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model-development.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center>\n",
" <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/Logos/organization_logo/organization_logo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\" />\n",
"</center>\n",
"\n",
"# Model Development\n",
"\n",
"Estimated time needed: **30** minutes\n",
"\n",
"## Objectives\n",
"\n",
"After completing this lab you will be able to:\n",
"\n",
"- Develop prediction models\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>In this section, we will develop several models that will predict the price of the car using the variables or features. This is just an estimate but should give us an objective idea of how much the car should cost.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some questions we want to ask in this module\n",
"\n",
"<ul>\n",
" <li>do I know if the dealer is offering fair value for my trade-in?</li>\n",
" <li>do I know if I put a fair value on my car?</li>\n",
"</ul>\n",
"<p>Data Analytics, we often use <b>Model Development</b> to help us predict future observations from the data we have.</p>\n",
"\n",
"<p>A Model will help us understand the exact relationship between different variables and how these variables are used to predict the result.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Setup</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Import libraries\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"load data and store in dataframe df:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"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": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# path of data \n",
"path = 'https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
"df = pd.read_csv(path)\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>1. Linear Regression and Multiple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Linear Regression</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>One example of a Data Model that we will be using is</p>\n",
"<b>Simple Linear Regression</b>.\n",
"\n",
"<br>\n",
"<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n",
"<ul>\n",
" <li>The predictor/independent variable (X)</li>\n",
" <li>The response/dependent variable (that we want to predict)(Y)</li>\n",
"</ul>\n",
"\n",
"<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
" Y: Response \\\\ Variable\\\\\n",
" X: Predictor \\\\ Variables\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" <b>Linear function:</b>\n",
"$$\n",
"Yhat = a + b X\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<ul>\n",
" <li>a refers to the <b>intercept</b> of the regression line0, in other words: the value of Y when X is 0</li>\n",
" <li>b refers to the <b>slope</b> of the regression line, in other words: the value with which Y changes when X increases by 1 unit</li>\n",
"</ul>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Lets load the modules for linear regression</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.linear_model import LinearRegression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Create the linear regression object</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm = LinearRegression()\n",
"lm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>How could Highway-mpg help us predict car price?</h4>\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": 5,
"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": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(X,Y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" We can output a prediction \n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
" 20345.17153508])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Yhat=lm.predict(X)\n",
"Yhat[0:5] "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>What is the value of the intercept (a)?</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"38423.3058581574"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>What is the value of the Slope (b)?</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([-821.73337832])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>What is the final estimated linear model we get?</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we saw above, we should get a final linear model with the structure:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b X\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plugging in the actual values we get:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b>price</b> = 38423.31 - 821.73 x <b>highway-mpg</b>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 a): </h1>\n",
"\n",
"<b>Create a linear regression object?</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lr = LinearRegression()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"lm1 = LinearRegression()\n",
"lm1 \n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1> Question #1 b): </h1>\n",
"\n",
"<b>Train the model using 'engine-size' as the independent variable and 'price' as the dependent variable?</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"X= df[['engine-size']]\n",
"Y = df['price']\n",
"lr.fit(X,Y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"lm1.fit(df[['engine-size']], df[['price']])\n",
"lm1\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 c):</h1>\n",
"\n",
"<b>Find the slope and intercept of the model?</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Slope</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([166.86001569])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lr.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Intercept</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-7963.338906281042"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lr.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"# Slope \n",
"lm1.coef_\n",
"# Intercept\n",
"lm1.intercept_\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 d): </h1>\n",
