{
"cells": [
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"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": 2,
"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": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'y')"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
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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": 18,
"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:.9f}')\n",
" plt.gcf().set_size_inches(10, 5)\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": [
"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": 7,
"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=1.3, intercept=.5)"
]
},
{
"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": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"\n",
"# computing / verifying MSE\n",
"show_fit(x, y, slope=0, intercept=np.mean(y))"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 3. , 0.5, 0. , -1. , -0.5, -2. ])"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_pred = x * 0 + np.mean(y)\n",
"error = y_pred - y\n",
"error"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.4166666666666665"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"error_sq = error ** 2\n",
"mse = np.mean(error_sq)\n",
"mse"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.4166666666666665"
]
},
"execution_count": 30,
"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": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(6,)"
]
},
"execution_count": 31,
"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": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(6, 1)"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = x.reshape((-1, 1))\n",
"x.shape"
]
},
{
"cell_type": "code",
"execution_count": 34,
"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": 35,
"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": 21,
"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\" 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": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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8du7cOWbPns2aNWs4ePAg8+bNS/J9ySjLZTxZ7w8ePEjyruz49+953qNhw4axfv16vL29mTt3rknu/o5XsmRJJk6cyKBBg1i6dClLly417suTJw8fffQRU6dOtbi14zI7JWaZkJOTEy1atGDp0qWsW7eOdu3asXz5cuLi4mjXrt1ThxBSIzWfoG7evEn//v2Jioqie/fuNGvWjHz58uHo6IiVlRUTJkzgxx9/NPYSmMrYsWPTNJTZrl07k8aRVtu2bWPgwIFYW1szceJEateunaZy4ns4/v333zSdb4rFfUNCQti/f7/x+5MnT1KpUqVUl/O0pw/EL5WR0mEuS2FtbU2hQoUIDQ1N8P7ET/i/efPmU8+NvxszX7586RJbnTp18PT0ZO3ateTOnRt7e3uaNm2a5vJKlCjBuHHjuHfvHr/99hvbt29P14Q5NDSUcePGpfq8tm3bJlg64mmcnJxwdXUlPDycmzdvJpkwxd89mdb3aOzYsSxZsgRPT0/mzp2b7JzDtGrYsCFVqlRh06ZNXLhwAYPBQMmSJXn99deNP29ZZR6opVBilkm98847xk9ALVu2ZOXKldjY2NC+ffsXHsvOnTuJioqiUaNGfPrpp4n2x99taGqbN29O06RbS0jMdu3aRd++fYmLi2P8+PHP1csZv4ZSevWsPIvBYGDQoEHcvn2bJk2asHPnTr777juqVq2aZe+wfVL8BPInb5YpUqQIDg4OhIWFcePGjUR/2KOjo41TANKrDm1sbGjevDlz5szh9u3bNG7c2CQ9JzVr1uS3335L9Yem1IqMjEyyB/VZqlWrlqLEDB73OB08eJDTp08nmbzEL0eR0htvnvTDDz8wZ84c3N3dmT9/frJPQ3heOXPmTHLuavySLU+7C1fShxKzTKpYsWJUq1aNQ4cOMXHiRIKDg2nQoEG6fOJ6lvjEIKnhz9DQUPbt25fkefHDZck9/iU5Ga33JN7+/fvp3bs3MTExjBo16rl6KQDjKuv/XcX/RZk7dy579uyhTJkyjBs3joCAAL7++mv69u1rXEU+qzp37hx//fUXkHDJBXt7e+rUqcNvv/3G+vXr+fDDDxOct23bNqKjoylTpky6/ky3atWKVatWAaRoeNFgMDxzXlz8B7E8efI8f4DJyJ8/P+fOnUvXa/j5+XHw4EHWr1+faJ7nrVu3OHr0KHZ2dokm1j/Ljz/+yPTp03F1dWXOnDkpWjfQ1I4ePcoff/xhsukvknKa0ZeJvfPOOwDMnj0bMM2k/7SIf3TIli1bEqzbFBkZyeDBg5867yz+F3dSk70zshMnTtC4ceMkH6Vz/PhxevbsSVRUFEOGDEnRH8Pr16/z888/J7pzKjY2lvnz5xsX/X333XdN8wJS4dSpU0yYMAFHR0fGjx+Pvb097du3p3Hjxly5ciXdnvX4ot26dcv4nv538c9FixYl2YZPnDjBJ598Ajy+o/m/icoHH3wAPP4jff78eeP2oKAgvvvuuwTHPMnf358SJUrQqVOn53tRPB7COnjwIAcPHkxRcnHu3Dk6d+7Mjh07kvxAtWXLFuNNSM/7gcMStG3blpw5c7J7924CAgKM26Ojoxk8eDAxMTHGY560aNEiGjduzMCBAxOVuXDhQiZMmICTkxOzZs1K917lEydOJLktvm0OGTIkyZs0JP2oxywTa9CgAV5eXgQFBVGgQAHq1q1rljjq169PyZIlOXv2LI0aNaJatWrY2tpy+PBhrK2tad26tfFT+ZPq1KlD9uzZ2bJlC2+//TYFCxbE2toaPz8/k63j87ymTp1qnFQff8PDvXv3EgwZt2vXLsHw6IMHD4y9JP/14YcfEhkZiaenJ3/++Sd//vlnksc9ebdZREQEQ4YMYezYsZQtW5bcuXMTERHB+fPnCQoKwsrKij59+qT6U/vzun//Pv369ePRo0cMHz48wd18I0aM4OTJk6xatYpatWrRvHnzFxpbclasWMGKFSsSbe/cubNxbqWvr2+Cx1I9evTI+J7+947VFStWMHz4cHx8fChcuDBWVlZcu3aNM2fOYDAYKF++fKK7NuHx3Ym9evVi6tSptG7dmlq1amFnZ8e+ffuIjIykTZs2SSY38Q+hN8Vc0tQyGAwcOHCAAwcO4OTkROnSpcmdOzf379/n0qVLxgVSmzZt+tQpAytWrEj2Bo+UzgF7EZycnPjuu+/o0aMHgwYN4ueff8bLy4tjx44RFBREyZIljY/PetKdO3f466+/Eq3rdubMGUaOHAk8XgJnyZIlLFmyJNH5Sd1pnJZ2C49/P3l7e1OsWDGcnZ25cuUKgYGBWFtbM3jwYBo2bJi6SpHnpsQsE7O1taVq1aqsXbuWDh06mO3Wezs7OxYtWsSUKVPYsWMHv//+Ozlz5sTPz48+ffqwfPnyJM/z9PRkxowZTJ06lTNnznDkyBEMBgNeXl4Wk5j9/fffiZKnmJiYBNtSkxDH9x7evn072fkxTyZmXl5edO3alZMnT3L16lX+/PNPDAYDefLkoUWLFrz11ltUrFgxxTGYyrfffsvVq1dp1qxZovWknJ2dGT9+PO+88w5DhgyhQoUKKV4/Kr0FBQUlmRCfPHnS+PV/HyCdnHfeeYc9e/Zw7tw59u3bZ7yDr0aNGjRt2pRWrVo99S7XTz75hJIlSzJ//nz++OMPDAYDRYoUoWPHjk9NbOJXmX/ag+7TU/HixVm4cCF79+7lyJEjXL9+3ViXuXLlolGjRrzxxhvJDo0dPXqUo0ePPnV/auaAvQh169Zl5cqVTJs2jUOHDhEYGEjevHnp3r073bt3T3Ytuv+KiIgw3gR15syZpz4xIKk7jdPabt977z0OHTrE8ePHiYyMJFeuXLRo0YL33nsvTXPj5PlZGUx9K5xYjPv371O3bl3js9rc3d3NHZKIpKOYmBiqVavGSy+9xC+//GK2D2MiknaaY5aJzZ07l/v379OsWTMlZSJZwIkTJ7h//z4DBgxQUiaSQanHLJO5fPkys2fPJigoiL1795ItWzbWrl1LgQIFzB2aiIiIPIPmmGUyt2/fZuXKlTg4OFC2bFkGDBjw1KRs27ZtbNu2LUXlmvuxNiIiIlmBesyyMH9/f6ZMmZKiY6tVq/bUVddFRETENJSYiYiIiFgITf4XERERsRBKzEREREQshBIzEREREQuhxExERETEQigxExEREbEQSsxERERELIQSMxERERELocRMRERExEIoMRMRERGxEErMRERERCyEEjMRERERC6HETERERMRCKDETERERsRBKzEREREQshBIzEREREQtha+4ATOXOnfvExRnS9RoeHk6EhNxL12tkJapP01Odmpbq0/RUp6al+jS99K5Ta2srcubM8dT9mSYxi4szpHtiFn8dMR3Vp+mpTk1L9Wl6qlPTUn2anjnrVEOZIiIiIhZCiZmIiIiIhVBiJiIiImIhlJiJiIiIWAglZiIiIiIWItPclfksjx5Fc/duGDEx0cTFxaapjH//tSYuLs7EkWVdqk/TM1edWlvbYGtrj7OzG3Z29i/8+iIimUWWSMwePLjP3bt3cHJyxcHBHWtrG6ysrFJdjq2tNTExSiRMRfVpeuaoU4PBQFxcLFFRD7hz51+cnXOSPfvT1+gREZGnyxKJ2b174bi55cLePpu5QxHJdKysrLCxscXR0RlbWzsiIkKVmImIpFGWmGMWG/sIOzsHc4chkunZ2TkQE/PI3GGIiKSKwWA5i/RmicQMSNPQpYikjn7ORCSjmTdvNi1aNLGY5CzLJGYiIiIiBoOB/fv38vDhQwCcnJzIlcuTu3cjzBzZY0rMREREJMs4dOggLVo0Yc2aVQC0bduBOXMW4uLiaubIHssSk/8leVevXmHbts00bdqcvHnzmTscERERk4mLi2PMmBHkyeNF167dqFatOjNmzKZx49cTHXt33Chistnx4OEjnAd+aYZo1WMmPE7M5s79iZs3b5g7FBERkedmMBi4du0qANbW1vz55zHOnz8LPJ4L27p1OxwdHROdF7U2gLAVK4haG/Aiw01APWaSatHR0djbaxFRERGxTGPHjmDGjGmcOHEWFxdXFi9ega1txkh51GOWgW3Zsok6dapw6tTJRPv8/SfQsGE97t+/l2wZGzas5csvBwDwySfdqVOnCnXqVOHo0T8AaNu2OV980Z+tWzfRqVN7XnmlBtu2bebmzRvUqVOFDRvWJiqzTp0qzJ79Y4JtV678xeDBg3j99QbUr1+Tzp07snnzxrS+dBEREaOQkBDGjBlu7CVr3rwVQ4eOND6JJKMkZaAes+eyPzCIVbsuERIRhYeLA619i1KzjNcLu76f36tMnfoDq1evoGzZcsbtUVEP2bBhHY0aNSFHDqdky6hZsw49evRm+nR/+vUbhI9PSQAKFy5sPOb06UCuXPmLLl0+wMMjF7lyeaYqzosXL9CjR1cKFXqJvn0/w9XVjR07tjFkyFc8ePCAZs1apqo8ERERg8HAgwcPcHR05OHDB0yZMomCBV/irbc6UaZMWcqUKWvuENNEiVka7Q8MYv7Gs0T/7/E3IRFRzN/4ePz6RSVntra2tGzZhoUL59K7dz/c3NwA2Lp1E3fvRtC6dbtnlpEzZ04KFCgEwEsvFU6Q4MULDw9jxow5CW4MSM18tKlTf8DNzQ1//x/Jnj07ANWq1SAiIpyZM6fTtOkbWFur81ZERFLGYDDQtu0b5M6dh+nTZ+HtnZ/jx8+SK1cuc4f23Mz21/DgwYOUKFEiyX+XLl0yV1gptmrXJWNSFi86Jo5Vu15s7C1atMZgMLB+/RrjttWrf6FixcoUKVLMJNcoXtwnzXdrRkVFcfToH9SrVx87OztiYmKM/2rWrE1oaAhXr14xSZwiIpJ53boVxOLFC4DHE/gbNHiNWrXqGPdnhqQMLKDHbMCAAVStWjXBtvz585spmpQLiYhK1fb04u7ugZ/fqwQErOLNNztx+nQg586dYejQ0Sa7hodH2ht7REQ4sbGxLFu2mGXLFid5THh4WJrLFxGRzM1gMGBlZcWKFcsYPvwb6tb1pWDBQvTs2dvcoaULsydmhQsXpmLFiuYOI9U8XBySTMI8XF78MznbtOnA5s0bOXhwH9u2bcHDIxe+vvVNVn5Sj9mJvyszOjo6wfb/JlnOzi5YW1vTtGlzWrZsk2CfjY01sbFxFCxYyGSxiohI5nDt2lW6devCwIFf4ef3Kp06daZp02bp9jdjf2AQxf/z/YucNx7P7IlZRtXat2iCOWYA9rbWtPYt+sJjKV26LKVLl2XBgrmcO3eGt9/unKo7UOzs7IDHw44p5e7ugb29A5cuXUywfc+eXQm+z5YtGxUrVubChfMUK+aTIC5bW2ti/jMcLCIiWdetW7f4998gypWrgJdXXrJly05sbAwArq5uuLq6pct14+eNj3hi24ueNx7P7InZN998wyeffEL27NmpUqUKvXv3pmxZy7+TIv6NMuddmU9q27YDw4Z9jY2NDS1atE7VuYULF