{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# DS 2500 Day 15\n",
"\n",
"Mar 3, 2023\n",
"\n",
"\n",
"## Content:\n",
"Regression \n",
"- like a classifier, but predicts a continuous feature instead of a nominal one\n",
"\n",
"## Admin:\n",
"- project teams:\n",
" - if your team was matched, one person should send a note to all others to set a first meeting\n",
" - if your team hasn't yet been created:\n",
" - see note on piazza\n",
" - email Alex when you've got team members\n",
"- project mentors:\n",
" - each team will be assigned one TA mentor, we hope to have this done for you the monday we're all back from break\n",
" - our TAs pick which projects they'd like to support, so you all get a mentor who's interested in your project!\n",
"\n",
"#### Data Credit:\n",
"The blue bike data was collected and cleaned by Piotr Sapiezynski (https://www.sapiezynski.com/) https://www.bluebikes.com/system-data"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Regression: Motivation\n",
"### How many people use Boston's bike sharing on a hot (or cold) day?"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"\n",
"sns.set(font_scale=1.5)\n",
"plt.scatter(df['temp'], df['trip_count'])\n",
"plt.xlabel('Temperature [F]')\n",
"plt.ylabel('Number of trips')\n",
"plt.gcf().set_size_inches(10, 5)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* Regression:\n",
" - predicting a continuous number from input data\n",
"* We will predict the number of blue bike trips in October 2019 based on the temperature:\n",
" * intuition from graph:\n",
" - higher temp -> more bike trips"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Linear regression\n",
"Regression seeks to find coefficients $a_0, a_1$ so that the function:\n",
"\n",
"$$ \\hat{y} = a_1 x + a_0 $$\n",
"\n",
"is able to predict $y$ from $x$.\n",
"\n",
"* $x$ is our input data \n",
" - (temperature on a given day)\n",
"* $y$ is the outcome we're predicting \n",
" - (number of bike trips on same day)\n",
"\n",
"To learn the function we \n",
"1. observe paired observations of $(x, y)$ \n",
" - (this is akin to observing the scatter plot above)\n",
"1. find the $a_i$ coefficients which best map $x$ to $y$.\n",
" - (this is akin to drawing a line through the scatter which \"best\" fits the points)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# What do $a_1$ and $a_0$ mean?\n",
"\n",
"## Algebraic meaning:\n",
"- $a_1$ is the slope of the line\n",
" - when x increases by 1, how much does y change?\n",
"- $a_0$ is the y-intercept of the line\n",
" - when x=0, what value is y?\n",
" \n",
"## Application meaning (from algebraic meaning):\n",
"Returning to our blue bike example where:\n",
"- x is the temperature\n",
"- y is the number of riders on a given day\n",
"\n",
"\n",
"- because $a_1$ is the increase in y when x increases by 1\n",
" - it represents the increase in riders because the temperature goes up by 1\n",
"- because $a_0$ is the value of y when x=0\n",
" - it represents the number of riders our model predicts when temperature=0"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Often there is no $a_1$ and $a_0$ which \"fits\" every observation...\n",
"\n",
"Specifying $a_1$ and $a_0$ is equivilent to specifying a straight line. \n",
"\n",
"Can we fit a straight line through all these observations? (very often: no)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'y')"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = [0, 1, 2, 3, 4, 5]\n",
"y_true = [0, 3, 2, 4, 3, 5]\n",
"\n",
"plt.scatter(x, y_true)\n",
"plt.gcf().set_size_inches(7, 5)\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## ... lets find the line which \"best\" fits these points"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Regression Recipe\n",
"1. Choose some \"form\" of the relationship between x and y:\n",
" - `y_pred = a_1 * x + a_0`\n",
" - this is a simple model, we could have chosen others too (more next lesson)\n",
" - a polynomial: `y_pred = a_2 * x ** 2 + a_1 * x + a_0`\n",
" - exponential: `y_pred = a_1 * np.exp(x)\n",
" - remember the $a_i$ coefficients define the position of the line above\n",
"1. Quantify what a \"good\" model is\n",
" - We want to minimize average distance from predicted y to observed y\n",
" - see MSE on next slide\n",
"1. `.fit()` the model parameters to maximize how \"good\" the model is\n",
" - Choose $a_0, a_1$ to draw a line which is as close as possible to all the points\n",
" - \"as close as possible\" = minimize average distance from predicted y to observed y"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Mean of Squared Errors (MSE): Intuition\n",
"Before formally defining **Mean of Squared Error (MSE)**, lets build our intuition of it:\n",
"- MSE measures how closely a line (i.e. $a_1, a_0$) comes to all observations $(x, y)$\n",
"- MSE is 0 when the line goes through all points exactly\n",
" - in other words, some $a_1, a_0$ has, for every pair $(x, y)$:\n",
" $$\\hat{y} = a_1 x + a_0 = y $$\n",
"- MSE is large when the line is far from many pairs $(x, y)$\n",
"\n",
"# The best line $(a_1, a_0)$ is the one which minimizes MSE"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"def get_mse(y_true, y_pred):\n",
" # calculate the mean squared distance between the predicted and actual y\n",
" return np.mean((y_pred - y_true) ** 2)\n",
"\n",
"def show_fit(x, y, slope, intercept):\n",
" plt.figure()\n",
" \n",
" # transform the input data into numpy arrays and flatten them for easier processing\n",
" x = np.array(x).ravel()\n",
" y = np.array(y).ravel()\n",
" \n",
" # plot the actual data\n",
" plt.scatter(x, y, label='y_true')\n",
" \n",
" # compute linear predictions \n",
" # x is a numpy array so each element gets mulitplied by slope and intercept is added\n",
" y_pred = slope * x + intercept\n",
" \n",
" # plot the linear fit\n",
" plt.plot(x, y_pred, color='black',\n",
" ls=':',\n",
" label='y_pred (regression)')\n",
" \n",
" # for each data point plot the error\n",
" for idx, (x_i, y_i) in enumerate(zip(x, y)):\n",
" # compute predicted position\n",
" y_pred_i = slope * x_i + intercept\n",
" \n",
" # plot error\n",
" plt.plot([x_i, x_i], [y_i, y_pred_i], \n",
" ls='--', lw=3, color='tab:red',\n",
" label='error' if idx == 0 else \"\")\n",
" \n",
" plt.legend()\n",
" plt.xlabel('x')\n",