"\n",
"<b>What is the equation of the predicted line. You can use x and yhat or 'engine-size' or 'price'?</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"#yhat = -7963.34 + 166*x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"# using X and Y \n",
"Yhat=-7963.34 + 166.86*X\n",
"\n",
"Price=-7963.34 + 166.86*engine-size\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Multiple Linear Regression</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>What if we want to predict car price using more than one variable?</p>\n",
"\n",
"<p>If we want to use more variables in our model to predict car price, we can use <b>Multiple Linear Regression</b>.\n",
"Multiple Linear Regression is very similar to Simple Linear Regression, but this method is used to explain the relationship between one continuous response (dependent) variable and <b>two or more</b> predictor (independent) variables.\n",
"Most of the real-world regression models involve multiple predictors. We will illustrate the structure by using four predictor variables, but these results can generalize to any integer:</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Y: Response \\\\ Variable\\\\\n",
"X_1 :Predictor\\\\ Variable \\\\ 1\\\\\n",
"X_2: Predictor\\\\ Variable \\\\ 2\\\\\n",
"X_3: Predictor\\\\ Variable \\\\ 3\\\\\n",
"X_4: Predictor\\\\ Variable \\\\ 4\\\\\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"a: intercept\\\\\n",
"b_1 :coefficients \\\\ of\\\\ Variable \\\\ 1\\\\\n",
"b_2: coefficients \\\\ of\\\\ Variable \\\\ 2\\\\\n",
"b_3: coefficients \\\\ of\\\\ Variable \\\\ 3\\\\\n",
"b_4: coefficients \\\\ of\\\\ Variable \\\\ 4\\\\\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The equation is given by\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>From the previous section we know that other good predictors of price could be:</p>\n",
"<ul>\n",
" <li>Horsepower</li>\n",
" <li>Curb-weight</li>\n",
" <li>Engine-size</li>\n",
" <li>Highway-mpg</li>\n",
"</ul>\n",
"Let's develop a model using these variables as the predictor variables.\n"
]
},
{
"cell_type": "code",
"execution_count": 35,
"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": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 36,
"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": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-15806.62462632922"
]
},
"execution_count": 37,
"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": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([53.49574423, 4.70770099, 81.53026382, 36.05748882])"
]
},
"execution_count": 38,
"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": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"B = df[['normalized-losses', 'highway-mpg']]\n",
"lm2 = LinearRegression()\n",
"lm2.fit(B, df['price'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"lm2 = LinearRegression()\n",
"lm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #2 b): </h1>\n",
"<b>Find the coefficient of the model?</b>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.49789586, -820.45434016])"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"lm2.coef_\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>2) Model Evaluation using Visualization</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we've developed some models, how do we evaluate our models and how do we choose the best one? One way to do this is by using visualization.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"import the visualization package: seaborn\n"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"# import the visualization package: seaborn\n",
"import seaborn as sns\n",
"%matplotlib inline "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Regression Plot</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>When it comes to simple linear regression, an excellent way to visualize the fit of our model is by using <b>regression plots</b>.</p>\n",
"\n",
"<p>This plot will show a combination of a scattered data points (a <b>scatter plot</b>), as well as the fitted <b>linear regression</b> line going through the data. This will give us a reasonable estimate of the relationship between the two variables, the strength of the correlation, as well as the direction (positive or negative correlation).</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Let's visualize **highway-mpg** as potential predictor variable of price:\n"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 48267.27106984383)"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"width = 12\n",
"height = 10\n",
"plt.figure(figsize=(width, height))\n",
"sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\n",
"plt.ylim(0,)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can see from this plot that price is negatively correlated to highway-mpg, since the regression slope is negative.\n",
"One thing to keep in mind when looking at a regression plot is to pay attention to how scattered the data points are around the regression line. This will give you a good indication of the variance of the data, and whether a linear model would be the best fit or not. If the data is too far off from the line, this linear model might not be the best model for this data. Let's compare this plot to the regression plot of \"peak-rpm\".</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 47414.1)"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(width, height))\n",
"sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
"plt.ylim(0,)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Comparing the regression plot of \"peak-rpm\" and \"highway-mpg\" we see that the points for \"highway-mpg\" are much closer to the generated line and on the average decrease. The points for \"peak-rpm\" have more spread around the predicted line, and it is much harder to determine if the points are decreasing or increasing as the \"highway-mpg\" increases.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #3:</h1>\n",
