx7s5LC9bw+zcWUVxWxoQLuvPjs9pTVe0sRKSSKBhi2Fdb9zBuWjZzVmxlYIcmTLy0N+3U9E5EKpmCIQaVljnPfrqSh95ZQvUqVbj/0l6M6tdG7SxE5KRQMMSYJRsKuXVaFl+u2cGQ7i24b0QvWjWsFe2yRCSJVHh2FjP7pZktMbNcM3swbHy8meUH64aGjfc1s+xg3WMW/BlsZjXN7OVgfJ6ZtatobfHkQEkZf3pvKRf9+WPWbNvLYz84nb9enaFQEJGTrkJnDGb2HWA40Nvdi8ysRTCeTmgGth6EpvZ8z8y6BLO4PQWMAeYCs4BhhGZxuxbY7u6dzGwU8ADw/YrUFy++WLODsVOzWLKxkOGnncJd3+tBk7o1ol2WiCSpil5Kuh6Y6O5FAO6+KRgfDrwUjK8MpuvsH8wL3cDd5wCY2WRgBKFgGA7cHew/FXjczCyR533ed6CUh99dwjOfrKRF/Vo8MzqDwd1bRrssEUlyFQ2GLsC3zOx3wH7gN+6+AGhN6IzgoIJgrDhYPnyc4PMaAHcvMbOdQFNgy+Hf1MzGEDrrIC0trYKHEB3/Wb6FcdOyWb1tL1cMSGPs+d1oUEtN70Qk+o4ZDGb2HlBe7+YJwf6NgYFAP2CKmXUAynt8xo8yzjHWHTroPgmYBKE5n49Wf6zZtb+Y+2ct5sX5q2nXtA4vXjeQQR2bRrssEZH/OmYwuPuQI60zs+uB6cHlnvlmVgY0I3Qm0CZs01RgXTCeWs44YfsUmFk1oCGw7fgPJfa9l7eRCa9ms7mwiDFnd+DmIV2oXUPtLEQktlT0qaRXge8CmFkXoAahSz8zgVHBk0btgc7AfHdfDxSa2cDgaaSrgRnB15oJjA6WLwPeT5T7C1t3F/HLFz/nJ5MzaVynBq/ecCa3XdBdoSAiMami9xj+BvzNzHKAA8Do4Jd5rplNAfKAEuCG4IkkCN2wfg6oTeim85vB+DPA34Mb1dsIPdUU19ydmV+u4+6ZuewuKuHmIV24/pyO1KhW4aeERUQqjcX7H+UZGRmemZkZ7TK+Zv3Ofdz+Sg6zF2/i9LRGPDiyN51b1o92WSIiAJjZQnfPKG+d3vkcYWVlzj/nr2bim4spLXPuvCid0We0U9M7EYkbCoYIWrllD+OmZTFv5TbO7NSU+y/pTVrTOtEuS0TkhCgYIqCktIxnPlnJw+8upUa1Kjwwshf/k6GmdyISnxQMFbRo/S7GTssiq2An56a35L4RPWnZQP2NRCR+KRi+oaKSUp54P58nP1xOw9rVefyHp3NhrxSdJYhI3FMwfAOfrd7O2KlZLNu0mxGnncKdanonIglEwXAC9h4o4aG3l/Lsf1aS0qAWz17Tj+90axHtskREIkrBcJw+zd/CuOlZrNm2j6sGtuXWYV2pr6Z3IpKAFAzHsHNfMb97I48pmQW0b1aXl8cMZEAHNb0TkcSlYDiKt3M3cMerOWzdc4Drz+nITYM7U6u6+huJSGJTMJRjc2ERd7+WyxtZ6+me0oBnRvejV2rDaJclInJSKBjCuDuvfL6W376ex96iUm4Z2pUxZ3egelU1vROR5KFgCKzdsY/bpmfz76Wb6ZPWiAcv602nFmp6JyLJJ+mDoazM+ce8r3jgzcU4cNf30rl6kJreiUjySupgWL55N+OmZbFg1Xa+1bkZv7+kF22aqOmdiCS3Cl08N7PTzGyumX1hZplm1j9s3XgzyzezJWY2NGy8r5llB+seC2ZyI5jt7eVgfJ6ZtatIbccyZcEazn/0Y5ZsKOTBy3oz+cf9FQoiIlR8as8HgXvc/TTgzuA1ZpZOaAa2HsAw4EkzO/ic51PAGELTfXYO1gNcC2x3907AI8ADFaztqNo3r8vgbi1479ffVidUEZEwFb2U5ECDYLkhsC5YHg685O5FwMpgus7+ZrYKaODucwDMbDIwgtD0nsOBu4P9pwKPm5lV1rzP/do1oV+7JpXxpUVE4lpFg+FXwNtm9hChs48zgvHWwNyw7QqCseJg+fDxg/usAXD3EjPbCTQFthz+Tc1sDKGzDtLS0ip4CCIiEu6YwWBm7wGtylk1ARgM3Ozu08zsf4BngCFAeddl/CjjHGPdoYPuk4BJEJrz+agHICIiJ+SYweDuQ460LrgUdFPw8l/A08FyAdAmbNNUQpeZCoLlw8fD9ykws2qELk1tO/YhiIhIJFX05vM64NvB8neBZcHyTGBU8KRRe0I3mee7+3qg0MwGBk8jXQ3MCNtndLB8GfB+Zd1fEBGRI6voPYbrgEeDv/D3E1z3d/dcM5sC5AElwA3uXhrscz3wHFCb0E3nN4PxZ4C/BzeqtxF6qklERE4yi/c/yjMyMjwzMzPaZYiIxBUzW+juGeWtU3c4ERE5hIJBREQOEfeXksxsM/DVCezSjHLeG5EEdNzJJ1mPXcd9fNq6e/PyVsR9MJwoM8s80nW1RKbjTj7Jeuw67orTpSQRETmEgkFERA6RjMEwKdoFRImOO/kk67HruCso6e4xiIjI0SXjGYOIiByFgkFERA6RVMFgZsOCqUbzzWxctOupLGbWxsw+MLNFZpZrZjcF403M7F0zWxZ8bhztWiPNzKqa2edm9nrwOuGPGcDMGpnZVDNbHPy7D0qGYzezm4Of8Rwze9HMaiXicZvZ38xsk5nlhI0d8TiPNLXy8UqaYAimFn0COB9IB34QTEGaiEqA/3X37sBA4IbgWMcBs929MzA7eJ1obgIWhb1OhmMGeBR4y927AacS+m+Q0MduZq2BG4EMd+8JVCXUfDMRj/s5/m8a5IPKPc5jTK18XJImGID+QL67r3D3A8BLhKYTTTjuvt7dPwuWCwn9kmhN6HifDzZ7ntC0qgnDzFKBC/m/eUEgwY8ZwMwaAGcT6lCMux9w9x0kwbET6hBdO+jwXIfQVAAJd9zu/hFfn5/mSMf536mV3X0lkE/o999xS6Zg+O/UoYHwaUUTlpm1A04H5gEtgzkxCD63iGJpleFPwK1AWdhYoh8zQAdgM/BscBntaTOrS4Ifu7uvBR4CVgPrgZ3u/g4JftxhjnScFf5dl0zBcNxThyYKM6sHTAN+5e67ol1PZTKzi4BN7r4w2