Skip to content

Instantly share code, notes, and snippets.

@johnleung8888

johnleung8888/model-development (1).ipynb

Created June 29, 2021 17:05
Show Gist options
  • Save johnleung8888/4fd6a5e6c6bdd539905d30d8661fb3d2 to your computer and use it in GitHub Desktop.
Save johnleung8888/4fd6a5e6c6bdd539905d30d8661fb3d2 to your computer and use it in GitHub Desktop.
Download ZIP
Display the source blob
Display the rendered blob
Raw
model-development (1).ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center>\n",
" <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Module%204/images/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\" />\n",
"</center>\n",
"\n",
"# Model Development\n",
"\n",
"Estimated time needed: **30** minutes\n",
"\n",
"## Objectives\n",
"\n",
"After completing this lab you will be able to:\n",
"\n",
"* Develop prediction models\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>In this section, we will develop several models that will predict the price of the car using the variables or features. This is just an estimate but should give us an objective idea of how much the car should cost.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some questions we want to ask in this module\n",
"\n",
"<ul>\n",
" <li>Do I know if the dealer is offering fair value for my trade-in?</li>\n",
" <li>Do I know if I put a fair value on my car?</li>\n",
"</ul>\n",
"<p>In data analytics, we often use <b>Model Development</b> to help us predict future observations from the data we have.</p>\n",
"\n",
"<p>A model will help us understand the exact relationship between different variables and how these variables are used to predict the result.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Setup</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Import libraries:\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Load the data and store it in dataframe `df`:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This dataset was hosted on IBM Cloud object. Click <a href=\"https://cocl.us/DA101EN_object_storage?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\">HERE</a> for free storage.\n"
]
},
{
"cell_type": "code",
"execution_count": 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://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/automobileEDA.csv'\n",
"df = pd.read_csv(path)\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>1. Linear Regression and Multiple Linear Regression</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Linear Regression</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>One example of a Data Model that we will be using is:</p>\n",
"<b>Simple Linear Regression</b>\n",
"\n",
"<br>\n",
"<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n",
"<ul>\n",
" <li>The predictor/independent variable (X)</li>\n",
" <li>The response/dependent variable (that we want to predict)(Y)</li>\n",
"</ul>\n",
"\n",
"<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Y: Response \\ Variable\\\\\\\\\n",
"X: Predictor \\ Variables\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b>Linear Function</b>\n",
"$$\n",
"Yhat = a + b X\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<ul>\n",
" <li>a refers to the <b>intercept</b> of the regression line, in other words: the value of Y when X is 0</li>\n",
" <li>b refers to the <b>slope</b> of the regression line, in other words: the value with which Y changes when X increases by 1 unit</li>\n",
"</ul>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Let's load the modules for linear regression:</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 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 called \"lm1\".</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",
"lm1 = LinearRegression()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm1 = LinearRegression()\n",
"lm1\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1> Question #1 b): </h1>\n",
"\n",
"<b>Train the model using \"engine-size\" as the independent variable and \"price\" as the dependent variable?</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"\n",
"\n",
"lm1.fit(df[[\"engine-size\"]],df[[\"price\"]])\n",
"lm1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm1.fit(df[['engine-size']], df[['price']])\n",
"lm1\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 c):</h1>\n",
"\n",
"<b>Find the slope and intercept of the model.</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Slope</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[166.86001569]])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.coef_\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Intercept</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-7963.33890628])"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# Slope \n",
"lm1.coef_\n",
"\n",
"# Intercept\n",
"lm1.intercept_\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 d): </h1>\n",
"\n",
"<b>What is the equation of the predicted line? You can use x and yhat or \"engine-size\" or \"price\".</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"#Price = 166.86001569*engine-size + -7963.33890628"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# using X and Y \n",
"Yhat=-7963.34 + 166.86*X\n",
"\n",
"Price=-7963.34 + 166.86*engine-size\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Multiple Linear Regression</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>What if we want to predict car price using more than one variable?</p>\n",
"\n",
"<p>If we want to use more variables in our model to predict car price, we can use <b>Multiple Linear Regression</b>.\n",
"Multiple Linear Regression is very similar to Simple Linear Regression, but this method is used to explain the relationship between one continuous response (dependent) variable and <b>two or more</b> predictor (independent) variables.\n",
"Most of the real-world regression models involve multiple predictors. We will illustrate the structure by using four predictor variables, but these results can generalize to any integer:</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Y: Response \\ Variable\\\\\\\\\n",
"X\\_1 :Predictor\\ Variable \\ 1\\\\\\\\\n",
"X\\_2: Predictor\\ Variable \\ 2\\\\\\\\\n",
"X\\_3: Predictor\\ Variable \\ 3\\\\\\\\\n",
"X\\_4: Predictor\\ Variable \\ 4\\\\\\\\\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"a: intercept\\\\\\\\\n",
"b\\_1 :coefficients \\ of\\ Variable \\ 1\\\\\\\\\n",
"b\\_2: coefficients \\ of\\ Variable \\ 2\\\\\\\\\n",
"b\\_3: coefficients \\ of\\ Variable \\ 3\\\\\\\\\n",
"b\\_4: coefficients \\ of\\ Variable \\ 4\\\\\\\\\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The equation is given by:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b\\_1 X\\_1 + b\\_2 X\\_2 + b\\_3 X\\_3 + b\\_4 X\\_4\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>From the previous section we know that other good predictors of price could be:</p>\n",
"<ul>\n",
" <li>Horsepower</li>\n",
" <li>Curb-weight</li>\n",
" <li>Engine-size</li>\n",
" <li>Highway-mpg</li>\n",
"</ul>\n",
"Let's develop a model using these variables as the predictor variables.\n"
]
},
{
"cell_type": "code",
"execution_count": 16,
"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": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 17,
"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": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-15806.62462632922"
]
},
"execution_count": 18,