" plt.ylabel('y')\n",
" \n",
" # compute mean squared error\n",
" y_pred = slope * x + intercept\n",
" mse = get_mse(y_true=y, y_pred=y_pred)\n",
" \n",
" # add title which shows model and MSE\n",
" plt.suptitle(f'y_hat = {slope:.2f} * x + {intercept:.2f}, MSE = {mse:.3f}')\n",
" plt.gcf().set_size_inches(10, 5)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"\n",
"sns.set(font_scale=1.5)\n",
"\n",
"x = [0, 1, 2, 3, 4, 5]\n",
"y = [0, 3, 2, 4, 3, 5]\n",
"show_fit(x, y, slope=-1, intercept=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The error of the j-th data point is the distance between our estimate $\\hat{y}$ and the observed $y$ (length of dotted red line above)\n",
"\n",
"$$\\texttt{Error}_j = \\hat{y} - y = a_1 x + a_0 - y$$\n",
"\n",
"This definition \"Mean of Squared Errors\" is more than a name, its a recipe:\n",
"\n",
"How to compute MSE:\n",
"1. Compute the error of every observation (length of red line)\n",
"1. Square each error\n",
"1. Compute average of all squared errors\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = [0, 1, 2, 3, 4, 5]\n",
"y = [0, 3, 2, 4, 3, 5]\n",
"show_fit(x, y, slope=1, intercept=.9)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# In Class Assignment 1\n",
"\n",
"Given the paired observations:\n",
"```python\n",
"x = np.array([0, 1, 2, 3, 4, 5])\n",
"y = np.array([1, 3.5, 4, 5, 4.5, 6])\n",
"```\n",
"1. Find an $a_1, a_0$ (slope, intercept) which get close to the minimum MSE (guess and check via `show_fit()`)\n",
"1. Compute the MSE of the line $a_1 = 0, a_0 =$ `np.mean(y)` by hand\n",
" - stuck? skip to the next part and come back to this computation\n",
"1. Verify your answer using `show_fit()`\n",
"1. This computation feels oddly familiar ... can you identify where we've seen it before?\n",
"\n",
"Use the `show_fit()` function to try and find $a_1, a_0$ which MSE is the smallest in the following dataset:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"source": [
"x = np.array([0, 1, 2, 3, 4, 5])\n",
"y = np.array([1, 3.5, 4, 5, 4.5, 6])"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# computing / verifying MSE\n",
"show_fit(x, y, slope=0, intercept=np.mean(y))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 3. , 0.5, 0. , -1. , -0.5, -2. ])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"y_pred = x * 0 + np.mean(y)\n",
"error = y_pred - y\n",
"error"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.4166666666666665"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"error_sq = error ** 2\n",
"mse = np.mean(error_sq)\n",
"mse"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.4166666666666665"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# what a coincidence ...\n",
"np.var(y)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## ICA 1 motivates two questions:\n",
"1. How can we avoid guessing and checking and find the best $a_0, a_1$?\n",
"1. What is the relationship between MSE and the sample variance of y?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## How can we avoid guessing and checking and find the best $a_0, a_1$?\n",
"\n",
"```python\n",
"from sklearn.linear_model import LinearRegression\n",
"\n",
"x = np.array([0, 1, 2, 3, 4, 5])\n",
"y = np.array([1, 3.5, 4, 5, 4.5, 6])\n",
"\n",
"reg = LinearRegression()\n",
"reg.fit(x, y)\n",
"slope = reg.coef_[0]\n",
"intercept = reg.intercept_\n",
"```\n",
"\n",
"which yields\n",
"\n",
" ValueError: Expected 2D array, got 1D array instead:\n",
" array=[0 1 2 3 4 5].\n",
" Reshape your data either using array.reshape(-1, 1) if your data has a single feature or array.reshape(1, -1) if it contains a single sample.\n",
" \n",
"### don't forget\n",
"\n",
"the input $x$ of all our sklearn models must have shape (n_samples, n_features)\n"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(6,)"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.array([0, 1, 2, 3, 4, 5])\n",
"x.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"this is a 1d array, sklearn can't identify whether its:\n",
"- a single sample with 6 distinct features? (no)\n",
"- 6 distinct samples each with one feature? (yes)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(6, 1)"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = x.reshape((-1, 1))\n",
"x.shape"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.linear_model import LinearRegression\n",
"\n",
"x = np.array([0, 1, 2, 3, 4, 5])\n",
"y = np.array([1, 3.5, 4, 5, 4.5, 6])\n",
"\n",
"# reshape x to specify it is 1 feature and many samples\n",
"x = x.reshape((-1, 1))\n",
"\n",
"# initialize sklearn model\n",
"reg = LinearRegression()\n",
"\n",
"# fit the model\n",
"reg.fit(x, y)\n",
"\n",
"# same as a_1\n",
"slope = reg.coef_[0]\n",
"\n",
"# same as a_0\n",
"intercept = reg.intercept_"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"show_fit(x, y, slope, intercept)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"ICA 1 motivates two questions:\n",
"1. ~How can we avoid guessing and checking and find the best $a_0, a_1$?~\n",
" - `from sklearn.linear_model import LinearRegression`\n",
"1. What is the relationship between MSE and variance of y?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## What is the relationship between MSE and the sample variance of y?\n",
"\n",
"Remember,\n",
"$$\n",
" MSE = \\frac{1}{n}\\sum_j{( \\hat{y_j} - y_j)^2}\n",
"$$\n",
"\n",
"Look familiar?\n",
"$$\\sigma^2 = \\frac{1}{n}\\sum_j{(\\bar{y} - y_j)^2} $$\n",
"where $\\bar{y}$ is the mean of our observed samples of $y$.\n",
"\n",
"\n",
"# Sample variance is the MSE of a line which predicts each $\\hat{y}_j = \\bar{y}$\n",
"\n",
"What kind of line would give the same prediction (the sample mean) for each sample?\n",
"- a horizontal line at the sample mean"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.array([0, 1, 2, 3, 4, 5])\n",
"y = np.array([1, 3.5, 4, 5, 4.5, 6])\n",
"y_sample_mean = y.mean()\n",
"show_fit(x, y, slope=0, intercept=y_sample_mean)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.4166666666666665"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# feel familiar? (see MSE in graph above)\n",
"np.var(y)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## An Intuition Honing Example: MSE and Variance of Y\n",
"\n",
"Whats the minimum MSE of predicting $\\hat{y} = a_1 x + a_0$ where:\n",