8HKyop16wLIkSMH9vb2FCxYCEfHHE89x8rKitdea8z69b/i7e1NsWI+nDkTyNatmxId+8kn/enV6wN69/6IFi1akyePF/fu3eXvv68RGHiSkSO/S/XrFRGRzKdTp/bExsbx2297sLe3JyBgwwu5bnLzxrNMYubs7Eznzp2pVq0abm5uXLp0iZkzZ/Lmm2+yaNEiKlSokKryPDyevizEv/9aY2trmvscniynboV81K1gGY8watDgVUaNGoqvb328vPKk6tz8+b3p06cfP/+8hN69PyI2NpapU2fy8stVgMdJWFL19+mn/bG2tmbJkoU8eBDJyy9XZfz4SbRq1Qxr6/8/p2TJEsybt5g5c35ixgx/wsLCcHFx5aWXCtOgQUOTvTfymLnr09raGk9PZ7PGYEqZ6bVYCtWpaWXk+ty5cycTJ05k5cqV2NnZMXXqFDw9PV/4awr939SkrcUbJNr+omOxMhgMhhd6xWTcvn2bZs2aUapUKebNm5eqc0NC7hEXl/RLCQq6ipfX849JW/LQ265d2/nqq4H4+/9IpUovmzucFLHk+syoLKFOTfXzZgk8PZ25ffuuucPIVFSnppUR6/P27dtkz54NJydntm3bzODBn7NkyQqTrSSQFp9N2/vUeePf9axt0mtZW1sl25lkUV0Vnp6e1KlThz///NPcoWQY165d4dChA0ydOokyZcplmKRMRESynhs3rlOpUikWLJgHgJ9fQ/btO2LWpAwezxu3/89og7nmjZt9jtl/xcWpByU1xo0bxalTJyhRohSDBw9NsM9gMBAbG5vs+TY2NknedSkiImIKa9euITj4Nu+99wH58nkzePC3NGzYCMBiFhd/ct54aEQU7macN25Ridnt27fZt29fhlw+w1ymTJn51H0bN65j1KihT90PMHnyDCpXrmLqsEREJAu7f/8+OXI8voFs3boALl++TJcuXbGysqJ794/NHF3SapbxomYZL7MPD5stMevfvz8FChSgTJkyuLi4cPnyZX766ScePnxIv379zBVWplK7dl1mzVqQ7DFaQ0xERExp9eqV9Ov3Cfv2/UHevPkYO3YCLi6uGp1JIbMlZiVKlGD9+vUsWrSIBw8e4ObmRrVq1ejRowc+Pj7mCitTSc81X0RERABiYmLYsGEtJUqUokSJklSuXIV27ToYEzE3t5xmjjBjsai7Mp9HVr8rMyNSfZqeJdSp7sqU5KhOTcuc9Rn/qKTw8DAqVChJ585dGTp0pFliMaX0rtNn3ZVpUXPMRERExPKNHDmUc+fOsmDBUlxd3diw4TdKlChp7rAyBcu4HUJEREQsVkxMDL/9toX4QbacOd3Jk8fLeOd/6dJlsLGxMWeImYZ6zERERCRZq1evpFevbgQEbKBWrTr07Nnb3CFlWkrMREREJIF79+4xZMiX+PrW5403WtG8eUucnJypXr2muUPL9DSUKSIiIsTGxvLXX5cBcHR05PjxY1y7dg2AbNmy0aTJ6xqufAHUYyYiIiL06vUhhw4d5NChP7G1tWXr1l0WszJ/VqIaF4tw9Ogf1KlThaNH/0jR8bNmzaBr107pHJVlu3nzBnXqVGHDhrXpdo179+7RuHF99uzZmW7XEBHzuHr1Cp9/3p979x4vDdGlywcMGzbauP6YkjLzUK1LhnPrVhBLly7kgw+6mzsUs/LwyMWMGXOpWbNOul3DycmJjh3fZurUScTExKTbdUTkxYiNjeX+/fsAhIQEs2TJQo4ePQJAjRq1aNbsDQ1XmpkSM3lu0dHRL/R6K1b8jIdHLmrWrJ3scTExMc98iLupxMXFvfDExd7enrJly5EzZ/quqt2iRWtu3rzBzp2/pet1RCR9PXz4kNq1q/DDD98DULlyFU6cOEe9eq+YNzBJQHPMMqgtWzYxbNhgZsyYS9my5RLs8/efwK+/BhAQsIEcOZ6+unC8DRvWMmrUUCZOnMr69b+yf//vGAxQs2Zt+vYdQM6c7sZj27ZtTvHiPvj5NWTBgjn8/fc1Bg78iqZNm/Pvv7eYNWsGBw/uIzw8HC+vfLRu3Zb27d9KcL0rV/5i8uTx/PnncbJlc6Bu3VeoU6deil73o0eP2LBhLa1bt0uw/ebNG7Rr9wY9e/YhMvI+Gzas5fbtf1m+fA158+bj1KkTzJ07i8DAE0RHP6JYseJ88EF3qlWrkaCcPXt2MmvWDK5du0quXJ60atWOBw8imTv3J37//f+HWevUqUK7dm+SN28+fvllGUFBN5k4cSqVK1fhypW/mDVrBseO/UFkZCQFCxbi7be78NprjY3nP3z4kJ9+ms7u3TsICQkmW7bs5M9fgM6du1K7dl0Azp07y6xZ0zlz5jT379/DzS0nJUuW4osvhuDi4mJ8zV9+OYSmTZsby96xYxuLFs3nr78uY2dnS4UKlejWrRfFihU3HjNy5Lfs2bOTmTPn8cMP4zl58jjOzi7Ur/8qH33UC3t7e+OxOXO6U7VqddasWcWrrzZK0fskIpbh/PlzHD36Bx07vk22bNlo1aotlSpVNu7X45IsT5bvMWvZsik//7wYePxHv2XLpqxY8TMAkZGRtGzZlICAXwCIiAinZcumrFv3KwAhISG0bNmUzZs3AnDr1i1atmzK9u1bAbh+/R9atmzKrl07gMcJScuWTdm373cALl68QMuWTdMUt5/fq3h45GL16hUJtkdFPWTDhnU0atQkRUnZk0aPHoaTkzPDho2hW7ce7N+/l08//ThRT9Dp04HMmTOTd97pwvffT6Z06bIEB9/mww87c+LEn3Tr1ovvvptEvXqvMHXqJH76abrx3JCQYD7+uBtXrvzFZ599zuDBw3j48CETJoxLUYynT58iIiKcihUrJ7l/+fIlnDlzmn79BjJ69Pc4O7tw6NABPv64G3FxsXzxxTeMHDkWD49cfPZZHw4dOmA898CBfXz11UDc3HIydOhoevb8hJ07f2PjxnVJXmvHjm1s3bqR7t0/ZuzYiXh75+fixQt8+GFngoJu0rfvZ4wdO5HSpcsybNhg1q0LMJ47efJ4Nm/ewNtvd2b8eH++/PIbatWqQ0REOPC47X36aS8ePXrEwIFfMWHCFHr2/ARnZ5dkeyjXrfuVr7/+HE9PT4YNG03//l/wzz9/06NHV65c+SvBsdHRj/j88/5Uq1ad0aPH07Rpc5YvX8LixfMTlVup0sucOHGcyMj7T722iFiGJ5+0OHfuT3z11SDj8OWgQV/x2mtNzBWapIB6zDIoW1tbWrZsw8KFc+ndux9ubm4AbN26ibt3IxL1KKVEuXIVGDDgcwCqV69JzpzuDBnyJTt2bKNhw//v7QkPD2PGjDnkzZvPuG3s2JFERT1k9uxF5MqVC4CqVasTE/OIpUsX0qHDW7i4uLJs2RLCw8OYP38pPj4+xMTEUbNmbfr06cm//956ZoynTp0AwMenRJL7HR0dGTduYoI5EhMmjMPHpyTjx/sbJ7PWqFGbrl07MXPmNGOv2axZM8iTx4vx4/2xtbX9Xz3Uol275okvxOMh3B9+mJYgAR4zZjhubm74+/9I9uzZAahWrQZhYWHMnDmdpk3fwNrampMn/+S11xrTsmUb47l16vgav7527QoREeH06tWX4sV9jNuffB/+Ky4ujunTp1CyZGlGjx5vnMBbuXIVOnRowdy5PzF06Kgn4o/io48+xte3PgBVqlTj3LkzbNmykffe+zBB2T4+JYmNjSUw8BRVq1Z/agwiYl7Hjh2he/euzJ+/lJIlS9G372f07/85OXLkMHdokkJZvscsIGADHTu+DYCdnR0BARto164j8PiPfEDABuMfTxcXVwICNtCs2RsAeHh4EBCwgUaNHn/6yJMnDwEBG/DzawiAt3d+AgI2GP/wvfRSYeOqyQDFihUnIGBDmmNv0aI1BoOB9evXGLetXv0LFStWpkiRYqku79VXX0vwva+vHzY2Nhw/fjTB9uLFfRIkZQAHDuzl5Zer4ubmRkxMjPFfzZq1iY6OJjDwJPD4l0axYsUTxffkMF9ygoODsbGxwdnZJcn9derUS5CU/fPP3/zzzzUaNmxsnAcWP/esRo1anDt3hsjISB48eMC5c2eoV+8VY1IGj9tA7dpJD7O+/HLVBElZVFQUR4/+Qb169bGzs0tUD6GhIVy9egWA0qXLsmHDWubO/YnAwFM8evQoQdn58xfE2dmFsWNHsHHjOm7cuP7Murl69QohIcG89lpjY1IGkCtXLqpWrc6xY0cSHG9jY2Nsi/GKFi3OrVtBicqOH84ODr79zDhE5MW6ePECZ8+eAaBgwZfw9s7PgweRwOO/S/EfliVjUI9ZBubu7oGf36sEBKzizTc7cfp0IOfOnWHo0NFpLC/hD6+trS2urm6Eh4cn2O7hkfiHPDQ0hF27dvDKKzUS7QMICwsDHg8H589fMNH+pMpMSlTUQ+zs7BIkHsmVExoaAsCkSd8zadL3SZ4TERGBtbUVBoMhwXy6eEltS+paERHhxMbGsmzZYpYtW5zkOeHhYQD07fsZuXJ5smXLRmbP/pHs2R2pW9eXHj164+mZGycnJ6ZMmcm8ebOYNGk89+7dJW9eb1q3bkfHjm8n+fojIiKAx+0iqVjjrx0ve/bs2NnZJdhmZ2eX5FBp/JyzqKiHSb4uETGPmJgYWrRoQpUq1Zg/fwkeHh6sWpX09AvJGJSYZXBt2nRg8+aNHDy4j23btuDhkcvYQ5daoaHBCb6PiYkhPDwMV1fXBNuTSgrc3Nzw8SlJ164fJVl2fA+bi4trouvA47lnKeHq6sbDhw+Jjo5OMEH9abHFD/F26fLBU28w8PDwICYmBisrK+7cCU20P6ltSV3L2dkFa2trmjZtnmCI8kkFCxYCHidFH37Ygw8/7MGdO6Hs3bubadP8uXUriKlTfwKgaNFiDB8+BoPBwMWLF1iz5hemTv0BZ2dnmjVrkajs+PcpPhl9UkhIMK6ubknGlBLxSd/zlCEiprF69UrWr1/LTz/Nw9bWlpkz5+LjU9LcYYmJKDHL4EqXLkvp0mVZsGAu586d4e23OycYikuNbdu2ULfuK8bvd+3aTmxs7FMn2j+pevVa/PHHIQoUKJjsTQeVK1dhyZIFXL58CR+f/79LcMuWTSmK8aWXCgOPb6woXLjIM48vUKAQ+fJ5c+nShWTXPbOzs6NkyVLs3r2THj0+MdZhZGQke/fuTlFs2bJlo2LFyly4cJ5ixXxS/D7kzOlOs2YtOXHiT3bt2p5ov5WVFcWL+/DppwNZuzaAixcvJFlOwYKF8PT0ZMuWTbRr96YxcQwNDeGPPw4lmMOWWvFDqYULF01zGSKSdpcvX6RAgULY2dkRHh7O9ev/EB4eRu7cLsY7uSVzUGKWCbRt24Fhw77GxsaGFi1ap7mckyf/ZPz4sdSt68u1a1eYOXM6xYr5UL/+q88898MPe3D48EF69OhK27YdyZ+/AA8ePOD69b/Zu3cPEyZMwcbGhvbt32T9+l8ZMOATPvqoJy4ubmzevIG//76aohgrVXoZgMDAkylKzKysrBgw4AsGDuzLwIF9adSoqXFY7+LFC4SEBDNw4FcAdO3anYED+9K/f2/atu1AbGwsS5YsJHt2R2OP0bN88kl/evX6gN69P6JFi9bkyePFvXt3uXr1CmfOBDJy5HcAdOvWhVq16lC0aDGcnJy5ePECO3dup2bNWgDs3buHgICV1K37Cnnz5iMuLo4tWzYSFxf31IcIW1tb07Nnb4YO/YYvvuhP8+atePAgknnzZmFtbcP773+Y5Hkpcfr0SdzdPYyJsYi8OIcPH+T11xsya9Z83nijFe+++x5dunQ1d1iSTpSYZQK+vn7Y2g6lbt1XyJXLM83lfPnlENatW8PXXw8iLs5ArVq16dNnQIp6fjw9czNr1gLmzp3F/PmzCQkJxsnJifz5C1KjRi3j3ZAeHrmYMmUmkyZ9z7hxo3BwyEa9eq/Qr99APv+8/zOvkzt3HipWrMzvv+9KcjgvKdWq1WDGjLksWDCHiRPHce/e4zXBihUrTpMmzYzH1ahRixEjxjF79gy++eYL3N09aNWqLcHBwWzatD5F1ypWrDizZy9i7tyfmD7dn/DwMFxcXClU6CXjTSHwOMHcs2cXP/+8mOjoaHLnzk2rVm3p0uUDAAoUKICjYw4WLZpHcHAw9vb2FC5cmOHDxyS7sG6TJs2wt8/GwoXz+PrrQdja2lGxYiWGDh1NwYIvpeg1/JfBYOD333cne0eoiJhOXFwcc+fOws3NjTZt2lO5chW+/XYkNWo8/tnXo5IyNyvDkwueZGAhIfeIi0v6pQQFXcXLq9BzX8PW1pqYmLjnLsfUdu3azldfDcTf/0djj1JqxC8wO3fuYooXT3oZivSQ1vrcsWMbQ4cOZvXqDU+dmG8qMTExdOnyFrly5eKHH6al67VMIT3a6NGjf/Dpp71YtGgFBQokvnHjv0z182YJPD2duX37rrnDyFRUp093926E8Y7z119viLe3NzNnzkv2HNWn6aV3nVpbW+Hh8fQpP0q7M7Br165w6NABpk6dRJky5dKUlGVEr7zSgOLFS7B48QKTlhsbG8vYsSPYsWMbx44d4bfftvDpp724evUv3n77XZNeKyOZP382r7/+RoqSMhFJm8mTJ1K1annjQrBLl658ZlImmZOGMjOwceNGcerUCUqUKMXgwUMT7TcYDM98VmRGfFitlZUVgwYN5uDBfSYv9+7dCCZPnkBY2B1sbW3x8SnJd99NomrVpJcByezu3btHhQqVaNWqrblDEclU7t+/z/LlS2natBl58nhRq1ZtHjyIJC7u8e9sFxfXZ5QgmZWGMlPBUocynyZ+iDI5kyfPoHLlKi8oooQyWn1mBJZQpxrKlORk9TqNi4vD2tqay5cvUbNmZUaP/v65bszJ6vWZHsw9lKkes0ysdu26zJqV/HBf/LpaIiKSfgwGA927v4+zsyvff/8DRYoUZc+eQwkeuSYCSswyNVdXNy0IKiJiJvfv32fv3t289loTrKysKFCgUIJnVj7tmb+StSkxExERSQczZ05j9OjhHD58gkKFXmLw4G/NHZJkALorU0RExARu3rxB585vceDA4xuT3nmnC2vXbtGUEUkV9ZiJiIikUWRkJLduBVG4cBFcXd04f/4sN2/eAMDT0xNPz7Qv+i1ZkxIzERGRNGrTphnW1jasX78VR0dH9u07YnxOrUhaKDETERFJoRMnjrNgwTzGjh2PjY0NAwZ8jqPj/0/oV1Imz0tzzERERJLx4MEDHj58CMDVq1dYu3Y1ly5dBKBBg9eSfX6tSGopMRMREXmKmzdvUKlSKZYuXQRAkybNOH78rJa6kHSjxExEROQJBw7sJyDgFwC8vPLy5pudKF++AgC2trZkz57dnOFJJqc5ZllUdHQ09vb2qd73vGWLiFii+EclAUybNomLFy/QokVrrKysGDJkuJmjk6xEPWaZwJUrfzF48CBef70B9evXpHPnjmzZssm4f8OGtdSpU4XDhw8wbNjXNGnix9tvP34o9ccfd6NLl7c4fPggH3zwLn5+tVi4cC4A16//wzfffEHTpo/L7dSpPWvWrEpw7aNH/6BOnSps2bKRCRPG0rz5a/j51XpxL15E5Dlt2rSBypXLEBwcDMCYMePZunW3JvKLWWT5HrP7c2byYO6sFB2bvUUrcgz4IsG2u+NGEbU2IGXnv/cBOd7vlmBb+KB+2JYomWh7Sl28eIEePbpSqNBL9O37Ga6ubuzYsY1hwwYTHf2QZs1aGo8dNWoYvr5+DBs2iqioKOP227dvMWbMcN59930KFCiIo6MjISHB9OzZFSsra3r2/AQPj1xs376V774bxZ07oXTp8kGCOKZNm8zLL1fhyy+HEBkZmabXIiLyIhgMBg4fPoSXlxcFCxaicOEilC9fgXv37pIrVy7y5fM2d4iShWX5xCyjmzr1B9zc3PD3/9E476FatRqEhYUxc+Z0mjZ9w3hsjRq16Nt3QKIywsPDGT16POXLVzRumzZtMqGhocydu4RixYoDULNmbe7du8fChXNp06YDzs7OxuNfeqkwX3+t7n4RsXx37oTSuvXrvPfeBwwfPoYSJUqyYMHP5g5LBNBQZoYWFRXF0aN/UK9efezs7IiJiTH+q1mzNqGhIVy9esV4fL16ryRZjptbzgRJGcCxY39QtGhxY1IWr3Hj14mKiiIw8GSC7fXq1TfFSxIRSRfTpvnTv38fANzdPVi69BcGDRps5qhEEsvyPWY53u+W4mFEW1trYmLiEmxzHvglzgO/TPP1XcdOSPO5ERHhxMbGsmzZYpYtW5zkMeHhYcavPTxyJXlMUtsjIiLw9i7w1GMjIsKfWYaIiLkYDAYCA09Rtmw5AMLD7xAcfJvY2FhsbGyoW9fXzBGKJC3LJ2YZmbOzC9bW1jRt2pyWLdskeUzBgoW4ceM68PQVqZPa7uLiSmhoSKLtISHBxv3PKkNExFxWr15J9+5d2bjxN15+uSqff/61fk9JhqDELAPLli0bFStW5sKF8xQr5oOtrenezpdfrsrixfO5ePFCguHMLVs24ODgQJky5Ux2LRGR5xUZGcmUKT9QpUpV/Pwa8tprjRkzZjwlSpQC9OFRMg7NMcvgPvmkP//8c43evT9i06b1HDt2hD17drJo0Ty++uqzNJfbocNbuLt78NlnfVi3bg0HDuxj1Kih7Nq1gy5dPkgw8V9ExFzie/bt7e1ZvvxnDh7cD4CTkzPvv/8hTk5O5gxPJNXUY5bBFStWnNmzFzF37k9Mn+5PeHgYLi6uFCr0En5+DdNcbs6c7syYMYcZM/yZNm0yDx5EUqBAQQYNGkzz5i1N9wJERNKof/8+7Nu3h717/8DW1pZdu/aTI0eOZ58oYsGsDAaDwdxBmEJIyD3i4pJ+KUFBV/HyKvTc10hq8r+knerT9CyhTk3182YJPD2duX37rrnDyFSep06Dg4NZvHg+3br1JHv27Gzduolr167y7rvvY2dnZ+JIMwa1UdNL7zq1trbCw+PpPbnqMRMREYsWfyfluXNnGDlyKGXLlqNBg9do2LCxuUMTMTnNMRMREYv08OFDXn+9IZMmjQegVq06HDx4nAYNXjNzZCLpx6ISM39/f0qUKEGLFi3MHYqIiJjB7du32bZtM/D4zvPSpcsaH5FkZWVF4cJFzBmeSLqzmKHMCxcu8NNPP5ErlxYqFRHJqkaPHsaqVSsJDLxIjhw5+O67ieYOSeSFsoges7i4OL766ivatWtHkSL6NCQiklWcPh3IG2805q+/LgPQp09/tm7dpbsrJcuyiB6zefPmERQUxJw5c+jRo0e6XMNgMGiBQZF0lklu8pZ0sD8wiFW7LhEaEYWjzQNerexFiwYv4+7uTkhIMDdv3qBw4SIUKvSSuUMVMSuzJ2Z///03kydP5vvvv0+3hQBtbOx49CgKe/ts6VK+iDz26FEUtrZZc9kCebr9gUHM33iW6Jg44uJiCfixJ3sLlCW312xqlsnL778f1gdnkf8x61CmwWBg8ODB1KlTh1dffTXdruPk5EpYWDD3798lNjZGn+pFTMhgMBAbG8P9+3cJCwsmRw7XZ58kWYr/7OUc3ToTAGtrG8rW/5Ci1duzatclQI9LEnmSWXvMli9fzqlTp9iwYcNzl5XcYm3gzMOHbty69S/h4beJiYl57uuJyP+ztbUlW7ZsFC1amGzZMlfPtKenHj+WFiEhIeTMmRNra2tu/H2JW5cO4VOzI/bZnMjrUwuA0Igo1a8JqA5Nz5x1arbELDQ0lO+++46PPvqI7NmzExERAUBMTAxxcXFERETg4OCAg4NDispLbuX/eI6OOXF0THvMWmHZtFSfpmfuOr179xF37z4y2/VNzdz1mVEdO3aEFi2aMHv2Aho2bEzlui0pXKkZVtY2CY5zd3FQ/T4ntVHTM/fK/2Ybyrx16xZ3795l/PjxVK1a1fjv6NGjnD9/nqpVq+Lv72+u8EREJIUMBgPr169l69ZNAJQtW54uXT6gSJGiALRrUAoH+4RzD+1trWntW/SFxypi6czWY1awYEEWLFiQaPuoUaOIjIxkxIgR5MuXzwyRiYhISsTExGBr+/jPyPjxY8mTJw8NGzbGzs6OYcNGGY+rWcYLwHhXpruLA619ixq3i8j/M1tiliNHDqpXr55ou4uLC0CS+0RExDLMmfMT06f78/vvh3FwcGDhwp/Jk+fpiVbNMl7ULOOloTeRZ7CIBWZFRMSyxcbGsnHjekJDQwAoVqw4dev6cv/+PQC8vfMbe89EJO0s7qdo4cKF5g5BRET+4/z5c3Tu/CYjRoyhW7ee1Kv3CvXqvWLusEQyHYtLzERExPwMBgNff/052bM78tVXQyhVqjSrVq2jRo1a5g5NJFPTUKaIiACPhyuPHTsCPF70NTIykgcPIo3769Spp+FKkXSmnzAREQFg8uQJjBs3isOHT5A/fwHGj5+sVflFXjD1mImIZFHBwcF8/nl//vzzGADt27/JjBmzjXdXKikTefGUmImIZCFxcXEEBwcDYG9vx5o1qzh58gTw+M7KFi1aY2enB9GLmIuGMkVEspB27VoAVvzyy6+4uLhy7NiZTPd8U5GMTImZiEgm9tdfl/nll+X07z8IKysr3nqrEzY2NhgMBqysrJSUiVgYJWYiIplMXFwccXFx2NracujQAX744XuaNWtByZKlaNOmvbnDE5FkaI6ZiEgmEhR0k9q1q7By5TIAWrZsw9GjpylZspSZIxORlFBiJiKSwV2+fImdO7cDkCePFxUrViZ37jwAODg4kDt3bnOGJyKpoKFMEZEMbtCgfly58heHDv2JlZUV06fPMndIIpJG6jETEclgdu/eyWuv+RIREQ7AyJHjWLdui9YdE8kElJiJiGQAf/11mVu3bgHg6uqKlZUVQUFBAPj4lDAuCisiGZsSMxERCxcaGkKdOlWZPt0fgAoVKrF58058fEqYOTIRMTXNMRMRsUDLli3hr78u8fnnX+Pu7sGUKT9Ss2Ztc4clIulMPWYiIhbi1q0g49cnT/7Jrl07iYmJAaBVq7Z4eeU1V2gi8oIoMRMRsQBr166hQoWSBAaeAuDrr4exYcM2bG01sCGSlSgxExExg+joaBYsmMuBA/sBqFOnLn369MPT8/GaYw4ODrrLUiQLUmImIvICRUdHG78eN24Ua9b8AkDOnO588cU3WgxWJItTH7lIJrA/MIhVuy4RGhGFu4sDrX2LUrOMlk+wNMOGfcPu3TvZunUX9vb2bN26S/PGRCQB9ZiJZHD7A4OYv/EsIRFRGICQiCjmbzzL/sCgZ54r6SsyMpKff15s7CUrW7Yc9es3MH6fN28+DVeKSALqMRPJ4FbtukR0TFyCbdExcazadUm9Zma2f//vfPJJD9zcctK4cVNat25n7pBExMIpMRPJ4EIiogBoeH6rcdtWn4bG7fLiREVF0bPnh1SrVp