"<b>Given the regression plots above is \"peak-rpm\" or \"highway-mpg\" more strongly correlated with \"price\". Use the method \".corr()\" to verify your answer.</b>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 30,
"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": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"df[['peak-rpm', 'highway-mpg', 'price']].corr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692 compared to \"peak-rpm\" which is approximate -0.101616. You can verify it using the following command:\n",
"df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Residual Plot</h3>\n",
"\n",
"<p>A good way to visualize the variance of the data is to use a residual plot.</p>\n",
"\n",
"<p>What is a <b>residual</b>?</p>\n",
"\n",
"<p>The difference between the observed value (y) and the predicted value (Yhat) is called the residual (e). When we look at a regression plot, the residual is the distance from the data point to the fitted regression line.</p>\n",
"\n",
"<p>So what is a <b>residual plot</b>?</p>\n",
"\n",
"<p>A residual plot is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n",
"\n",
"<p>What do we pay attention to when looking at a residual plot?</p>\n",
"\n",
"<p>We look at the spread of the residuals:</p>\n",
"\n",
"<p>- If the points in a residual plot are <b>randomly spread out around the x-axis</b>, then a <b>linear model is appropriate</b> for the data. Why is that? Randomly spread out residuals means that the variance is constant, and thus the linear model is a good fit for this data.</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"width = 12\n",
"height = 10\n",
"plt.figure(figsize=(width, height))\n",
"sns.residplot(df['highway-mpg'], df['price'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<i>What is this plot telling us?</i>\n",
"\n",
"<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, which leads us to believe that maybe a non-linear model is more appropriate for this data.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Multiple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n",
"\n",
"<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>: We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First lets make a prediction \n"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"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": [
"plt.figure(figsize=(width, height))\n",
"\n",
"\n",
"ax1 = sns.distplot(df['price'], hist=False, color=\"r\", label=\"Actual Value\")\n",
"sns.distplot(Y_hat, hist=False, color=\"b\", label=\"Fitted Values\" , ax=ax1)\n",
"\n",
"\n",
"plt.title('Actual vs Fitted Values for Price')\n",
"plt.xlabel('Price (in dollars)')\n",
"plt.ylabel('Proportion of Cars')\n",
"\n",
"plt.show()\n",
"plt.close()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can see that the fitted values are reasonably close to the actual values, since the two distributions overlap a bit. However, there is definitely some room for improvement.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 3: Polynomial Regression and Pipelines</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p><b>Polynomial regression</b> is a particular case of the general linear regression model or multiple linear regression models.</p> \n",
"<p>We get non-linear relationships by squaring or setting higher-order terms of the predictor variables.</p>\n",
"\n",
"<p>There are different orders of polynomial regression:</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center><b>Quadratic - 2nd order</b></center>\n",
"$$\n",
"Yhat = a + b_1 X +b_2 X^2 \n",
"$$\n",
"\n",
"<center><b>Cubic - 3rd order</b></center>\n",
"$$\n",
"Yhat = a + b_1 X +b_2 X^2 +b_3 X^3\\\\\n",
"$$\n",
"\n",
"<center><b>Higher order</b>:</center>\n",
"$$\n",
"Y = a + b_1 X +b_2 X^2 +b_3 X^3 ....\\\\\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We saw earlier that a linear model did not provide the best fit while using highway-mpg as the predictor variable. Let's see if we can try fitting a polynomial model to the data instead.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We will use the following function to plot the data:</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [],
"source": [
"def PlotPolly(model, independent_variable, dependent_variabble, Name):\n",
" x_new = np.linspace(15, 55, 100)\n",
" y_new = model(x_new)\n",
"\n",
" plt.plot(independent_variable, dependent_variabble, '.', x_new, y_new, '-')\n",
" plt.title('Polynomial Fit with Matplotlib for Price ~ Length')\n",
" ax = plt.gca()\n",
" ax.set_facecolor((0.898, 0.898, 0.898))\n",
" fig = plt.gcf()\n",
" plt.xlabel(Name)\n",
" plt.ylabel('Price of Cars')\n",
"\n",
" plt.show()\n",
" plt.close()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"lets get the variables\n"
]
},
{
"cell_type": "code",
"execution_count": 42,
"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": 43,
"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": 44,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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9KFz2GPUHHJ/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": 45,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.55663829e+00, 2.04754306e+02, -8.96543312e+03, 1.37923594e+05])"
]
},
"execution_count": 45,
"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": 47,