"- y = stock price increase on a given day\n",
"- x = number of coffees consumed by CEOs parents on the same day"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"1. As x increases, we don't observe changes in y\n",
" - assume: x and y uncorrelated\n",
"1. Therefore, slope = $a_1 = 0$\n",
"1. To minimize MSE our best y prediction is to assign intercept = $a_0 = \\bar{y}$\n",
"1. From above, an estimate of MSE of this model is sample variance: `np.var(y)`"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"# Variance of Y is the \"worst\" (minimum) MSE you will get\n",
"\n",
"- At worst, if you try to predict some y using uncorrelated x\n",
" - MSE = Var(y)\n",
"- As x shows some stronger correlation with y (making it useful for prediction)\n",
" - MSE decreases\n",
" \n",
"#### Don't forget: \n",
"MSE is always positive\n",
" - error is a \"distance\" from `y_true` to `y_pred`"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## $R^2$ is the percentage of variance of y which can be explained by the model\n",
"\n",
"$$R^2 = 1-\\frac{MSE}{\\sigma_y^2}$$\n",
"\n",
"$R^2$ is the percent of variance of y explained by x (under model)\n",
"\n",
"Intuition:\n",
"- $R^2 = 0$\n",
" - x, using this model, doesn't explain any of the variance of y\n",
"- $R^2 = .5$\n",
" - x, using this model, explains half the variance of y\n",
"- $R^2 = 1$\n",
" - x, using this model, explains all the differences in y"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.metrics import r2_score\n",
"\n",
"x = np.array([0, 1, 2, 3]).reshape(-1, 1)\n",
"y = np.array([1, 3.5, 4, 5])\n",
"\n",
"reg = LinearRegression()\n",
"reg.fit(x, y) \n",
"\n",
"# get the slope\n",
"slope = reg.coef_[0]\n",
"\n",
"# get the intercept\n",
"intercept = reg.intercept_\n",
"\n",
"# same as y_pred = slope * x + intercept\n",
"y_pred = reg.predict(x)\n",
"\n",
"show_fit(x, y, slope, intercept)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.8992805755395683\n"
]
}
],
"source": [
"# computing R2 from our formula (just to check that Prof Higger isnt pulling our leg)\n",
"R2 = 1 - (get_mse(y_pred, y) / np.var(y))\n",
"\n",
"# computing R2 from sklearn (easy to work with, doesn't inspire our intuition with its use)\n",
"R2_easy = r2_score(y_true=y, y_pred=y_pred)\n",
"\n",
"assert R2 == R2_easy, 'r2_score() doesnt agree with our formula'\n",
"\n",
"print(R2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our linear fit explains 89% of variance."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Guess that $R^2$: part 0"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's try with data than can be fit perfectly.\n",
"x = np.array([0, 1, 2]).reshape(-1, 1)\n",
"y = np.array([1, 3, 5])\n",
"\n",
"reg = LinearRegression()\n",
"reg.fit(x, y) \n",
"slope = reg.coef_[0]\n",
"intercept = reg.intercept_\n",
"\n",
"show_fit(x, y, slope, intercept)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# two lines below compute the same thing:\n",
"y_pred = slope * x + intercept\n",
"y_pred = reg.predict(x) \n",
"\n",
"# computing R2 from sklearn\n",
"r2 = r2_score(y_true=y, y_pred=y_pred)\n",
"r2"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Guess that $R^2$: part 1"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAnYAAAFwCAYAAAA15TZ5AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAABakklEQVR4nO3dd1wT5x8H8E8gIKgsgZ8DcWJQ3FsRRXHTqnFVW2fVUmddVeuqdYt146SgddvWga3ioo460ba4EbfWgTIMiAgIud8fNqkxARkJgcvn/Xr5kjx3z3PPl+RyX+557k4iCIIAIiIiIir0zIzdASIiIiLSDyZ2RERERCLBxI6IiIhIJJjYEREREYkEEzsiIiIikWBiR0RERCQSUmN3gMQrICAAK1euxMiRIzFq1Chjd6dQuHDhAgIDA3H58mWkpKSgXLly6Nq1K/r37w+pNOe7a3p6OjZt2oQ9e/bg4cOHsLKyQu3ateHn54cGDRpkWu/FixdYtWoVjh49iufPn8PBwQFeXl4YNWoUypQpk+v4fHx8MHLkSHTr1i3XbRQWycnJCAsLw5UrV3DlyhVERkYiJSUF7du3x4oVK/LUdlpaGnbs2IH9+/fj7t27SE1NhaOjI2rWrIkBAwagfv366nV3796NyZMnf7DNxo0bY9OmTXnqF/Dffg8AlStXRmhoaKbrBgcHY+HChQAAFxcXHD16VGudiIgIbNmyBREREXj+/DksLCzg6OgIV1dX1K9fH+3atYNMJlOv/+jRI7Ru3fqD/axatSr27t2b0/AMbufOndixYwfu3LkDc3NzVKtWDQMGDECbNm1y1d7Zs2exadMmXL58GQqFAlZWVqhSpQo6deqEXr166fxeUSqV2LVrF/bs2YNbt24hOTkZdnZ2qFGjBvr06QNvb2+d20pKSsL69etx6NAh/PPPP7C0tETVqlXRp08fdOzYMVf9p5xjYkeiIIYkcvfu3Zg6dSoAoGHDhrC3t0d4eDj8/f1x9uxZrFmzJkfJXXp6Or788kucOnUK9vb28Pb2hkKhwMmTJ3Hy5EksWLAAXbp00ar37Nkz9OrVC0+fPkWFChXQtm1b3L17F7t378bvv/+OrVu3okqVKtnqw5s3b2BhYZHr5YXZgwcPMGHCBL23Gxsbi0GDBiEqKgr29vaoX78+ihQpgidPnuDo0aOoWrWqRmKn+uMgM4cOHUJycjIaNWqk977euXMHly9fRq1atXQuDwkJybJ+UFAQFi1aBEEQUK5cOXh5eaFYsWJ4+vQpIiIicObMGbx69QqTJk3SWT+ruEuXLp3tOPLLlClTsGvXLhQtWhSenp5IS0vD2bNncf78eYwdOxZDhw7NUXs//vgj5s+fDwCoUaMGGjZsiBcvXuCvv/5CREQEjhw5guDgYJibm6vrCIKAUaNGISwsDBYWFqhfvz4cHBzwzz//4MSJEzhx4oTO79m4uDj07dsXd+/ehYODAzw9PfHq1StcunQJFy5cwMWLF7P1BwbpgUBkICtWrBBkMpmwYsUKUW3LEB49eiTUqFFD8PDwEE6fPq0uVygUQpcuXQSZTCYEBQXlqM1169YJMplMkMvlgkKhUJefPn1a8PDwEGrWrCk8ffpUq96gQYMEmUwmTJ48WcjIyFCXq37HnTp10ijPSu/evYVZs2YJiYmJgiAIQqtWrYRdu3YJgiAIp06dEtq1ayf88ccfOYqrsHjw4IEwefJkYevWrcKlS5eE7du3CzKZTBg1alSu23zz5o3QtWtXQSaTCbNnzxZSUlI0lr948UK4e/duttu7f/++IJPJBHd3d+HRo0e57te7VJ8TVT9nzpypc72rV68KMplM6NatmyCTyYRWrVppLI+MjBSqVq0qeHh4CPv27dOqn5KSIhw4cEDYu3evRvk///wjyGQyQSaT6SWe/LJv3z5BJpMJLVu2FJ48eaIuj4yMFOrVqye4u7sLly5dynZ7z549E6pXry5Uq1ZNOHr0qMayBw8eCJ6enoJMJhN2796tsezgwYOCTCYTmjVrJjx8+FBjWVhYmFC1alWhatWqWsuGDx8uyGQyoW/fvhrfNzdv3hS8vLwEmUwm/P7779nuP+Ue59gRFQAbN25EWloaunfvDk9PT3W5nZ0dZsyYAeDtsFVGRka22svIyMD69esBADNmzICdnZ16maenJ7p3747U1FRs3LhRo96NGzdw6tQp2NnZYfr06TAz++8rYuTIkahUqRKioqJw4sSJbPVj0qRJiIyMRMeOHbFv3z4AQExMDMaNG4dRo0ahc+fOWQ4J57fw8HC4u7sjICAgz22VK1cO8+bNw2effYZatWrB0tIyz21u374d165dQ4sWLTBt2jQUKVJEY7m9vT0qVqyY7fZ2794N4O0wrIuLS577965GjRrBxcUF+/fvR1pamtbyPXv2AMj8rNqBAwegVCrRvn17fPTRR1rLixQpgg4dOqBz58567bex/PDDDwCAr7/+WuNsYtWqVeHn5wdBEBAUFJTt9iIiIvDmzRvUrl0brVq10lhWrlw59OjRAwBw6dIljWXnz58HAHTv3h2urq4ay1q3bo3atWtDqVTiypUr6vLo6GiEhYXB3Nwcc+bM0fi+qVKlCsaMGQMAWLt2bbb7T7nHxM5EPXnyBB4eHurT/bo8f/4c1atXR6NGjZCSkpKn7T179gyTJ09Gs2bNULNmTXTs2DHT+Ty3bt3CsmXL0KtXL3h5eaFGjRpo1qwZRowYgb/++ktrfR8fH/WcnpUrV8Ld3V39Tx8H6Pygmlv08ccfay2rW7cuXFxcEBcXh4sXL2arvYiICLx48QIuLi6oU6eO1nLVgfL333/XKFe9bt26NaytrTWWSSQS+Pr66qyXmTp16mDbtm347rvvsHLlSjx+/BgrVqyAjY0Njhw5ghEjRmhtR5fJkyfD3d1dfYB4V3p6Oj755BO4u7tj1apV2epXYbVt2zYAwJAhQ/LcliAI+PXXXwFkPWSZWxKJBJ07d4ZCocDx48c1lr158wb79++Hi4sLGjZsqLN+fHw8AMDJyUnvfStonj59isjISFhaWqJt27Zay1X76x9//JHp9/X7sjvFwcHBIc/1rl69CuDtPMny5ctrrav6Y/XSpUt49uxZttqn3GNiZ6LKlCmDVq1aIS4uDkeOHNG5