rVEQTWgD/CUu58O7CExLp8cVXBNfTjQHjgFqGtmV0a3qphQ4d91yRQMR5puNCGZWXVCofCCu08PhjeaWUqwPgXYFK36KsGZwMVmtorQZcLvmtk/SOxjPqgAKHD3ecHrqYSCItGPfQiw0t03u3sxMB04g8Q/7oOOdJwV/l2XTMGwAOhsZu3NrAahmzMzo1xTpQimTX0GWOTuD4etCp8+dTT/N61q3HP38e6e6u7tCP3bvu/uV5LAx3yQu28A1phZ12BoMKHZExP92FcDA82sTvAzP5jQ/bREP+6DjnSc5U6tfEJf2d2T5gO4AFgKLAcmRLueSjzOswidOmYBXwQfFwBNCT29sCz43CTatVbS8Z8DvB4sJ8sxnwZkBv/mrwKNk+HYgXuAxUAO8HegZiIeN/AiofsoxYTOCK492nECE4Lfc0uA80/0+6klhoiIHCKZLiWJiMhxUDCIiMghFAwiInIIBYOIiBxCwSAiIodQMIiIyCEUDCIicoj/D004giL15DQmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(new_input, yhat)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Decision Making: Determining a Good Model Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now that we have visualized the different models, and generated the R-squared and MSE values for the fits, how do we determine a good model fit?\n",
    "<ul>\n",
    "    <li><i>What is a good R-squared value?</i></li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>When comparing models, <b>the model with the higher R-squared value is a better fit</b> for the data.\n",
    "<ul>\n",
    "    <li><i>What is a good MSE?</i></li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>When comparing models, <b>the model with the smallest MSE value is a better fit</b> for the data.</p>\n",
    "\n",
    "<h4>Let's take a look at the values for the different models.</h4>\n",
    "<p>Simple Linear Regression: Using Highway-mpg as a Predictor Variable of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.49659118843391759</li>\n",
    "    <li>MSE: 3.16 x10^7</li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>Multiple Linear Regression: Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.80896354913783497</li>\n",
    "    <li>MSE: 1.2 x10^7</li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>Polynomial Fit: Using Highway-mpg as a Predictor Variable of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.6741946663906514</li>\n",
    "    <li>MSE: 2.05 x 10^7</li>\n",
    "</ul>\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Regression Model (SLR) vs Multiple Linear Regression Model (MLR)</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Usually, the more variables you have, the better your model is at predicting, but this is not always true. Sometimes you may not have enough data, you may run into numerical problems, or many of the variables may not be useful and even act as noise. As a result, you should always check the MSE and R^2.</p>\n",
    "\n",
    "<p>In order to compare the results of the MLR vs SLR models, we look at a combination of both the R-squared and MSE to make the best conclusion about the fit of the model.\n",
    "<ul>\n",
    "    <li><b>MSE</b>: The MSE of SLR is  3.16x10^7  while MLR has an MSE of 1.2 x10^7.  The MSE of MLR is much smaller.</li>\n",