2PPupF/fqvsnbtFqpVq27u0EQkg1BiJpLBebg4EBIRRcMLvxm3bfVpiIeLgxmjyjoePHjAmTOBVK5cBQcHB2JiYjAYDABYW1tTvXoNM0coIhmJEjORDK61b1HmbzybYJu9rTWtfYuaKaKs5csvP2Pt2jX8+edZcuTIwfz5S8wdkohkYJr8L5LB1SzjRecmJRNs69ykpOaXpZPLly/SrVsXbt68AcBHH/Vi3rzFODo6mjkyEckM1GMmkgnULONF8H++F9N5+PAh9+/fx8PDA2trG3bv3smZM4HkzZuPkiVLAaXMHaKIZBJKzEREkhETE0OdOtWoXbsOkyZN46WXCnPixHns7e3NHZqIZEIayhQR+Y/jx48yefIEAGxtbfnkk09p166jcb+SMhFJL0rMRER4vNRF/N2U27dvw9//B0JDQwF49933qFOnnjnDE5EsQomZiGR5J0/+SaVKpdm7dw8A3br14Nix07i7u5s5MhHJajTHTESypCNHDvPoUQw1atSkePES1Kvni7OzMwBOTs5mjk5EsiolZiKS5RgMBnr37k7evPn45Ze1ZMuWjRkz5pg7LBERJWYimYVD85Zkz2bHg4ePzB2KRVqx4mfmzJnJ2rVbsLW1ZdasBRQsWNDcYYmIJKDETCSTcB74JZ6ezty+fdfcoViMY8eOULy4D05OzuTI4UTOnO6EhoaSO3duSpcuY+7wREQS0eR/EcmUzpw5TaNG9Vm27PEjkpo2bcaSJSvJnTu3mSMTEXk69ZiJSKZgMBiYPHkCdnb29OzZm1KlSjN9+ixee62xuUMTEUkxJWYikqH988/f5M9fACsrK44fP0a2bNmM+9q0aW/GyEREUk+JmUgmcXfcKGL+N/nfeeCX5g7nhZg2zZ9Ro4Zy9OhpcufOzcyZc7GzszN3WCIiaabETCSTiFobQNT/vs6siVlERDhz5vxE06bN8fEpQePGTbCxscbRMTuAkjIRyfBSNfm/UaNGzJw5k9u3b6dXPCIiiTx48ACAR49imDjxO3bu/A2AIkWK8dFHvbQgrIhkGqnqMbO1tWXChAlMnjyZevXq0a5dO3x9fbG21s2dIpI+3n+/E48eRbNw4TI8PDz4449TeHp6mjssEZF0karEbP369Rw/fpyVK1eyceNGduzYQa5cuWjdujVt2rTRYo0i8txCQkLYsGEt77zTGSsrK2rXrktMzCMMBgNWVlZKykQkU7MyGAyGtJz44MEDNmzYwMqVKzl27BhWVlZUrVqVdu3a0ahRI+zt7U0da7JCQu4RF5eml5JiWrzTtFSfphVct5rx61x7DpkxkrSJT7zmzZvNwIGfsnPnfrMvAqs2anqqU9NSfZpeeteptbUVHh5OT9+f1oKzZ89OmzZtWLp0KRs3bqRp06YcOnSIgQMHUrduXUaNGsWNGzfSWryIZBH//vsvLVs2Ze3aAADatevI7t0HzZ6UiYiYw3NNDouNjWXr1q2MGTOGjRs3YmVlRfXq1alQoQKLFi2iadOmbNu2Lclzjx49SteuXalbty7lypWjRo0avPvuu+zatet5QhKRDODOnVCOHz8KgIeHBzY2NsTFxQGQI0cOSpYsZc7wRETMJk3LZVy6dImVK1fy66+/EhISgoeHB++//z7t27c3zjO7evUqffv25bvvvuPVV19NVEZERASFCxemdevW5MqVi4iICJYtW0a3bt2YMGECr7/++vO9MhGxWB980Jm//77GgQPHsLGx4Zdf1po7JBERi5CqxGzlypWsXLmSP//8E4BatWrRvn17GjRogK1twqIKFSpEp06dGDx4cJJlvfLKK7zyyisJttWvX58GDRqwbNkyJWYimciRI4eZNGk806fPJkeOHHz11RCyZcuuO7pFRP4jVYnZ4MGDyZUrF926daNdu3bkz58/2eOLFStGixYtUh6MrS3Ozs5aJFIkEwgLu4OVlRWurm48ehTDqVMn+euvy5QtW47KlauYOzwREYuUqsTM398fPz8/bGxsUnR8+fLlKV++fLLHxMXFERcXR0hICMuWLePKlSsMHDgwNWGJCJD9vQ/I4ejA/cioZx+czu7cCaVy5bL06PExAwd+SfXqNTh06M9EPesiIpJQqn5LNmzY0OQB9O3bl82bNwPg5OTEDz/8QL169Ux+HZHMLsf73fD0dAYz3Tr/229buHTpIt269SRnTne++GIwder4AmBlZaWkTEQkBdK8jpmp/P3339y5c4fg4GDWrVvHli1bGDNmDM2aNTNnWCKSApGRkTg6OgLQrVs3du3aRWBgoJIwEZE0Mnti9l/du3fn6NGjHDhwIFUTg7XAbMaj+jS9F1mnW7duolu39/ntt90UKVKM8PAwcuRwylRJmdqo6alOTUv1aXoZdoHZ9FKuXDnCw8MJDQ01dygi8oS4uDi2bt3EyZMnAChfvhJvvNESG5vHiZirq1umSspERMzBon6LGgwGDh06hIuLC25ubuYORyRDCR/Uj4f2tkRFx+A6doLJyo1/VNLDhw/p1asbzZq1YMIEf/LkycOkSdNMdh0RETFjYta/f3+8vb0pU6YMOXPm5Pbt26xevZoDBw7w9ddf65O3SCo92vc7j0xc5uTJE/j9990sXx6Ao6Mjq1dvwMenhImvIiIi8cyW/VSqVIm1a9eybNky7t69i7OzM2XLlmX69On4+fmZKyyRLC0uLo7du3dSt64vNjY2uLi4kjt3HqKionBwcKBMmbLmDlFEJFOzuMn/aaXJ/xmP6tO0gutWM36da8+hNJWxefNGOnXqwMKFy2jUqImpQsuw1EZNT3VqWqpP09PkfxExm6ioKL76aiA//7wYgAYNGjJr1nzq129g5shERLImJWYiWUxcXBx//XUZAHt7e44fP8aVK4+/t7W15Y03WmFvb2/OEEVEsizNsBfJYj7/vD/r1q3h6NHTZMuWjV9/3ZTix6yJiEj6Uo+ZSCZ38+YNvv76C4KDgwHo0OEthg0bbUzGlJSJiFgOJWYimZDBYOD+/fsAREREMGfOTA4e3A/Ayy9XpW3bDtjZ2ZkzRBERSYKGMkUyoVdfrUfVqtUYM2Y8JUqU5NSpC+TM6W7usERE5BmUmIlkAleu/MWTN183b96CwoWLGL9XUiYikjEoMRPJoOIflQSwePEC/g0OZty4sRgMtvR9o5WZoxMRkbTQHDORDOjs2TP4+tbgyJHDAHTv/jGfb/+d/O+/TzYlZSIiGZZ6zEQyiGvXrnL37l3KlClL/vz5cXf3ICoqCgAPDw8zRyciIqagxEwkAzAYDLRp05yCBQvxyy9rcXJyJiBgg7nDEhERE9NQpoiF2rJlI507v0VcXBxWVlZMnjwdf/8Z5g5LRETSkRIzEQvyzz9/8+DBA+Dx+mPXrl3l339vAVCzZm3y5fM2Z3giIpLOlJiJWIizZ89QpUo5Vq9eCUDr1u3Yvv13vLzymjkyERF5UTTHTMSMli5dBMCbb75DiRIl+frrYdSr9woA1tb63CQiktUoMRN5we7du4uTkzMAAQG/AI8TMysrK3r1+sScoYmIiJnpI7nICzRv3mwqVChFWNgdAGbOnMvPP68yc1QiImIplJiJpKOHDx/y88+LuXr1CgBVq1bn3XffIy4uDgBXVzfj6v0iIiJKzETSgcFgACAs7A79+vU2TugvU6YsQ4YMx91dC8KKiEhimmMmYmIDBvTl/v17TJ8+Cy+vvGzfvpcSJUqaOywREckA1GMm8pyioqLYunWT8XsvLy/y5fM29pqVLFlKw5UiIpIi6jETeU4LF87lyy8HsmPHPsqUKcuAAZ+bOyQREcmg1GMmkkohISF07/4+v/22BYB27TqyYsUaSpcuY+bIREQko1NiJpICUVFRXL58CQAXFxcCA09x48YN4PGdlb6+9TVcKSIiz01DmSIp0KlTB4KCbrJr1wHs7OzYteuAVuYXERGTU2ImkoSzZ88wa9aPjBw5FgcHB3r16mNcewz0uCQREUkf+usi8j/R0dFERkYCcOPGdVatWsGZM4EA+PrWp379BhquFBGRdKXETITHC8G+/HJZZs+eCUD9+g04ceIsFStWNnNkIiKSlSgxkyzrzz+P8csvywFwc8tJhw5vUbnyywBYWVkZHzQuIiLyomiOmWQpcXFxxvlhM2ZMZe/ePbRo0RpbW1sGD/7WvMGJiEiWpx4zyTL27NlFlSrluH79HwC++WYYv/9+CFtbfT4RERHLoL9IkqmdOHEcJycnihQpxksvFaZ4cR/u3bsHQN68+cwcnYiISELqMZNM6/79+7Ro0ZTJkycCUKBAQZYtW60HiouIiMVSj5lkKgsWzOXQoQNMmfIjOXLkYMGCpZQvX8HcYYmIiKSIeswkwztz5jQGgwF4vOzFrVtBPHz4EIC6dX1xdXUzY3QiIiIpp8RMMrRt2zbj61uD3bt3AtC796esWLGGbNmymTcwERGRNFBiJhlKdHQ0kydPZP36tQDUrfsKI0aMoUKFigBamV9ERDI0JWaSIYSF3QHAzs6OlSt/5vffdwHg4OBAt249cXPLac7wRERETEKT/8XiDR36NatXr+Tw4RPY2dmxYcM2rcovIiKZknrMxOKEhd1h6tTJRESEA+Dn9yoffNCdmJgYACVlIiKSaanHTCxG/OOSrl69wtChg8mXLx+tWrWlbl1f6tb1NXd4IiIi6U49ZmJ2sbGxtG/fkuHDhwBQoUIl9u8/QqtWbc0cmYiIyIulxEzMIizsDuvXrwfAxsYGH58S5M9fwLi/aNHi5gpNRETEbDSUKWYxfvw45syZyYkT5/Hw8GDEiLHmDklERMTs1GMmL8Tlyxdp27YFgYGnAOjevRcHDx7Ew8PDzJGJiIhYDiVmkm4iIsK5evUKADlzunP9+t/cvHkdAG/v/FSqVMmM0YmIiFgesw1l7t+/nzVr1nDs2DGCgoJwdXWlfPny9O7dmxIlSpgrLDERg8HAa6+9QpEiRVmyZCU5c7qzb98RrcwvIiKSDLMlZkuXLiUsLIwuXbpQtGhRgoODmTVrFm3btmXhwoVUrFjRXKFJGh04sI/Vq1cyZsx4rKysGDJkBPny5TPuV1ImIiKSPLMlZkOGDEk0v6hOnTo0aNCA2bNn4+/vb6bIJDXu3o0gW7bs2NnZcfHiBTZuXE/fvgPImzcfTZq8bu7wREREMhSzzTFLatK3i4sLhQoVIigoyAwRSWqdP3+O8uVLsm7dGgDat3+TI0dOkTdvvmecKSIiIkmxqMn/oaGhXLhwgeLFtYaVpdq+fSvr168FoFix4nTq1IUSJUoBYG9vj52dnTnDExERydCsDAaDwdxBwOPJ4h9//DG7d+8mICCAokWLmjsk+Z/Y2FhsbGwAqFevHrGxsezdu9fMUYmIiGQ+FpOYjR07ljlz5jB69Ghat26d6vNDQu4RF5e+L8XT05nbt++m6zUszfLlSxkzZgS7dx/EycmJ69f/wdMzN/b29s9ddlasz/SmOjUt1afpqU5NS/Vpeuldp9bWVnh4OD19f7pdORUmTpzInDlz+Oqrr9KUlInpGAwGduz4jVu3Hs/zK1KkKNWr1+T+/XvA4/XHTJGUiYiISGJmT8wmTZrEjBkz+Oyzz3j33XfNHU6W988/f9OxY2sWLZoPQJUq1Zg+fRZ58niZOTIREZHMz6zPypwyZQrTpk2jT58+fPDBB+YMJUsbM2Y49+7dY8SIsRQoUJCVK3+lWrUa5g5LREQkyzFbYjZnzhz8/f2pX78+tWrV4vjx48Z99vb2lC5d2lyhZXoGg4ETJ45TocLjRyLdvXuXu3fvYjAYsLKyom5dXzNHKCIikjWZLTHbsWOH8f/4r+N5e3uzfft2c4SVJcyZM5MvvviMvXv/oHhxH0aMGKtV+UVERCyA2RKzhQsXmuvSWU54eBgTJnxHkyavU6NGLd54ozU5cjhRoEBBQI9KEhERsRRmn/wv6cNgMBAcHAyAg0M2fvllOceOHQXA09OTjh3fJlu2bOYMUURERP7DrJP/Jf289947BAXdYNOmHWTLlo1Dh/7E0dHR3GGJiIhIMtRjlklcv/4P338/hpiYGADatGlH585diYuLA1BSJiIikgGoxywDMxgMxMbGYmtry/Hjxxg/fiyvvOJHlSrVaN68pbnDExERkVRSj1kGFR4eRv36tZk/fzYAjRs35Y8/TlKlSjUzRyYiIiJppcQsA7l+/R+2b98GgKurG+XLV8DLKx8ANjY2eHvnN2d4IiIi8pw0lJmBDB78OQcP7ufEiXPY2toyefJ0c4ckIiIiJqQeMwt2+PBBmjTx499//wVg8OAhbN68A1tb5dMiIiKZkf7CW5gbN65jZWVF3rz5yJnTnQcPHhIUdIPcuXNTtGhxc4cnIiIi6Ug9Zhbk/v371K5dlfHjxwFQrFhxduzYS/nyFc0bmIiIiLwQ6jEzs7Vr13D06B8MGTKcHDly8MMPU6hU6WXjfj0uSUREJOtQj5kZ/PvvvxgMBgACA0+yfftWHj58CECLFq0pWLCQOcMTERERM1Fi9oLt3LmdihVLcvjwIQA+/fQzdu7cr+dWioiIiBKz9BYTE8Py5UvZvXsnAFWrVqd794/x9vYGwMHBQcOVIiIiAigxSzePHj0CHs8RGzduND//vBiAHDly8M03w7QYrIiIiCSiyf/pYOLE7/jll+Xs3n0QGxsbfv11I3nz5jN3WCIiImLh1GNmAtHR0fzyy3Lu378PQMmSpXnlFT8iIyMByJfPW8OVIiIi8kxKzEzg6NEj9OjxAevX/wpAkyavM2LEWJycnMwcmYiIiGQkSszSIDY2lo8//ogffvgegOrVaxAQsIG2bTuYOTIRERHJyJSYpVB0dDSHDj1e4sLGxoZHj6ITTPCvVasO1taqThEREUk7Tf5PoeHDhzB//myOHz+Du7sHP/4419whiYiISCajxCyFunR5nzfeaIqbW05zhyIiIiKZlBKzFCpatDg1alTm9u275g5FREREMiklZil0f85McHTgfmQUOd7vZu5wREREJBNSYpZCD+bO4sH/vlZiJiIiIulBtxGKiIiIWAglZiIiIiIWQomZiIiIiIVQYiYiIiJiIZSYiYiIiFgIJWYiIiIiFkKJmYiIiIiFUGImIiIiYiGUmImIiIhYCK38n0IOzVuSPZsdDx4+MncoIiIikkkpMUsh54Ff4unprIeYi4iISLrRUKaIiIiIhVBiJiIiImIhlJiJiIiIWAjNMUuhu+NGEfO/yf/OA780dzgiIiKSCSkxS6GotQFE/e9rJWYiIiKSHjSUKSIiImIhlJiJiIiIWAglZiIiIiIWQomZiIiIiIUw6+T/oKAgZs2aRWBgIGfPniUyMpIFCxZQvXp1c4YlIiIiYhZm7TG7evUq69evx9HRkRo1apgzFBERERGzM2tiVrVqVfbv38/s2bNp06aNOUNJ1v7AoGS/FxERETEFsyZm1taWP8Vtf2AQ8zeeTbBt/sazSs5ERETE5Cw/MzKzVbsuER0Tl2BbdEwcq3ZdMlNEIiIiklllmpX/PTyc0qXc0IjH6/1vLd4g0XZPT+d0uWZWojo0PdWpaak+TU91alqqT9MzZ51mmsQsJOQecXEGk5fr7uJASEQUW30aJtp++/Zdk18vK/H0dFYdmpjq1LRUn