zi+//IL09HR07doVVlZWud7WkydP0L17d5w+fRq1a9dGnTp1cP/+fcydO1fngfjHH3/E2rVr8fr1a9SoUQM+Pj4oUaIEwsLC0K9fP+zfv19j/fbt26Nq1aoA3v5127VrV/W/atWq5brf+SUpKQn//PMPAKB69eo611GVR0ZGZqvN69evA3g7ryar9h48eICkpCR1uar9D/VD1X52SSQSjddmZmZaZVmZPn06KlasiAMHDuDnn3/WWLZs2TJcunQJjRo1wrBhw3LUr8Lk2bNnuHv3LqytrVG/fn1cvnwZS5cuxbfffovly5fjzz//zFF7586dw5MnT1CsWDG0b9/eIH1WJYzvz6U7ceIE4uPj0blz50w/B6VKlQLwdg7g8+fPDdK/gkK1P1WpUkXnmd2yZcvC3t4er1+/xv3797PVZt26dVG8eHFcunRJK7F++PAhdu7cCQsLC60zns2bNwcA7Nq1S/29pPL777/j0qVLqFChgsY8ztevXwN4e8ZYl3fLs/sdRrnHiydMWJ8+fRAWFobt27drDXUolUrs3LkTEokEvXv3ztN2du/ejV69emHatGnqL62DBw9i9OjRCAoKwueff46iRYuq1+/SpQtGjhypNbn56NGj+OqrrzBz5kz4+Pioz/RMmjQJAQEBuHHjBtq0aZOriyd8fHzw+PHjHNXp2rUrFixYkONtvU+1XVtbWxQrVkznOiVLltRY90OePHkC4L+D4/uKFy+O4sWLIykpCU+ePFFfVfiheqry7PbjypUrWLhwIe7du4dJkyZh6dKl6NWrF27cuIG2bdviiy++wMCBAz/4h0PRokWxbNky9OzZE3PnzkW9evXg5uaGM2fOICgoCA4ODli0aJHG0LHY3Lp1CwDg6uqKhQsXag2jr169Gm3atMH333+vsT9lRjUM27Fjx2ydNc2N8uXLo27duvjjjz8QHx+PEiVKAPgv0ZPL5ZmegerSpQt++OEHREdHo3379mjZsiXq1asHDw8P1KhRQ2sY2pDevdI3J6KiorK1nmq/y+qCjpIlS0KhUODx48caVwFnxsHBAfPmzcOECRPw5ZdfombNmnB1dUV8fDz++usvuLi4YNGiRVpD982aNcPgwYMRHByMjh07okGDBnBwcMDDhw9x7do1NG7cGPPmzdNIQB0dHQG8vSJZl3fLM1uH9IeJnQnz9PREpUqVcOHCBdy+fRtubm7qZcePH8eTJ0/QtGnTHM3Z0cXFxUUjqQOADh06QCaT4ebNm7hy5QoaN26sXpbZ1Xk+Pj5o37499u3bh/DwcLRs2TJP/XpX+/bt8eLFixzVefcv1rx49eoVAGR5cFUlfKp19dFm0aJFkZSUpNGm6ufMEgNVeXb7MXfuXHh4eGD16tWwsbHB0qVL4ezsjC+//BKnT5/GrFmz4OHhgRYtWnywrapVq2LSpEmYPXs2xo4di7Vr12LixIkQBAHz589XJ79ilZCQAAC4e/cubt68iZ49e2Lw4MFwcnLChQsX8N133yEsLAwzZ86Ev79/lm0lJSWpz9Qb+tYzXbt2RUREBPbt24f+/fvjxYsXOH78OOrWrYsKFSrg5s2bOuuVLVsW69atw5QpU/Do0SOEhoaqb51iYWGB5s2bw8/PD3Xr1s102+7u7pkuy8kV9NWqVTPIcLVKdvfXd9fNjvbt28PZ2RljxoxR33YHAKRSKRo3bowKFSrorDdx4kRUqFABs2fPxtmzZ9XlDg4OaNSokdbweK1atWBlZYX4+HiEhYVp3Zrlp59+0oqVDIeJnYn77LPPMGfOHOzYsQPTpk1Tl+/YsQMA8ny2Dng7MVvX8ELFihVx8+ZNxMTEaC17+fIljh07hhs3biAxMRHp6ekA/jtrkd3hiOzK7HYJ+UEQBADaw5XGaFPffdm8eXOmc3aaNWuGffv25eh2J3379sWZM2fw+++/o3PnzkhKSsKAAQO0Jod/SHx8vPr+ae9SfRbDwsJ0npXs0aOH0S72UCqVAN7OKfT29sacOXPUy3x8fODs7IyePXti7969GDlypNbE93cdPHgQr1+/1hpSMwRfX1/MnTsXISEh6N+/P/bt24c3b95kK1Fq3LgxDh06hNOnT+PUqVMa9wM8evQojh8/jhkzZmT6PZXVNnIyTaNNmza5vo9cdhjiOwB4O61l4cKFaN68OdasWYOKFSsiJiYGO3bswIYNG3Ds2DFs27ZN47OSlpaGyZMnIzQ0FJ9//jl69+4NJycn3Lt3D8uWLcOKFStw5swZbNy4UX37peLFi6N///4IDAzElClTkJycjBYtWiA5ORm7du3C1q1bIZVKkZ6ervcYSRsTOxPXtWtXLFmyBCEhIRg/fjysra3x+PFjnDx5Es7Oznr5MstsWE/1F+j7QzFHjhzBlClTkJiYmGmb784LK+ju3LmjvuLtXaokQXU2Ljk5OdM2VMsyG6p9X3baVM2LebfND50Z1FUnKx9K2nJzD7t58+ahdevWSEpKgkwmw9dff53jNpKTk9VXZepy48YN3LhxQ6u8UaNGRkvs3v2df/LJJ1rLa9asierVq+Pq1asIDw/PMrH70BWp+mRjYwMfHx8cOHAAt27dwp49e2BpaZntG9ZKpVJ4e3urb4qbmpqKkydPYtGiRbh37x7mzJkDb29vncOY+pgqkR9yu79m5fz585g/fz6qVq2KVatWqZOw8uXLY9KkSXj9+jW2b9+O5cuXY9GiRep6gYGB2LdvH/r27YuJEyeqy6tXr47Vq1eje/fu+PPPP7Fnzx707NlTvXz06NGIjY3F7t27te7f2K5dOyQnJ6vvqUmGxcTOxBUvXhxdunTB9u3bsW/fPvTs2RM///wzlEolevbsmaunHbwvJ/Oenj59ivHjxyM1NRVDhw7Fxx9/jDJlyqBo0aKQSCRYsmQJ1q1bp/4LV1/8/f1zNRT77hdbZmJjY3UmEaokQXWbicTERLx69UrnF7fqSrLsPvVBtV50dLTO5a9evcLLly+12ixTpgyuX7+eaT1VeW5vjaHryQI5dfz4cXViHx0djZiYmBz3p2zZsjrnP4WHh6N///4F8kbX78aYWdJWtmxZXL16FbGxsZm2888//+Cvv/6CmZkZ5HK5vrupU9euXXHgwAEsWrQI165dQ8eOHWFra5urtooUKYI2bdqgZs2aaN++PV6/fo2TJ0/qTHb1JSwsDGFhYTmul93EUrUPPn36NNN1VPtedr8DVE/VaN++vc7v8Y8++gjbt2/HuXPndNbTlXhbWFigXbt2iIqKwrlz5zS+/6RSKebPn4++ffvi2LFjePbsGWxsbODl5QVPT0+0a9cOALJ9c3PKPSZ2hL59+2L79u3Yvn075HI5du7cCXNzc4N+UWbm+PHjSE1NRfv27TF27Fit5Q8ePDDIdg8dOpTjiycAZCuxa9y4cZaTqG1sbFC2bFk8evQI169f13n7B9XtBLI7fOTh4QEAuHbtms7lqvZcXV1RvHhxdXm1atUQFhb2wXqqq5Dz2/379zFz5kxYWFio51uOHz8eW7Zs0csfIQVZxYoVYW1tjdevX0OhUOhcR1We1cUTu3fvhiAIaNasWaZn0/XNy8sLzs7O6qsz9XGmsGTJkqhUqRKuXbumvjWKoURGRmZ5hjcz2U3sVPvr7du3kZaWpjV15dGjR+rHgWV3zrMqEbSxsdG5XFX+/siIKrnMrJ4qIVfN+Xxf9erVta6q/+eff/DgwQPY2tpmesU96Y+4vwkpW9zc3NCoUSOcP38eS5cuRWxsLFq3bm2UR+6ovix0HXDi4+Nx5swZnfVUQ3qquXg5pY8zSXnh4+ODTZs2Yf/+/VqJ3aVLl/D48WOUKFEiy4ni76pbty7s7e3x6NEjnY90Uk1Cf3+ovXXr1ggICMDRo0eRkpKicbWqIAg4ePCgznr5IS0tDePGjUNycjImTpyIgQMH4tmzZ7hw4QICAgJ0/iEgJpaWlvD29sbBgwdx9uxZjQuOgLfzUlW3zcjs4CkIgvqMTH4Mw6qYm5uje/fu2LFjB+zt7eHl5fXBOoIgZDkfKyMjQ/3HmKET1FGjRhn0DG6ZMmVQtWpV3LhxA2FhYer7Raqo9tcWLVpk+0bXzs7OAN5+f/Tr109r+eXLlwFon33/3//+h8ePH+Py5cs6Lz5R3dA4J2fJAwMDAbydfqKPG3VT1sR7bwDKkb59+wJ4+3QDQD8XTeRGpUqVAACHDx/WGE5KTk7GtGnTMp13p7oi8u7du4bvpAEMGDAAFhYW2Llzp8ZVaImJiZg5cyYAYNCgQRrPdASAxYsXo0OHDli8eLFGuVQqxeeffw4A+O677zR+b2fPnsXOnTthaWmJ/v37a9SrVq0amjVrBoVCgTlz5qgn7APAqlWrcPv2bchkMr1ekZxdixcvxrVr1+Dl5aX+XXz//fewt7dHYGCg1pBSYbVlyxZ06NBBY36Tip+fHyQSCTZu3Khx37q0tDT1++zh4YF69erpbDs8PByPHz+GjY2Nzhvhvs/Hxwfu7u7qW6PkxdixYxEeHo5Dhw5pfY51WbZsGebNm4c7d+5oLUtKSsK0adOgUChQrFixbF1VXdCpbjq9aNEijakQUVFR6sRI142pBwwYgA4dOmjdj1T1/u7fvx8HDhzQWBYVFYXly5cDgFYSqaq3fPly9cVqKqGhoer7iL5f78mTJ1pTADIyMrBu3Tr8/PPPKF26NEaMGJFZ+KRHPGNHAN6eqSlVqhSio6Ph6uqqvkllfmvVqpX6L9f27dujUaNGkEqluHDhAszMzNCtWzedBxkvLy9YW1vj8OHD6NOnD8qVKwczMzP4+PigdevWRogkZ8qWLYvvvvsO06ZNw6BBg9C4cWPY2toiPDwcCoUCXl5e6kTtXTExMbh3757OK4sHDx6M8PBwnDlzBu3atUOjRo2QmJiI8PBwCIKAOXPm6JyvM3fuXPTq1Qu//PILLly4AA8PD9y7dw+RkZGwsbExyv3iTpw4gY0bN8LJyQn+/v7qMzmlS5fG3LlzMWLECEyYMAF79+5V3yutIBgxYoT6vVENF4aHh2tMc5gxY4bGGbYXL17g3r176jMu76pevTq++eYbzJ8/H/3790ft2rVRokQJXL16FdHR0XB2dsbixYszPdOlGk709fXN1n3gVIm9MYa5k5OTsWnTJmzcuBEuLi6QyWQoVqwYYmNjcfXqVSQlJcHS0hILFizI9D3/5ptvstxGQbq4olOnTjh9+jT27NmDjh07wtPTE2/evMGZM2fw5s0bfPXVV6hdu7ZWvX/++QePHz9Wz5lVad26NeRyOUJCQjBmzBisXbsWFSpUQGxsLC5evIj09HTUrVtXK1kcMWIEzp49i6ioKMjlctSpU0d9VaxqSsmAAQO0zhifO3cO06ZNg4eHB8qUKQNBEHDx4kU8f/4cpUuXxvr16zWmfZDhMLEjAG+/uBs2bIjffvsNvXr1Mtol6RYWFtiyZQtWrlyJY8eO4dSpU3BwcICPjw9Gjx6t9dQBFWdnZ6xduxarVq1CZGQk/vrrLwiCgFKlShWKxA54O0zh6uqKwMBAXL58GampqShXrpz6Jr45PbhaWFggMDAQGzduREhICI4fP44iRYqgWbNm+PLLLzN9lFPp0qUREhKCVatW4ejRozhy5Ajs7e3RtWtXjBo1Su/PFP2QmJgY9QHa399f6x5abdq0wWeffYZt27Zh8uTJWLt2bYG5pUJkZKTW3E2FQqExRy6nV3gPHDgQMpkM69evV9+brFSpUujfvz++/PLLTB/B9erVKxw+fBhA9u5dFx8fj+joaJQoUQI+Pj456qM+DB8+HLVr18bp06cRGRmJK1euQKFQoEiRInB1dUXjxo3Rt29flCtXLtM2PjQvriAldgAwf/581K9fHzt27MCZM2cgkUhQu3ZtfP7557ma/uDv748WLVpg165duH79Om7dugVra2vUqFEDHTt2RJ8+fbSuTLe1tcXPP/+MTZs24fDhw4iMjERqaipsbW3RokUL9OrVS2dfqlevjo4dO+LSpUu4ffs2JBIJypUrh169emHgwIFM6vKRRND35YVUKL169QrNmzfHmzdvcOLEiQJ11oOI8l9oaCjGjh2LqVOnag3ZE1HBxTl2BADYsGEDXr16hY8//phJHRHh7NmzKFu2rNHm2xJR7vCMnQm7e/cugoODER0djdOnT8PKygq//fZbljc2JSIiooKLc+xMWExMDHbu3IkiRYqgRo0a+PrrrzNN6nJyg85KlSrBz89Pn10lIiKibOAZO8qWgIAArFy5MlvrNmrUCJs3bzZwj4iIiOh9TOyIiIiIRIIXTxARERGJBBM7IiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERERiQQTOyIiIiKRYGJHREREJBJM7IiIiIhEgokdERERkUgwsSMiIiISCSZ2RERERCIhNXYHCooXL15BqRQM1r6jY3HExSUZrP2CzpTjN+XYAdOOn7GbZuyAacdvyrEDho/fzEwCB4dimS5nYvcvpVIwaGKn2oYpM+X4TTl2wLTjZ+ymy5TjN+XYAePGz6FYIiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSBjt4om///4bq1atws2bN6FQKFCsWDHIZDIMHjwY3t7eH6z/8OFDLFiwAOHh4VAqlWjQoAEmTZoENze3fOg9ERERUcFjtMQuMTERFStWRLdu3eDk5ITExET89NNP8PPzw5IlS/DRRx9lWjcuLg6fffYZHB0d4e/vD3Nzc6xZswZ9+/ZFSEgISpUqlY+REBGZhjdv0vDypQLp6WlQKjOyXPf5czMolcp86lnBY8rxm3LsQO7jNzMzh1RqCRsbe1hYWOZ6+xJBEArMNcnp6elo3bo1ypcvj02bNmW63sKFC7FlyxYcOXIEJUuWBAC8ePECrVu3RqdOnTBz5swcbzsuLsmglyc7O9sgJualwdov6Ew5flOOHTDN+M9ei8buE3cQn5iKErZF0M27MppWL9x/cL5+/QovX75A8eJ2KFLEGmZm5pBIJJmuL5WaIT3ddA/uphy/KccO5C5+QRCgVGYgNfU1kpISYGPjAGtr3feqMzOTwNGxeKZtFag5dlKpFDY2NrCwsMhyvbCwMHh6eqqTOgBwcHBAq1atcOTIEUN3k4goU2evRWPjgRuIS0yFACAuMRUbD9zA2WvRxu5aniQlJcDe3glFi9rA3FyaZVJHRDkjkUhgbi5F0aI2sLd3wqtXCbluy+iJnVKpRHp6Op49e4YVK1bg/v37GDBgQKbrp6Sk4OHDh5DJZFrL3N3dERcXh7i4OEN2mYgoU7tP3EHae3+tp6UrsfvEHSP1SD8yMt7AwqKIsbtBJHoWFkWQnv4m1/WN/uSJMWPG4NChQwCA4sWLY9myZWjRokWm6yckJEAQBNjZ2Wkts7e3BwAoFAo4OjrmqB9ZndbUF2dnG4NvoyAz5fhNOXbAtOKPT0wFALS9+d/owRFZW8Qnphbq38Pz52awsDDPUR2p1OjnDozKlOM35diBvMdvZmaW6+8Loyd2EyZMwJAhQxAbG4t9+/ZhzJgxWLBgAT7++OMs6+l7GIBz7AzLlOM35dgB04u/hG0RxCWmou2t39VlR2RtUcK2SKH+PbwdXcn+vCHOszLd+E05dkA/8SuVyky/Lwr8HDtXV1fUqlULPj4+WLJkCby8vDBr1qxMryixs7ODRCKBQqHQWqYqU525IyLKb928K8Pyvb/WLaVm6OZd2Ug9IiJTYvTE7n01a9ZEQkIC4uPjdS63srKCq6srbt68qbXs5s2bKFGiRI6HYYmI9KVp9VIY0LGqRtmAjlUL/VWxlLUHD+4jOHgdnj59YuyukIkrUImdIAg4f/48bG1tszzr1qZNG5w5cwYxMTHqMoVCgWPHjqFt27b50FMiosy9n8QxqRO/Bw/uY8OGH5jYkdEZbY7d+PHj4eLigurVq8PBwQExMTHYs2cPzp07h+nTp0Mqfdu1fv364fz584iKilLXHTx4MH799Vf4+flhxIgRkEqlWLNmDaRSKYYOHWqskIiIiLIlLS0Nlpa5vwktUWaMdsaubt26CA8Px7fffouBAwdi1qxZEARB/QSJrDg5OWHr1q0oVaoUJk6ciLFjx8LGxgZbtmxBmTJl8ikCIiIq7A4fPggvrwa4evWK1rKAgCVo27YFXr1KyrKN0NDfMGXK1wCAr74aCi+vBmjSpB7+/vtPAECPHp0wefJ4HDlyEP36fYKWLZsgLOwQnj59Ai+vBggN/U2rTS+vBggOXqdRdv/+PUybNgkffdQarVo1xYABvXH48MHchk4iZbQzdn379v1gAgcAmzdv1lleoUIFrFmzRt/dIiKifKR6SkdcYiocjfCUDh+fNli1ahn27PkFNWrUVJenpqYgNHQf2rfviGLFsr4dVtOmXhg2bBTWrAnAuHGTIJNVhVQqgatrBfU6169fw/379zBw4BA4OjrByck5R/28ffsWhg0bjPLlK2DMmAmws7PHsWNhmDVrGtLSUvDxx/IctUfiZfTbnRARkWlSPaVDdUNn1VM6gPyblyiVSiGXd8fmzRswatQ49fzuI0cO4uXLRHTr1vODbTg4OMDVtTwAoEKFiqhRo6bWLS8SEhRYu3Y9Spf+b1QpJ/PxVq1aBnt7ewQErIO1tTUAoFGjJlAoFAgMXANf384wMytQ0+bJSPgpICIioygoT+no0qUbBEHA/v171WV79uxCnTr1UKmSm162UaWKTCOpy4nU1FT8/fefaNGiFSwsLJCenq7+17RpM8THx+HBg/t66ScVfjxjR0RERhH371M6sltuKCVKOMLHpw1CQnbj00/74fr1a4iKisTMmfP1tg1HR6dc101MTEBGRgZ++mkrfvppq851EhIUuW6fxIWJHRGRARTpJIe1lQVep+T+mY9i5/jvUzp0lee37t174dChAwgPP4OwsMNwdHSCt3crvbWv62lJqqti09LSNMrfT9JsbGxhZmYGX99OkMu762y/XLny+ukoFXpM7IiIDMBm4hSTe5xaTnXzrqwxxw4w3lM6PDxqwMOjBjZt2oCoqEj06TNAfdut7LCwsADwdtg0u0qUcISlZRHcuXNbo/zkyRMar62srFCnTj3cunUTbm6yHPWLTA8/HUREZBSqCySMeVXsu3r06IVZs6bD3NwcXbp0y1HdihUrQSKRYN++EBQrVgzW1lZwcXFF0aLFMq0jkUjQrl0H7N//K1xcXODmJkNk5DUcOaJ9C5OvvhqPESOGYNSoL9GlSzeULFkKSUkv8eDBfURGXsPcud/nOF4SJyZ2RERkNE2rlyowT+bw9vaBVDoTzZu3zPHtSEqVKo1Ro8bi55+3Y9SoL5GRkYEVK9aiXr0GWdYbNWosJBIJtm3bjNevk1GvXgMsXLgMPXp00ljPza0KgoO3YMOGH7BmTQASEhSwtbVD+fIV4OPDJy7RfySCIAjG7kRBEBeXBKXScL8KUx+SMeX4TTl2wLTjF1Ps0dEPUKpU9udxvX+7j8LgxImjmDp1IgIC1qFu3fp5aqswxq8vphw7oJ/4s9rfzMwkcHTM/N6KPGNHRGQALxfOQ/q/F0/YTJxi7O5QFh4+vI/o6GisWrUc1avXzHNSR2RMTOyIiAwg9bcQqKbRM7Er2BYunIerVy/D3b0apk2bqbFMEARkZGRkWd/c3FznVa9ExsDEjoiITNrKlYGZLjtwYB/mzZuZ6XIA2ZpLR5RfmNgRERFlolmz5ggK2pTlOryHHBUkTOyIiIgyYWdnDzs7e2N3gyjb+KxYIiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJJnZEREREIsHbnRARGYD150NQrGgRvEpO/fDKRER6wjN2REQGUGyQH5xHjUSxQX7G7gqZiL///hNeXg3w999/Zmv9oKC1GDy4n4F7VbA9ffoEXl4NEBr6m8G2kZSUhA4dWuHkyeMG28a7mNgRERGZmGfPorF9+2YMGTLU2F0xKkdHJ6xduwFNm3oZbBvFixdH7959sGrVcqSnpxtsOypM7IiIiIwsLS0tX7f3yy874OjohKZNm2W5Xnp6OjIyMvKlT0qlMl8Sn3dZWlqiRo2acHBwMOh2unTphqdPn+D48d8Nuh2Ac+yIiMhEHT58ELNmTcPatRtQo0ZNjWUBAUvw668hCAkJRbFixT/YVmjob5g3byaWLl2F/ft/xdmzpyEIApo2bYYxY76Gg0MJ9bo9enRClSoy+Pi0xaZN6/HPPw8xceJU+Pp2wvPnzxAUtBbh4WeQkJCAUqXKoFu3Hvjkk880tnf//j2sWLEYly5FwMrKCs2bt4SXV4tsxf3mzRuEhv6Gbt16apQ/ffoEPXt2xvDho5Gc/Aqhob8hJuY5fv55L0qXLoOrVy9jw4YgXLt2GWlpb+DmVgVDhgxFo0ZNNNr544/jWLduNR4+fAAnJ2d07doTr18nY8OGH3Dq1H/DxF5eDdCz56coXboMdu36CdHRT7F06SrUq9cA9+/fQ1DQWkRE/Ink5GSUK1ceffoMRLt2HdT1U1JS8MMPa/DHH8cQFxcLKytrlC3rigEDBqNZs+YAgKioGwgKWoPIyOt49SoJ9vYOqFq1GiZPngFbW1t1zFOmzICvbyd128eOhWHLlo24d+8uLCykqF27Lvz8RsDNrYp6nblzv8PJk8cRGPgjli1bjCtXLsLGxhatW7fFF18Mh6WlpXpdB4cSaNiwMfbu3Y02bdpn633KLZ6xIyIygIRJ4/DP0GFImDTO2F0xOLncFzt2bAXwNmmQy33x8887AADJycmQy30RErILAJCYmAC53Bf79v0KAIiLi4Nc7otDhw4AAJ49ewa53BdHjx4BADx+/AhyuS9OnDgG4G1CI5f74syZUwCA27dvQS73zVW/fXzawNHRCXv2/KJRnpqagtDQfWjfvmO2krp3zZ8/C8WL22Du3AXw8xuGs2dPY+zYkVpnoq5fv4b16wPRt+9ALFq0Ah4eNRAbG4MvvhiAy5cvwc9vBL7/fjlatGiJVauW44cf1qjrxsXFYuRIP9y/fw/jx3+DadNmISUlBUuWLMxWH69fv4rExATUqVNP5/Kff96GyMjrGDduIubPXwQbG1ucP38OI0f6QanMwOTJ32LuXH84OjphwoTROH/+nLruuXNn8M03X8Pe3gEzZ87H8OFf4fjx33HgwD6d2zp2LAxHjhzA0KEj4e+/FC4uZXH79i188cUAREc/xZgxE+DvvxQeHjUwa9Y07NsXoq67YsViHDoUij59BmDx4gBMmfItPD29kJiYAODtZ2/s2BF48+YNJk6ciiVLVmL48K9gY2Ob5RnS0NDfMH36N3B2dsasWfMxfvxkPHr0D4YNG4z79+9prJuW9gbffDMejRo1xvz5i+Hr2wk7dmzF1q0btdqtW7c+Ll++iOTkV5luWx94xo6IyADenDmFN8buBGVJKpVCLu+OzZs3YNSocbC3twcAHDlyEC9fJmqd0cqOmjVr4+uvv4FUaoYGDZrAwaEEZsyYgmPHwtC27X9nmxISFFi7dj1Kly6jLvP3n4vU1BQEB2+Bk5MTAKBhw8ZIT3+D7ds3o1evz2Bra4efftqGhAQFNm7cjkqV3AAATZs2w+jRw/H8+bMP9vHq1csAAJnMXefyokWLYuHCpTA3N1eXLVmyEDJZVSxeHAAzs7fnhJo0aYbBg/shMHC1+qxdUNBalCxZCosXB0AqfZtiNG7siZ49O2lvCG+HoJctW62RQC9YMBv29vYICFgHa2trAECjRk2gUCgQGLgGvr6dYWZmhitXLqFduw6Qy7ur63p5eat/fvjwPhITEzBixBhUqSJTl7/7PrxPqVRi3bqVqFrVA/PnL4ZEIgEA1KvXAL16dcGGDT9g5sx57/Q/FV9+ORLe3q0AAA0aNMLNmzdw+PABfP75Fxpty2RVkZGRgWvXrqJhw8aZ9iGveMaOiIjyJCQkFL179wEAWFhYICQkFJ980hvA2yQhJCRUffC1tbVDSEgoPv64MwDA0dERISGhaN++IwCgZMmSCAkJhY9PWwCAi0tZhISEqg+cFSpUREhIKDw93052d3OrgpCQ0Fz3vUuXbhAEAfv371WX7dmzC3Xq1FMnTTnRpk07jdfe3j4wNzfHxYt/a5RXqSLTSOoA4Ny506hfvyHs7e2Rnp6u/te0aTOkpaXh2rUrAICIiL/g5lZFq3/vDlNmJTY2Fubm5rCxsdW53MurhUZS9+jRP3j06CHatu2gngenmnvXpIknoqIikZycjNevXyMqKhLe3q3USR3w9jPQrJnuYeL69RtqJHWpqan4++8/0aJFK1hYWGj9HuLj4/DgwX0AgIdHDYSG/oYNG37AtWtX8eaN5p9SZcuWg42NLfz95+DAgX148uTxB383Dx7cR1xcHNq166BO6gDAyckJDRs2RkTEXxrrm5ubqz+LKm5uVfDsWbRW26rh+NjYmA/2Iy94xo6IiExWiRKO8PFpg5CQ3fj00364fv0aoqIiMXPm/Fy256TxWiqVws7OHgkJCRrljo6a6wFAfHwcTpw4hpYtm2gtAwCFQgHg7XB22bLltJbralOX1NQUWFhYaCQuWbUTHx8HAFi+fBGWL1+ks05iYiLMzCQQBAElSjhqLX93jmFW20pMTEBGRgZ++mkrfvppq846CQkKAMCYMRPg5OSMw4cPIDh4Hayti6J5c28MGzYKzs7/Q/HixbFyZSB+/DEIy5cvRlLSS5Qu7YJu3Xqid+8+OuNPTEwEAJ0xODo6qbetYm1tDQsLC40yCwsLnUO9qjl3qakpOuPSFyZ2RERk0rp374VDhw4gPPwMwsIOw9HRSX2GMKfi42M1XqenpyMhQQE7OzuNcl1Jhb29PWSyqhg8+EudbavO8Nna2mltB3g79y477OzskZKSgrS0NI0J/pn1TTVEPXDgkEwv0HB0dER6ejokEok6EXzXixfxOuu9vy0bG1uYmZnB17eTxhDru8qVKw/gbVL1xRfD8MUXw/DiRTxOn/4Dq1cH4NmzaKxa9QMAoHJlN8yevQCCIOD27VvYu3cXVq1aBhsbG3z8cRettlXvk64Y4uJiYWdnr7NP2aFKGvPSRnYwsSMiIpPm4VEDHh41sGnTBkRFRaJPnwEaQ4k5ERZ2GM2bt1S/PnHiKDIyMjK9UOFdjRt74s8/z8PVtVyWF23Uq9cA27Ztwt27d1CpUmV1+eHDB7PVxwoVKgJ4e2FKxYqVPri+q2t5lCnjgjt3bmV53zsLCwtUrVoNJ04cw9Cho9S/w+TkZJw+/Ue2+mZlZYU6derh1q2bcHOTZft9cHAogY8/luPy5Us4ceKo1nKJRIIqVWQYO3YifvstBLdv39LZTrly5f89C3gQPXt+qk484+Pj8Oef5zXm8OWUaii4YsXKH1gzb5jYERGRyevRoxdmzZoOc3NzdOnSLdftXLlyCYsX+6Nly5a4d+8eAgPXwM1Nhlat2nyw7hdfDMOFC+EYNmwwevTojbJlXfH69Ws8fvwPTp8+iSVLVsLc3ByffPIp9u//FV9//RW++GIY7O0dcOhQKP7550G2+li3bn0AwLVrV7KV2EkkEnz99WRMnDgGEyeOQfv2vuphydu3byEuLhYTJ04FAAwePBQTJ47B+PGj0KNHL2RkZGDbts2wti6qPmP1IV99NR4jRgzBqFFfokuXbihZshSSkl7iwYP7iIy8hrlzvwcA+PkNhKenFypXdkPx4ja4ffsWjh8/iqZNPQEAp0+fREjITjRv3hKlS5eBUqnE4cMHoFQq0bhxU53bNjMzw9ChIzFnzgxMnjwenTp1xevXyfjxxyCYmZlj0KAvdNbLjuvXr6BECUd1Ym0oTOyIiMjkeXv7QCqdiebNW8LJyTnX7UyZMgP79u3FlCmToFQq4enZDKNHf52tM0/Ozv9DUNAmbNgQhI0bgxEXF4vixYujbNlyaNLEU301qqOjE1auDMTy5Yvw/ffzYWVlhRYtWmLcuIn45pvxH9zO//5XEnXq1MOpUyd0Dkfq0qhRE6xduwGbNq3H0qULkZT09p5wbm5V0LHjx+r1mjTxxPz53yMwcA2+/XYySpRwRNeuPRAbG4uDB/dna1tublUQHLwFGzb8gDVrApCQoICtrR3Kl6+gvqgGeJugnjx5Ajt2bEVaWhr+97//oWvXHhg4cAgAwNXVFUWLFsOWLT8iNjYWlpaWqFixImbPXpDljZk7dPgI1tbW2Lz5R0yfPglSqQXq1KmLmTPno1y5CtmK4X2CIODUqT+yvCJXXySCIAgG30ohEBeXBKXScL8KZ2cbxMS8NFj7BZ0px2/KsQOmG39s80bqn51OnjdiT/QjOvoBSpUqn+31pVIzpKcrDdgj/Tpx4iimTp2IgIB16jNaOaG6QfGGDVtRpYp7gY//2LEwzJw5DXv2hGZ6YUNuvR97eno6Bg78DE5OTli2bLVet1UQ6Xrv//77T4wdOwJbtvwCV1ftC1/el9X+ZmYmgaNj5kP1vN0JERGZrIcP7+P8+XNYtWo5qlevmaukrjBq2bI1qlRxx9atm/TabkZGBubNm41jx8IQEfEXfv/9MMaOHYEHD+6hT5/+et1WYbJxYzA++qhztpK6vOJQLBERmayFC+fh6tXLcHevhmnTZmotFwThg89Kffeeb4WFRCLBpEnTEB5+Ru/tvnyZiBUrlkCheAGpVAqZrCq+/345GjbUfRsXsUtKSkLt2nXRtWuPfNkeh2L/xaFYwzLl+E05dsB040/5dQ+KF7dCUlIKrDp3NXZ38kzsQ7GZUQ2xZmXFirWoV6+BRplY4s8NU44d0E/8eRmK5Rk7IiIDsOrcFQ7ONkg3waRWTJo1a46goKyHK1X3VSMqCJjYERERZcLOzt7gN5Ql0idePEFEREQkEkzsiIiIiESCQ7FERAbwYnB/JEnN8CZdCYdg/d5SgogoM0zsiIgMIOPmDWR9kwwiIv3jUCwRERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERHlQlpaWq6W5bVtoqwwsSMiIpN3//49TJs2CR991BqtWjXFgAG9cfjwQfXy0NDf4OXVABcunMOsWdPRsaMP+vR5+1D3kSP9MHDgZ7hwIRxDhvSHj48nNm5cDwB4/PgRvv12Mnx937bbr98n2Lt3t8a2//77T3h5NcDhwwewZIk/OnVqBx8fz/wLnkTFaLc7OXv2LPbu3YuIiAhER0fDzs4OtWrVwqhRo+Du7p5l3YCAAKxcuVKr3MnJCadPnzZUl4mISIdX6wPxekNQttYt0kkOm4lTNMpeLpyH1N9CslXf+vMhKDbIT6MsYdI4SN2rapVn1+3btzBs2GCUL18BY8ZMgJ2dPY4dC8OsWdOQlpaCjz+Wq9edN28WvL19MGvWPKSmpqrLY2KeYcGC2ejffxBcXcvBxqY44uJiMXz4YEgkZhg+/Cs4Ojrh6NEj+P77eXjxIh4DBw7R6Mfq1StQv34DTJkyA8nJybmKhchoid327duhUCgwcOBAVK5cGbGxsQgKCkKPHj2wefNm1KlT54NtbNiwAUWLFlW/trCwMGCPiYhIjFatWgZ7e3sEBKyDtbU1AKBRoyZQKBQIDFwDX9/O6nWbNPHEmDFfa7WRkJCA+fMXo1atOgAAqdQMK1YsQ3x8PDZs2AY3tyoAgKZNmyEpKQmbN29A9+69YGNjo26jQoWKmD59tgEjJVNgtMRuxowZcHR01Cjz8vJC69atERwcjICAgA+2UaNGDdja2hqqi0REJHKpqan4++8/0aNHb1hYWCA9PV29rGnTZjh58jgePLivLmvRoqXOduztHdRJnUpExJ+oXLmKOqlT6dDhI5w8eRzXrl1Bkyb/Dbm2aNEqT7EQAUZM7N5P6gDA1tYW5cuXR3R0tBF6RESkPzYLFsPO1hoJia+N3RWDKzbIT2sYVCo1Q3q6Mlv1bSZO0RqezQk7/yW5rpuYmICMjAz89NNW/PTTVp3rJCQo1D87OjrpXEdXeWJiIlxcXDNdNzEx4YNtEOVUgXqkWHx8PG7duoWPPvooW+v7+voiLi4Ojo6OaNmyJcaOHaszYSQiym9FmjWHjbMNUmJeGrsrlAUbG1uYmZnB17cT5PLuOtcpV648njx5DACQSCQ619FVbmtrh/j4OK3yuLhY9fIPtUGUUwUmsRMEAdOnT4dSqcTgwYOzXNfV1RXjxo1DtWrVYGFhgb///htBQUE4e/Ysdu/eDTs7uyzrExERAYCVlRXq1KmHW7duws1NBqlUf4fF+vUbYuvWjbh9+5bGcOzhw6EoUqQIqlevqbdtEakUmMRu4cKFCAsLw/z581G5cuUs15XL5RqvmzZtijp16mDQoEHYunUrhg8fnuPtOzoWz3GdnHJ2tvnwSiJmyvGbcuyAaccvltifPzeDVJqzO2TldH1jGTv2awwdOgRffTUUXbt2Q8mSpZGU9BL379/H9etXsWDBIpiZvT2bZm6u/XuQSCSQSLTj/eyzvjh4cB8mTBgNP7+hcHJyxu+/H8GJE8cwbNhIODjYqdt8+7+k0PzOPkQsceRWXuM3MzPL9XdHgUjsli5divXr12Pq1Kno1q1brtpo1qwZnJ2dcfHixVzVj4tLglIp5Kpudjg72yDGhIdkTDl+U44dMO34xRS7UqnM9pw5IGdz7IytYkU3BAdvxoYNP2DlyhVISFDA1tYO5ctXgI9PW6SnK9XHh4wM7d+DIAgQBGiUS6VmsLW1x5o167F2bQACApbj9etkuLqWw6RJ09Cpk1y9fkaG6n+h0PzOslKY3ntD0Ef8SqUy0+8OMzNJliejJIIgGC6byYbly5dj9erVmDBhAoYMGfLhCllo1qwZatasibVr1+a4LhM7wzLl+E05dsB044+X+8LMTAKlUkCJkFBjdyfPoqMfoFSp8tlenwd3043flGMH9BN/VvvbhxI7o56xW7lyJVavXo3Ro0fnOak7deoUYmNjUbt2bT31jogo95RxsTDdQxsRGYvRErv169cjICAArVq1gqenp8YQqqWlJTw8PAAA/fr1w/nz5xEVFaVeLpfLIZfLUbFiRUilUkRERCA4OBjly5dHnz598jsUIiIiogLBaIndsWPH1P+rflZxcXHB0aNHM61bqVIlbNu2Dc+fP0d6ejpKlSqFnj17Yvjw4bxhMREREZksoyV2mzdvzvV6S5bk/maURERERGJl2tcjExEREYkIEzsiIsoWI99Egcgk5HU/Y2JHREQfZG5ugTdvUo3dDSLRe/MmFVKpRa7rM7EjIqIPKl7cDgpFLF69eomMjHSevSPSI0EQkJGRjlevXkKhiEWxYrl/NGqBePIEEREVbNbWxSCVWiApSYFXrxKgVGZkub6ZmRmUStO9k58px2/KsQO5j9/MzBwWFpZwcPgfLCwsc719JnZERJQtqoNOdpjqE0dUTDl+U44dMH78TOyIiAzAPmgj7O2LQaF4ZeyuEJEJYWJHRGQAUvdqsHa2QZIJn7kgovzHiyeIiIiIRIKJHREREZFIMLEjIiIiEgnOsSMiMoDY5o0Q++/PTifPG7UvRGQ6eMaOiIiISCSY2BERERGJBBM7IiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERERiQQfKUZEZAAOe/bDsURxxMUnGbsrRGRCmNgRERmAuZMzLJxtYG5mbeyuEJEJ4VAsERERkUgwsSMiIiISCQ7FEhEZQEZsDN4oXyMjPgnmTs7G7g4RmQgmdkREBvCi60d48e/PTifPG7UvRGQ6OBRLREREJBJM7IiIiIhEgokdERERkUgwsSMiIiISCSZ2RERERCLBxI6IiIhIJJjYEREREYkEEzsiIiIikWBiR0RERCQSTOyIiIiIRIKPFCMiMgCnk+fh7GyDmJiXxu4KEZkQnrEjIiIiEgkmdkREREQiwcSOiIiISCQ4x46IyADSoyLx+lkxpCteQepezdjdISITwcSOiMgAFEMGQPHvz04nzxuzK0RkQjgUS0RERCQSTOyIiIiIRIKJHREREZFIMLEjIiIiEgkmdkREREQiYbSrYs+ePYu9e/ciIiIC0dHRsLOzQ61atTBq1Ci4u7t/sP7Dhw+xYMEChIeHQ6lUokGDBpg0aRLc3NzyofdEREREBY/Rztht374dT548wcCBA/HDDz/gm2++wZMnT9CjRw9cvHgxy7pxcXH47LPP8PjxY/j7+2PJkiVISEhA3759ER0dnT8BEBERERUwOTpj1759e3Tv3h1du3aFs7NznjY8Y8YMODo6apR5eXmhdevWCA4ORkBAQKZ1g4ODkZiYiF27dqFkyZIAgDp16qB169ZYs2YNZs6cmae+ERERERVGOTpjJ5VKsWTJErRq1QrDhw/HsWPHoFQqc7Xh95M6ALC1tUX58uU/eNYtLCwMnp6e6qQOABwcHNCqVSscOXIkV/0hIiIiKuxylNjt378fO3bsgFwuR3h4OIYPHw5vb28sXboUDx8+zHNn4uPjcevWLVSpUiXTdVJSUvDw4UPIZDKtZe7u7oiLi0NcXFye+0JElBdmjk6QOjvDzNHJ2F0hIhOS44sn6tSpgzp16mDq1KkIDQ3Fzp07sW7dOgQGBqJhw4bo2bMn2rdvD0tLyxy1KwgCpk+fDqVSicGDB2e6XkJCAgRBgJ2dndYye3t7AIBCodB5RjArjo7Fc7R+bjg72xh8GwWZKcdvyrEDphm/8+mTxu6C0Zni+/4uU47flGMHjBt/rq+Ktba2Rvfu3dG9e3fcu3cPK1euxP79+3HhwgXMmTMHXbp0wcCBA1GmTJlstbdw4UKEhYVh/vz5qFy58gfXl0gkue26TnFxSVAqBb22+S5nZxvExLw0WPsFnSnHb8qxA6YdP2M3zdgB047flGMHDB+/mZkky5NReboqNiMjA0eOHMGCBQtw4MABSCQSNG7cGLVr18aWLVvg6+uLsLCwD7azdOlSrF+/HlOnTkW3bt2yXNfOzg4SiQQKhUJrmapMdeaOiIiIyJTk6ozdnTt3sHPnTvz666+Ii4uDo6MjBg0ahE8++QTlypUDADx48ABjxozB999/jzZt2mTa1vLly7F27VpMmDAB/fv3/+C2rays4Orqips3b2otu3nzJkqUKJHjYVgiIiIiMchRYrdz507s3LkTly5dAgB4enrik08+QevWrSGVajZVvnx59OvXD9OmTcu0vZUrV2L16tUYPXo0hgwZku1+tGnTBlu3bkVMTIz6tisKhQLHjh3DRx99lJOQiIgMIvX0Sby0tUZq4msUadbc2N0hIhORo8Ru2rRpcHJygp+fH3r27ImyZctmub6bmxu6dOmic9n69esREBCAVq1awdPTU+OmxJaWlvDw8AAA9OvXD+fPn0dUVJR6+eDBg/Hrr7/Cz88PI0aMgFQqxZo1ayCVSjF06NCchEREZBAvvxkP1SybIifPG7UvRGQ6cpTYBQQEwMfHB+bm5tlav1atWqhVq5bOZceOHVP/r/pZxcXFBUePHs20XScnJ2zduhX+/v6YOHEiBEFA/fr1sWXLlmxfrEFEREQkNjlK7Nq2bau3DW/evDlP61WoUAFr1qzRW3+IiIiICjujPSuWiIiIiPSLiR0RERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERERiQQTOyIiIiKRyNWzYomIKGvmsqqwkJrhTbrS2F0hIhPCxI6IyAAcgjfB2dkGMTEvP7wyEZGecCiWiIiISCSY2BERERGJBBM7IiIiIpHgHDsiIgNI+XUPXhS3QkpSCqw6dzV2d4jIRDCxIyIygKTv5yPp35+Z2BFRfuFQLBEREZFIMLEjIiIiEgkmdkREREQiwcSOiIiISCSY2BERERGJBBM7IiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSPDJE0REBmDh6YUillKkpqUbuytEZEKY2BERGYCd/xI4O9sgJualsbtCRCaEQ7FEREREIsHEjoiIiEgkmNgRERERiQTn2BERGcCr9YFA0SJ4lZyKYoP8jN0dIjIRTOyIiAzg9YYgvP73ZyZ2RJRfOBRLREREJBJM7IiIiIhEgokdERERkUgwscsnLVu2xI4dWwEAb968gVzui19+2QEASE5Ohlzui5CQXQCAxMQEyOW+2LfvVwBAXFwc5HJfHDp0AADw7NkzyOW+OHr0CADg8eNHkMt9ceLEMQDA/fv3IJf74syZUwCA27dvQS73xfnz4QCAyMjrkMt9ERHxFwDgypXLkMt9ceXKZQBARMRfkMt9ERl5HQBw/nw45HJf3L59CwBw5swpyOW+uH//HgDgxIljkMt98fjxIwDA0aNHIJf74tmzZwCAQ4cOoGXLloiLiwMA7Nv3K+RyXyQmJgAAQkJ2QS73RXJyMgDgl192QC73xZs3bwAAO3ZshVzuq/5dbt78I7p376x+vX79D+jdu5v6dWDgavTr10v9etWqFfj8877q1ytWLIGf30D168WL/TFs2BD16wUL5uCrr4apX8+Z8x3Gj/9K/XrGjKmYNGmc+vW0aZMwbdok9etJk8Zhxoyp6td+fn6YM+c79euvvhqGBQvmqF8PGzYEixf7v7P+QKxYsUT9+vPP+2LVqhXq1/369UJg4Gr16969u2H9+h/Ur7t374zNm39Uv5bLfY362WvZsqVRP3tyua/RPnvvy+/P3vjxX5n0Z8+Y33u//fabUT97xv7eM+XPnrExscsHr9YH4qOXSah0/pyxu0JE+cT68yG4WbcuDjuUMHZXiCifvFofiJiAlW+vijcSiSAIgtG2XoDExSVBqTTMryK2eSP1z04nzxtkGwWdKT9ayZRjB0w7fsZumrEDph2/KceeH8d7MzMJHB2LZ77cIFslIiIionzH+9jlA6eT5036LxgiIiJTUBCO9zxjR0RERCQSTOyIiIiIRIKJHREREZFIcI5dPkiPisTrZ8WQrngFqXs1Y3eHiIiIDKAgHO+Z2OUDxZABUPz7s6ne7oSIiEjsCsLxnkOxRERERCLBxI6IiIhIJJjYEREREYkEEzsiIiIikWBiR0RERCQSTOyIiIiIRMKotzuJjo5GUFAQrl27hhs3biA5ORmbNm1C48aNP1g3ICAAK1eu1Cp3cnLC6dOnDdFdIiIiogLNqIndgwcPsH//fnh4eKBJkyY4evRojtvYsGEDihYtqn5tYWGhzy4SERERFRpGTewaNmyIs2fPAgDCwsJyldjVqFEDtra2+u4aERERUaFj1MTOzMw0pviZOTrBzEwCpVIwdleIiIjIQArC8b7QP1LM19cXcXFxcHR0RMuWLTF27Fg4Ojoau1saSoSEwtnZBjExL43dFSIiIjKQgnC8L7SJnaurK8aNG4dq1arBwsICf//9N4KCgnD27Fns3r0bdnZ2OWrP0bG4gXr6H2dnG4NvoyAz5fhNOXbAtONn7KbLlOM35dgB48ZfaBM7uVyu8bpp06aoU6cOBg0ahK1bt2L48OE5ai8uLsmgp06NncEbmynHb8qxA6YdP2M3zdgB047flGMHDB+/mZkky5NRoprk1qxZMzg7O+PixYvG7goRERFRviu0Z+wyIwhCgbsoI/X0Sby0tUZq4msUadbc2N0hIiIiAygIx3tRJXanTp1CbGwsateubeyuaHj5zXioTsoWOXneqH0hIiIiwygIx3ujJ3YHDx4EAFy5cgUAcOHCBbx48QLW1tbw9vYGAPTr1w/nz59HVFSUup5cLodcLkfFihUhlUoRERGB4OBglC9fHn369Mn/QIiIiIiMzOiJ3ejRozVeBwQEAABcXFyyvGFxpUqVsG3bNjx//hzp6ekoVaoUevbsieHDh/OGxURERGSSjJ7YvXsWLjObN2/WKluyZIkhukNERERUaBWsqwyIiIiIKNeY2BERERGJBBM7IiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSBj9diemwFxWFRZSM7xJVxq7K0RERGQgBeF4z8QuHzgEb4Kzsw1iYl5+eGUiIiIqlArC8Z5DsUREREQiwcSOiIiISCSY2BERERGJBOfY5YOUX/fgRXErpCSlwKpzV2N3h4iIiAygIBzvmdjlg6Tv5yPp35+Z2BEREYlTQTjecyiWiIiISCSY2BERERGJBBM7IiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgk+OSJfGDh6YUillKkpqUbuytERERkIAXheM/ELh/Y+S+Bs7MNYmJeGrsrREREZCAF4XjPoVgiIiIikWBiR0RERCQSTOyIiIiIRIJz7PLBq/WBQNEieJWcimKD/IzdHSIiIjKAgnC8Z2KXD15vCMLrf39mYkdERCROBeF4z6FYIiIiIpFgYkdEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERERiQQTOyIiIiKR4JMn8kGRTnJYW1ngdcobY3eFiIiIDKQgHO+Z2OUDm4lT4Oxsg5iYl8buChERERlIQTjecyiWiIiISCSY2BERERGJBBM7IiIiIpHgHLt88HLhPKT/O5nSZuIUY3eHiIiIDKAgHO+Z2OWD1N9CkPrvz0zsiIiIxKkgHO85FEtEREQkEkzsiIiIiESCiR0RERGRSDCxIyIiIhIJoyZ20dHRmDNnDj799FPUrVsX7u7uCA8Pz3b9hw8fYvjw4ahfvz7q1q2LL774Ardv3zZgj4mIiIgKLqMmdg8ePMD+/ftRtGhRNGnSJEd14+Li8Nlnn+Hx48fw9/fHkiVLkJCQgL59+yI6OtpAPSYiIiIquIya2DVs2BBnz55FcHAwunfvnqO6wcHBSExMRGBgINq0aYNWrVph3bp1SEtLw5o1awzU45w7ey06y9dERERU+BWU471REzszs9xvPiwsDJ6enihZsqS6zMHBAa1atcKRI0f00b08O3stGhsP3NAo23jgBpM7IiIiESlIx/tCefFESkoKHj58CJlMprXM3d0dcXFxiIuLM0LPNO0+cQdp6UqNsrR0JXafuGOkHhEREZG+FaTjfaF88kRCQgIEQYCdnZ3WMnt7ewCAQqGAo6Njttt0dCyur+6pxSe+vf/0kSqttcqdnW30vr2CzhRjVjHl2AHTjp+xmy5Tjt/UYi9Ix/tCmdipSCQSvbUVF5cEpVLQW3sAUMK2COISU3FE1larPCbmpV63VdA5O9uYXMwqphw7YNrxM3bTjB0w7fhNMfb8PN6bmUmyPBlVKIdi7ezsIJFIoFAotJapylRn7oypm3dlWEo1f8WWUjN0865spB4RERGRvhWk432hPGNnZWUFV1dX3Lx5U2vZzZs3UaJEiRwNwxpK0+qlALwde49PTEUJ2yLo5l1ZXU5ERESFX0E63hfKxA4A2rRpg61btyImJgbOzs4A3p6tO3bsGD766CMj9+4/TauXQtPqpUzy1DQREZGpKCjHe6MndgcPHgQAXLlyBQBw4cIFvHjxAtbW1vD29gYA9OvXD+fPn0dUVJS63uDBg/Hrr7/Cz88PI0aMgFQqxZo1ayCVSjF06ND8D4SIiIjIyIye2I0ePVrjdUBAAADAxcUFR48ezbSek5MTtm7dCn9/f0ycOBGCIKB+/frYsmULypQpY9A+ExERERVERk/s3j0Ll5nNmzfrLK9QoUKBesoEERERkTEVyqtiiYiIiEgbEzsiIiIikWBiR0RERCQSRp9jV1CYmenvKRbG3EZBZsrxm3LsgGnHz9hNlynHb8qxA4aN/0NtSwRB0O9ztIiIiIjIKDgUS0RERCQSTOyIiIiIRIKJHREREZFIMLEjIiIiEgkmdkREREQiwcSOiIiISCSY2BERERGJBBM7IiIiIpFgYkdEREQkEnykWDa9evUKS5cuxcGDB5GYmAg3NzeMGDECrVu3/mDdhw8fYsGCBQgPD4dSqUSDBg0wadIkuLm5aa27adMmbN26FY8fP0apUqXQq1cvDB48GGZmxsvBcxv7L7/8gt9//x1RUVGIi4tDqVKl0KJFCwwfPhwlSpTQWNfd3V1nG9999x0+/fRTvcWSG7mNPyAgACtXrtQqd3JywunTp7XKxfTe+/j44PHjxzqXVaxYEQcPHlS/LqjvfXR0NIKCgnDt2jXcuHEDycnJ2LRpExo3bpyt+oV9v89L/IV9389L7GLY7/MSf2He98+ePYu9e/ciIiIC0dHRsLOzQ61atTBq1KhM+/qugrLPM7HLppEjR+L69ev4+uuvUbZsWezZswcjR47E2rVr4e3tnWm9uLg4fPbZZ3B0dIS/vz/Mzc2xZs0a9O3bFyEhIShVqpR63dWrVyMgIABDhw5FkyZNEBERgWXLliEhIQFff/11foSpU25jX7FiBRo3boxx48ahZMmSuH37NlatWoWjR48iJCQEtra2Guv7+vpiwIABGmWurq4GiSknchu/yoYNG1C0aFH1awsLC611xPber1y5EmlpaRplN2/exPTp09GmTRut9Qvie//gwQPs378fHh4eaNKkCY4ePZrtumLY7/MSf2Hf9/MSu0ph3u/zEn9h3ve3b98OhUKBgQMHonLlyoiNjUVQUBB69OiBzZs3o06dOpnWLVD7vEAfdPz4cUEmkwmHDx9WlymVSqF3795Chw4dsqzr7+8v1KxZU4iOjlaXxcfHC3Xr1hW+/fZbjbKaNWsKs2fP1qi/ZMkSwcPDQ3j69KmeosmZvMQeGxurVRYeHi7IZDJh06ZNGuUymUyYM2eOfjqtR3mJf8WKFYJMJhMSEhKyXE+M770us2fPFmQymXD37l2N8oL63mdkZKh/PnLkiCCTyYRz585lq25h3+8FIW/xF/Z9Py+xF/b9XhDyFr8uhWXf1/W5TUhIEBo0aCCMHDkyy7oFaZ/nHLtsOHLkCGxsbDSGnyQSCbp27Yq7d+/i9u3bmdYNCwuDp6cnSpYsqS5zcHBAq1atcOTIEXXZyZMnkZqaiq5du2rU79q1K9LT0/H777/rMaLsy0vsjo6OWmU1a9YE8PZUf2GQl/izS4zv/fvS0tLw22+/oX79+qhYsaIhuqt3eRkSKez7PZC3+Av7vp8fw6Bife/fV5j2fV2fW1tbW5QvX/6Dn9uCtM8zscuGW7duwc3NTevDrhpzv3nzps56KSkpePjwIWQymdYyd3d3xMXFIS4uTr0NiUSCKlWqaKxXoUIFWFlZ4datW/oIJcdyG3tmzp07BwBacQLA3r17UatWLdSsWRM9e/ZEaGhoLnutP/qI39fXF9WqVYOXlxemTZumfs/f3YbY3/uwsDAoFAp0795d5/KC+N7nlhj2e0MobPt+XhXW/V7fCvu+Hx8fj1u3bun83KoUtH2ec+yyQaFQoEKFClrldnZ26uW6JCQkQBAE9Xrvsre3V9d1dHSEQqGAtbU1LC0ttda1tbXNdBuGltvYM2trzpw5qFChAnx9fTWWderUCd7e3ihdujSeP3+O7du3Y+zYsYiJidGaf5Gf8hK/q6srxo0bh2rVqsHCwgJ///03goKCcPbsWezevVujDbG/97t27ULRokXRsWNHrWUF9b3PLTHs9/pWGPf93Crs+72+FeZ9XxAETJ8+HUqlEoMHD850vYK2zzOxyyaJRJKrZdlZntftG1peYld5/fo1RowYgYSEBGzZskXrQ71o0SKN1x06dEC/fv2wbNky9OrVC1ZWVjnvuJ7kNn65XK7xumnTpqhTpw4GDRqErVu3Yvjw4XnevqHp472Pjo7GmTNn0K1bN43J5CoF+b3Pi8K+3+tLYd73c0MM+72+FPZ9f+HChQgLC8P8+fNRuXLlD65fUPZ5DsVmg729vc4sOiEhAQB0ZumqcolEorOuqkyVzdvb2+P169daVxMBQGJiYqbbMLTcxv6ulJQUDBs2DNevX0dgYCCqVq36wTpmZmbo3LkzkpOTczzcq0/6iP9dzZo1g7OzMy5evKixDbG+9wCwe/duKJXKTIdi3ldQ3vvcEsN+ry+Fed/Xp8K03+tTYd73ly5divXr12Pq1Kno1q1blusWtH2eiV02uLm54c6dO1AqlRrlqg+ernF1ALCysoKrq6vOD+jNmzdRokQJ9WRNNzc3CIKgNb7+4MEDpKSkZDm+b0i5jV0lNTUVw4cPx8WLF7Fu3TrUq1cv29tWbdOY93PKa/y6CIKgEZNY33vgbax79uxBpUqVCt17n1ti2O/1obDv+/pWWPZ7fSnM+/7y5cuxdu1aTJgwAf379//g+gVtnxfPXmNAbdu2RWJiota9fEJCQlCxYkWdNx9UadOmDc6cOYOYmBh1mUKhwLFjx9C2bVt1WYsWLWBpaYm9e/dq1N+zZw+kUil8fHz0FE3O5CX2tLQ0DB8+HH/++SdWr16NRo0aZXu7SqUSv/32G4oVK2bUL7i8xK/LqVOnEBsbi9q1a6vLxPjeq5w/fx4PHz7M9l/sQMF57/OisO/3eSWGfV+fCtN+ry+Fdd9fuXIlVq9ejdGjR2PIkCHZrleQ9nnOscsGb29vNG7cGFOnToVCoUDZsmUREhKCv/76C6tXr1av169fP5w/fx5RUVHqssGDB+PXX3+Fn58fRowYAalUijVr1kAqlWLo0KHq9RwcHPDll19i9erVsLGxQePGjXHx4kUEBQWhf//+KF26dL7GrJKX2L/66iucOnUKI0aMQNGiRTWGIUqUKIFy5coBAIKDg3Hv3j00adIEzs7OiI2Nxfbt2/HXX3/h22+/RZEiRfIt3vflJX65XA65XI6KFStCKpUiIiICwcHBKF++PPr06aNeT4zvvcquXbsglUq15h2pFOT3HoD6LvlXrlwBAFy4cAEvXryAtbW1+gbNYtzvVXIbvxj2/dzGXtj3e5Xcxq9SGPf99evXIyAgAK1atYKnp6fG59bS0hIeHh4ACv4+LxEEQchzKyYgKSkJS5YswaFDhzQerfTunbQz+5Dfv38f/v7+CA8PhyAIqF+/PiZNmqT1F4kgCNi4cSO2bduGJ0+e4H//+x969eqFL774wqinpXMbe1aPYOnatSsWLFgAADh69CiCgoJw9+5dvHz5EtbW1qhevToGDBhQIP5qzW3848aNw9WrV/H8+XOkp6ejVKlS8PHxwfDhw9XzLVTE9t6r6np5eaFp06ZYs2aNzvYL+nuf2WfYxcVFfSZTrPs9kPv4xbDv5zZ2Mez3QN4++4V131fFo0th2ueZ2BERERGJBOfYEREREYkEEzsiIiIikWBiR0RERCQSTOyIiIiIRIKJHREREZFIMLEjIiIiEgkmdkREREQiwcSOiIiISCSY2BERERGJBBM7IiIiIpFgYkdEpAfp6eno3bs36tatizt37mgs++mnn+Du7o7ly5cbqXdEZCr4rFgiIj15/Pgx5HI5ypQpg59//hlFihTBrVu30KNHD1SvXh2bN2+Gubm5sbtJRCLGM3ZERHri4uKCuXPn4saNG/D390dKSgrGjRuHIkWKYNGiRUzqiMjgpMbuABGRmLRr1w6ffvoptm7diuvXr+PmzZsICAhAmTJljN01IjIBHIolItKz1NRUfPzxx3j48CE++eQTzJ4929hdIiITwaFYIiI9i4qKwtOnTwEAt27dQnp6upF7RESmgokdEZEeJSUlYezYsbC3t8fYsWMRERGBgIAAY3eLiEwE59gREenRt99+iydPnmD9+vVo2rQpIiMjERgYiKZNm6JJkybG7h4RiRzP2BER6ckvv/yC/fv3w8/PD02bNgUAzJ49G6VLl8aECRPw4sULI/eQiMSOF08QEenBnTt30L17d1StWhVbtmyBVPrfgEhERAT69u2L5s2bY+3atUbsJRGJHRM7IiIiIpHgUCwRERGRSDCxIyIiIhIJJnZEREREIsHEjoiIiEgkmNgRERERiQQTOyIiIiKRYGJHREREJBJM7IiIiIhEgokdERERkUgwsSMiIiISif8Dj1dh0DHr6R8AAAAASUVORK5CYII=\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's try with data that is a little bit correlated\n",
"x = np.array([0, 1, 1.5, 2, 2.1]).reshape(-1, 1)\n",
"y = np.array([1, 1, 2, 1, 3])\n",
"\n",
"reg = LinearRegression()\n",
"reg.fit(x, y) \n",
"slope = reg.coef_[0]\n",
"intercept = reg.intercept_\n",
"\n",
"show_fit(x, y, slope, intercept)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.3209379240162824"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.metrics import r2_score\n",
"\n",
"# computing R2 from sklearn\n",
"y_pred = reg.predict(x)\n",
"r2 = r2_score(y_true=y, y_pred=y_pred)\n",
"r2"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Whats a 'good' $R^2$ value?\n",
"\n",
"... it depends:\n",
"\n",
"- if you're predicinting price changes in stock market: cross validated $R^2 = .01$ is fantastic!\n",
" - if you keep using your model to make bets, you'll come out ahead\n",
" - if this is the case, give me a call: I'd like to invest in your startup :)\n",
"- if you're predicting how many people will rent a blue bike (y) given weather (x): cross validated $R^2 = .01$ is not so great\n",
" - adding weather information into your model barely changes predictions\n",
" \n",
" \n",
"More generally, $R^2$ should be interpretted in the context of the application. Like Accuracy, its context dependent:\n",
"\n",
"- baseball player who \"accurately\" gets base hit 50% of at-bats is better than any hitter to every play the game\n",
"- pilot who \"accurately\" lands the plan without crashing 50% of the time might not be as celebrated ..."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Shouldn't you be cross-validating $R^2$?\n",
"\n",
"... we're `.fit()` ing and `.predict()`ing on the same samples!\n",
"\n",
"- one cross-validates $R^2$ values to \n",
" - estimate performance in predicting new samples\n",
"- it is also common to **not** cross-validate an $R^2$ when we want to examine a model's parameters\n",
" - how many more riders get on a blue bike when the temperature goes up 1 degree fahrenheit?\n",
" - `y_pred = a_1 * temp + a_0`"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# In Class Assignment 2\n",
"\n",
"Predict y=`trip_count` from x=`temp` by ...\n",
"1. `.fit()`ing a LinearRegression to predict y from x\n",
"1. visually inspect your results using `show_fit()`\n",
"1. store the following values in a new dataframe `df_regress` (see table immediately below)\n",
" - slope \n",
" - intercept\n",
" - mse\n",
" - r2\n",
"1. Repeat the three steps above for each new x value below. (Use a loop)\n",
" - x=`wind`\n",
" - x=`rain`\n",
" - x=`temp_c` (temperature in celsius)\n",
" - `temp_c` = (`temp` - 32) / 1.8\n",
" \n",
"Your final `df_regress` should look similar to below:\n",
"\n",
"| | r2 | mse | slope | intercept |\n",
"|-------:|---------:|-------------:|-------------:|-------------:|\n",
"| temp | 0.150487 | 3.548955e+06 | 144.646765 | 1157.497714 |\n",
"| temp_c | 0.150487 | 3.548955e+06 | 260.364178 | 5786.194210 |\n",
"| wind | 0.137007 | 3.605272e+06 | -119.156711 | 11469.348993 |\n",
"| rain | 0.271195 | 3.044684e+06 | -2224.622727 | 10644.350000 |\n",
" \n",
"Using the results above, answer the following questions\n",
"1. Which of the four features, `temp`, `wind`, `rain` or `temp_c` best predicts changes in `trip_count`? \n",
"1. Explain, to a non-technical expert, the meaning of each value in the slope column above\n",
" - i.e. if \"slope\" of \"temp\" is 144.64, what does this mean?"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"