    "    <li><b>R-squared</b>: In this case, we can also see that there is a big difference between the R-squared of the SLR and the R-squared of the MLR. The R-squared for the SLR (~0.497) is very small compared to the R-squared for the MLR (~0.809).</li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "This R-squared in combination with the MSE show that MLR seems like the better model fit in this case compared to SLR.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Model (SLR) vs. Polynomial Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li><b>MSE</b>: We can see that Polynomial Fit brought down the MSE, since this MSE is smaller than the one from the SLR.</li> \n",
    "    <li><b>R-squared</b>: The R-squared for the Polynomial Fit is larger than the R-squared for the SLR, so the Polynomial Fit also brought up the R-squared quite a bit.</li>\n",
    "</ul>\n",
    "<p>Since the Polynomial Fit resulted in a lower MSE and a higher R-squared, we can conclude that this was a better fit model than the simple linear regression for predicting \"price\" with \"highway-mpg\" as a predictor variable.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression (MLR) vs. Polynomial Fit</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li><b>MSE</b>: The MSE for the MLR is smaller than the MSE for the Polynomial Fit.</li>\n",
    "    <li><b>R-squared</b>: The R-squared for the MLR is also much larger than for the Polynomial Fit.</li>\n",
    "</ul>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Conclusion</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing these three models, we conclude that <b>the MLR model is the best model</b> to be able to predict price from our dataset. This result makes sense since we have 27 variables in total and we know that more than one of those variables are potential predictors of the final car price.</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thank you for completing this lab!\n",
    "\n",
    "## Author\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Joseph Santarcangelo</a>\n",
    "\n",
    "### Other Contributors\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
    "\n",
    "Bahare Talayian\n",
    "\n",
    "Eric Xiao\n",
    "\n",
    "Steven Dong\n",
    "\n",
    "Parizad\n",
    "\n",
    "Hima Vasudevan\n",
    "\n",
    "<a href=\"https://www.linkedin.com/in/fiorellawever/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Fiorella Wenver</a>\n",
    "\n",
    "<a href=\"https:// https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "## Change Log\n",
    "\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description                            |\n",
    "| ----------------- | ------- | ---------- | --------------------------------------------- |\n",
    "| 2020-10-30        | 2.2     | Lakshmi    | Changed url of csv                            |\n",
    "| 2020-09-09        | 2.1     | Lakshmi    | Fixes made in Polynomial Regression Equations |\n",
    "| 2020-08-27        | 2.0     | Lavanya    | Moved lab to course repo in GitLab            |\n",
    "\n",
    "<hr>\n",
    "\n",
    "## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python",
   "language": "python",
   "name": "conda-env-python-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}