"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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VDTmVtKrVrC1bSmNACSo0BpTF5dWJDs0YY+LGEk0M7R56CoowWd8lzSekCKT5hHGlOYkOzRhj4saazmIo2Ksfjf0PZ0jF69xx7rdYXF7NuNIcazYzxvQolmhirG7oqeS9cxuHZ29n9JGDWt/AGGO6GWs6i7HdQ04FIGvViwmOxBhjEsMSTYwFckupL5lE7w/vR3bvSHQ4xhgTd5Zo4qDqC9ciDTXkLvy/RIdijDFxZ4kmDvyFB1M74iv0WvEkqdui3a3aGGO6H0s0cVI94SqCGXnkvX1zl5r/zGY0MMZ0lCWaOPloeyov972UjI0LySp7IdHhtMmSjbVc/exK7n1nI1c/u9KSjTFmv1iiiYOmE/b3ysaxWIeT+/r1pG9YkOiwWrW4vNpmNDDGdFjCE42I+ERksYi84JYLRWSOiKx0vwtC1r1WRMpE5BMROT2kfLyILHHP3SEi4sozRORJV/6uiAyJ+xtk7wnbryn8T8OP2J4+gMIXryBt8+JEhNNm40pzbEYDY0yHJTzRANcAK0KWfw68qqrDgVfdMiIyApgGjASmAHeJiM9tczdwOTDc/Uxx5ZcBO1R1GHA7cGts30pkoSfsal8eS4/7G8FefSia/W3Sti5LREhtMro4mzvOHc7lk4ptIlBjzH5LaKIRkVLgTODvIcXnADPc4xnA1JDyJ1S1XlVXA2XARBEpBnJVdb6qKvBQ2DZN+3oaOLmpthNP4SfsQ4YewLazHiCYnkPRC5eQsfb1eIfUZqOLs7nkyAGWZIwx+y3RNZo/Az8FgiFl/VV1I4D73c+VlwDrQtYrd2Ul7nF4ebNtVNUPVAFF4UGIyOUislBEFm7btq2Dbymy8BN2oPdAKs5+FH/uARS+9F2ylzzUpUajGWNMWyUs0YjIWcAWVV3U1k0ilGmU8mjbNC9QvVdVJ6jqhKKiffJQzAR7D2Db2Y+w+4ATyZv/O/Le+jUEA3F7fWOMiYdE1miOAc4WkTXAE8BJIvIIsNk1h+F+b3HrlwOhs1KWAhtceWmE8mbbiEgqkAdsj8Wb2V+a1osdp95BzZhLyV7+OAWv/ggCDYkOyxhjOk3CEo2qXquqpao6BK+Tf66qXgzMAqa71aYDz7vHs4BpbiTZULxO/wWuea1aRCa5/pdLwrZp2tf57jWSr31KUtg56SdUTfoZWatfomj2t5GGmkRHZYwxnSLRfTSR3AKcKiIrgVPdMqq6DJgJLAdeBK5U1aZ2pivwBhSUAZ8Bs135/UCRiJQBP8SNYEtWtWO+wY4TbyV940KK/n0p0mAXSBpjuj5Jxi/4iTR27FidPXt26yvGUMaauRTOuZr6kklsP/0u8KUnNB5jjGlNSUnJIlWdEOm5ZKzR9Hj1Q06i8vibyCx/i/zXrwMNtr5RFMk6X1myxmWM6Vx2h80kVXfIefh2bSX3vT8T7NWXnZN+sl/7aZr+pjGgpPk2Jc2Fl8kalzGm81mNJonVHH45tSO+Su+P/kHmqpf2ax/JOl9ZssZljOl8lmiSRMRmJBGqjv45Df3Gkv/6dfh2rm33fpN1vrJkjcsY0/lsMECYRAwGaN6MJPs0I/mq19P3mS/jzyml4pzH9hkcsGRjLYvLqxlXmhOx+am15xMlWeMyxrRftMEA1keTBCI1I4WeeD+oyadm4I/58urryX33D+w8+hd7nmtLX8fo4uykPJEna1zGmM5lTWdJIFozUlMi+cnHBzEjOIXeSx8mff38Pc9bX4cxJtlZokkC0abjD00ktzROY3tGKflv3IA07gKsr8MYk/ys6SxJtNSMNK40B1/KJjSg+FMyKBv/Sya+fTk5C+9g5xd+vidJdcW+DuujMaZnsETTJeie3zuKjqD2sIvIXvIQdQdOobH/4V2yr8OuozGm57CmsyS3uLyaQNBLNYGgt7zzqB8TzO5P/hvXd9mZnq1vyZiewxJNkovUB6Ppvak89pek7Sgje+nDiQ5xv1jfkjE9hzWdJbmW+mDqDziR3YMnk/P+XdQNO4tgdv8ER9o+o4uzueb4UuaVVTJ5WL41mxnTjVmNpgsIvw10k6qjr0WCfoLzbulyk1Mu2VjLX94oZ+G6av7yRnmXit0Y0z6WaLqwQO5gVh14CQPXv8jid+dy9bMru8wJ2/pojOk5LNF0cc/2+jLrtQ83pj5IMODvMidsb9i2IIAvxfpojOnOLNF0caMH9+V3wa9zWMo6Lk6d28VO2Br22xjTHVmi6eJGF2fzpXO+yue9x3Ft5jOMKfR36v5jdXOySMO2jTHdU8ISjYhkisgCEflQRJaJyK9ceaGIzBGRle53Qcg214pImYh8IiKnh5SPF5El7rk7RERceYaIPOnK3xWRIXF/o3EwemBvsk6/gTR/NTmL/tpp+226qPLedzZ2ev+PDW82pudIZI2mHjhJVccChwNTRGQS8HPgVVUdDrzqlhGREcA0YCQwBbhLRHxuX3cDlwPD3c8UV34ZsENVhwG3A7fG4X0lhL/oEHYdegHZyx4ntXJVp+wzlh320eZ3M8Z0LwlLNOqpcYtp7keBc4AZrnwGMNU9Pgd4QlXrVXU1UAZMFJFiIFdV56t3c52HwrZp2tfTwMlNtZ3uqHrC99DUTHLn39Ip+4t1raOlYdvGmO4loX00IuITkQ+ALcAcVX0X6K+qGwHc735u9RJgXcjm5a6sxD0OL2+2jar6gSqgKEIcl4vIQhFZuG3btk56d/EXzCqievx3yVz3XzLWvt7h/VmtwxjTGRKaaFQ1oKqHA6V4tZNRUVaPVBPRKOXRtgmP415VnaCqE4qK9slDXUrtyK/hzxtC3vxbOmUeNKt1GGM6KilGnalqJTAPr29ls2sOw/3e4lYrBwaFbFYKbHDlpRHKm20jIqlAHrA9Fu8hafjSqfrCz0mtWkP2sscSHY0xxiR01FlfEcl3j7OAU4CPgVnAdLfadOB593gWMM2NJBuK1+m/wDWvVYvIJNf/cknYNk37Oh+Y6/pxurX6wSewe9Bx5Cz6Kym7KhIdToueW1rB958r47mlyRujMabjEjmpZjEww40cSwFmquoLIjIfmCkilwFrgQsAVHWZiMwElgN+4EpVDbh9XQE8CGQBs90PwP3AwyJShleTmRaXd5YEqr5wLf2eOpuchX+h6vhfJzqcfTy3tILb5npdbgvWeqPZpo7qk8iQjDExkrBEo6ofAeMilG8DTm5hm5uBmyOULwT26d9R1d24RNXTBPKHUjvqYrKXzGDXYdNo7Dsy0SE1M6+scp9lSzTGdE/tajoTkQIRGROrYEznqh7/XYJZReS9+SsIBlrfII4mD8uPumyM6T5aTTQiMk9EckWkEPgQeEBE/hT70ExHaXoOO7/wM9K3LqHXx08lOpxmpo7qw09PGsTEwTn89KRBVpsxphtrS40mT1V3AucBD6jqeLyOe9MF1B10JvUDJ5G74HZS6pLrGqGpo/rw56nDLMkY0821JdGkumHGFwIvxDge09lEqDr2esRfR+47v090NMaYHqgtieZXwEtAmaq+JyIHAitjG5bpTP78A6kZcym9Vj5P+oYFiQ5nj1jNDG2MSS5RE40bejxIVceo6ncBVHWVqn45LtGZTlNzxLfx5w4m//XrkMbEn9hjOTO0MSa5RE007jqVs+MUi4khTc2i8oSb8VWXk/tu4sdyLC6vpsHvZob2262cjenO2tJ09raI3Ckix4nIEU0/MY/MdLqG4gnUjvo62csfI339OwmNJTcrdc+kc0G3bIzpntry3320+31TSJkCJ3V+OCYWlmysZXF5NeNKcxgz8ftkrnud/Nf/l63nz0LTEzNZ5s46P8LeWVF31nXunUGNMcmj1USjqifGIxATG019IY0BJc23iTvOHc4RJ/yOPrO+Rt5bN1E5+RZIwC16xpXmkJ66ycVld9g0pjtrU3uFiJyJd2fLzKYyVb2p5S1Msoh0l8zRR46jevyV5C66k4YB49l12IVxj6vpXjdNNS27DYEx3VeriUZE7gF6AScCf8ebBTl5xsiaqLy7ZO5bc6g54grSNy8m7+2baew7ksY+8Z8LbXRxtiUYY3qAtgwGOFpVLwF2qOqvgC/Q/L4wJom1eJdMSaHyxNsIZhZSMOf7SH1V3GPryHU0dg2OMV1HW5rO6tzvXSIyENgGDI1dSKaztVRzCGYVsv2UP9Fn1iUUvvJ9tk35G/jS4xJTpL6jttZulmys5apnVuIPKKm+Tdx5nt1m2phk1pYazQvuBmW/B94H1gBPxDAmE0eN/cdRecKvyVj/DgWv/SxuszxH6jtqq9krttMYUBRv29kruvdNU43p6toy6qzprln/FJEXgExVjX87i4mZuoOnklK3nbx3f08ws4CqY65v80i00KHT7alVtNR31DbhN0nt9jdNNaZLazHRiMjFgKjqw01lqlovIpeISK2q2g3pu5HasZfiq9tG74/+QTCtF9UTf9RqsulI81dHRp2dcVgR/16xDX8AUn3ecrjnllYwr6ySycPybXZoYxIsWo3mR8DxEcqfAOYBHUo0IjIIeAgYgHdx+L2q+hd335sngSF4zXQXquoOt821wGVAALhaVV9y5ePZeyvn/wDXqKqKSIZ7jfF4fUsXqeqajsTdne086sdIYy05H96Pb9dWKo//ddQ+m4hDp9uRMPZ31Nno4mzuPO/gFpOU3SbamOQSrY/Gp6r7NJy7srROeG0/8CNVPQyYBFwpIiOAnwOvqupw4FW3jHtuGt71PFOAu9yknwB3A5cDw93PFFd+Gd5ouWHA7cCtnRB39yVC1bE3sHPCNfRaOYuiF7+NNLTcd+I1fwkpQtwvuhxdnM0lRw6ImKgi3SbaGJM40RJNmojs818sIjlAh4cmqepGVX3fPa4GVgAlwDnADLfaDGCqe3wO8ISq1qvqaqAMmOjulZOrqvNVVfFqMKHbNO3raeBkkQRcBt+ViFBzxHfYMfl3pG9YSN9nzid906KIq44uzuaa40uZMCiHa44vTZqRX3abaGOSS7Sms/uBp0XkiqbmJhEZAvzVPddp3H7HAe8C/VV1I3jJSET6udVKgNCZIMtdWaN7HF7etM06ty+/iFQBRUBFZ8bfHdUdPJVATin5866laNbXqR09nZ1HXgOpeyaHYMnGWv7yRjmNAeXDDTUcVJSVFMmmqZnM+miMSQ4tJhpV/YOI1ACvi0hvvKE9tcAtqnp3ZwXg9v1P4PuqujNKhSPSExqlPNo24TFcjtf0RklJyT4b9FQNxROYd+xjFLz3R8YveZDMVS9Rc/hl7DrkfEjN6HAfzf6OWGuLqaP6WIIxJklEHd6sqvcA97hkIJH6bDpCRNLwksyjqvqMK94sIsWuNlMMbHHl5TSfkaAU2ODKSyOUh25TLiKpQB6wz0UXqnovcC/A2LFjbayss2RjLVf/az2NgYs4JnUMd6Q/T8FbvyHn/XuoHfk1jsk/ngd8sl9DlFu76DKWScgYE19tuWATVa2JQZIRvCa4FaoaeieuWcB093g68HxI+TQRyRCRoXid/gtcM1u1iExy+7wkbJumfZ0PzHX9OKYNQm9O9lbjYfztgD9TcdYM/IXDyF34F4577cssLLiORwe/wBOT1nF470po4+GNdtFlW+6+aVPQxI8da9NRibzb1DHA14ElIvKBK/sFcAswU0QuA9YCFwCo6jIRmQksxxuxdqW7AyjAFewd3jzb/YCXyB4WkTK8msy0GL+nbmWfm5P1SqNh4ES2DZxISs1GslbPIXP1y0za/CSy+TFYCMG03gR6DyCQ3Z9tFLChPoOCgkL6FhagqVloaiaa1oviHdWMEWUnvdiq+Wzf1bDndZsSnLL37pvhtZ39vX4n0bpaTa0rH2uTPKJdsHmBqj4lIkPdKK9OpapvErkPBeDkFra5Gbg5QvlCYFSE8t24RGXaL/RmZOE3Jwv2LqZ29CXUjr4E/LtJ2/4paRXLSN3xGb7azTRUbiBlxwoOpY6crXX77PtnABl7l3dvzCL1yf7484Zwmn8gW1Jy+UCHsUqL97n7Zkf7hloTq2TQFU/asT7WpmeIVqO5FngKrw/Fbt3cA4We4JUot1tOzaSx3xga+43ZU/TQe5u4d/NGggo+CXLVkXl8ZUwu0liHNO7irU/W88LiNeSyi75SyZmD/RycuZPUylWMrXyTI9K9pFahuVQsH0dW2mnsPuAkNDO/g9PXRBfLZNAVT9qxPNam54iWaLaJyGvAUBGZFf6kqp4du7BMMujI7ZbHlebgS9mEBpSUFB8jDigm2GvvSfXZd9J5I7h36piPJZdbTj0IgKXrq/jz8/9lrH7CJN/HnLb7Y7Jefx2VVOpLjmLi8LP5v7OP4/2N9S3WOqLVSqI9F8tkEHpMfCld46RtN6gznSFaojkTrybzMPDH+IRjkklHb7fsd539/sC+AwQqav0tLo8qyeOs4ycxr+xQBg2bzo6RRdRULCNz1UtkrXqRgtd+xuT0fHIKvkhD0VeBg5rtK9qIttZGu8X+G