"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": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([53.49574423, 4.70770099, 81.53026382, 36.05748882])"
]
},
"execution_count": 19,
"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": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2 = LinearRegression()\n",
"P= df[[\"normalized-losses\", \"highway-mpg\"]]\n",
"lm2.fit(P, df[\"price\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm2 = LinearRegression()\n",
"lm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n",
"\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #2 b): </h1>\n",
"<b>Find the coefficient of the model.</b>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.49789586, -820.45434016])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm2.coef_\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>2. Model Evaluation Using Visualization</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we've developed some models, how do we evaluate our models and choose the best one? One way to do this is by using a visualization.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Import the visualization package, seaborn:\n"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"# import the visualization package: seaborn\n",
"import seaborn as sns\n",
"%matplotlib inline "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Regression Plot</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>When it comes to simple linear regression, an excellent way to visualize the fit of our model is by using <b>regression plots</b>.</p>\n",
"\n",
"<p>This plot will show a combination of a scattered data points (a <b>scatterplot</b>), as well as the fitted <b>linear regression</b> line going through the data. This will give us a reasonable estimate of the relationship between the two variables, the strength of the correlation, as well as the direction (positive or negative correlation).</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's visualize **highway-mpg** as potential predictor variable of price:\n"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 48275.413199456496)"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"width = 12\n",
"height = 10\n",
"plt.figure(figsize=(width, height))\n",
"sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\n",
"plt.ylim(0,)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can see from this plot that price is negatively correlated to highway-mpg since the regression slope is negative.\n",
"\n",
"One thing to keep in mind when looking at a regression plot is to pay attention to how scattered the data points are around the regression line. This will give you a good indication of the variance of the data and whether a linear model would be the best fit or not. If the data is too far off from the line, this linear model might not be the best model for this data.\n",
"\n",
"Let's compare this plot to the regression plot of \"peak-rpm\".</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 47414.1)"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAuAAAAJNCAYAAABwXMA5AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAABcJUlEQVR4nO3de3xj533f+e8PBwDvnOFcqFFmKEus5YytVLKlsWo3ek2nttsom1R2tkoiddt4s3Y9TZzabdZpnO5GbafprtVk68rbxjuKktpJ2sjutEmm2dip48l04lSybrbkjkVbKkc2Z6QR58I7SAI45+kfOCABECRBEjjAAT7vl2mADwnyQBgQXzzn9/wec84JAAAAQDQSzT4AAAAAoJMQwAEAAIAIEcABAACACBHAAQAAgAgRwAEAAIAIEcABAACACCWbfQBR27dvn7v55pubfRgAAABoc88+++xV59z+yvGOC+A333yznnnmmWYfBgAAANqcmX2n2jglKAAAAECECOAAAABAhAjgAAAAQIQI4AAAAECECOAAAABAhAjgAAAAQIQI4AAAAECECOAAAABAhAjgAAAAQIQI4AAAAECECOAAAABAhAjgAAAAQIQI4AAAAECECOAAAABAhAjgAAAAQIQI4AAAAECECOAAAABAhAjgAAAAQISSzT4AYLvOjk3q5LlxTUxlNDLUq+NHR3Xs8HCzDwsAAGBDzIAjls6OTeqh0+c1Obek3T0pTc4t6aHT53V2bLLZhwYAALAhAjhi6eS5caU8U286KbPCZcoznTw33uxDAwAA2BABHLE0MZVRT8orG+tJebo4lWnSEQEAANSGAI5YGhnq1WLOLxtbzPk6NNTbpCMCAACoDQEcsXT86KhyvlMmm5dzhcuc73T86GizDw0AAGBDBHDE0rHDwzpx320aHujWzGJOwwPdOnHfbXRBAQAALY82hIitY4eHCdwAACB2mAEHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAiRAAHAAAAIkQABwAAACJEAAcAAAAilGz2AQAA4ufs2KROnhvXxFRGI0O9On50VMcODzf7sAAgFpgBBwBsydmxST10+rwm55a0uyelybklPXT6vM6OTTb70AAgFgjgAIAtOXluXCnP1JtOyqxwmfJMJ8+NN/vQACAWCOAAgC2ZmMqoJ+WVjfWkPF2cyjTpiAAgXqgBR2xRgwo0x8hQrybnltSbXn0JWcz5OjTU28SjAoD4YAYcsUQNKtA8x4+OKuc7ZbJ5OVe4zPlOx4+ONvvQACAWCOCIJWpQgeY5dnhYJ+67TcMD3ZpZzGl4oFsn7ruNM1AAUCNKUBBLE1MZ7e5JlY1RgwpE59jhYQI3AGwTM+CIpZGhXi3m/LIxalABAEAcEMARS9SgAgCAuCKAI5aoQQUAAHFFDThiixpUAAAQR8yAAwAAABEigAMAAAARangANzPPzL5mZn8Qfr7HzL5kZi+Fl0Ml3/sLZvaymX3LzH6gZPwuM/tG+LVPmZmF411m9rlw/KtmdnOj7w8AAACwE1HMgH9U0osln39c0pedc7dK+nL4uczsLZIekHSbpHsl/aqZeeFtPi3pQ5JuDT/uDcc/IGnKOfdGSZ+U9HBj7woAAACwMw0N4GZ2SNIPSXqsZPi9kj4bXv+spPeVjD/unFt2zl2Q9LKku83sRkmDzrknnHNO0m9W3Kb4s05JendxdhwAAABoRY2eAf+Xkv6BpKBk7Abn3GuSFF4W21gclDRR8n0Xw7GD4fXK8bLbOOfykmYk7a3rPQAAAADqqGEB3Mx+WNKkc+7ZWm9SZcxtML7RbSqP5UNm9oyZPXPlypUaDwcAAACov0bOgH+/pPvM7BVJj0t6l5n9tqTXw7IShZeT4fdflDRScvtDkl4Nxw9VGS+7jZklJe2SdL3yQJxzjzrnjjjnjuzfv78+9w4AAADYhoYFcOfcLzjnDjnnblZhceUZ59zflHRa0vvDb3u/pN8Pr5+W9EDY2eQWFRZbPhWWqcyZ2TvC+u6fqLhN8WfdH/6ONTPgAAAAQKtoxk6Yn5D0eTP7gKTvSvpRSXLOnTezz0v6pqS8pA875/zwNj8l6TOSeiR9IfyQpF+X9Ftm9rIKM98PRHUnAAAAgO2wTpswPnLkiHvmmWeafRgAAABoc2b2rHPuSOU4O2ECAAAAESKAAwAAABEigAMAAAARIoADAAAAESKAAwAAABEigAMAAAARIoADAAAAESKAAwAAABEigAMAAAARIoADAAAAESKAAwAAABEigAMAAAARIoADAAAAESKAAwAAABEigAMAAAARIoADAAAAESKAAwAAABEigAMAAAARIoADAAAAESKAAwAAABEigAMAAAARIoADAAAAESKAAwAAABEigAMAAAARIoADAAAAESKAAwAAABFKNvsAAABAazs7NqmT58Y1MZXRyFCvjh8d1bHDw80+LCC2mAEHAADrOjs2qYdOn9fk3JJ296Q0Obekh06f19mxyWYfGhBbzIADALaMGdHOcfLcuFKeqTddiAy96aQy2bxOnhvnMQe2iRlwAMCWMCPaWSamMupJeWVjPSlPF6cyTToiIP4I4ACALSmdETUrXKY808lz480+NDTAyFCvFnN+2dhiztehod4mHREQfwRwAMCWMCPaWY4fHVXOd8pk83KucJnznY4fHW32oQGxRQAHAGwJM6Kd5djhYZ247zYND3RrZjGn4YFunbjvNuq/gR1gESYAYEuOHx3VQ6fPK5PNqyflaTHnMyPa5o4dHiZwA3XEDDgAYEuYEQWAnWEGHACwZcyIAsD2MQMOAAAARIgADgAAAESIEhQAscHuiwCAdsAMOIBYYPdFAEC7IIADiAV2XwQAtAsCOIBYYPdFAEC7IIADiAV2XwQAtAsCOBBDZ8cm9eCjT+qeh8/owUef7Ig66ONHR5XznTLZvJwrXLL7IgAgjgjgQMx06mJEdl8EALQL2hACMVO6GFGSetNJZbJ5nTw33vZhlN0XAQDtgBlwIGZYjAgAQLwRwIGYYTEiAADxRgAHYobFiAAAxBsBHIiZY4eHdf+dB3VlblkvXp7Tlbll3X/nQWqjAQCICQI4EDNnxyZ16rlL2j/QpTcfGND+gS6deu5S23dBAQCgXRDAgZhhS3YAAOKNAA7EDF1QAACINwI4EDN0QQEAIN4I4EDM0AUFAIB4I4ADMcOW7AAAxBtb0QMxxJbsAADEFzPgAAAAQIQI4AAAAECEKEEBYujs2KROnhvXxFRGI0O9On50lJIUAABighlwIGbOjk3qodPnNTm3pN09KU3OLemh0+fZCRMAgJhgBhyImdKdMCWpN51UJpvXyXPjzIIDaAjOugH1xQw4EDPshAkgSpx1A+qPAA7EDDthAohS6Vk3s8JlyjOdPDfe7EMDYosADsQMO2ECiBJn3YD6I4ADMcNOmACixFk3oP5YhAnEEDthAojK8aOjeuj0eWWyefWkPC3mfM66ATvEDDgAAFgXZ92A+mMGHAAAbIizbkB9MQMOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiJ0wAQDAhs6OTerkuXFNTGU0MtSr40dH2RkT2AFmwAEAwLrOjk3qodPnNTm3pN09KU3OLemh0+d1dmyy2YcGxBYBHAAArOvkuXGlPFNvOimzwmXKM508N97sQwNiixIUIIY4HQwgKhNTGe3uSZWN9aQ8XZzKNOmIgPhjBhyIGU4HA4jSyFCvFnN+2dhiztehod4mHREQfwRwIGY4HQwgSsePjirnO2WyeTlXuMz5TsePjjb70IDYIoADMTMxlVFPyisb43QwgEY5dnhYJ+67TcMD3ZpZzGl4oFsn7ruNsjdgB6gBB2JmZKhXk3NL6k2vPn05HQygkY4dHiZwA3XEDDgQM5wOBgAg3gjgQMxwOhgAgHijBAWIIU4HAwAQXwRw1IS+0wAAAPVBCQo2Rd9pAACA+iGAY1P0nQYAAKgfAjg2Rd9pAACA+iGAY1NsQwwAAFA/BHBsir7TAAAA9UMAx6boOw0AAFA/tCFETeg7DQAAUB/MgAMAAAARYgYcALBlbM4FANvHDDgAYEvYnAsAdoYADgDYEjbnAoCdIYADALaEzbkAYGcI4ACALWFzLgDYGQI4AGBL2JwLAHaGAA4A2BI25wKAnaENIQBgy9icCwC2r2Ez4GbWbWZPmdnzZnbezP5JOL7HzL5kZi+Fl0Mlt/kFM3vZzL5lZj9QMn6XmX0j/NqnzMzC8S4z+1w4/lUzu7lR9wcAAACoh0aWoCxLepdz7g5Jb5V0r5m9Q9LHJX3ZOXerpC+Hn8vM3iLpAUm3SbpX0q+aWXGZ/aclfUjSreHHveH4ByRNOefeKOmTkh5u4P0BAAAAdqxhAdwVzIefpsIPJ+m9kj4bjn9W0vvC6++V9Lhzbtk5d0HSy5LuNrMbJQ06555wzjlJv1lxm+LPOiXp3cXZcQAAAKAVNXQRppl5ZvZ1SZOSvuSc+6qkG5xzr0lSeFksIjwoaaLk5hfDsYPh9crxsts45/KSZiTtbcidAQAAAOqgoQHcOec7594q6ZAKs