6anOjUt1afppXedWltbJduZpKHMZ2jtWxR724TVZG9rTWvfomaKSERERDKrTNNjll5qlvECHs81C42Iwt3Fgda+RY3bRURERExFiVkK1CzjRc0yXuoyFhERkXRl9sRs06ZNAJw8eRKAw4cPc+fOHbJnz46vr685QxMRERF5ocyemPXp0yfB9/7+/gB4e3uzfft2c4QkIiIiYhZmT8zOnTtn7hBERERELILuyhQRERGxEErMRERERCyEEjMRERERC2H2OWamYm1tlamuk1WoPk1PdWpaqk/TU52alurT9NKzTp9VtpXBYDD9c4xEREREJNU0lCkiIiJiIZSYiYiIiFgIJWYiIiIiFkKJmYiIiIiFUGImIiIiYiGUmImIiIhYCCVmIiIiIhZCiZmIiIiIhVBiJiIiImIhMs0jmdLq/v37TJw4kU2bNhEREUGxYsXo1asXDRo0eOa5165dY8yYMRw8eJC4uDiqVKnCoEGDKFas2AuI3DKltT79/f2ZMmVKou25cuVi79696RWuxQsKCmLWrFkEBgZy9uxZIiMjWbBgAdWrV0/R+WqjiT1PnaqdJrZ//37WrFnDsWPHCAoKwtXVlfLly9O7d29KlCjxzPPVRhN6nvpU+0za0aNHmTp1KufPnycsLIwcOXLg4+ND165d8fX1feb5L7qNZvnE7OOPP+b06dMMGDCA/Pnzs3r1aj7++GNmzJiR7BsWEhLCW2+9hYeHB2PHjsXGxobp06fzzjvvEBAQgJeX1wt8FZYjrfUZb+7cuTg6Ohq/t7OzS89wLd7Vq1dZv349pUuXpkaNGmzfvj3F56qNJu156jSe2un/W7p0KWFhYXTp0oWiRYsSHBzMrFmzaNu2LQsXLqRixYpPPVdtNLHnqc94ap8JRUREULhwYVq3bk2uXLmIiIhg2bJldOvWjQkTJvD6668/9VyztFFDFrZz506Dj4+PYcuWLcZtcXFxho4dOxoaN26c7Lljx441lCtXzhAUFGTcFhoaaqhUqZLhm2++SbeYLdnz1OfkyZMNPj4+hvDw8PQOM0OJjY01fr1161aDj4+P4cCBAyk6V200ac9Tp2qniQUHByfaFh4ebqhSpYrh448/TvZctdHEnqc+1T5T7tGjR4Z69eoZOnXqlOxx5mijWXqO2datW3F2dk4wzGZlZUWrVq24fPkyFy9efOq527Zto1atWuTJk8e4LWfOnNSvX5+tW7ema9yW6nnqU5JmbZ32H1G10aQ9T51KYh4eHom2ubi4UKhQIYKCgpI9V200seepT0k5W1tbnJ2dn9mbaI42mqV/Q124cIFixYol+kUdP45//vz5JM97+PAh165dw8fHJ9G+EiVKEBISQkhIiOkDtnBprc8nNW3alFKlSlGnTh0GDx6cJevRFNRG05faafJCQ0O5cOECxYsXf+oxaqMpl5L6fJLaZ9Li4uKIiYnh1q1bTJ48mStXrtC5c+enHm+uNpql55iFhYXx0ksvJdru6upq3J+U8PBwDAaD8bgnubm5Gc9N6pNPZpbW+gQoUKAA/fr1o1SpUtjZ2XH06FFmzZrF/v37WbVqVZJ1LU+nNpo+1E6fzWAw8PXXXxMXF0fXrl2fepzaaMqktD5B7fNZ+vbty+bNmwFwcnLihx9+oF69ek893lxtNEsnZvB4qC0t+1KyPytKa322bNkywfc1a9akYsWKvP/++yxevJiePXuaKsQsRW3UtNROn23cuHFs27aN0aNHU7Ro0WcerzaavNTUp9pn8j777DM++OADgoODWbduHX379mXMmDE0a9Ys2fNedBvN0omZm5tbkr044eHhAE/9dOHq6oqVlVWS58Zvi8+ms5K01ufT1K5dG09PT44fP26C6LIWtdEXR+30/02cOJE5c+bw1Vdf0bp162SPVRt9ttTU59Ooff6/AgUKUKBAAQD8/Pzo3r07w4YNo2nTpknOPTVXG83Sc8yKFSvGpUuXiIuLS7A9fi5UUuPKANmyZaNAgQJJzpk6f/487u7uWbL7Pa31mRyDwaDJ2mmgNvpiqZ3CpEmTmDFjBp999hnvvvvuM49XG01eauszOWqfSStXrhzh4eGEhoYmud9cbTRLv1MNGzYkIiIi0TpGAQEBFC5cONnF41599VX27dvH7du3jdvCwsLYsWMHDRs2TLeYLdnz1GdSfv/9d4KDg6lQoYIpw8wy1EZfDLVTmDJlCtOmTaNPnz588MEHKT5PbTRpaa3PpKh9Js1gMHDo0CFcXFyS7fUyRxvN0kOZvr6+VK9ena+++oqwsDDy589PQEAAR44cYdq0acbjOnXqxKFDhzh37pxxW9euXfn111/p1q0bvXr1wtbWlunTp2Nra0v37t3N8XLM7nnqs2XLlrRs2ZLChQtja2vLsWPHmD17NoUKFeLtt982x8uxGJs2bQLg5MmTABw+fJg7d+6QPXt246K9aqOpk9Y6VTtNbM6cOfj7+1O/fn1q1aqVYMjM3t6e0qVLA2qjKfU89an2mbT+/fvj7e1NmTJlyJkzJ7dv32b16tUcOHCAr7/+Glvbx6mQpbTRLJ2YWVlZMW3aNCZMmMDEiRONjxCaMmUKfn5+yZ6bK1cuFi9ezNixYxk4cCAGg4GXX36ZRYsWkS9fvhf0CizL89RnkSJFWLJkCf/++y8xMTF4eXnRrl07evbsiYuLywt6BZapT58+Cb739/cHwNvbO9lV69VGny6tdap2mtiOHTuM/8d/HU9tNPWepz7VPpNWqVIl1q5dy7Jly7h79y7Ozs6ULVuW6dOnW+TfeiuDwWBIl5JFREREJFWy9BwzEREREUuixExERETEQigxExEREbEQSsxERERELIQSMxERERELocRMRERExEIoMRMRERGxEErMRERERCyEEjMRERERC6HETERERMRCKDETEQFiYmLo2LEjlSpV4tKlSwn2LVu2jBIlSjBp0iQzRSciWYWelSki8j/Xr1+nZcuW5MuXj+XLl+Pg4MCFCxdo27YtZcqUYeHChdjY2Jg7TBHJxNRjJiLyP97e3owcOZKzZ88yduxYHj58SL9+/XBwcOD7779XUiYi6c7W3AGIiFiS1157jTfffJPFixdz+vRpzp8/j7+/P/ny5TN3aCKSBWgoU0TkP6KiomjWrBnXrl2jffv2DB8+3NwhiUgWoaFMEZH/OHfuHDdv3gTgwoULxMTEmDkiEckqlJiJiDzh3r17fPrpp7i5ufHpp59y7Ngx/P39zR2WiGQRmmMmIvKEb775hhs3bjBnzhxq1qzJmTNnmDlzJjVr1qRGjRrmDk9EMjn1mImI/M+KFStYv3493bp1o2bNmgAMHz6cvHnz8tlnn3Hnzh0zRygimZ0m/4uIAJcuXaJNmzaULFmSRYsWYWv7/wMKx44d45133qFu3brMmDHDjFGKSGanxExERETEQmgoU0RERMRCKDETERERsRBKzEREREQshBIzEREREQuhxExERETEQigxExEREbEQSsxERERELIQSMxERERELocRMRERExEIoMRMRERGxEP8Hkbazcy5MSXgAAAAASUVORK5CYII=\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": 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\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": 31,
"metadata": {},
"outputs": [
{
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