7yG/U5+doM601HRrqNpAN4RkaNVdaubEUBVtSZ+4ZlE6si32bvfWt/slHr3W+u56/yD9zx/1sgilm/e1Wy5SeQLQUfR2HcU1RN/wIYlr7Hj7Qc5adPjBDY9yeYh55B+9HcJ5HjXQDWNaIO9I9qaYo/2XEffc2sWl1cTCHrHIxCkSzSdGdMZ2jLqrL+IvAwU4o1K3gpMV9WlsQ3NJIPWvs221Az1+Y7dzdYLX4529X7U5itJ4ZX6kdzb+EOKdSvfTZvFtLWzSFn3L3Ydej7V469i+67GZq/VfLn1WwzE6hu89XeYnqotieZe4Ieq+hqAiEx2ZUfHLizTFUTrOPelNB9QGL4McFBRFjvr/BxUlNWsvLUTctPzGwN9uUm/RenJP2DChkfotWImWWUv8OWci3iH42hwc78W9tr7MW/LLQZixfo7TE/VlkST3ZRkAFR1XqTJNk3PE63mkRI2lVD4crQk1doJOfz54cXZVB14A7UjLyb3nVs5Z93fGZX+b67zX8r84EgO7ter2bbRbjEQa9bfYXqitiSaVSJyPd6gAICLgU6/rsZ0PdFqHoeX9OblT3Y0Ww7V2uiu1k7IkZ73FxzE9jPu5V//+idT1t/B4+k383TgeBZv/B6ENM3Zyd6Y+GrLFDSXAn2BZ9xPH+CbsQzKJI9o04801Swun1S8z/UmvdKaf7TCl2N5L5sV2UdyWsNt/NV/NuekvMW1n3+LzFUvdtr+jTHt02qNxt3d8uo4xGKSTFsuXmy5dhDeJ9N8ueleNk2DATqzhtHUD/MH/zT+o0fzWP4MCl/5AXUHvkTVMdcTzCqMun1XmyamM/TE92ziJ5FznZkk19qcY9DyCeqMwwpdp7uS6hPOOKxwn+1uf70cf0BZvL7997KJdmIcXZzND04Y5JLYMdSOOBP58H5yFv2V9A0LqDr+JnYPiTjLUZecJqajeuJ7NvHVptmbTc+0z6SaYVPQRJtleXRxNhce3peSvHQuPLzvPieuaLM3t6a12Z2brsNZuK6av7xRzpLN9dSM+zZbz3uaYHZ/Cl++ivx5v0Aa9r0kLFLfUWdKxpmQY/2ejbFEY1rUNAUNRJ6CJtoJ6rmlFTy6aAvlVQ08umgLzy0Nv6lp69eztKS1E2Po7Q0a/Huf9xcezNapT1A97ttkrXyevk+fTfqGBc22jWXfUVtuf5AIsXzPxkAbEo2IHCwir4rIUrc8RkSui31oJtG8KWi8E1B6akvXs0Q+Qc1cvKXZuuHLZxxWRJrPS2Bp7byepbUTY3VDoNmsBNUNgb1P+tKpPvL7VJz9KKSkUfTCN8idfyv464HoAxygYzWSZK05tPaejemotvTR3Af8BPgbgKp+JCKPAb+JZWAm8dpyPUtLHfq7/cFm64Yvd+R6ltbiWhl2W4LwZYDG/oez9cvPkvvObfRe8iAZ5W9SOfkWGvuObHGAQ0f7MpJ5ZgAb8m1iqS2JppeqLpDmF9y1fRpf06VFOwF5Hfrr8Adg8frqZh36A3LS2VS9d+qXATnp7dp3R+LKD+tLCl9uNpDguBvZfcBJ5L9xPX2eu4iacd9mfvHXeX/D7n2SWEdndraZAUxP1ZY+mgoROQjXiC4i5wMbYxqV6RJmr9hGYwDXoe8tNxlSmNls3fDlWKoM60sKXW6avflv8zdy1TNeP0n94OPZcsEs6g76Ijnv30XpC9N485239zzfpC19Gc8treD7z5VF6JPyjC7O5pIjB1iSMT1KWxLNlXjNZoeKyHrg+3i3TjY9XsvXynSkD6ajJg/Lb3G5pdFumpFH5Um3cf+AG+hLJc+lX8+P5FFeWbZhz7at9WU8t7SC2+auY8Haam6bu67FZGP2SsZReKbzteWCzVXAKW5+sxRV7bQeTBH5B3AWsEVVR7myQuBJYAiwBrjQXTSKiFwLXAYEgKtV9SVXPh54EMgC/gNco6oqIhnAQ8B4YBtwkaqu6az4e7qD+2W1uJzIOcWizQwdfWZnWNL7aP5SX8K1qY/zndQXqFi7CFn7S+oHT271dV9Ytm2f5dDXBrswMpRdv9NztGXU2W9FJF9Va1W1WkQKRKSzBgI8CEwJK/s58KqqDgdedcuIyAhgGjDSbXOXiPjcNncDlwPD3U/TPi8DdqjqMOB24NZOitvQ+vDnRDYTTR3Vhz9PHbbPiT50JudIy2ccVkRtSm+u9f8PX228jsyMdIpevILCF7/DZytXcNUzn7pmt0/3+Rae7pOoy5Ga7XqyZB2FZzpfW5rOzlDVyqYFV7v4Yme8uKq+AYRfqXcOMMM9ngFMDSl/QlXrVXU1UAZMFJFiIFdV56uq4tVgpkbY19PAyRI2qsHsv9aGPyej0JmcIy0Dey7peTc4grcnP0HVUT8hfeN7fOG1i/iFzKCIqn36pABqG/xRlztykWp3ZNfv9BxtGXXmE5EMVa0HEJEsICOGMfVX1Y0AqrpRRPq58hLgnZD1yl1Zo3scXt60zTq3L7+IVAFFQLPGcxG5HK9GRElJCaZtOjqKKhHNSKG1rki1sEcXbabpztMBhUcWb2fUWZdSN/wsPn7mZr5eO4eLfPP4R2AKy2umAYP3bLu1pvm+wpdbu0j1uaUVEZv7uqtYzndnkktbEs0jwKsi8gDef8al7K0lxFOkmohGKY+2TfMC1XvxbubG2LFju87N3JPA/g5RTlT7fOjFm/tczAl8unVXxOVgr378I/8afrXjdH6Q+jRXpT5P/eYX8b95LjWjpxPIG8KQwkw+2LC3OSx8pN0ZhxXxr2XbCCj4pPkAiaaBBAAL1npNSN092US+ZXeckk2wkbSK5aRvWYKvZgO+6g2k1FVASirqy0DTetFYOJzGvqNp6DsKzSyIT1zdVFsGA9wmIkuAk/FO3L9u6oSPkc0iUuxqM8VA0yXl5cCgkPVKgQ2uvDRCeeg25SKSCuSxb1OdSYCOXpOyv1q7mLMhEGxxubBXKm9oMVc3fo87/Ofy675zmfTxP+m1/EnqS77AVUUn8b0NB1KHl2BOO7T5RKKfbatrVlv6bFvdnvccaSaF7p5o4v0ZSNm1hcxVc8hc+xrpmxaT4ve+RKgvA3/vgQR79YWgn5SGGlKq1pC56iXEfS+tL57IrkPPp27oqZAav6H63UWbZm9W1dnA7BjH0mQWMB24xf1+PqT8MRH5EzAQr9N/gaoGRKRaRCYB7wKXAP8Xtq/5wPnAXNePYxIsUVfJTx6Wv6fG0LQcKsOXgjeoMXTZE3ob6M9TStl5wm/YnPcLspc/SdbK5zhl/W94LyOTecHDeS1wOO8un9QsWcwrq2z2WvPKKvc839pMCh2VjKPd4vEZkMZdZK56kV6fPk/6xvcQlMb8g6g7eCr1A4+kof84gr36QYSuW2mo8Wo9G9+j18pZFLz2U/LeyqVm9CXUjvkmmhahf89E1GKiEZE3VfVYEammeXOTAKqquR19cRF5HJgM9BGRcuAGvAQzU0QuA9YCF+C94DIRmQksx5uZ4EpVbTojXMHe4c2hSfF+4GERKcOryUzraMymcyTqKvmpo/qwvqqe18sqOSFCX0j/nDQ2hsxo0D8nrVnM4UO2g2RTPeEqqsd/l+vum8mpgTc42beYs3zvQOU9NM48iMa+o2joO5qv9u3HurXCZgoIktIsyaWmND/RhS8DEGggpb7K/exE6qtIaahGGmrYsn0HW7dXMbC30DcL0ABICoiPrbuCLP+kjt2axZz3sik6ZgSDBw0mkN0fTc+NeJKNh1h+BlK3f+q+AMwipbEGf94Qao64groDp+AvHA64PrE5lUwe5tvnc7C3v+xApo6fSM0RV5C+cSHZSx8hd9GdZH/8FDuP/D51w8/2jrOJSuwLfnNjx47V2bPjVXkz8da8b0j26Ru64ulP+TCkn2XswGzuPv/gZtu3dGKc/tgKVlbsBpSR8jnn5SzjawPWk7Z1Kb66veNPGtTHFgrIzM4nJ68QTevFW5/X0BgUBCWdRnql+BnX34c01OxJJin+fedsCxVUoYFUUtPSSfGlgiqoH39jI+k0Rt4mPRd//hCW1vdnfs0AMktH88UTjkMz89txVJNE0E/mmrlkL3uUjI0LUF86dUNPZ9dhF9IwYHyzhBraJwbw05MG7Uk20Z4DSN+0iNz5t5C+dSn1A49ix4m3EszuH4c32A4aJPPz12joM4Jg7+K4vGRJSckiVZ0Q6bmoTWcikgJ81HQxpTFdXWv9AlVho9CqIkxf493MbRN3ntc8SRXnZrhEIyzTIRT1GcsZUw4EVVJqN3Hff96kbuvnDJYt9JVKDvDXM1oDpOzawiCpJShec9lu0iAlnWBaHppdTDC9N5rem2BGPsHMPILpuWhGHsGMXILpOcxcXsc9i6qo1QxSRLj8iGIuOXLAnri++vByynfUksMucmUXY3J28avjsvDVbiZ151o2ff4JxTWLuFK2w+fAQ+DPHUxD/8Np6H8EDQOOwF8wLGE1n9ak7Kqg18dPkb1iJr7aTfh7D2TnxB9Re+iXW+zEj9aMGe05gIYB46mY+iS9PvknuW/fQr+nz6HyhN+we8gpbYo31s2YvqrPyX/jejI2vkcwrRc7J/6QXSO+ktCaV9REo6pBEflQRAar6tp4BWVMrIwrzcGXsgkNKL6UffsFBhdksmZHfbPlJk3XwcDe62DadKIQIdi7mKIRJzb/pnzcIAa6E9h1z5U16zuaODiHP585rE3v6eChtfg/WElKC30dNQ0B/KSyg1x2aC61gVR2HzR6z/PTP1tGeX0D+VQzMmUNx2at5RuFm8kof4teK2cBEMgspKH4SOoHTqShZBL+vKGJTTwaJH39O/T65J9krZ6DBBvZXXI0Vcdcx+7BkyHFF3XzaH11rfXjASAp7Dr0AuoHTKBg7k8ofPl71Iz6Ojsn/RRSWj6txnS0pSrZSx8mZ8Ht4Euj6uhfkLH2DfLf+g1ZZf+h8qTbCOQk5vKNtgwGKAaWicgCYE+bgqqeHbOojIkpDfu919fG9+etNVUEguBL8Zb33S7ycmuzDkSbGmdDVX2zdcOXo2mtr2PHLn/U5V2NXldnJTm8FRzNCj2cc04bA6r4qteRvnERGRveJX3DArJWewNOA736UT/wKOpLJtEw8KiYncCaXVs0sojUHSvJWvUiWZ8+T2rNBoIZedSOmEbtiK8QyB/a5v1G+1tEey5cIH8oFec8Ru67f6D30odJrVzFjpP/hGZE7sKO5Ui77CUPkvfObewefCKVx91IMLsftSMvJmvl8+S9+WuCr9/GQ/2vTciAkLYkml/FPApj4mRxeTWBoJciAkH2+UcfXZzNXV+OPEdb6Kiz1AgThbb2PHgnsUgnrhEDsimvami23B7RrmcSoVlODK+IbN8ViLwsQiB3MHW5g6k75Nw9iSdj/TveT/lb9Cr7FwD+3gNpGDCehgFH0NB/HP6Cg6J+s2+L55ZW8Je5nzE+5VPYsJSsxR9QULcWRWgoOYrqiT+kbsgpkLp/14+39Ldo7bl9+NLZefQv8BceTN5/f0Wf56axfcrdBPIO2GfVWI20y1zzCrnv/J66A6ew4+Q/7m0mE6Hu4KnUrFpA4eezeXD1V3nAlxH3eeWijTrLBL4DDAOWAPerqt2HxnRpbflHb+mk3dpEoR2ZSPTAsIs7w5c74qThBbz8yY5my6HC8lDEq5y9J7zEsyt3MLsOuxBUSd1R5tV2Nr5Hxvr5exKP+jJoLDyYxqJD+bCuL29V5jN4yHBOGH0gwYx88IXcn0gVadxFSl0Fvl1bSd3xGWnbP+XElR9wWcZKMqQRv6bwsX8Ucuw32D3kFO+alySz69Dz8ecOpmDONfR5/itsn3IPjf3GNFsnFiPt0iqWkT/3pzT2Hc2Oyb+L2BfzdtokLpJnOVqWMi9wRNyuW2sS7SvHDLzpXf4LnAGMAK6JR1DGxEqsh1Xv70wJ40pzyEjd/2+60TqYvzymL3M+2bFnGo0vj2l+kk7zQegECWlh3Rst7lsEf+Fw/IXDqR11