9nft8G3V5u5dhuMb3Sb8h9s9iEze8bMnrly5comRw0AAAA0TiRtCJ1z05LOqlC7/XpYVqLwcjL8touSRkpudkjSq+H4oSrjZbcxs6SkXZKuV/n9jzrnjjjnjuzfv78+dwoAAADYhkZ2QdlvZrvD6z2S3iNpTNJpSe8Pv+39kn4/vH5a0gNhZ5NbVFhs+VRYpjJnZu8I67t/ouI2xZ91v6QzYZ04AAAA0JIa2Qf8RkmfDTuZJCR93jn3B2b2hKTPm9kHJH1X0o9KknPuvJl9XtI3JeUlfdg5V9zr+KckfUZSj6QvhB+S9OuSfsvMXlZh5vuBBt4fAAAAYMes0yaMjxw54p555plmHwYAAADanJk965w7UjnOVvQAAABAhAjgAAAAQIQI4AAAAECECOAAAABAhAjgAAAAQIQI4AAAAECECOAAAABAhAjgAAAAQIQI4AAAAECECOAAAABAhAjgAAAAQIQI4AAAAECEks0+AMTD2bFJnTw3rompjEaGenX86KiOHR5u9mEBAADEDjPg2NTZsUl97NTz+trElF6fXdLXJqb0sVPP6+zYZLMPDQAAIHYI4NjUJ77woqYzOblA8szkAmk6k9MnvvBisw8NAAAgdihBwaYuXMsoYVIiYZIkM8kFTheuZZp8ZAAAAPHDDDgAAAAQIQI4NjW6r0+BkwLn5OQUOKfAFcYBAACwNQRwbOrn7z2sod6UTFLeD2SShnpT+vl7Dzf70AAAAGKHAI5NHTs8rF++/w697aYh3birR2+7aUi/fP8dtCEEAADYBhZhoibHDg8TuAEAAOqAGXAAAAAgQgRwAAAAIEIEcAAAACBCBHAAAAAgQgRwAAAAIEIEcAAAACBCBHAAAAAgQgRwAAAAIEIEcAAAACBCBHAAAAAgQgRwAAAAIEIEcAAAACBCBHAAAAAgQgRwAAAAIEIEcAAAACBCBHAAAAAgQgRwAAAAIEIEcAAAACBCBHAAAAAgQgRwAAAAIEIEcAAAACBCBHAAAAAgQslmHwDi4ezYpE6eG9fEVEYjQ706fnRUxw4PN/uwAAAAYocZcGzq7NikHjp9XpNzS9rdk9Lk3JIeOn1eZ8cmm31oAAAAsUMAx6ZOnhtXyjP1ppMyK1ymPNPJc+PNPjQAAIDYIYBjUxNTGfWkvLKxnpSni1OZJh0RAABAfBHAsamRoV4t5vyyscWcr0NDvU06IgAAgPgigGNTx4+OKuc7ZbJ5OVe4zPlOx4+ONvvQAAAAYocAjk0dOzysE/fdpuGBbs0s5jQ80K0T991GFxQAAIBtoA0hanLs8DCBGwAAoA6YAQcAAAAiRAAHAAAAIkQABwAAACJEDXgbYJt4AACA+GAGPObYJh4AACBeag7gZvYGM3tPeL3HzAYad1ioFdvEAwAAxEtNAdzM/rakU5JOhkOHJP1eg44JW8A28QAAAPFS6wz4hyV9v6RZSXLOvSSJIuMWwDbxAAAA8VJrAF92zmWLn5hZUpJrzCFhK9gmHgAAIF5qDeD/xcz+oaQeM/srkv69pP/UuMNCrdgmHgAAIF7Muc0nss0sIekDkv6qJJP0R5Iec7XcuMUcOXLEPfPMM80+DAAAALQ5M3vWOXekcrzWPuA9kn7DOfdr4Q/zwjFW+gEAGoI9DgC0q1pLUL6sQuAu6pH0x/U/HAAA2OMAQHurNYB3O+fmi5+E12mzAQBoCPY4ANDOag3gC2Z2Z/ETM7tL0mJjDgkA0OnY4wBAO6u1BvzvSfr3ZvZq+PmNkn68IUcEAOh4I0O9mpxbUm969WWKPQ4AtIuaZsCdc09LOizppyT9tKQ3O+eebeSBAQA6F3scAGhnG86Am9m7nHNnzOx/rvjSrWYm59x/bOCxAQA61LHDwzqhQi34xamMDtEFBUAb2awE5S9JOiPpr1X5mpNEAAcANMSxw8MEbgBtacMA7pz7R+EmPF9wzn0+omMCAAAA2tamNeDOuUDSz0RwLAAAAEDbq7UN4ZfM7GNmNmJme4ofDT0yAAAAoA3V2obwf1Oh5vunK8ZZjg4AAABsQa0B/C0qhO97VAjifyrp/2vUQQEAAADtqtYA/llJs5I+FX7+YDj2Y404KAAAAKBd1RrAv9c5d0fJ539iZs834oAAAK3v7NikTp4b18RURiP06AaALal1EebXzOwdxU/M7C9I+rPGHBIAoJWdHZvUQ6fPa3JuSbt7UpqcW9JDp8/r7Nhksw8NAGKh1hnwvyDpJ8zsu+HnN0l60cy+Ick5525vyNEBqAtmK1FPJ8+NK+WZetOFl5DedFKZbF4nz43z7woAalBrAL+3oUcBoGGKs5Upz8pmK09IhCVsy8RURrt7UmVjPSlPF6cyTToiAIiXmgK4c+47jT4QAI3BbCXqbWSoV5NzSyv/piRpMefr0FBvE48KAOKj1hpwADE1MZVRT8orG2O2Ejtx/Oiocr5TJpuXc4XLnO90/ChbQwBALQjgQJsbGerVYs4vG2O2Ejtx7PCwTtx3m4YHujWzmNPwQLdO3HcbZ1QAoEa11oADiKnjR0f10OnzymTz6kl5Wsz5zFZix44dHm544GbxMIB2xQw40OaYrUQc0eoQQDtjBhzoAFHMVgL1xOJhAO2MGXAAQMth8TCAdkYABwC0HBYPA2hnBHAAQMuh1SGAdkYABwC0nGOHh3X/nQd1ZW5ZL16e05W5Zd1/50HqvwG0BQI4AKDlnB2b1KnnLmn/QJfefGBA+we6dOq5S3RBAdAWCOAAgJZT2gXFrHCZ8kwnz403+9AAYMcI4ACAlkMXFADtjAAOAGg5dEEB0M4I4G3g7NikHnz0Sd3z8Bk9+OiT1EgCiD26oABoZwTwmDs7NqmfO/W8vvbdKV2eWdTXvjulnzv1PCEcQKwdOzysE/fdpuGBbs0s5jQ80K0T991GFxQAbYGt6GPu4S+OaSqTk5cwJb2EnJOmMjk9/MUxXqgAxNqxw8P8HQPQlgjgMTd+dUEJkxJmkiQzyZnT+NWFJh8ZAAAAqqEEBQAAAIgQATzmbtnbq8BJQeDknFMQOAWuMA4AAIDWQwCPuY//4Ju1uzclS0i+c7KEtLs3pY//4JubfWgAAACoggAec8cOD+tX7r9DbxsZ0oHBbr1tZEi/cv8dLFwCAABoUSzCbAN0CgAAAIgPZsABAACACBHAAQAAgAgRwAEAAIAINSyAm9mImf2Jmb1oZufN7KPh+B4z+5KZvRReDpXc5hfM7GUz+5aZ/UDJ+F1m9o3wa58yK+w6Y2ZdZva5cPyrZnZzo+4PAAAAUA+NnAHPS/rfnXNvlvQOSR82s7dI+rikLzvnbpX05fBzhV97QNJtku6V9Ktm5oU/69OSPiTp1vDj3nD8A5KmnHNvlPRJSQ838P4AAAAAO9awAO6ce80591x4fU7Si5IOSnqvpM+G3/ZZSe8Lr79X0uPOuWXn3AVJL0u628xulDTonHvCOeck/WbFbYo/65SkdxdnxwEAAIBWFEkNeFga8jZJX5V0g3PuNakQ0iUV++cdlDRRcrOL4djB8HrleNltnHN5STOS9jbkTgAAAAB10PA+4GbWL+k/SPp7zrnZDSaoq33BbTC+0W0qj+FDKpSw6KabbtrskAGgYc6OTerkuXFNTGU0MtSr40dH6eMPAB2moTPgZpZSIXz/W+fcfwyHXw/LShReTobjFyWNlNz8kKRXw/FDVcbLbmNmSUm7JF2vPA7n3KPOuSPOuSP79++vx10DgC07Ozaph06f1+Tcknb3pDQ5t6SHTp/X2bHJzW8MAGgbjeyCYpJ+XdKLzrl/UfKl05LeH15/v6TfLxl/IOxscosKiy2fCstU5szsHeHP/ImK2xR/1v2SzoR14gDQck6eG1fKM/WmkzIrXKY808lz480+NABAhBpZgvL9kv6WpG+Y2dfDsX8o6ROSPm9mH5D0XUk/KknOufNm9nlJ31Shg8qHnXN+eLufkvQZST2SvhB+SIWA/1tm9rIKM98PNPD+AMCOTExltLsnVTbWk/J0cSrTpCMCADRDwwK4c+4rql6jLUnvXuc2/0zSP6sy/oyk76syvqQwwANAqxsZ6tXk3JJ606t/ehdzvg4N9TbxqAAAUWMnTACIyPGjo8r5TplsXs4VLnO+0/Gjo80+NABAhAjgABCRY4eHdeK+2zQ80K2ZxZyGB7p14r7b6IICAB2m4W0IAQCrjh0ebnjgptUhALQ2ZsABoI3Q6hAAWh8z4ABQIu6zx6WtDiWpN51UJpvXyXPjsbofUvwfCwBYDzPgABBqh9njiamMelJe2VgcWx22w2MBAOshgANAqB02yhkZ6tVizi8bi2Orw3Z4LABgPQRwAAi1w+xxu7Q6nJjKKO8HGr8yr7HLsxq/Mq+8H8TqsQCA9RDAASDUDrPH7dLqsD/t6dL0kvK+k2emvO90aXpJfWlv8xsDQItjESYAhI4fHdVDp88rk82rJ+VpMefHcvY4ilaHjWYWbqRsWt1T2ZWMA0CMEcBbECv/geY4dnhY91+c1mNfuaCFrK++tKcP3nNLXZ9/PL9rM7ec18Hd3bo6n1XWD5T2Ejow2KX55XyzDw0AdowA3mKKK/9TnpWt/D8h8SKNjtfo8Hp2bFKnnruk/QNduimcAT/13CXdfmh3XX4Pz+/ajQz1anJuSaP7+1fGMtm8hge6m3hUAFAf1IC3GFb+A9VF0Zau0c8/nt+1a5fFpABQDQG8xbRDFwagEaIIr41+/vH8rt2xw8O6/86DujK3rBcvz+nK3LLuv/Ng3c8UnB2b1IOPPql7Hj6jBx99kj7jACJBAG8x7dCFAWiEKMJro59/PL9rV1oO9OYDA9o/0KVTz12qa0Bmsx8AzdJxATybD3R5ZknXF7KaX84rmw8a/ju3MsPCaVeguijCa6Offzy/axfFGQ9KggA0S8cFcKmwkGc6k9Xk7JIuTmX0ytUFXZpe1NX5Zc0u5bSU8+Wcq8vv2uoMS7v08AXqLYrw2ujnH8/v2kVxxoOSIADNQhcUSYFzWs75Wq6YXUt5CXUlE+pKekonE0onE/ISW+tBWzrDIkm96aQy2bxOnhtf90W3HXr4AvV27PCwTqjwnLo4ldGhBrXwa/Tzj+d3bYpdUIp/O6X6n/GI4ncAQDUE8A3k/EA5PyjrO5tMFIJ4VxjI08mEUt76JxImpjLa3ZMqG2OGBVFrl97ThNfOcfzoqH7u1PO6NLWofBAomUhooDupX/yht9T1d7TDxksA4ocAvkX5IFA+GyiTXR1LmK2E8ZVw7iVkZsywoOnoPY24cpJk4e6XFn5eR1GdVQGASgTwOgic01LO11JJCYuZKZkw/diRQ/qV//xtBUFOPWlPSzlf+UDMsCAy2ymDAprt5Llx7epJ6cZdPStjjfh3y1kVAM3QkYswo+CcU84PdMfIbv3dv/xG7epJ6/pCVoPdaf3MsT+nNx0Y0OTckqYzWS2E3VjqtfATKMVCM8TRxFRGeT/Q+JV5jV2e1fiVeeX9gH+3ANoCM+ARuHt0j+4e3VM2tpTzpdza7015YSmLV1uNObAZyqAQRwNdSb00OS8vYfISpnzgdGl6SbcO929+YwBocQTwFlNc+LlQMlZZY54Ou7OYba0jCzoTC80QRytnBIsnBl3FOADEGAE8BqrVmEurbRJLg3mS2XJUYKFZa2mXjjSNNp/1dXB3t67OZ5X1A6W9hA70d2kh629+YwBocQTwCDw1fl2PPz2h12YXdeNgjx54+8iakpTtKM6Wa3l1zEvYSt/yLkpYEGKhWWugI03tiqVTo/tXS04y2byGB7qbeFQAUB8kswZ7avy6Hjnzkq4tLGuwO6lrC8t65MxLemr8ekN+nx+4lZ0+X59d0sT1wk6fr5bs9Lmcr99OnwBqx9bntYti51MAaBZmwBvs8acnlPd9TWd85fxAKS+h/i5Pjz89UZdZ8Fqs1yYx5Vn5gk9KWICGYmOu2lE6VTvKmoD4IYA32HeuL2huMSdLmBLhSv6phZzywcLmN24g55yyeadsPigb9xKroTyVTCiVSCjlGcEcqIN26kgTReijdGpzlDUB8UQAb7BsPpCs0MlEkswk39YG31bhB06LWV+LKl/olDALA7mF9eWFOnMvQScWRCfuM33t0pGG0Nc62GgLiCemNRss5RUCahA4OecUBIXa67QXr+AaOKflnK/55byuL2T12syivnNtQRPXM5qcXdJMJqelHLXlaJyzY5P62Knn9bWJKb0+u6SvTUzpY6ee19mxyWYfWs2OHR7Wiftu0/BAt2YWcxoe6NaJ+26LXVCilr11sNEWEE/MgDfYzXv7dXFqQQvZ1RrwvnRSh4b6mn1odVHsxDK/nF8ZK86Qd6XCTiwePcuxc5/4wouazuTkmckzkwuk6UxOn/jCi7ELsNJqe+s4mpjKyDNp/Mr8SovAff1pQl8TtFNZE9BJmAFvsAfePqJU0tO+/i7dsq9P+/q7lEp6euDtI80+tIbJ5gPNLeV0dW5Zl6YW9cq1jC6VdGFZyvkrZwKAWl24llEQOC37gZbygZb9QEHgdOFafEJfsXRjcm6prHQjTrP4UmGXykvTS8oHrmyXyv4u5nSidvzoqGYXc3rp9Tm9+NqMXnp9TrOLudiVNQGdhr+WDXb36B59VLfq8acndHl2UQfq2Ac8LlxYvrLMRkLYgZwfqHLlRBCOx0W71OuyS2VrcZJkhe5WsnifXQE6BQE8AneP7umowF2rahsJJROJsk2E0smEkgmjhAVa76RJnE6mtEsbQnapbB0nz41rV09KN+7qWRmL45s6oNMQwNFS8kGgfDZQJls+nkwklPSs8BFep0Ui4qZd6nXZpbJ1tMubOqDTkFwQC/kg0FLO1/xSYZfPq3PLem1mUd8Nd/q8NL2oybklTS1kNb+cb9k2j9i+9VpexqkVZrvs7tgu96MdjAz1arGivC+Ob+qATkMAR+yttEhcymsqk9Xk7JIuThWC+Wszi7o2v6z55XysaoWx1n23H9jSeCs6dnhY9995UFfmlvXi5TldmVvW/XcejF2pQLu0U2wHvBkC4okSFLStwJVsKrSYk1SYLU15CaW8wqLPdJIylrj45AN3SnpOp1+4LD/svnHf7QfC8Xg4OzapU89d0v6BLt0UbsRz6rlLuv3Q7tiG1xiV4LelY4eHdUKFWvCLUxkdiuEGVUAnsk5btX77W+90v/elc80+DLSY4k6fxVBe7F+eiFF5A1rfg48+uaYGvFg7/TsfekcTj2xrSnfCLN3Rk1lwAChnZs86545UjjMDDmi1jKWyVWKxK0tpq8R0ktlybE+7bGDTLu0UAaBZCODABqp1ZUmYrQnlxdIWYCP9aU8vTc4rcIXSjbzv6+LUom4d7t/0tq2EzhtohLNjkzp5blwTUxmNUEqDNkcAB7YocE5LOV9LFbPlZqZkotAq0UsU2iR2pzx1pxL0Ma+TuL9AL2R9+U4yFT4kyXeKXf/sdmmniNZRWtZUukvsCSlWz3GgVkzZAXXinFPOD7SYXe3I8trMol65ltFrM4uazmTXhHbUrh22cZ+cW1YyIRXfj5lJyURhfCNnxyb14KNP6p6Hz+jBR59s+n2m8wbqrbSsyaxwmfJMJ8+NN/vQgIYggAMN5sJuLNcXsnp1elGvXF3Q5ZklXV/Iam4pp+W8zxbeNWiXF+iEmbqSnrpTnrqSnhKbnB1pxTcetCFEvU1MZdST8srGKGtCO6MEBYhYEM4YVu72mVppi1hojVhslxinjWYaqR3qjm/Z26uXryzIAiczyTkpcNIb961futGqCx6PHR4mcKNuKGtCpyGAAy0i5wdVNwtKWKGuPO0llPQSq9cTndW/vB1eoD/+g2/Wx049r/nl/Eov891dKX38B9+87m3a4Y3HdsW95h+1O350VA+dPq9MNl/W2pKyJrSrznn1BmIqcE7ZfKD55bymM1ldnVvWq9OL+u71jC5cXdDE9Yxen13StfllzS7ltJj1lW/DXT/boe742OFh/cr9d+htI0M6MNitt40M6Vfuv2PDUNmpW423YukNGoeyJnQaNuIB2lTlzHmxrCXOGwwVZ0Q7ace/s2OT+rlTz2tuKa98ECiZSGigO6lf3iS4x127bFoEoLOxEQ/QYQoz54XZ80rJREKpZFhnXnq9xUtaOrXu2EmSFVpdyjpj+/dOLr0B0P46LoBfuLagv/+5r2tXT0q7elIaDC+rfdC/Ge2qsMGQtKi1vcxT4ax5Kqw3b6XFoJ1YE3zy3Lh29aR0466elbFWWITZaO1Q8w8A6+m4AJ7NB3r+4kxN35vybE0oLwb2we7iWLLs610VbZSAOHEbzJp74aLPVHjpJVY3HkomGh/QO3Wjjk6dCWZRHoB21nEBfHigS3/rHTdpZjGvmcWcZhZzml3MaTq8zAerJ3dzvtPV+ayuzmc3+InlupOJdWfVV8eTZWOtftofkCQ/cPIDX+ttGVO6E2gyUag5T4bdWuoxg96q7fgarVNngo8dHtYJqeNq/gF0ho4L4EO9af3k999S9WuFzgr+SjCfWcxpdimvmUy2cFkyXgzuM4s5lWR2LeUDLc0tb7qzXam+tFc1tA+GQb3ya4PdqZYoBwBKFXYCdSo07Fi742exvCVVDOXJQv15scxlM8wEd95McKfW/ANofx0XwDdiZurrSqqvK6nv2d2z+Q1UWOi2sFwZzsPPqwT32cWc5pbyZYuoFrK+FrK+XptZqvlYB7qTFaUwqzPrg1Vm3Qe6k5vuuAc00kblLVJhYWhh9ny1xCXlWeEykWAmmJlgAGgbBPAdSphpoDulge6UDg3Vdhs/cJqvMqO+Ouu+dmxhuXxGcW4pr7mlvKTFGo9TGiipW99o8Wnxa31pj0WoiEw+CLRONpck/chbv0f/9xfHdHEqs7KJTX9XUj//A4eV9wN5CWvbf6/MBANAeyGAN4GXMO3qTWlXb2rzbw7l/ECzxZKYasE9UwjusyW17aWbdwROK+NbOs6VspfkmoBO5xhEqVjq5dzqR+Ck6wtZffd6oQzFS1i4OHS1Bj3trV5vBZ3YyQUAUI4AHhMpL6G9/V3a299V822y+aCsVr3qbHtJycz0YlY5f7U4xg+cri9kdX2h9kWoG3WOqTrb3p2kcwxq8vjTE+rvSmp/yXNgMefr8acndPfoHknFhaJOWa2dSi9uTJQq6eDilXzQyQUAEBUCeBtLJxPaP9Cl/QO1hXbnnJbC0F6cUV8vtJfOtO+4c0wqUVHLTucYrPXa7KIGu8v/ZHWnEro8W1sZ1kYbExUlrLA4NF2cOa/zBkWd2skFAFCOAI4VZqaelKeelKcDg9013aZq55hqC1IXiyUyVTrH5AIt5XbWOWawSkinc0x7uXGwR9cWltVTcsZkKRfowGBtC6ZrETin5Zyv5dzaDYoqWyx6Je0VE2Y1/fvq1E4uANDqnHOF8sbidYXljiqMq+JzV3q78Guq+HrKW/91gQCOHalH55jpzGpte7VymWLte6l6d46pFtr76RzTUh54+4geOfOSFnO+ulMJLeUC5QOnB94+0vDfvVmLxSIzk2cmMymRMCVM4eeF6wcGu3V1fnllBtxMWszm9T27e1YWlgJAuygNtSufa/1gu3q9erBd9+sKv75yfW1YXjmWKuON0te1fswmgCNy2+0cM7dUDOT5lY2TKjvHTJeUztSjc0wxrA/SOabp7h7do4/qVj3+9IQuzy7qwGCPHnj7yEr9dytwzilf/GNeJafff+chPXLmJflBruxNxI+89aC+c21BklZm01Ne2CO92J4xvJ7ooJDOglVgeypD5UYzu4UF7a7wEZRcd6uhdqNAq4qvSY0Ptu3AOu0/0O1vvdP93pfORfo7nxq/rsefntBrs4u6sQVDQ1xt9t815weaq+gaUxrQZ6uML+U26INXg9LOMaXtHtercadzTOcp/rvd7puI4mx6MagXS2ASppVWjMXrieJsfMm/L6v4WSa1ZKgvXbBaugHRiftuI4QjckFQCKVOhYBaDK0rl1qdqZWqBNXi11UeaovKviatO2tb/r2lt++sLBcXfV1JHdjV86xz7kjl1wjgDfbU+HU9cuYlJRNWNuP10XfdSgjfgUb9d12vc0zpjPtGnWO2Y6udY3b1pJROsggV9VUI8avlM6ZCiYzJwstQOFapmPELtwuDfXjD0jcBxTBSuK6ywFLqg599Rlfnl9WT9lZ+Xyab1/6BLv2bn7xbiZJjS5S8KVnvzUTlqfBqVu5zzN4QF+9bPd9IFbPBdv5bFG9bGRRXxlc+L359/UdlOxGl9OcGriQAB5sH42Kg9oPy68B2bBTAKUFpsMefnlAyYSsLx4ozOaWt07B1jfrvupPOMWtC+5rZ9tXZeL8OnWMqF5nSOQY7UTztLGmjMvfITExlNNidlO+vpvSUZ5q4ntHk7MZrP1bCfvj5diaaim8iyt6EVDmzkCjW/Scq3giE14sB1lZ+7urvCFyhvK44k+qHj4ELVq8XZl7DzwO3MhO6Xv3qyu9OrJ4lMSvtnb/6+9ZbULbRf5P11GMyj7PF6CQE8Abbaes0VNcq/10b0TlmuqTN48qs+1L1zjGvz26/c8xm7R4H6ByDJtpJ15ugDmFwZaZ+9f9iYeWN1M6q6apq5Bnz0rOag91JXVtY1iNnXtJHxdlitCcCeINF0TqtE8X5v+t2O8fMLeXLF54u5jSzlNdMJrtmh9R6dI4xFTrHVAvtgz0p7arytUZ3jmmHGbLf+q+v6PPPXtRizldPytOP3XVIf+sv3tzsw2o5zex6g+hxthidhgDeYLyINEan/XdN2GqdeK33sNg5ZrqiBGbtbPtqaF/IrtYeOEmzS3nNLuV1car2zjED3auz6fXsHNMOM2S/9V9f0Wef/E64SFJazvv67JPfkaTYhfBGvxmKQ9cb1E+rnNUEokIAbzBeRBqD/66b8xKm3b1p7e5N13ybnB9otiSYV5tZn67YJbW0c0zgtDK+leOs1jmm8uM3/uyC5Jy6kp7k4jlD9vlnL4bhO6zHN0lBoM8/ezFWATzqN0PxKQDBdsX5rCawHQTwCPEiUl93j+6JTfCKi5SX0N7+Lu3tr20RqiQt5/yVoD69TjlM5Wx7aecYP3C6vpDV9YVaF6EuyxQuhkuYXp9d0j/9g2/GonPMYs5X5VpYs8J4nERRLtAOZzxQu047qwkQwBuMFxG0u66Up/0pb2udY3JBeUhfKu8gUz7bnl/TOcZJygdOxZWpf/KtK5v+3srOMZu1exzsTipZ584xPSlPy3m/rBm3C2fz4ySKcgFqgjsLZzXRaQjgDcaLCFDOzNST9tST9nRgV+2dY/7021f1r8++LDNTMlE4PZ0LnO66aUh9Xcny4L6Y01wLdo75sbsOFWq+g2ClNVzgCuNxEkW5ADXBnYezmugkBPAG40UE2Dkz09Hv3a/vXFuouYNI4JzmS8phCrPs1bvGFD/mGtw5Zt9gt/7ym/brz/77NS3nA/WkErHsgvLA20f08B+N6fXZJfmBk5codPb58LE31u13UBNcu3boDgR0GgJ4g/EiAtTHU+PX9cVvvq49femVGtEvfvN1fe+BwaphI2GmwTD4brVzzGooLwb17Epv9soymZ10jsnkAv3mV7+r33v+tSolMcl1S2V6a+wc03Dh5jRVNsbcMWqCa0OZIxBPBPAG40UEqI/Hn55QLu9rOusr5wdKeQn1pb26lnPtpHPMTJWuMTOZ6vXtlZ1jpsOymVolSzrHbBbai5fdyUTdQvvjT0+ovyup/SWLdetdWkdNcG0ocwTiiQDeYLyIAPXxyrV5zS/nZSpstZ33naYXc/KD+aYe1047x6z5WCe0l3aOyQdO1xayulZz5xgpnUxo1xZ7tK/XOSaq0jpqgjdHmSMQTwTwCPAiAuxczncKAsmpsEV4sfIh68evwedOOsdUC+flwX012Jd2jsnmA12ZX9aV+doXofakvKo92k2mq/NZdSc9eYnCmYOc73TDQG2LalE/lDkC8UQABxAbQcl1p87prb/dzjELWX/dGfVqob2yc8xiztdiztfl2fUWoZaXzbw6s6S/9q++UtHOcWedY7AxyhyBeCKAA4gNU3noJratz8zU35VUf1dSB1XbbKgfOM0v51dq2ks3UqpclDo5u6ypTE6+K38btLDsa2HZ16vT9ekcU+zJXjre351UohUWobYAyhyBeCKAA4gF54I1M95OklxQ5buxHV7J4s6tdI5ZmWHP5DSztE5oL5mJz+ygc4wkJUwrM+ux6xzTAJQ5AvFDAAcQC2YJmQrBrVgDXvhC87eY72RewjTUm9ZQb1raW9ttsvmgot1jIajPVpTIvDazqMm55bIFqFL9O8dUhvVGdI4BgFIEcLQlM1PCJJOp+PqZSFhh4V44rpXrKvQzDr/XwttXfu9Kz2Otfk9R4JxcULgMXGGRYOBcuNOhU+AKNbmlnxd/fuHnrR5n8bgSZiu/P7FRr2VXPIbCAsXASUFQ+rvao1I6nUxoOefLErayi6QL3LqdOtpJu220kk5u3jmm2N/6wGC3ulMJZbK+cr7Tjx8Z0cienuqhfam8dKaVOscAQCkCODZUDIErYTAMtlJ5YFXJWFFZoFwZqwi2VhKCq3x9JaBWCc3F7y39XcxWVRcEbiX4l74xcCq8MZBWa6tdDasbXfgNzpXebvXnuPDNQPi/lc8rv7/0vUHxevH7Vn9W4ZM37OnTpekFzS+v9gHv70nq4O6+7f1HiYlO3Wilsr91XzqpxZyvP33pqv7Fj9+x6e1LO8eU7oY6XbEodbastr1xnWPWC++D3UklPUI70GkI4DFVDMIJMyUSq9eLYTkRhtOEmSxRHliL31f4ORvM/BJm20YiYUrEeMmic04fefcb9Y9On9dAd0rd4WYjed/pp4/9Od24q7DIsDTkF89KrJwVKJ6dKDkLEYczBZ260cpO+1vvqHPMmsWn5cG9NLRvvXPMWn1dXpVgvv5se393ks4xQMwRwBtkvZnjYjmBWXnoLX5NptWva7UUofgzE1aouSQco5OYmd715hv03y7N6LGvXNBC1ldf2tMH77lFf/X7DtTt96zM4jutOTvgh2HdLwb5oHC9MO5WrgfhuKtToO/UjVaa0d+6rHPM7tp+T+Cc5is2VSqG9+nFnGZLZteLAX5uKV/2M7bbOaZaGUy1Vo+7elLq66JzDNBKOi6AF2dFpIoSh/D/KmeDS4PxSqBWxcxx5awzMxNA3Z0dm9Sp5y5p/0CXbgpngU89d0m3H9qtY4eH6/I7im9sV3PK6nO5JAfWJAhWQ3nOD+QHTvnArV76Tvlg8w4uNw72rC296fLavvQmLv2tE2YrwXcrnWMqN1WaXTPbnl8Zn13MaWGdzjETW+gcs14pzHqhvScVbeeYdlvrAGyk4wJ4yrOV09UA4uPkuXGlPFNvuvBnqzedVCab18lz43UL4PVULPtJeVL3OundudVAXgzluSAoC+93vWG3Xrg0HZ4Zk3J+oGsLgX74z++K+B5Fq537W3sJ056+tPb0pWu+Tc4PKoJ6vspse3mgX8qvvsELnDSVyWkqU3vnmJRn5YF9pfXj+u0e1/u3vplOXeuAztVxARzoRGfHJnXy3LgmpjIaGerV8aOjLRlaNzIxldHunlTZWE/K08WpTJOOaOfMTEnPlNwgs3zztTkND3RpdjGnrB8o7SXU353UN16dVX9XUlk/UN5v3Rr2naC/9aqUl9C+/i7t26BzTKWlnK/ZsnCeX1vfXtG3vbRzTM53ujaf1bX52jvHdCUT68y0l4T2ih7u6WSiY9c6oHMRwIE2d3ZsUh879bzml/PyA6er88v62Knn9Sv33xGrED4y1KvJuaWVGXCpsODt0FBvE4+q8SamMtrX36X9A6sLCZ1zen12ScODq2OFmfRCGM8HTvmw7CW3hXKXVkNJws50pzx1p7yyfycbKe0cM72YLatf32i2vXQR6nI+0OTcsibnttY5ZjnvK+Ul5CVMnlnhMiHNLOb0X759hc4xaDsEcKDNfeILL2o6kyu8qJnJBdJ0JqdPfOHFWAXw40dH9dDp88pk8yuzYznf6fjR0WYfWkPV+sajEFg8da3zV905p1wYxAsBvRDSWzWgU5IQvW13jln2V+vXK4L7bMkse7G2fXYxV9bpdDFXqG9fzlf/N/hP/tM314zROQZxRwAH2tyFa5lCm8rE6gJDFzhduBav0o1jh4d1QoVa8ItTGR2KaSnNVtXrjYeZKZ00pbX+zGHeD9bUo+f9wiLSfFC/zi61oCQhHsxM/d1J9XcndXCotvVVfuA0v7xaDjOdyen5iWn95xdfX9nmtrhwebA7peV8oPnl+nWOWW/nUzrHIEoEcACxcezwcNsH7kpRvvFIeokN69GLAT0X1p0XA3q+ATPondp+sRN4CVsJuUX33LpPb795T8mi2/6ykqO8H5R1hqkshZldKp91n87kVmbWpfLOMWqjzjGILwJ4C2qHBXNoHaP7+jR2eU5Zf/XFyCQdPtDfvIPClrTKG49iQK/W6cI5t1raEmy/7WJRM/qAo7k2WnSb9BJb7hyTzQdVWz1WtnksrXNfrmPnmPKSmPp3jkG8EcBbzNmxST10+rxSnml3T0qTc0t66PR5nZBa4gUY8bO7J7lmZ3kXjgP1YmZKeRb2S68eKILAKesHyvmBcmFpSzZf+LxSXPqAo3Wlk9vvHLMayvNratlnKj4i6RxTUeueTrIINe54BW4xcet1jNb31HemtzTeyjg7FG+JhKk74a2Z8SudPS+WtbzrzcNKJU2//eR39dpMe/UBR+vaTueYxZy/pmNMte4xpR877RzTm/ZKZtmTVctkKoM7i1BbCwG8xbRjr2M0lx/+pS8tS3RudTwuODvUvkpnz3tKZs//+l0j+ut3jZR1cMmF3VtKa9HbsQd6J4pj20mzwoRZbzq5pc4x88v5tW0ei+UymdLZ9tUZ+NJ/5Zmsr0zW12sztS1ClaT+ruTKzPp6gb00tPd30TmmkQjgLWZkqFevXJvX7GJ+ZdONwZ6kbt5LvS62x0tY1bAdtz+snB3qXJt1cCnrgd7k7i3Ynk5qO2lmGuhOaaA7tfXOMZlcWV179dn2Qmiv7Bwzv5zX/HJel6ZrO86ElYb26rPqlR99XSxCrRUBvMW8c3SPnnrleqFtnElZP9DkXFYPvr29/gC1s1Yrk7jv9gP63a+/psoMct/tB5pzQNvE2SGsZ7Me6Gu7thT6nxc3K0Lz0XZyY9U6x2xmTeeYNTXsec1kspoJe7PPLOaUya4u1g/caueYiRo7x3jhG6ithPbuVKIjQzsBvMU8MX5d+/vTmltanQEf6E7qifHr+kizD67FtFrQLR5Tq5VJfPKBOyU9p9MvXJYfOHkJ0323HwjH46NTd8LEzqW8xJrylqLKDYpy+cJlNs/seZRoO1l/O+4cs2a2vaRkJvza9GJO2ZLOMX7gdtQ5ZldPSru6i6G9vTvHEMBbzHrbTjPLV64Vg67UumUS733rIV2eza68WXnvWw817Vi2q1N3wkRjbVbeki92bGH2vKFoO9katts5prwMpkqLx6XV2vaZTE75gM4xBPAWwyxfbVo16LZimUSrvlnZqk7dCRPNVex9Xm32PAjWbkZUXBzqhz3QURvaTsZXsXPMDVvsHFNWv57JlZXCVH5tdmnnnWN6Ul5ZUN+sc8xgd1JJr3GhnQDeYpjlq00rBl2pNd9Ateqble1olQ1pAKnQVrFrg9rzyoCe9YPVxaKUt5S5e3SPPqpbS3bCjEcXFGxdaeeYG3fVdoYjcE4Ly/k1s+zF3VCrBfe5pXxZ55jFnK/FnK/Ls63ROYYA3mKY5atNKwZdqTXfQLXqmxVgM624zmMrNgrozhU3JXIrmxGttylRp9hoJ0x0tkRJ55hDQ7Xdxg+c5pc26M9epZvMwrJf9jO20zlmoHt1ln1P3/qlPATwFsQs3+ZaMehKrfkGamSoVxeuzq9Z2HvLPlpbonW1S+nUesxMXckwnJe8RjvntFwWyIsLQtcP5nHsnw00mpcw7epNaVfvDjrHrAntpbPw1TvHFL++GQI4YqkVg27psbXCcRRVa215ZT6rv3E3L9DNEPdZ3ai0U+nUVpjZSk1tqSAozJhn/UC5kmD+X1++2jH9s4FG23HnmIrgvrDs61fW+131OeS1zOw3JP2wpEnn3PeFY3skfU7SzZJekfRjzrmp8Gu/IOkDknxJH3HO/VE4fpekz0jqkfSHkj7qnHNm1iXpNyXdJemapB93zr3SqPuD1tNqQbdVPTF+XcMD6TWbO9HaMnrtPqtbT5ROlUskTN2JtcH8H5y6pO5UQj2ppJxz6utKKJPN0z8biMhGnWP6upLrBvBG9mT5jKR7K8Y+LunLzrlbJX05/Fxm9hZJD0i6LbzNr5pZ8a/MpyV9SNKt4UfxZ35A0pRz7o2SPinp4Ybdk4idHZvUg48+qXsePqMHH31SZ8cmm31IiLGJqYzSFSu5016iY4NMM5XO6hYXIqU808lz480+tJYzMtSri1MZnX91Rt+4NKPzr86snO3CqovTi+pLFxZ+Jb2EUl5Cg90pXZ1f0vfs7tH+gS7t7k2H/9Zaqw0b0MkaNgPunDtnZjdXDL9X0rHw+mclnZX08+H44865ZUkXzOxlSXeb2SuSBp1zT0iSmf2mpPdJ+kJ4m38c/qxTkv6VmZmL+bJyZshQb/1pTy9fWZBnJs9Med/p0vSS3ri/r9mHFiv1KB2ZmMrIM2n8yvzK2Yh9/WneDFVxYDCtJ8ZXt9IOnDS9mNeBwdpPDXeC9Rakj+zpq1rKUlz8WawvZ/En0BxRvx2+wTn3miSFl8VXr4OSJkq+72I4djC8XjledhvnXF7SjKS9DTvyiDBDhnpb2eLXSj5Kx7Gp4hvjybmlsjfGWz07NdCV1KXpJeXDHUnzQeHNUP96few62B99s/p/2/XGO9Xxo6PK+U6ZbF7OFS43WpBeXPw50J3Snr60bhjs1sieXt2yr08Hh3o0PNit3b1p9XUxYw40Uqv81a+WBNwG4xvdZu0PN/uQCmUsuummm7ZzfJGh7hH1Nrec18Hd3bo6n12ZdT0w2KX55fzmN4ak+i0IXDlBV/xL5SrGsaLYWaD0faJzKus4gPotSN+oK0u2oiPLZl1ZAGwu6gD+upnd6Jx7zcxulFScyrgoqXS7q0OSXg3HD1UZL73NRTNLStol6Xq1X+qce1TSo5J05MiRln6la9X+1oivkaFevXJtvmws6we6eS9tCGtVrzfG81l/7Zuh/i4tECrXMCsE7mrjKNfIBemrwbx6V5blMJAXu7MEvJkEahL1+aXTkt4fXn+/pN8vGX/AzLrM7BYVFls+FZapzJnZO6xwvvwnKm5T/Fn3SzoT9/pvaeunE4HNvHN0jybnCoGv2IZwci6rd9IhoWYjQ71azJWH5O28MR4Z6lW2otY26we8wa7i4GBhGta51Y/ScTRXIlFol7irJ6X9A106uLtHN+/r08ieXt0w2K2hcOFnMkEZC5rnqfHr+tnPPa8Hf+1J/eznntdT41XnaZuiYc8MM/sdSU9I+l4zu2hmH5D0CUl/xcxekvRXws/lnDsv6fOSvinpi5I+7Jwrvtr9lKTHJL0s6b+rsABTkn5d0t5wwebPKuyoEnfHDg/rxH23aXigWzOLOQ0PdOvEfbexALMKusXU5onx69rfn1baSyhwhQ4o+/vTeqKF/hC1unq9MebNUO1+6Udu10CXp+KuzgmTBro8/dKP3N7cA8OGUl5CfV1JDfWldWBXt27a26s37O3Tjbt6tLevS/3dSaWTCdagoOGeGr+uR868pGsLy2U98lslhFsbTBpvyZEjR9wzzzzT7MPADpV2iyndCZM3K2vd8/AZ7e5Jlb3gOec0s5jTn/78u5p4ZPFS7IKykzrbBx99ct1dSX/nQ+9o0JHHVz3+m6M1FWvLS+vKqS1HPf3s557XtYVl9ZR0AlrM+drb16V/8eN3RHIMfV1JHdjV86xz7kjl11plESawJZ26S952sK6gvnYyZTExldG+/i7tH+he/XnOsch6HS9cnNb5V2e0kPU1s5jTCxeneX63ifUWffpBoTUiteXYqddmF+WZNDG1rJwfKOUlNNSb0uXZxWYfmiQCOGKKbjG1O350VB/93Nc0u7iw0lposCepX/yhtzT70GKjXv35eTNUu0/98bf1yJmXlTApmSj8d3rkzMuSpI+8501NPjo0ipcweVV2/CyGcWbLUau+dFLfubagRMKUCNu+vj67rDfsbY09MFgdgViq16K4TvDCxWnNLpa3HJxdzOuFi9PNOaAYqld/fhZZ1+6xr1wIw3dCCUuEl4VxdJ50MqH+rqT2UFuOWpW2fS1+lI43GTPgiKXjR0f10OnzymTzZTXgBJm1HvvKBSU9K+tGkA8CPfaVC8wk1qheZ1zq1bO5EyxkfSUrpogSJlo2VlGPXVrjyEuYetKeetKepMLz0zlXqCtntrzjLeR83TDYpalMrqQEJa1MrjX+hhDAW1Cn/jHdCoJM7QgyO9eI0pHWmINpXX3pwhvrRMmEZuAK41hVr/KodmFmSidN6WRiTW15MYwv+/7KxkKd1oiik9w42KNrC8saKfk7vZjzNdzXGq1MCeAthj+mtWvk5hPtpC/taSGbl3O+nCtsZGJWqI+Lm0/98bf12FcuaCHrqy/t6YP33BLJLH69zrjw/K7dB++5RY+ceVn5oNCyMXCFjw/ec0uzD62lnDw3rmze17X58s46LEgvt95sedlMuR8ol3fMlreJB94+okfOvKTFnK/uVEJLuUD5wOmBt49sfuMIUAPeYupVawoUvfvwfvlBIbw4FS79oDAeJ8VFeYs5v2xR3qf++NsN/9316s/P87t2H3nPm/TRd71RPSlP+aBQ8vPRd72RsqkK3359VtcWssr7Tp6Z8r7TtYWsXnp9ttmH1vKKnVgGulPa29+lG3f16Ka9vbp5b58ODvVoONxQqL+L+vI4unt0jz76rlu1t69Lc0t57e3r0kffdavubpF9F+I3Bdbm6O6BenvxtTmZykseLByPk9JFeVKhjCbKWvZ6nHHh+b01H3nPmwjcm8j5hWd2IqzVMStuE09pxXYlEqauxNoWiaUz5ssl9eW0SGxdd4/uaZnAXYkA3mJoU4Z6u3Ato5Rn8koWYfpBoAvX4hX62qGWnec36i2dTGgx6ytwTmZhgwdXGEd9rfYu9zRQMl7sW76c85X1Ay3nCOXYHAG8xdDdA43gB075oKQGXFLSi9fp1L60p4XlvJzK70dfV3z+jG33+d2pC7M79X5vxa3DA3rl2rxmF1drwAf7Urp5b3+zD61jpLyEUl6hTWJR6WZCy/nCok8/IJRjFW+RW0y9ak2BouGBLvmuogbcFcbj5N2H91e9H3GqZd/O87u4cHNybqls4ebZsckIjzx6nXq/t+r40VGlPE8HdnXre28Y0IFd3Up5HpM2TVYM5Hv60rpxV4/esLdPN+3p1YFdhbryvq6kUh4RrJPFZ+qog9DdA/Xk1lnRv954q7o8m9VQb1Izi3kFrlB+sqsnqcuz2WYf2pZs9fldunBTknrTSWWy+bbvctGp93uraMkaH0kvoaSXUG96daxQr19SUx7WmNMesf0RwIE2d3muekB9fZ3xVjUxldHB3b06NLRaOuOci90Cxq2WVXTqws1Ovd/bwaRNfCUSpu6Ep+5UeX/70jBe6Fle+ED7IIADbW69usN8zOoRR4Z6deHqvOaWyvsd37IvPrWu2+kDPjLUu7bGtyfZ9jW+LFhFJ0snE2s2EyrOlheDeY6+5bFGARKAWHjn6B5dmc8q6xc2Zsn6ga7MZ/XOFm0xVc12+oC/c3SPJufK7/fkXLzu93YcPzqqnO+UyeblXOGSBenoZImEqTvlabA7pX0lfcvfsLdP37O7R3v7uzTQnaJneUwwAw60ucoe4KXjcfLE+HUND6TXzAQ/MX5dH2n2wdVoYiojz6TxK/Mr92Fff3rDsoonxq9rsNvTzGJeuZLa9zjd7+2gthmojZcweRVlLM65QmvEki4sOd9RW95CCOCILVqU1SaRkKqdoUzE7PzXxFRGe/u6tK+/e2UsbjXgA11JvTQ5H75gmvKB06XpJd06vH45yUuTc5pf8pXyEit9nueXfL00Ga+NlLbjhYvTOv/qjBayvmYWc3rh4jTP8Sr4W4hKZoXZ8kIoL6ylKN1IqLTGnPaIzUEARyxtp5a2U+XXKQ9cb7xVtUNNsHOFGahs3smpcBYiYdpwViqbDySTElay06G5wngb+9Qff1uPnHk53P208Fg/cuZlSWJ3zBL8LUStSjcSKpX3yxd8LudZ8BmFmM2BIU7Ojk3qwUef1D0Pn9GDjz5Z1/69J8+NK5v3dXlmSd96fU6XZ5aUzfsb1tIi3tqhJvjqQrawU2Gx/iec0b66sH5HmlS4YVIQFMJ7EM5WpWO2kdJWPfaVC2H4TihhifCyMI5V21lXAJQqtEZMandvWsOD3RrZ06tb9hXqyvcNdGmwJ6XulLcyCYD6YAYcDdHoWZlvvz6r2aW8EjJ5Zsr7TtcWssr7szs/eLSkdqgJzuYDeZ4pWVL/kw+CDWez33TDYJXuL6lYdX/ZjoWsr4SclvOrO596VhjHKto1ohHKS1hW5SpmyrP5gC4s20QAR0OcPDeunO/r2nz5grl6baKR8wuzgIlEyWn5wCnrU8vWzuLe7zjlmRZzhX+rxXpuaePZ7OL29Qd2Jbe0fX3cdXkJZXKrYduFu6D2pjhxW6odSrMQHykvoZSXUF9Je0Q/cCsLPSlhqR1/ydAQL03O6epcVvnArSw2uzqXrdvCsXQyITkpcE5OToEr7E+eTvJPulJinWy33jga5003DKov7SkXBFrKB8oFgfrSnm69YXDd22xn+/p24CWqv5leb7xTtUNpFuLNS9iaEpabi60R+7rU353ktbkKZsDREI1eOHbr8MDazUn6Um2/Ocl2dKc8Zaqctq88tRgHce/28M7RPXrqlevyEqaUFWZ055b9TXt6x33mfzvms9X/Vqw33qnaoTQL7ad8h8/VLiyVrRHbfTH5RgjgaIjtnGrfik49Lb8de3qSVQP4np54Pf3bodvDE+PX1ZNKaH559fHo7/Lavqf3dhT/ZpSu+3JudRyr2uUN2qf++Nt67CsXtJD11Zf29MF7bqHjTRtZrzViaShfznVO+Uq8XoERG41eOMaszxYkEhrsSmh2efWP2mBXQhazRuCl3R4kqTedVCabr9u6giicf3VG88t+2SZI88u+zr8607RjalW9Ka9QA+7WjqP90HayM1UL5YX1XIGWc4GW/fYN5QRwNEQUM9TtMuvTaP1pT69Ol//xms8G+p7d8Qoy7dDtYaWDR2kCd3T2qObv/KVR/csvv6TSPUISVhhH+ym0l3TyAykfdr2xsO0kAbyzVCtfCQK30nVlOe+3xUJPAjga4tjhYd1/cXrN6UQCc/SuLmRVudFZsEnv6VbUDt0eij28K8soAnaiW6MYuihJ6Azzy3kFLnxvaqtdb+aX880+NLSARMLUk/bUk14N5X7gygL5ci5eLREJ4GiIs2OTOvXcJe0f6NJN4Qz4qecu6fZDuwnhEbs2Xz1orzfeqo4fHdXHTj2vS9OL8sPuOv1dSf3iD72l2YdWs4Hu5EqgKPa2lqT+Lv4UV/OR97yJwN0hrLhYqGSTKrlwHKjCKwvlBcWWiMu51u9THq8iUMQGu7O1jvXmVuM452qS5MKt2115JUccfPCeWyQVZvZceFk6DnSqnlTh2VxcaFs8S9SbituzHM1UbIk41JfWgV3dumlvr27a06sbBrs11JtWbzopr0V68DLtgoZoh3pdtJaT58aV9ExewuS7wmUyfFMXl7Mqtx/arb60p4Wsr8AVapr70p5uP7S72YcGNNXIUJ9evLx2n4hDQ31NOBq0k6SXULJi86C8Hyhbsatn1DXlBHA0RDvU67aL8Exu1fE4eWlyTlMLWQWS5KR84GspXNwbFyfPjWt4sLvseRG3Ti5R+vuPP6fTL1xeKTm67/YD+uQDdzb7sNAAzjklEybPbKV1re9c4WwXUGfFUN6bXh1b6b4ShvJiQG/Uv0ECOBqi2AUlk83Tp7vJEgmTX2WRX6JFTsPVKrPsyy8tO3GSH47HxcRURp5J41fmV9pz7utPx/LMUKM3Rfr7jz+n3/36ayuf+4ELP3+OEN6G5rO+Du7u1tX57Mpz40B/Fx2CEJny7isFzrmymfLi9WqvqVv+fTv+CUAVnbp9divqWaeGMm61lVm/8ELsSj5Kx+NgoCupS9NLyoczuvnA6dL0UuwWYRY3RZqcWyrbFOns2GTdfsfpFy5LWm1HV1yLVxxHexkZ6tVyxa6Iy/mAs6ZoKjNTV9LTQHdKe/u7dOOuHr1hb19ZXXlfV1Ipb+txOl5/9REr9OluDYd292rs9fk14wd3x+uFzUsk5FxQCN/FPsHheFysnMosvntwFeMxEcWmSOvNMNVj5gmt552je/TUK9eVsMLaiKwf6Mp8Vn/j7j3NPjRgjWp15ZUbCGXzwYalnvF55QKwLeudwo3bqd3RfX0yM6W8hLpSCaW8hMxMo/vis0ireJo96Zl855T0TAd3d8fusZiYyqinYkfKei+yLnYqqOyK0SodDFBfT4xf1/BAWmkvocBJaS+h4YG0nhi/