savxlJO++QPStq0grWI5KWUvc7S/iqMBPnQ/QNCXCZKCBgOoBknV5qPigmnZ5GcOZUbdabwdHMF7wUO58piDmToiuS9ibRg4kYqpj1P0n8speuEb7DjlT/vM/N2ZdzNNqd1M4YvfJZiZz/bT72TJ1gCLyzft87cqOPR4qsuyOMP3Hm/p+LjPKxct0YxQ1dEAInI/sCA+IRkTW8k4bU5HEmBrcS0ur0bEG+0ssm9z4eRhzWs8k4cVtHnfzYgQyB1EXe4g6oZ/CYBvPfkJ5Zu3cIBsYZBsYURuA5eMziSlfidbaxqYW1aJPyjslN5MGX8IA4tL8OcPJdB7oJfIllawq6ySK7vQ/G+BvCFUnPMYhS9+h8KXrqLquBvYdegFnf464q+j8KUrkcYatp39GB9W9WrxbzWqJJ/q0smctekt8qYMZVQS9dHs+YrhJqSMQzjGJK9YT5myvwmwtbhaay688fQhALyzZieThuTuWW7LvlvTJzuN5fRmifZmiR5ITWEe5407EIAn39vEvY0bCSqkCASkmEsGDWi2fbv6SpJIsFcftn1pBgWv/ID8N36Jr3o91ROu6byReqrkz/sFaRXL2X76X/EXHcLi9zZF/VtljjiDrPWzOYLlNPCFzomjjaIlmrEistM9FiDLLXfazADGdCWJmjanNa3F1ZbaUmhyac++WxNtFF+yHs/OomnZbD/9r+S9+WtyFv8NX/V6Kk+4uXn/1H7q/f5dZK16kaqjfkz9AScCrR/P+kHHEvRlkrV6Dg0l8U00NjNAGJsZwESTjHOGQWzj6ui+o22frMezU6nS+4P7yH3vduoHjGfHyX8imN2v9e1a0GvZY+S/9Wt2HTyVyhN+26yW1NrxLHj5atK3fMDmr83r9As4o80MYIkmjCUaY0wsZH72H/Jfvw5N68WOk/5AQ8mkdu+j9wf3kbvgT+wefCLbT/1zu2tHWWUvUDD3J2w95zEa+49r9+tHEy3R2GxwxhgTB7sP+iIV584kmJFP0X8uI2fhHeDf3baNVclZ8CdyF/yJXcPOYvtpf9mvJrjdg09AU9LIWv1Ku7ftCEs0xhgTJ/6CYVSc+yR1w84i5/276f/kGWR9+hxoy7eFSN/0Pn1mfZWcD+6j9rCLqJx8C6Sktbh+NJqeQ2PRIaRu/2Q/38H+6dilu8YYY9pF07KpPPFWdh16Prnv/J6CedeSs/hv7B50HA3FR9JYMAxf7SZSq8vJWPsGWWteIdCrLzuO/w11h5zX4ZFr/tzBpG9Z0knvpm0s0RhjTAI0FB9JxdQnyPpsNr0++Se9VjxF76UPN1snmJbNzglXUzt6eqfdaC2QOwjfqpcg2LjfNaP2skRjjDGJIinUDTuTumFnQqCB9K1L8FWtJdC7mEBOKYHeAzo8Z1w4f+5gRAP4qjdEnI8tFizRGGNMMvClezdoGzA+pi8TyB0MQOrOdXFLNDYYwBhjehC/SzS+nfG7xViPSDQiMkVEPhGRMhH5eaLjMcaYRAn26kvQl0mqJZrOIyI+4K/snYH6KyIyIrFRGWNMgrjJT30717W+bifp9okGmAiUqeoqVW0AngDOSXBMxhiTMP68waTu/Dxur9cTEk0JEJq6y13ZHiJyuYgsFJGF27Zti2twxhgTb4HcwaTuLI96oWhn6gmJJtLVTc0meFPVe1V1gqpOKCra9/a7xhjTnfhzByOBelJqt8Tl9XpCoikHBoUslwIbEhSLMcYkXCDXOyXGa0BAT0g07wHDRWSoiKQD04BZCY7JGGMSxp/rXT8Tr0TT7S/YdHcHvQp4CfAB/1DVZQkOyxhjEibQewAqqXEbedbtEw2Aqv4H+E+i4zDGmKSQkkogZ6A1nRljjIkdf94BcZsdwBKNMcb0QIGcQaTuXAdxuMuyJRpjjOmB/HmDSWmoJqW+MuavZYnGGGN6oHhOrmmJxhhjeqA9twuoskRjjDEmBvw5pShiNRpjjDExkppBIHtAXIY4W6IxxpgeKth7AL44zHdmicYYY3qoYEa+jTozxhgTO8HMfFJ2V8b8dSzRGGNMDxXMzEcs0RhjjImVYEY+KYHd4N8d09exRGOMMT1UMCMPgJT6qpi+jiUaY4zpoYKZ+QAx76exRGOMMT3UnkQT45FnlmiMMaaHCmbkA1ajMcYYEyPWdGaMMSamuvVgABG5QESWiUhQRCaEPXetiJSJyCcicnpI+XgRWeKeu0NExJVniMiTrvxdERkSss10EVnpfqbH7Q0aY0xXkJpJ0JfZbftolgLnAW+EForICGAaMBKYAtwlIj739N3A5cBw9zPFlV8G7FDVYcDtwK1uX4XADcBRwETgBhEpiOF7MsaYLkfjMDtAQhKNqq5Q1U8iPHUO8ISq1qvqaqAMmCgixUCuqs5XVQUeAqaGbDPDPX4aONnVdk4H5qjqdlXdAcxhb3IyxhhDfKahSbY+mhJgXchyuSsrcY/Dy5tto6p+oAooirKvfYjI5SKyUEQWbtu2rRPehjHGdA3xmFgzZolGRF4RkaURfs6JtlmEMo1Svr/bNC9UvVdVJ6jqhKKioijhGWNM9xKP+c5SY7VjVT1lPzYrBwaFLJcCG1x5aYTy0G3KRSQVyAO2u/LJYdvM24+YjDGm2wpm5HXPUWdRzAKmuZFkQ/E6/Reo6kagWkQmuf6XS4DnQ7ZpGlF2PjDX9eO8BJwmIgVuEMBprswYY4zjNZ1VgUZs8OkUMavRRCMi5wL/B/QF/i0iH6jq6aq6TERmAssBP3ClqgbcZlcADwJZwGz3A3A/8LCIlOHVZKYBqOp2Efk18J5b7yZV3R77d2eMMV1HMDMf0QDSUI1m5MbkNRKSaFT1WeDZFp67Gbg5QvlCYFSE8t3ABS3s6x/APzoUrDHGdGOh850FYpRokq3pzBhjTBztmR0ghgMCLNEYY0wPtrdGE7sBAZZojDGmB4vHDM6WaIwxpgfTONyTxhKNMcb0YMH0XBSxGo0xxpgYSfGhGbmWaIwxxsROMCMPsaYzY4wxsRLMzLdRZ8YYY2InmJFnTWfGGGNiJ9a3CrBEY4wxPVysb35micYYY3q4YGY+KY21EGiIyf4t0RhjTA+3Z3aAGA0IsERjjDE9XKznO7NEY4wxPZzGeAZnSzTGGNPDBWM835klGmOM6eFiPYOzJRpjjOnh9tRoulOiEZHfi8jHIvKRiDwrIvkhz10rImUi8omInB5SPl5Elrjn7hARceUZIvKkK39XRIaEbDNdRFa6n+nxfI/GGNNVaGovNCUtZvOdJapGMwcYpapjgE+BawFEZAQwDRgJTAHuEhGf2+Zu4HJguPuZ4sovA3ao6jDgduBWt69C4AbgKGAicIOIFMT+rRljTBcj4k1D051Gnanqy6rqd4vvAKXu8TnAE6par6qrgTJgoogUA7mqOl9VFXgImBqyzQz3+GngZFfbOR2Yo6rbVXUHXnJrSk7GGGNCxHJ2gGToo7kUmO0elwDrQp4rd2Ul7nF4ebNtXPKqAoqi7GsfInK5iCwUkYXbtm3r0JsxxpiuyJvBuTIm+06NyV4BEXkFGBDhqf9V1efdOv8L+IFHmzaLsL5GKd/fbZoXqt4L3AswduzYiOsYY0x3Vl9yDOKvi8m+Y5ZoVPWUaM+7zvmzgJNdcxh4tY5BIauVAhtceWmE8tBtykUkFcgDtrvyyWHbzNuPt2KMMd1ezRHfidm+EzXqbArwM+BsVd0V8tQsYJobSTYUr9N/gapuBKpFZJLrf7kEeD5km6YRZecDc13iegk4TUQK3CCA01yZMcaYOIpZjaYVdwIZwBw3SvkdVf2Oqi4TkZnAcrwmtStVNeC2uQJ4EMjC69Np6te5H3hYRMrwajLTAFR1u4j8GnjPrXeTqm6P+TszxhjTjOxttTLg9dHMnj279RWNMcbsUVJSskhVJ0R6LhlGnRljjOnGLNEYY4yJKUs0xhhjYsoSjTHGmJiyRGOMMSambNRZGBHZCnzegV30ASo6KZzOZHG1j8XVPhZX+3THuA5Q1b6RnrBE08lEZGFLQ/wSyeJqH4urfSyu9ulpcVnTmTHGmJiyRGOMMSamLNF0vnsTHUALLK72sbjax+Jqnx4Vl/XRGGOMiSmr0RhjjIkpSzTGGGNiyhLNfhKRf4jIFhFZGlJ2o4isF5EP3M8XExDXIBF5TURWiMgyEbnGlReKyBwRWel+FyRJXAk9ZiKSKSILRORDF9evXHmij1dLcSX8M+bi8InIYhF5wS0n9HhFiSvhx0tE1ojIEvf6C11Zwo9XC3HF5HhZH81+EpHjgRrgIVUd5cpuBGpU9Q8JjKsYKFbV90UkB1gETAW+AWxX1VtE5OdAgar+LAniupAEHjN3I71sVa0RkTTgTeAa4DwSe7xaimsKCf6Mufh+CEwAclX1LBG5jQQeryhx3Uji/yfXABNUtSKkLOHHq4W4biQGx8tqNPtJVd/Au9FaUlHVjar6vntcDawASoBzgBlutRl4J/lkiCuh1FPjFtPcj5L449VSXAknIqXAmcDfQ4oTerygxbiSVcKPVzxZoul8V4nIR65pLSHNB01EZAgwDngX6O9uiY373S9J4oIEHzPX3PIBsAWYo6pJcbxaiAsS/xn7M/BTIBhSlvDj1UJckPjjpcDLIrJIRC53ZclwvCLFBTE4XpZoOtfdwEHA4cBG4I+JCkREegP/BL6vqjsTFUe4CHEl/JipakBVDwdKgYkiMireMUTSQlwJPV4ichawRVUXxfN1WxMlroR/voBjVPUI4AzgStfsngwixRWT42WJphOp6mZ3cggC9wETExGHa9P/J/Coqj7jije7fpKm/pItyRBXshwzF0slMA+vHyThxytSXElwvI4Bznbt+08AJ4nIIyT+eEWMKwmOF6q6wf3eAjzrYkj08YoYV6yOlyWaTtT0wXHOBZa2tG4MYxDgfmCFqv4p5KlZwHT3eDrwfDLElehjJiJ9RSTfPc4CTgE+JvHHK2JciT5eqnqtqpaq6hBgGjBXVS8mwcerpbgSfbxEJNsNfkFEsoHTXAyJ/nxFjCtWxyu1M3bSE4nI48BkoI+IlAM3AJNF5HC8ts81wLcTENoxwNeBJa59H+AXwC3ATBG5DFgLXJAkcX0lwcesGJghIj68L14zVfUFEZlPYo9XS3E9nASfsUgS/flqyW0JPl79gWe971mkAo+p6osi8h6JPV4txRWTz5cNbzbGGBNT1nRmjDEmpizRGGOMiSlLNMYYY2LKEo0xxpiYskRjjDEmpizRGNMGIjJEQmbqDnvuJhE5pZXtbxSRH8cmOmOSm11HY0wHqeovEx2DMcnMajTGtJ1PRO4T7/4wL7sr9hGRB0XkfPf4iyLysYi8KSJ3iLsvijNCROaJyCoRudqt/9OQx7eLyFz3+GQ3tQsicreILJTm96U5WUSebdqxiJwqIs8QRrx7jvxWROa7fRwhIi+JyGci8h23zmQReUNEnhWR5SJyj4ikuOcuE5FPXdz3icidMTiuppuzRGNM2w0H/qqqI4FK4MuhT4pIJvA34AxVPRboG7b9ocDpePNH3eDmfnsDOM49PwHo7cqPBf7ryv9XVScAY4ATRGQMMBc4TESaXuObwAMtxL1OVb/g9vcgcD4wCbgpZJ2JwI+A0XiTKp4nIgOB6926p7r4jWk3SzTGtN1qVf3APV4EDAl7/lBglaqudsuPhz3/b1Wtdzea2oI3DcgiYLybd6oemI+XcI5jb6K5UETeBxYDI4ER6k3p8TBwsZsT7QvA7BbinuV+LwHeVdVqVd0K7G6aTw1YoKqrVDXg4j4WL/m8rqrbVbUReCrq0TGmBdZHY0zb1Yc8DgBZYc9LO7dPVdVGN+PwN4G3gY+AE/FqFStEZCjwY+BIVd0hIg8CmW4fDwD/AnYDT6mqv5XXDYbFEGTvOSB8Liptw/sxpk2sRmNM5/kYOFC8G7sBXNTG7d7ASyZv4NVivgN84GotuUAtUCUi/fHuHQLsmeZ9A3AdXpNYR0wUkaGub+YivFtHL8BrqisQkVTCmgqNaSur0RjTSVS1TkS+C7woIhV4J+q2+C/wv8B8Va0Vkd2uDFX9UEQWA8uAVcBbYds+CvRV1eUdDH8+3gzMo/ES3rOqGhSR3+LdCXUDsByo6uDrmB7IZm82phOJSG9VrXH33/krsFJVb4/h690JLFbV+zuwj8nAj1X1rAjPNb2fVLybY/1DVZ8NX8+YaKzpzJjO9T/ufjvLgDy8UWgxISKL8EaiPRKr1wBudO9nKbAaeC6Gr2W6KavRGGOMiSmr0RhjjIkpSzTGGGNiyhKNMcaYmLJEY4wxJqYs0RhjjImp/wdmPomsHi7sZAAAAABJRU5ErkJggg==\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",
"f11= np.polyfit(x,y,11)\n",
"p11 = np.poly1d(f11)\n",
"print(p11)\n",
"PlotPolly(p11,x,y,'highway mpg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"# calculate polynomial\n",
"# Here we use a polynomial of the 11rd order (cubic) \n",
"f1 = np.polyfit(x, y, 11)\n",
"p1 = np.poly1d(f1)\n",
"print(p1)\n",
"PlotPolly(p1,x,y, 'Highway MPG')\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2)polynomial with two variables is given by:</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b_1 X_1 +b_2 X_2 +b_3 X_1 X_2+b_4 X_1^2+b_5 X_2^2\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can perform a polynomial transform on multiple features. First, we import the module:\n"
]
},
{
"cell_type": "code",
"execution_count": 48,
"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": 49,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [],
"source": [
"Z_pr=pr.fit_transform(Z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The original data is of 201 samples and 4 features \n"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 4)"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"after the transformation, there 201 samples and 15 features\n"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 15)"
]
},
"execution_count": 52,
"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": 53,
"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": 55,
"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": 56,
"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": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pipe=Pipeline(Input)\n",
"pipe"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can normalize the data, perform a transform and fit the model simultaneously. \n"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.partial_fit(X, y)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.fit(X, y, **fit_params).transform(X)\n"
]
},
{
"data": {
"text/plain": [
"Pipeline(memory=None,\n",
" steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False))])"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pipe.fit(Z,y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Similarly, we can normalize the data, perform a transform and produce a prediction simultaneously\n"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" Xt = transform.transform(Xt)\n"
]
},
{
"data": {
"text/plain": [
"array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ypipe=pipe.predict(Z)\n",
"ypipe[0:4]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #5:</h1>\n",
"<b>Create a pipeline that Standardizes the data, then perform prediction using a linear regression model using the features Z and targets y</b>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.pipeline import Pipeline\n",
"from sklearn.preprocessing import StandardScaler"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.partial_fit(X, y)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.fit(X, y, **fit_params).transform(X)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" Xt = transform.transform(Xt)\n"
]
},
{
"data": {
"text/plain": [
"array([13699.11161184, 13699.11161184, 19051.65470233, 10620.36193015,\n",
" 15521.31420211])"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"Input = [('scale', StandardScaler()), ('model', LinearRegression())]\n",
"pipe = Pipeline(Input)\n",
"pipe.fit(Z,y)\n",
"\n",
"ypipe = pipe.predict(Z)\n",
"ypipe[0:5]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"</div>\n",
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
"\n",
"pipe=Pipeline(Input)\n",
"\n",
"pipe.fit(Z,y)\n",
"\n",
"ypipe=pipe.predict(Z)\n",
"ypipe[0:10]\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 4: Measures for In-Sample Evaluation</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n",
"\n",
"<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n",
"<ul>\n",
" <li><b>R^2 / R-squared</b></li>\n",
" <li><b>Mean Squared Error (MSE)</b></li>\n",
"</ul>\n",
" \n",
"<b>R-squared</b>\n",
"\n",
"<p>R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.</p>\n",
" \n",
"<p>The value of the R-squared is the percentage of variation of the response variable (y) that is explained by a linear model.</p>\n",
"\n",
"<b>Mean Squared Error (MSE)</b>\n",
"\n",
"<p>The Mean Squared Error measures the average of the squares of errors, that is, the difference between actual value (y) and the estimated value (ŷ).</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Model 1: Simple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2\n"
]
},
{
"cell_type": "code",
"execution_count": 63,
"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": 64,
"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": [
"lets import the function <b>mean_squared_error</b> from the module <b>metrics</b>\n"
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.metrics import mean_squared_error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we compare the predicted results with the actual results \n"
]
},
{
"cell_type": "code",
"execution_count": 66,
"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": 67,
"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": 68,
"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": 69,
"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": 71,
"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": 72,
"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": 73,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361218"
]
},
"execution_count": 73,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_squared_error(df['price'], p(x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 5: Prediction and Decision Making</h2>\n",
"<h3>Prediction</h3>\n",
"\n",
"<p>In the previous section, we trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction. Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 74,
"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": 75,
"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": 76,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 76,
"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": 77,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-7796.47889059, -7629.6188749 , -7462.75885921, -7295.89884352,\n",
" -7129.03882782])"
]
},
"execution_count": 77,
"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": 78,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(new_input, yhat)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Decision Making: Determining a Good Model Fit</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Now that we have visualized the different models, and generated the R-squared and MSE values for the fits, how do we determine a good model fit?\n",
"<ul>\n",
" <li><i>What is a good R-squared value?</i></li>\n",
"</ul>\n",
"</p>\n",
"\n",
"<p>When comparing models, <b>the model with the higher R-squared value is a better fit</b> for the data.\n",
"<ul>\n",
" <li><i>What is a good MSE?</i></li>\n",
"</ul>\n",
"</p>\n",
"\n",
"<p>When comparing models, <b>the model with the smallest MSE value is a better fit</b> for the data.</p>\n",
"\n",
"<h4>Let's take a look at the values for the different models.</h4>\n",
"<p>Simple Linear Regression: Using Highway-mpg as a Predictor Variable of Price.\n",
"<ul>\n",
" <li>R-squared: 0.49659118843391759</li>\n",
" <li>MSE: 3.16 x10^7</li>\n",
"</ul>\n",
"</p>\n",
" \n",
"<p>Multiple Linear Regression: Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n",
"<ul>\n",
" <li>R-squared: 0.80896354913783497</li>\n",
" <li>MSE: 1.2 x10^7</li>\n",
"</ul>\n",
"</p>\n",
" \n",
"<p>Polynomial Fit: Using Highway-mpg as a Predictor Variable of Price.\n",
"<ul>\n",
" <li>R-squared: 0.6741946663906514</li>\n",
" <li>MSE: 2.05 x 10^7</li>\n",
"</ul>\n",
"</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Simple Linear Regression model (SLR) vs Multiple Linear Regression model (MLR)</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Usually, the more variables you have, the better your model is at predicting, but this is not always true. Sometimes you may not have enough data, you may run into numerical problems, or many of the variables may not be useful and or even act as noise. As a result, you should always check the MSE and R^2.</p>\n",
"\n",
"<p>So to be able to compare the results of the MLR vs SLR models, we look at a combination of both the R-squared and MSE to make the best conclusion about the fit of the model.\n",
"<ul>\n",
" <li><b>MSE</b>The MSE of SLR is 3.16x10^7 while MLR has an MSE of 1.2 x10^7. The MSE of MLR is much smaller.</li>\n",
" <li><b>R-squared</b>: In this case, we can also see that there is a big difference between the R-squared of the SLR and the R-squared of the MLR. The R-squared for the SLR (~0.497) is very small compared to the R-squared for the MLR (~0.809).</li>\n",
"</ul>\n",
"</p>\n",
"\n",
"This R-squared in combination with the MSE show that MLR seems like the better model fit in this case, compared to SLR.\n"
]
},
{
"cell_type": "markdown",
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"<h3>Simple Linear Model (SLR) vs Polynomial Fit</h3>\n"
]
},
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"<ul>\n",
" <li><b>MSE</b>: We can see that Polynomial Fit brought down the MSE, since this MSE is smaller than the one from the SLR.</li> \n",
" <li><b>R-squared</b>: The R-squared for the Polyfit is larger than the R-squared for the SLR, so the Polynomial Fit also brought up the R-squared quite a bit.</li>\n",
"</ul>\n",
"<p>Since the Polynomial Fit resulted in a lower MSE and a higher R-squared, we can conclude that this was a better fit model than the simple linear regression for predicting Price with Highway-mpg as a predictor variable.</p>\n"
]
},
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"source": [
"<h3>Multiple Linear Regression (MLR) vs Polynomial Fit</h3>\n"
]
},
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"cell_type": "markdown",
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"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"
]
},
{
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"source": [
"<h2>Conclusion:</h2>\n"
]
},
{
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"source": [
"<p>Comparing these three models, we conclude that <b>the MLR model is the best model</b> to be able to predict price from our dataset. This result makes sense, since we have 27 variables in total, and we know that more than one of those variables are potential predictors of the final car price.</p>\n"
]
},
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"source": [
"### Thank you for completing this lab!\n",
"\n",
"## Author\n",
"\n",
"<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
"\n",
"### Other Contributors\n",
"\n",
"<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
"\n",
"Bahare Talayian\n",
"\n",
"Eric Xiao\n",
"\n",
"Steven Dong\n",
"\n",
"Parizad\n",
"\n",
"Hima Vasudevan\n",
"\n",
"<a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a>\n",
"\n",
"<a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
"\n",
"## Change Log\n",
"\n",
"| Date (YYYY-MM-DD) | Version | Changed By | Change Description |\n",
"| ----------------- | ------- | ---------- | --------------------------------------------- |\n",
"| 2020-09-09 | 2.1 | Lakshmi | Fixes made in Polynomial Regression Equations |\n",
"| 2020-08-27 | 2.0 | Lavanya | Moved lab to course repo in GitLab |\n",
"\n",
"<hr>\n",
"\n",
"## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
]
}
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