3uxDA2qSSBR29dzVm9LwQLcODfVqeLB73e9nBhxoc5dnlrY03qp+/t7D+rlTz2tuKa+8HyiZSGioN6Wfv/dwsw+tZsXFyaP7+1fGMtm8hgfW/yPdikaGevXKtXnNLuZX6nUHe5K6eW//5jeu0d1v2K0nLkxVHUf7mZjKaG9fl/b1rz4XnHOxXB8B1IIZcKDN5cOpw8pa2nzMyh6OHR7WL99/h95205Bu3NWjt900pF++/45YlTkdPzqqnO+UyeblXOEyjouT3zm6R5NzhcVyxXKBybms3jlav3KBievVg9d644i3kaFeLebKzwTROQvtjAAOtDkvDNxrTuXH+Ex+vN46rGqXxclPjF/X/v7ycoH9/fUtF7g0s7ylccRbu7w5BWpFCQrQ5m4dHtC3Ls/JWcniRVcYj5Ni542UZ2WdN05IsQqw7bA4eWIqo339Xdo/0LhygXbawRWbO3Z4WCdUWOB7cSqjQw1obQm0EgI40ObKaqeDQu30QHcyVrXTUjSdN1CbKDbaapcNpFC7dnhzCtSKEhSgzbVD7bQUTecN1CaKcoGDu6svTF1vHADihBlwoAO0w8xSFLOuqE0U5QK/9L4/r4/8znOaz/oKXKE3dH/a0y+978/X7XcAQLMQwAHEwvGjo3ro9Hllsnn1pDwt5nwWaTVRo9/UHTs8rE89eCc1wQDaEiUoAGKhXTqIoHYvXJzW+Vdn9OrMks6/OqMXLk43+5AAoC6YAQcQG+1QSnN2bFInz41rYiqjEWZ11/WpP/62HjnzshImJROFcqNHzrwsSfrIe97U5KMDgJ1hBhzoAGfHJvXgo0/qnofP6MFHn9TZsclmH1JHKrZSnJxbKmulyOOx1mNfuSAXOOV8p+V84dIFTo995UKzDw0AdowADrQ5Ql/rKG2laFa4THmmk+fGm31oLWduKa+gYiwIxwEg7ihBAdpcO/XPjnv5xsRURrt7UmVjtFKsjo14ALQzAjjQ5qIKfY0Ox1HthNnI+0ErRQCARAkK0PZGhnq1mPPLxuod+qIoc4mifKPR9yOKDWzaxWB3cs2ulxaOA0DcEcCBNhdF6IsiHEexE2aj7wetFGv3wXtuUSJhSnmmrmThMpEwffCeW5p9aACwY0wlAG0uil0LoyhziaJ8I4r70Q6tFKNQbDX42FcuaCHrqy/t6YP33EILQgBtgQAOdIBGh74ownEUO2FSo91aPvKeNxG4AbQlSlAA7FgUZS5RlG9Qow0AiII511lNnY4cOeKeeeaZZh8G0HaK3UMaVeYSlXa5HwCA5jOzZ51zR9aME8ABAACA+lsvgFOCAgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEKPYB3MzuNbNvmdnLZvbxZh8PAAAAsJFYB3Az8yT9a0k/KOktkh40s7c096gAAACA9cU6gEu6W9LLzrlx51xW0uOS3tvkYwIAAADWFfcAflDSRMnnF8MxAAAAoCUlm30AO2RVxtyabzL7kKQPhZ/Om9m3GnpUiNo+SVebfRCIFI95Z+Hx7iw83p2l3R/vN1QbjHsAvyhppOTzQ5Jerfwm59yjkh6N6qAQLTN7xjl3pNnHgejwmHcWHu/OwuPdWTr18Y57CcrTkm41s1vMLC3pAUmnm3xMAAAAwLpiPQPunMub2c9I+iNJnqTfcM6db/JhAQAAAOuKdQCXJOfcH0r6w2YfB5qK8qLOw2PeWXi8OwuPd2fpyMfbnFuzZhEAAABAg8S9BhwAAACIFQI4WpaZeWb2NTP7g/Dzf2xml8zs6+HH/1Tyvb9gZi+b2bfM7AdKxu8ys2+EX/uUmVVrXYkWYGavhI/V183smXBsj5l9ycxeCi+HSr6fxzzG1nm8eY63KTPbbWanzGzMzF40s3fy/G5f6zzePL9LEMDRyj4q6cWKsU86594afvyhJJnZW1TogHObpHsl/aqZeeH3f1qFHvC3hh/3RnLk2K6/HD62xZZUH5f0ZefcrZK+HH7OY94+Kh9vied4u3pE0hedc4cl3aHC33ae3+2r2uMt8fxeQQBHSzKzQ5J+SNJjNXz7eyU97pxbds5dkPSypLvN7EZJg865J1xhscNvSnpfo44ZDfFeSZ8Nr39Wq48fj3ln4fGOMTMblHRU0q9LknMu65ybFs/vtrTB472ejny8CeBoVf9S0j+QFFSM/4yZvWBmv1FyuvKgpImS77kYjh0Mr1eOozU5Sf/ZzJ61wu61knSDc+41SQovh8NxHvP4q/Z4SzzH29GopCuS/k1YVviYmfWJ53e7Wu/xlnh+ryCAo+WY2Q9LmnTOPVvxpU9L+nOS3irpNUn/T/EmVX6M22Acren7nXN3SvpBSR82s6MbfC+PefxVe7x5jrenpKQ7JX3aOfc2SQsKy03WweMdb+s93jy/SxDA0Yq+X9J9ZvaKpMclvcvMfts597pzznfOBZJ+TdLd4fdflDRScvtDkl4Nxw9VGUcLcs69Gl5OSvpdFR7f18PTkAovJ8Nv5zGPuWqPN8/xtnVR0kXn3FfDz0+pENB4frenqo83z+9yBHC0HOfcLzjnDjnnblZhYcYZ59zfLP6hDv2IpP8WXj8t6QEz6zKzW1RYqPFUeEpzzszeEa6c/glJvx/dPUGtzKzPzAaK1yX9VRUe39OS3h9+2/u1+vjxmMfYeo83z/H25Jy7LGnCzL43HHq3pG+K53dbWu/x5vldLvY7YaKj/HMze6sKp6BekXRckpxz583s8yr8Qc9L+rBzzg9v81OSPiOpR9IXwg+0nhsk/W7YYSop6d85575oZk9L+ryZfUDSdyX9qMRj3gbWe7x/i+d42/q7kv6tmaUljUv6SRUmAXl+t6dqj/eneH6vYidMAAAAIEKUoAAAAAARIoADAAAAESKAAwAAABEigAMAAAARIoADAAAAESKAAwDKmNlnzOz+Zh8HALQrAjgAYEfMzGv2MQBAnBDAAaBNmNnNZjZmZp81sxfM7JSZ9ZrZXWb2X8zsWTP7o5Ltv/+2mT1tZs+b2X8ws94qP/OfhjPiiYrxY2b2J2b27yR9Y73fHX7vK2b2f5nZE2b2jJndGR7HfzezvxPJfxwAaCEEcABoL98r6VHn3O2SZiV9WNL/K+l+59xdkn5D0j8Lv/c/Oufe7py7Q9KLkj5Q+oPM7J9LGpb0k865oMrvulvS/+Gce8s6v/unS753wjn3Tkl/qsLOdvdLeoekEzu8vwAQOwRwAGgvE865Pwuv/7akH5D0fZK+ZGZfl/R/SjoUfv37zOxPzewbkv4XSbeV/JxflLTbOXfcrb9l8lPOuQsb/O57Sr52Orz8hqSvOufmnHNXJC2Z2e4t30sAiLFksw8AAFBXlWF5TtL5cPa50mckvc8597yZ/a+SjpV87WlJd5nZHufcdTP7C5JOhl97SIUZ7oVNfnfp58vhZVByvfg5r0UAOgoz4ADQXm4ys2LYflDSk5L2F8fMLGVmxZnuAUmvmVlKhRnwUl+U9AlJ/7+ZDTjnvuqce2v4cVrVVf7ur9TrTgFAOyGAA0B7eVHS+83sBUl7FNZ/S3rYzJ6X9HVJfzH83l+U9FVJX5I0VvmDnHP/XtKvSTptZj3b+N2f3tldAYD2ZOuX9gEA4sTMbpb0B8657+uk3w0AccMMOAAAABAhZsABAACACDEDDgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAAROh/ANyA2wIoaViIAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(width, height))\n",
"sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
"plt.ylim(0,)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Comparing the regression plot of \"peak-rpm\" and \"highway-mpg\", we see that the points for \"highway-mpg\" are much closer to the generated line and, on average, decrease. The points for \"peak-rpm\" have more spread around the predicted line and it is much harder to determine if the points are decreasing or increasing as the \"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": 26,
"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": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692 compared to \"peak-rpm\" which is approximate -0.101616. You can verify it using the following command:\n",
"\n",
"df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Residual Plot</h3>\n",
"\n",
"<p>A good way to visualize the variance of the data is to use a residual plot.</p>\n",
"\n",
"<p>What is a <b>residual</b>?</p>\n",
"\n",
"<p>The difference between the observed value (y) and the predicted value (Yhat) is called the residual (e). When we look at a regression plot, the residual is the distance from the data point to the fitted regression line.</p>\n",
"\n",
"<p>So what is a <b>residual plot</b>?</p>\n",
"\n",
"<p>A residual plot is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n",
"\n",
"<p>What do we pay attention to when looking at a residual plot?</p>\n",
"\n",
"<p>We look at the spread of the residuals:</p>\n",
"\n",
"<p>- If the points in a residual plot are <b>randomly spread out around the x-axis</b>, then a <b>linear model is appropriate</b> for the data.\n",
"\n",
"Why is that? Randomly spread out residuals means that the variance is constant, and thus the linear model is a good fit for this data.</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"width = 12\n",
"height = 10\n",
"plt.figure(figsize=(width, height))\n",
"sns.residplot(df['highway-mpg'], df['price'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<i>What is this plot telling us?</i>\n",
"\n",
"<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, leading us to believe that maybe a non-linear model is more appropriate for this data.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Multiple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n",
"\n",
"<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>. We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, let's make a prediction:\n"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"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>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": 30,
"metadata": {},
"outputs": [],
"source": [
"def PlotPolly(model, independent_variable, dependent_variabble, Name):\n",
" x_new = np.linspace(15, 55, 100)\n",
" y_new = model(x_new)\n",
"\n",
" plt.plot(independent_variable, dependent_variabble, '.', x_new, y_new, '-')\n",
" plt.title('Polynomial Fit with Matplotlib for Price ~ Length')\n",
" ax = plt.gca()\n",
" ax.set_facecolor((0.898, 0.898, 0.898))\n",
" fig = plt.gcf()\n",
" plt.xlabel(Name)\n",
" plt.ylabel('Price of Cars')\n",
"\n",
" plt.show()\n",
" plt.close()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's get the variables:\n"
]
},
{
"cell_type": "code",
"execution_count": 31,
"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": 32,
"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": 33,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"PlotPolly(p, x, y, 'highway-mpg')"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.55663829e+00, 2.04754306e+02, -8.96543312e+03, 1.37923594e+05])"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.polyfit(x, y, 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can already see from plotting that this polynomial model performs better than the linear model. This is because the generated polynomial function \"hits\" more of the data points.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #4:</h1>\n",
"<b>Create 11 order polynomial model with the variables x and y from above.</b>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 11 10 9 8 7\n",
"-1.243e-08 x + 4.722e-06 x - 0.0008028 x + 0.08056 x - 5.297 x\n",
" 6 5 4 3 2\n",
" + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"f_1 = np.polyfit(x, y, 11)\n",
"p_1 = np.poly1d(f_1)\n",
"print(p_1)\n",
"PlotPolly(p_1,x,y, 'Highway MPG')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# Here we use a polynomial of the 11rd order (cubic) \n",
"f1 = np.polyfit(x, y, 11)\n",
"p1 = np.poly1d(f1)\n",
"print(p1)\n",
"PlotPolly(p1,x,y, 'Highway MPG')\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2) polynomial with two variables is given by:</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b\\_1 X\\_1 +b\\_2 X\\_2 +b\\_3 X\\_1 X\\_2+b\\_4 X\\_1^2+b\\_5 X\\_2^2\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can perform a polynomial transform on multiple features. First, we import the module:\n"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.preprocessing import PolynomialFeatures"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We create a <b>PolynomialFeatures</b> object of degree 2:\n"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"Z_pr=pr.fit_transform(Z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the original data, there are 201 samples and 4 features.\n"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 4)"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"After the transformation, there are 201 samples and 15 features.\n"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 15)"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z_pr.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Pipeline</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Data Pipelines simplify the steps of processing the data. We use the module <b>Pipeline</b> to create a pipeline. We also use <b>StandardScaler</b> as a step in our pipeline.</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.pipeline import Pipeline\n",
"from sklearn.preprocessing import StandardScaler"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We create the pipeline by creating a list of tuples including the name of the model or estimator and its corresponding constructor.\n"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [],
"source": [
"Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We input the list as an argument to the pipeline constructor:\n"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Pipeline(memory=None,\n",
" steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False))])"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pipe=Pipeline(Input)\n",
"pipe"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, we convert the data type Z to type float to avoid conversion warnings that may appear as a result of StandardScaler taking float inputs.\n",
"\n",
"Then, we can normalize the data, perform a transform and fit the model simultaneously.\n"
]
},
{
"cell_type": "code",
"execution_count": 45,
"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": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z = Z.astype(float)\n",
"pipe.fit(Z,y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Similarly, we can normalize the data, perform a transform and produce a prediction simultaneously.\n"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ypipe=pipe.predict(Z)\n",
"ypipe[0:4]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #5:</h1>\n",
"<b>Create a pipeline that standardizes the data, then produce a prediction using a linear regression model using the features Z and target y.</b>\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([13699.11161184, 13699.11161184, 19051.65470233, 10620.36193015,\n",
" 15521.31420211, 13869.66673213, 15456.16196732, 15974.00907672,\n",
" 17612.35917161, 10722.32509097, 10722.32509097, 17804.80307397,\n",
" 18063.72662867, 19320.78745066, 26968.56492801, 27674.72007721,\n",
" 28191.0677239 , 650.62317688, 5648.50489642, 5813.27443123,\n",
" 5478.81383232, 5370.64136587, 8739.61952024, 5799.04215638,\n",
" 5902.61157827, 5902.61157827, 9036.2046829 , 11863.43973759,\n",
" 18767.70667001, 4808.3090102 , 5693.32889063, 4006.47212651,\n",
" 6118.73075572, 6194.05397163, 6448.26982534, 6514.17763926,\n",
" 9478.65495235, 9728.16310506, 9798.77861998, 10118.90228761,\n",
" 11178.86719942, 10423.81935057, 9463.46710755, 12626.61544369,\n",
" 34470.03895495, 34470.03895495, 43996.52260522, 5265.67702191,\n",
" 5565.15645357, 5588.69495854, 5777.00299832, 5800.5415033 ,\n",
" 7337.21461795, 7337.21461795, 7360.75312292, 10536.2966792 ,\n",
" 11015.41658913, 11133.109114 , 11015.41658913, 11133.109114 ,\n",
" 10579.12325046, 11203.72462892, 15570.21546943, 13087.15905929,\n",
" 23142.39640924, 24248.70614297, 23048.24238935, 24342.86016287,\n",
" 29819.13398143, 29560.21042672, 38084.86726826, 36887.82152897,\n",
" 19534.15717412, 5839.59780174, 5853.82556115, 6136.28762083,\n",
" 8819.65043715, 11606.18674596, 10961.06060934, 18871.2760919 ,\n",
" 19285.55377942, 19309.0922844 , 11135.24554614, 11323.55358593,\n",
" 11761.54087878, 11761.54087878, 6019.99158096, 6831.56582665,\n",
" 6156.51490981, 6250.6689297 , 6655.53121524, 6311.86904263,\n",
" 6674.36201921, 6406.02306252, 6716.73132817, 6580.20799932,\n",
" 11332.74595339, 11229.17653151, 22445.30557997, 23391.55347988,\n",
" 22388.7085116 , 22868.45917635, 25256.2976354 , 23188.58284399,\n",
" 14248.73095747, 17908.4883867 , 15237.34816634, 18716.92280791,\n",
" 14400.66302373, 18167.4119414 , 15389.2802326 , 18975.84636261,\n",
" 14507.65451218, 18167.4119414 , 18315.31025055, 5676.5372741 ,\n",
" 8739.61952024, 5799.04215638, 5902.61157827, 7505.80928975,\n",
" 11863.43973759, 18800.66057698, 18205.88219608, 24959.72677135,\n",
" 24959.72677135, 25166.86561511, 13791.57395935, 13231.35754099,\n",
" 13465.74809145, 13639.93302825, 13696.42544019, 13936.51819091,\n",
" 16774.57547431, 16958.1758131 , 6741.87395228, 8001.94145676,\n",
" 8566.86557611, 8817.44061256, 8885.05720205, 10197.10379314,\n",
" 9514.59898547, 11798.66814761, 9319.76981269, 10702.4319187 ,\n",
" 9823.59847554, 12241.40135396, 5761.92432539, 5984.79039128,\n",
" 5867.09786641, 7078.58114117, 6945.37070703, 10805.68552262,\n",
" 7058.89617998, 7190.71180783, 8165.5554308 , 8562.18780779,\n",
" 7480.67118107, 7143.73945431, 7228.47807221, 7365.00140105,\n",
" 7529.77093586, 9883.47450995, 10048.24404476, 15341.58541261,\n",
" 15322.75460863, 15393.37012355, 15995.95585086, 16160.72538567,\n",
" 17389.43534526, 11237.74316189, 9931.88932009, 11579.90587178,\n",
" 11579.90587178, 11787.04471555, 21623.36319906, 21811.67123885,\n",
" 22085.5781321 , 21364.42951378, 7186.34609846, 9252.57850626,\n",
" 7200.46920145, 9266.70160925, 9563.28677191, 8171.0947085 ,\n",
" 10411.30048253, 9551.61632807, 9396.26219524, 14558.59519649,\n",
" 9250.86701184, 10971.41942458, 16506.09239741, 17080.43191875,\n",
" 16614.36952029, 17118.09352671, 18586.83451761, 19114.09702901,\n",
" 16694.4004372 , 19503.67920162, 20475.45837959, 17804.03881343,\n",
" 17104.07508015])"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"ninput = [('scale',StandardScaler()),('model',LinearRegression())]\n",
"pipe2 = Pipeline(ninput)\n",
"pipe2.fit(Z,y)\n",
"npipe2 = pipe2.predict(Z)\n",
"npipe2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
"\n",
"pipe=Pipeline(Input)\n",
"\n",
"pipe.fit(Z,y)\n",
"\n",
"ypipe=pipe.predict(Z)\n",
"ypipe[0:10]\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>4. Measures for In-Sample Evaluation</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n",
"\n",
"<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n",
"<ul>\n",
" <li><b>R^2 / R-squared</b></li>\n",
" <li><b>Mean Squared Error (MSE)</b></li>\n",
"</ul>\n",
"\n",
"<b>R-squared</b>\n",
"\n",
"<p>R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.</p>\n",
"\n",
"<p>The value of the R-squared is the percentage of variation of the response variable (y) that is explained by a linear model.</p>\n",
"\n",
"<b>Mean Squared Error (MSE)</b>\n",
"\n",
"<p>The Mean Squared Error measures the average of the squares of errors. That is, the difference between actual value (y) and the estimated value (ŷ).</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Model 1: Simple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2:\n"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The R-square is: 0.4965911884339176\n"
]
}
],
"source": [
"#highway_mpg_fit\n",
"lm.fit(X, Y)\n",
"# Find the R^2\n",
"print('The R-square is: ', lm.score(X, Y))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can say that ~49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\".\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the MSE:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:\n"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The output of the first four predicted value is: [16236.50464347 16236.50464347 17058.23802179 13771.3045085 ]\n"
]
}
],
"source": [
"Yhat=lm.predict(X)\n",
"print('The output of the first four predicted value is: ', Yhat[0:4])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's import the function <b>mean_squared_error</b> from the module <b>metrics</b>:\n"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.metrics import mean_squared_error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can compare the predicted results with the actual results:\n"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The mean square error of price and predicted value is: 31635042.944639888\n"
]
}
],
"source": [
"mse = mean_squared_error(df['price'], Yhat)\n",
"print('The mean square error of price and predicted value is: ', mse)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Model 2: Multiple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2:\n"
]
},
{
"cell_type": "code",
"execution_count": 57,
"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": 58,
"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": 59,
"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": 60,
"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": 61,
"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": 62,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361218"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_squared_error(df['price'], p(x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>5. Prediction and Decision Making</h2>\n",
"<h3>Prediction</h3>\n",
"\n",
"<p>In the previous section, we trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction. Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 63,
"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": 64,
"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": 65,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 65,
"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": 66,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([37601.57247984, 36779.83910151, 35958.10572319, 35136.37234487,\n",
" 34314.63896655])"
]
},
"execution_count": 66,
"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": 67,
"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 even act as noise. As a result, you should always check the MSE and R^2.</p>\n",
"\n",
"<p>In order to compare the results of the MLR vs SLR models, we look at a combination of both the R-squared and MSE to make the best conclusion about the fit of the model.\n",
"<ul>\n",
" <li><b>MSE</b>: The MSE of SLR is 3.16x10^7 while MLR has an MSE of 1.2 x10^7. The MSE of MLR is much smaller.</li>\n",
" <li><b>R-squared</b>: In this case, we can also see that there is a big difference between the R-squared of the SLR and the R-squared of the MLR. The R-squared for the SLR (~0.497) is very small compared to the R-squared for the MLR (~0.809).</li>\n",
"</ul>\n",
"</p>\n",
"\n",
"This R-squared in combination with the MSE show that MLR seems like the better model fit in this case compared to SLR.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Simple Linear Model (SLR) vs. Polynomial Fit</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<ul>\n",
" <li><b>MSE</b>: We can see that Polynomial Fit brought down the MSE, since this MSE is smaller than the one from the SLR.</li> \n",
" <li><b>R-squared</b>: The R-squared for the Polynomial Fit is larger than the R-squared for the SLR, so the Polynomial Fit also brought up the R-squared quite a bit.</li>\n",
"</ul>\n",
"<p>Since the Polynomial Fit resulted in a lower MSE and a higher R-squared, we can conclude that this was a better fit model than the simple linear regression for predicting \"price\" with \"highway-mpg\" as a predictor variable.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Multiple Linear Regression (MLR) vs. Polynomial Fit</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<ul>\n",
" <li><b>MSE</b>: The MSE for the MLR is smaller than the MSE for the Polynomial Fit.</li>\n",
" <li><b>R-squared</b>: The R-squared for the MLR is also much larger than for the Polynomial Fit.</li>\n",
"</ul>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Conclusion</h2>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Comparing these three models, we conclude that <b>the MLR model is the best model</b> to be able to predict price from our dataset. This result makes sense since we have 27 variables in total and we know that more than one of those variables are potential predictors of the final car price.</p>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Thank you for completing this lab!\n",
"\n",
"## Author\n",
"\n",
"<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Joseph Santarcangelo</a>\n",
"\n",
"### Other Contributors\n",
"\n",
"<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
"\n",
"Bahare Talayian\n",
"\n",
"Eric Xiao\n",
"\n",
"Steven Dong\n",
"\n",
"Parizad\n",
"\n",
"Hima Vasudevan\n",
"\n",
"<a href=\"https://www.linkedin.com/in/fiorellawever/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\">Fiorella Wenver</a>\n",
"\n",
"<a href=\"https://www.linkedin.com/in/yi-leng-yao-84451275/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDA0101ENSkillsNetwork20235326-2021-01-01\" target=\"_blank\" >Yi Yao</a>.\n",
"\n",
"## Change Log\n",
"\n",
"| Date (YYYY-MM-DD) | Version | Changed By | Change Description |\n",
"|---|---|---|---|\n",
"| 2020-10-30 | 2.2 | Lakshmi |Changed url of csv |\n",
"| 2020-09-09 | 2.1 | Lakshmi | Fixes made in Polynomial Regression Equations |\n",
"| 2020-08-27 | 2.0 | Lavanya | Moved lab to course repo in GitLab |\n",
"\n",
"<hr>\n",
"\n",
"## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python",
"language": "python",
"name": "conda-env-python-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.13"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment