Praktikum_Machine_Learning/Regression/SyahdanFaizM-202310715258-Reg-NoneLinearRegression.ipynb

859 lines
312 KiB
Plaintext
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p style=\"text-align:center\">\n",
" <a href=\"https://skills.network\" target=\"_blank\">\n",
" <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
" </a>\n",
"</p>\n",
"\n",
"\n",
"# Non Linear Regression Analysis\n",
"\n",
"\n",
"Estimated time needed: **20** minutes\n",
" \n",
"\n",
"## Objectives\n",
"\n",
"After completing this lab you will be able to:\n",
"\n",
"* Differentiate between linear and non-linear regression\n",
"* Use non-linear regression model in Python\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the data shows a curvy trend, then linear regression will not produce very accurate results when compared to a non-linear regression since linear regression presumes that the data is linear. \n",
"Let's learn about non linear regressions and apply an example in python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"importing_libraries\">Importing required libraries</h2>\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Although linear regression can do a great job at modeling some datasets, it cannot be used for all datasets. First recall how linear regression, models a dataset. It models the linear relationship between a dependent variable y and the independent variables x. It has a simple equation, of degree 1, for example y = $2x$ + 3.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"y = 2*(x) + 3\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"#plt.figure(figsize=(8,6))\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Non-linear regression is a method to model the non-linear relationship between the independent variables $x$ and the dependent variable $y$. Essentially any relationship that is not linear can be termed as non-linear, and is usually represented by the polynomial of $k$ degrees (maximum power of $x$). For example:\n",
"\n",
"$$ \\ y = a x^3 + b x^2 + c x + d \\ $$\n",
"\n",
"Non-linear functions can have elements like exponentials, logarithms, fractions, and so on. For example: $$ y = \\log(x)$$\n",
" \n",
"We can have a function that's even more complicated such as :\n",
"$$ y = \\log(a x^3 + b x^2 + c x + d)$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a look at a cubic function's graph.\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"y = 1*(x**3) + 1*(x**2) + 1*x + 3\n",
"y_noise = 20 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, this function has $x^3$ and $x^2$ as independent variables. Also, the graphic of this function is not a straight line over the 2D plane. So this is a non-linear function.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some other types of non-linear functions are:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Quadratic\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = X^2 $$\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"\n",
"y = np.power(x,2)\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exponential\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An exponential function with base c is defined by $$ Y = a + b c^X$$ where b ≠0, c > 0 , c ≠1, and x is any real number. The base, c, is constant and the exponent, x, is a variable. \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"\n",
"Y= np.exp(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Logarithmic\n",
"\n",
"The response $y$ is a results of applying the logarithmic map from the input $x$ to the output $y$. It is one of the simplest form of __log()__: i.e. $$ y = \\log(x)$$\n",
"\n",
"Please consider that instead of $x$, we can use $X$, which can be a polynomial representation of the $x$ values. In general form it would be written as \n",
"\\begin{equation}\n",
"y = \\log(X)\n",
"\\end{equation}\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
" This is separate from the ipykernel package so we can avoid doing imports until\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"Y = np.log(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sigmoidal/Logistic\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = a + \\frac{b}{1+ c^{(X-d)}}$$\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"\n",
"Y = 1-4/(1+np.power(3, X-2))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"ref2\"></a>\n",
"# Non-Linear Regression example\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For an example, we're going to try and fit a non-linear model to the datapoints corresponding to China's GDP from 1960 to 2014. We download a dataset with two columns, the first, a year between 1960 and 2014, the second, China's corresponding annual gross domestic income in US dollars for that year. \n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2025-10-20 11:50:18 URL:https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv [1218/1218] -> \"china_gdp.csv\" [1]\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Year</th>\n",
" <th>Value</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1960</td>\n",
" <td>5.918412e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1961</td>\n",
" <td>4.955705e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1962</td>\n",
" <td>4.668518e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1963</td>\n",
" <td>5.009730e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1964</td>\n",
" <td>5.906225e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>1965</td>\n",
" <td>6.970915e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>1966</td>\n",
" <td>7.587943e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>1967</td>\n",
" <td>7.205703e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>1968</td>\n",
" <td>6.999350e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>1969</td>\n",
" <td>7.871882e+10</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Year Value\n",
"0 1960 5.918412e+10\n",
"1 1961 4.955705e+10\n",
"2 1962 4.668518e+10\n",
"3 1963 5.009730e+10\n",
"4 1964 5.906225e+10\n",
"5 1965 6.970915e+10\n",
"6 1966 7.587943e+10\n",
"7 1967 7.205703e+10\n",
"8 1968 6.999350e+10\n",
"9 1969 7.871882e+10"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"#downloading dataset\n",
"!wget -nv -O china_gdp.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv\n",
" \n",
"df = pd.read_csv(\"china_gdp.csv\")\n",
"df.head(10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Did you know?__ When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: [Sign up now for free](http://cocl.us/ML0101EN-IBM-Offer-CC)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting the Dataset ###\n",
"This is what the datapoints look like. It kind of looks like an either logistic or exponential function. The growth starts off slow, then from 2005 on forward, the growth is very significant. And finally, it decelerates slightly in the 2010s.\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,5))\n",
"x_data, y_data = (df[\"Year\"].values, df[\"Value\"].values)\n",
"plt.plot(x_data, y_data, 'ro')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Choosing a model ###\n",
"\n",
"From an initial look at the plot, we determine that the logistic function could be a good approximation,\n",
"since it has the property of starting with a slow growth, increasing growth in the middle, and then decreasing again at the end; as illustrated below:\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAjcAAAGwCAYAAABVdURTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAgAElEQVR4nOzdd3zU9eHH8ddlXXZIAkkghL33DigOFA2golUrjgqI2No6qqkoKKMORK1aVKy0qEVqVRQt/BiCglJBEGSjjLBCQiB7r7vk7vv7IzUaGebgku8leT8fj3tAvnff5B0fcnnn+/0Mi2EYBiIiIiKNhJfZAURERETcSeVGREREGhWVGxEREWlUVG5ERESkUVG5ERERkUZF5UZEREQaFZUbERERaVR8zA5Q35xOJydPniQkJASLxWJ2HBEREakFwzAoKiqiVatWeHmd+9pMkys3J0+eJC4uzuwYIiIich5SU1Np3br1OV/T5MpNSEgIUPUfJzQ01OQ0IiIiUhuFhYXExcVV/xw/lyZXbn64FRUaGqpyIyIi0sDUZkiJBhSLiIhIo6JyIyIiIo2Kyo2IiIg0Kio3IiIi0qio3IiIiEijonIjIiIijYrKjYiIiDQqKjciIiLSqJhabr766iuuu+46WrVqhcViYenSpb94zvr16xkwYABWq5VOnTqxcOHCug8qIiIiDYap5aakpIS+ffvy+uuv1+r1x44d45prrmHEiBHs2rWLhx56iMmTJ7NmzZo6TioiIiINhanbL4wePZrRo0fX+vXz58+nffv2vPTSSwB0796djRs38te//pWEhIQznmOz2bDZbNUfFxYWXlhoERER8WgNaszN5s2bGTlyZI1jCQkJbN68+aznzJkzh7CwsOqHdgQXERFp3BpUuUlPTyc6OrrGsejoaAoLCykrKzvjOdOmTaOgoKD6kZqaWh9RRUREmhSn06DYVsmpgjJO5p/5Z3J9afS7glutVqxWq9kxREREPJ5hVBWU/NIKckvs5JXaKSirIL/0f48yO4VllRSUVVBYXkFhWdWjyFZJsa0Sw6j6PPHtI1j8u2GmfR8NqtzExMSQkZFR41hGRgahoaEEBASYlEpERMRzOZwGuSV2sopsZBaVk1VkI6vYRk6xnZxiGzkldrL/9/e8UjsVDuOCvp6PlwWLxU3hzzeDuV/eNcOGDWPVqlU1jn3++ecMG2ZeOxQRETGLw2mQUVjOyfwyThaUcyq/6pZQemE5GYU2MgrLySyy4XC6VlgCfL2JCPIjLMCX8CBfwgJ8CQuo+rhZoC+h/r6EBvj8709fQvx9qh5WX/x9vbCY3G5MLTfFxcUcPny4+uNjx46xa9cuIiIiaNOmDdOmTSMtLY1FixYBcO+99zJv3jweffRRJk2axBdffMGHH37IypUrzfoWRERE6oxhGOSXVnA8t5TjOSUczynlRF4pqbllnMgv5VR+OZW1KC4WC0QG+dEixJ8WIVZaBFtpHuxH82ArkcF+RAT5ERlU9ffwQD8C/Lzr4burO6aWm23btjFixIjqjxMTEwGYMGECCxcu5NSpU6SkpFQ/3759e1auXMnDDz/MK6+8QuvWrXnzzTfPOg1cRESkIbBVOjiWXcLRrBKOZBZzNLuEo1nFHMsuobC88pzn+npbiAnzp2VYAK3C/GnZrOrPqFB/okP9iQn1p3mwHz7eDWoO0QWxGIZxYTfXGpjCwkLCwsIoKCggNDTU7DgiItKEOJ0Gx3NL2X+qkAPpRRzKKCIpo4jknNJz3jqKDrXSNiKINpGBtIkIJC4igNbhgcSFBxIVYsXLy+RBLvXAlZ/fDWrMjYiISENR4XCSlFHE3hMF7E0rqC40pXbHGV8fYvWhY1QwHVoE0bFFMB2aB9G+RRBtI4Ia/G2i+qZyIyIicoEMw+BEXhk7UvLYmZLPrtR89p0qxF7pPO21Vh8vusaE0C0mhC7RIXSODqFLdDAxof6mD8RtLFRuREREXORwGuw7WciWYzl8m5zLjpR8sopsp70uxN+HPq3D6BUbRs9WYfRoGUK7yKAmNf7FDCo3IiIiv8DpNNh3qpCvD2fzzdEctiXnUWSrOdDX19tCj1ZhDGjTjH5xzejbuhltIwN1NcYEKjciIiJnkF5QzldJWWw4nM2mw9nklNhrPB9i9WFw+wiGtI9gUNtwesWG4e+rsTGeQOVGRESEqltNu0/k8+WBTNbtz2TfqcIazwf5eTO0QyTDOkYytEMk3VuG4t0EZik1RCo3IiLSZNkrnWw+msPq707x+b4Msot/vDpjsUDf1s24tHNzhnduQb+4Zvj5aKxMQ6ByIyIiTYq90smGQ1ms3HOKtfszaiySF2L14dIuLbiiWxSXd21BZLA2Xm6IVG5ERKTRczoNth3PY9muNFbuPUV+aUX1c82DrST0jGZUrxiGdojEVzOZGjyVGxERabRSc0v5aPsJPt5+grT8surjLUKsXNunJWN6t2RAm3CNnWlkVG5ERKRRKa9w8Nm+DD78NpWvj2TzwyZDwVYfRvWK4YZ+sQzrGKlC04ip3IiISKOQll/Gv785zgffppL7k2nbF3eK5JZBcST0jNFU7SZC5UZERBoswzDYfCSHdzYn8/m+DH7YezIm1J9bBrXm14PiiIsINDWj1D+VGxERaXAqHU5W7j3F/P8eZf9P1qO5qGMk44e1Y2T3KG1x0ISp3IiISINRaq/kw29TWbDhWPUA4QBfb24e2Jrxw9rSOTrE5ITiCVRuRETE45XYKvnXN8f5x1dHq8fTRAb5MfGidvxmaFvCg/xMTiieROVGREQ8Vqm9kn9tPs7ff1Jq2kYGcs8lHbh5YGsNEJYzUrkRERGPY6908u8tx5n3xeHqDSvbRgby4BWdub5fK42nkXNSuREREY9hGAYr957ihdUHScktBaBNRCAPXNGJX/WPVamRWlG5ERERj7DlaA7PfnqA3an5QNUqwg+N7Mwtg+K0JYK4ROVGRERMdaqgjGdXHWD57pMABPp587tLOzL5kvYEWfVjSlyn/2tERMQU9konb208xmtfHKLU7sDLArcOacPDI7vQIkS7ccv5U7kREZF69/XhbGYs/Y6j2SUADGwbzpNje9IrNszkZNIYqNyIiEi9KSit4JmV+/ho+wkAmgdbeXxMN37VPxaLRRtZinuo3IiISL34dO8pZv7f92QV2bBY4M6hbXkkoSuh/r5mR5NGRuVGRETqVHaxjen/+Y7V36cD0LFFEC/c3IeBbSNMTiaNlcqNiIjUmbX7Mnjs4z3klNjx8bLw+8s7ct+ITlpZWOqUyo2IiLhdia2SZ1bu5/2tKQB0iwnh5Vv60aNVqMnJpClQuREREbfalZrPQx/sJDmnFIsFJg9vz5+u7qqrNVJvVG5ERMQtDMPgrY3HeO7TA1Q6DVqF+fPiLX25qGNzs6NJE6NyIyIiF6ygrIJHl+xmzfcZAFzTuyXP3tibsADNhJL6p3IjIiIXZO+JAv7w3nZSc8vw9bYw49oe3Dm0rdatEdOo3IiIyHlb/G0KM5Z+j93hpHV4AH+7YwB9WjczO5Y0cSo3IiLisgqHk9kr97NwUzIAV/WI5sWb+xIWqNtQYj6VGxERcUleiZ373tvBpiM5ADw8sgsPXNEJLy/dhhLPoHIjIiK1djC9iMmLviU1t4xAP29evqUfo3rFmB1LpAaVGxERqZUNh7L4/bs7KLZVEhcRwILxg+gWo0X5xPOo3IiIyC/6aFsq0z7ZS6XTIL59BPN/M5DwID+zY4mckcqNiIiclWEYvLruMH9dmwTA9f1a8cLNfbD6aLVh8VwqNyIickYVDifT//Mdi7elAvD7yzsy5equGjgsHk/lRkRETlNe4eD+93awdn8mXhZ46vpe/GZoW7NjidSKyo2IiNRQYqvknkXb2HQkB6uPF6/fPoCRPaLNjiVSayo3IiJSraC0gokLt7IzJZ8gP2/emjiYoR0izY4l4hKVGxERASCryMadb23hQHoRYQG+vDNpCP3itJWCNDwqNyIiQkZhObf94xuOZpfQPNjKu5OHaA0babBUbkREmrjMwnJuW1BVbGKbBfDu5HjaNw8yO5bIeVO5ERFpwrKKbFXFJquq2Hzw26HERQSaHUvkgniZHUBERMyRXWzj9gXfcCSrhJZh/rx/j4qNNA4qNyIiTVBOsY07FmzhUGYxMaFVxaZNpIqNNA4qNyIiTUxReQUT/rmVgxlFRIVYef+3Q2mnMTbSiKjciIg0IeUVDia/s43v0gqJDPLjvXuGavCwNDoqNyIiTUSlw8n97+1ky7Fcgq0+vDNpCJ2igs2OJeJ2KjciIk2A02nw2Md7Wbs/Az8fL96cMIhesWFmxxKpEyo3IiKNnGEYzF61n493nMDby8Lrtw/QlgrSqKnciIg0cm9tPMZbG48B8MJNfbhKm2BKI6dyIyLSiH269xSzV+0H4PEx3bhpYGuTE4nUPZUbEZFGakdKHg8t3oVhwJ1D23LPJR3MjiRSL0wvN6+//jrt2rXD39+f+Ph4tm7des7Xz507l65duxIQEEBcXBwPP/ww5eXl9ZRWRKRhOJ5Twj3vbMNW6eSKblHMuq4HFovF7Fgi9cLUcrN48WISExOZNWsWO3bsoG/fviQkJJCZmXnG17/33ntMnTqVWbNmsX//ft566y0WL17M448/Xs/JRUQ8V16Jnbv++S05JXZ6xYby2m398fE2/XdZkXpj6v/tL7/8Mvfccw933XUXPXr0YP78+QQGBvL222+f8fWbNm3i4osv5vbbb6ddu3ZcffXV3Hbbbb94tUdEpKmocDi5993t1Tt8vz1hMEFW7ZEsTYtp5cZut7N9+3ZGjhz5YxgvL0aOHMnmzZvPeM5FF13E9u3bq8vM0aNHWbVqFWPGjDnr17HZbBQWFtZ4iIg0Vk8u/756kb63Jw4mKtTf7Egi9c60Op+dnY3D4SA6uuaUxOjoaA4cOHDGc26//Xays7MZPnw4hmFQWVnJvffee87bUnPmzOHJJ590a3YREU/07y3HefebFCwWeOXWfnSNCTE7kogpGtRN2PXr1/Pss8/yt7/9jR07dvDJJ5+wcuVKnn766bOeM23aNAoKCqofqamp9ZhYRKR+bDmaw6xl3wPwyNVdubK71rKRpsu0KzfNmzfH29ubjIyMGsczMjKIiYk54zkzZszgzjvvZPLkyQD07t2bkpISfvvb3/LEE0/g5XV6V7NarVitVvd/AyIiHiI1t5Tf/3sHlU6D6/q24g+XdzQ7koipTLty4+fnx8CBA1m3bl31MafTybp16xg2bNgZzyktLT2twHh7ewNVy4uLiDQ1pfZKfvuv7eT+b2bUCzf10ZRvafJMHUKfmJjIhAkTGDRoEEOGDGHu3LmUlJRw1113ATB+/HhiY2OZM2cOANdddx0vv/wy/fv3Jz4+nsOHDzNjxgyuu+666pIjItJUGIbBE//5jv2nCmke7Mc/7hxEgJ/eC0VMLTfjxo0jKyuLmTNnkp6eTr9+/Vi9enX1IOOUlJQaV2qmT5+OxWJh+vTppKWl0aJFC6677jpmz55t1rcgImKad7ek8J+dadWbYbZqFmB2JBGPYDGa2P2cwsJCwsLCKCgoIDQ01Ow4IiLnZVdqPr+ev4kKh8HjY7rx20s1zkYaN1d+fjeo2VIiIgK5JXbu+/cOKhwGo3rGaM8okZ9RuRERaUAcToOHFu8iLb+M9s2DeOHXGkAs8nMqNyIiDchrXxziq6Qs/H29eOM3Awj19zU7kojHUbkREWkgNh/J4dV1hwB49le96RajcYMiZ6JyIyLSAOSW2Hlo8U6cBtwyqDU3DmhtdiQRj6VyIyLi4QzD4NElu8kotNGxRRB/HtvT7EgiHk3lRkTEwy3clMza/Zn4+Xjx2m0DCPQzdYkyEY+nciMi4sG+SytgzqoDADwxpjs9WmmcjcgvUbkREfFQJbZKHnh/J3aHk6t6RDN+WFuzI4k0CCo3IiIe6ukV+ziWXULLMH/+crPWsxGpLZUbEREP9Pm+DD74NhWLBV6+pR/NAv3MjiTSYKjciIh4mOxiG1M/3gPAPZd0YFjHSJMTiTQsKjciIh7EMAymfryHnBI73WJC+NPVXcyOJNLgqNyIiHiQxd+mVk379vbir+P6YfXxNjuSSIOjciMi4iGO55Tw1Ip9ADyS0IXuLTXtW+R8qNyIiHgAh9Mg8cPdlNodxLeP4O7hHcyOJNJgqdyIiHiAf359jO3H8wi2+vDSLX3x9tK0b5HzpXIjImKyo1nF/GXNQQCmX9Od1uGBJicSadhUbkRETORwGkxZsgdbpZNLOjdn3OA4syOJNHgqNyIiJvrp7ajnbtIqxCLuoHIjImKSY9kl1bejHh/TndhmASYnEmkcVG5EREzgcBpM+Wg3tkonwzs157Yhuh0l4i4qNyIiJli0OZltx/MI8vNmzo29dTtKxI1UbkRE6llafln17aipo7sRF6HZUSLupHIjIlKPDMNg+n/2Ump3MKhtOHfEtzU7kkijo3IjIlKPlu85xZcHs/Dz9mLOjb3x0mJ9Im6nciMiUk/yS+08tfx7AP4woiOdo0NMTiTSOJ13uUlOTmbdunWUl5e7M4+ISKM1e+V+sovtdIoK5veXdzQ7jkij5XK5yc3NZdSoUXTo0IGrr76akydPAjBx4kQeeeQRtwcUEWkMNh3O5qPtJwB47sbeWH28TU4k0ni5XG4SExNxOBwcPXqUwMAfR/jfeuutfPrpp24NJyLSGJRXOHj8P3sB+M3QNgxqF2FyIpHGzcfVE9asWcOnn35Ku3btahzv0qULx48fd1cuEZFG42/rj5CcU0p0qJVHR3UzO45Io+fylZuioiKCg4NPO56Xl4efn59bQomINBZHs4qZv/4IADOv7Umov6/JiUQaP5fLzfDhw3n33XerP7ZYLBiGwYsvvsiIESPcGk5EpCEzDIOZy77H7nByaZcWjOkdY3YkkSbB5dtSf/nLX7jiiivYvn07drudadOm8f3335ORkcHXX39dFxlFRBqk5XtOsfFwNn4+Xjw1tqe2WBCpJy5fuenduzdJSUkMGjSIa665htzcXK655hp27txJ586d6yKjiEiDU1hewdMr9gFw/4hOtGseZHIikabD5Ss3AOHh4cyaNcvdWUREGo2XP0siq8hGh+ZB/O6yDmbHEWlSalVu9u3bV+tP2KNHj/MOIyLSGHyXVsCizckAPH1DL61pI1LPalVuevXqVT1w+Ex+eM5iseBwONwaUESkIXE6DaYv/Q6nAWP7tuLiTs3NjiTS5NSq3Bw6dKiuc4iINApLdpxgV2o+QX7eTL+mu9lxRJqkWpWbjh21B4qIyC8pKKvg+U8PAPDQyC5EhfqbnEikaTqvAcVHjhzhtddeY//+/QB0796d++67T7OlRKRJm7s2iZySqo0xJ17czuw4Ik2Wy1PBly5dSvfu3fn666/p2rUrXbt2ZdOmTfTs2ZOlS5fWRUYREY93IL2QRZurtqD583U98fV2+e1VRNzE5Ss3U6ZMYcqUKcyePbvG8enTp/PII49www03uC2ciEhDYBgGs5Z9j8NpMLpXDMM7axCxiJlc/tUiLS2NiRMnnnZ8woQJnDx50h2ZREQalOV7TrHlWC7+vl48oUHEIqZzudxccsklbNq06bTjmzZt4uKLL3ZLKBGRhqLEVsmzK6vGH953eSdahweanEhEanVbatWqVdV/v+mmm3j00UfZuXMnQ4cOBeCbb77hgw8+4KmnnqqblCIiHuqN9UdILyynTUQg91yqlYhFPIHFONvKfD/h5VW7CzwNYRG/wsJCwsLCKCgoIDQ01Ow4ItKApeaWcuXL/8Ve6eTvdw4koad2/RapK678/K7VlZuKigq3BBMRaUzmfLofe6WTizpGcnWPaLPjiMj/1KrceHtrXxQRkZ/65mgOq/am42WBmdf1wGKxmB1JRP7nvBbxKysrY8OGDaSkpGC322s894c//MEtwUREPJXDafDk8qoNhW+Pb0O3GN3iFvEkLpeb3bt3M2bMGAoKCigvLyc0NJT8/HwCAgKIjIxUuRGRRm/xt6nsP1VIqL8PiVd1NTuOiPyMy1PBH374YUaNGkVBQQEBAQFs27aNI0eOMHDgQF599dW6yCgi4jEKyip46bODQNX+URFBfiYnEpGfc7nc7NixgylTpuDt7Y23tzc2m4327dvz/PPPM23atLrIKCLiMV5bd4icEjsdWwRx57C2ZscRkTNwudz4+Pjg41N1NysqKoqUlBQAIiIiOH78uHvTiYh4kOTsEt7ZnAzA9Gt7aP8oEQ/l8pib/v378+2339KpUycuvfRS/vznP5Ofn8+iRYvo1atXXWQUEfEIz68+QIXD4NIuLRjRNcrsOCJyFi7/2jF79myioqr+UT/zzDMEBQVx1113ceLECf7+97+7PaCIiCfYeiyXT7+rmvr9xBjtHyXiyVy+cjNkyJDqv8fExLB27Vq3BhIR8TROp8EzK6umft86pA1dY0JMTiQi52L6DePXX3+ddu3a4e/vT3x8PFu3bj3n6/Pz87nvvvto2bIlVquVLl261Nj7SkTE3ZbtTmPPiQKCrT48PLKL2XFE5BfU6srNkCFDWLNmDeHh4QwePPicK3H+Ujn5qcWLF5OYmMj8+fOJj49n7ty5JCQkcPDgwepbXz9lt9u56qqriIqKYsmSJcTGxnL8+HGaNWtW668pIuKKMruDF1ZXTf3+w4iOtAixmpxIRH5JrcpNQkICVmvVP+hRo0a57Yu//PLL3HPPPdx1110AzJ8/n5UrV/L2228zderU017/9ttvk5uby6ZNm/D19QWgXbt2bssjIvJzb244yqmCcmKbBTDp4vZmxxGRWqjVruA/cDgcbNmyhR49elzw1RK73U5gYCBLlizhhhtuqD4+YcIE8vPzWbZs2WnnjBkzhoiICAIDA1m2bBktWrTg9ttv57HHHjvr/lc2mw2bzVb9cWFhIXFxcdoVXER+UWZhOZe/uJ5Su4NXb+vP2L6tzI4k0mS5siu4S2NuvL29GTFiBHl5eRcUECA7OxuHw0F0dM2ddKOjo0lPTz/jOUePHmXJkiU4HA5WrVrFjBkzeOmll3jmmWfO+nXmzJlDWFhY9SMuLu6Cs4tI0/DXtUmU2h30i2vGdX1amh1HRGrJ5QHFvXr1Ijk5uQ6i/DKn00lUVBT/+Mc/GDhwIOPGjeOJJ55g/vz5Zz1n2rRpFBQUVD9SU1PrMbGINFRJGUUs/rbq/WL6Nd2167dIA+LyVPBnn32WRx55hNmzZzNw4ECCgoJqPB8YGFirz9O8eXO8vb3JyMiocTwjI4OYmJgzntOyZUt8fX1r3ILq3r076enp2O12/PxO3+PFarVWjxcSEamt5z49gNOAhJ7RDGoXYXYcEXGBy1duRo8ezc6dOxkzZgwxMTGEhITUeNSWn58fAwcOZN26ddXHnE4n69atY9iwYWc85+KLL+bw4cM4nc7qY0lJSbRs2fKMxUZE5HxsOpLNFwcy8fGy8NiobmbHEREXuXzl5vPPP3fbF09MTGTChAkMGjSIIUOGMHfuXEpKSqpnT40fP57Y2FjmzJkDwO9//3vmzZvHH//4Rx544AEOHTrEs88+y4MPPui2TCLStDmdBs+u2g/AHfFt6NAi2OREIuIql8vNlVde6bYvPm7cOLKyspg5cybp6en069eP1atXVw8yTklJwcvrx4tLcXFxrFmzhocffpg+ffoQGxvLH//4Rx577DG3ZRKRpm3Z7jS+SyskxOrDg1d2NjuOiJwHl6aC/5TNZiM1NRW73V7jeI8ePdwSrK64MpVMRJqW8goHV770X9Lyy5iS0JX7RnQyO5KI/I8rP79dvnKTnZ3N5MmTWb58+Rmfdzgcrn5KERGPsHBTMmn5ZbQM8+fu4VqwT6ShcnlA8cMPP0xmZiZff/01AQEBrFixgrfeeotOnTqdceE9EZGGIK/EzutfHgbgT1d3xd/3zAuDiojnc/nKzdq1a1m6dCnx8fF4eXnRqVMnRo8eTbNmzXjhhRe49tpr6yKniEidev3LwxSVV9ItJoRf9Y81O46IXACXr9wUFxdXD/gNDw8nMzMTgL59+7Jt2zb3phMRqQepuaUs2nwcgKmju+HtpQX7RBoyl8tN165dSUpKAqBPnz68+eabZGRksGDBgrMuvici4sle/jwJu8PJRR0juaxLC7PjiMgFcvm21IMPPsiJEycAmDlzJqNGjWLRokX4+vry9ttvuz2giEhd+v5kAUt3pQEwbbS2WRBpDFwuN+PHj6/+++DBg0lOTmb//v20bdv2tE0wRUQ83XOfHsAw4Lq+rejdOszsOCLiBrW+LfXII49w4MCB046HhIQwZMgQFRsRaXA2Hspmw6FsfL0tTLm6q9lxRMRNal1uli1bRs+ePbnooot4++23KSkpqctcIiJ1yuk0mPPpD9sstKVNZO02/RURz1frcnPo0CG+/PJLunTpwh//+EdiYmKYNGkSmzZtqst8IiJ1Yvmek3x/spBgqw8PXKGViEUaE5dmS1166aUsXLiQ9PR0XnnlFQ4dOsTw4cPp3r07L774IhkZGXWVU0TEbeyVTl787CAAv7u0A5HBVpMTiYg7uTwVHCAoKIhJkyaxYcMGkpKSuPHGG5kzZw5t2rRxdz4REbd7b8txUnPLaBFi5e5LtM2CSGNzXuXmByUlJWzYsIH//ve/5OXl0aFDB3flEhGpE8W2Sl77omqbhT9e2ZlAP5cnjYqIhzuvcrNx40YmTZpEy5YtefDBB+nSpQsbNmxg//797s4nIuJWC746Sk6JnfbNgxg3OM7sOCJSB2r9K8upU6d45513WLhwIUlJSQwdOpSXX36ZW2+9leDg4LrMKCLiFllFNhZsOArAlISu+Hpf0MVrEfFQtS43cXFxREZGcuedd3L33XfTvXv3uswlIuJ2r31xiFK7g76twxjdS9vFiDRWtS43H374IWPHjsXHR/enRaThOZ5TwntbUgB4bHQ3bbMg0ojVuqnceOONdZlDRKROvfhZEpVOg8u6tOCijs3NjiMidUg3nEWk0fsurYDlu08C8OgobbMg0tip3IhIo/f86qp98a7v14qerbQ5pkhjp3IjIo3apsM/bo75pyHBMkQAACAASURBVKt01UakKXC53EyaNImioqLTjpeUlDBp0iS3hBIRcQfDMKqv2tw+pI02xxRpIlwuN++88w5lZWWnHS8rK2PRokVuCSUi4g6ffpfO7hMFBPp5c/8Vnc2OIyL1pNazpQoLCzEMA8MwKCoqwt/fv/o5h8PBqlWriIqKqpOQIiKuqnQ4eXFN1eaYky/pQIsQbY4p0lTUutw0a9YMi8WCxWKhS5cupz1vsVh48skn3RpOROR8fbjtBEezS4gI8uMebY4p0qTUutx8+eWXGIbBFVdcwccff0xERET1c35+frRt25ZWrVrVSUgREVeU2R3MXZsEwP0jOhHi72tyIhGpT7UuN5dddhkAx44dIy4uDi8vTbQSEc/0z03HyCyy0To8gDuGtjE7jojUM5f3Umjbti35+fls3bqVzMxMnE5njefHjx/vtnAiIq7KL7XzxvojACRe1QWrj7fJiUSkvrlcbpYvX84dd9xBcXExoaGhNfZnsVgsKjciYqo31h+hqLySbjEhXN8v1uw4ImICl+8t/elPf2LSpEkUFxeTn59PXl5e9SM3N7cuMoqI1MqpgjIWbkoGqrZZ8PbS5pgiTZHL5SYtLY0HH3yQwEAthiUinmXu54ewVToZ0i6CEV21NIVIU+VyuUlISGDbtm11kUVE5Lwdzizio+2pADw2uluNW+Yi0rS4PObmmmuuYcqUKezbt4/evXvj61tziuXYsWPdFk5EpLb+suYgTgOu6hHNwLbhZscRERNZDMMwXDnhXFPALRYLDofjgkPVpcLCQsLCwigoKCA0NNTsOCLiBjtS8rjxb5vwssCahy6lc3SI2ZFExM1c+fnt8pWbn0/9FhExk2EYPP9p1eaYNw1orWIjIq6Pufmp8vJyd+UQETkv65Oy2HIsFz8fLx666vStYUSk6XG53DgcDp5++mliY2MJDg7m6NGjAMyYMYO33nrL7QFFRM7G6fzxqs2EYW2JbRZgciIR8QQul5vZs2ezcOFCXnjhBfz8/KqP9+rVizfffNOt4UREzmXZ7jQOpBcR4u/DHy7vZHYcEfEQLpebRYsW8Y9//IM77rgDb+8flzXv27cvBw4ccGs4EZGzsVU6eOmzqs0xf395R8KD/H7hDBFpKs5rEb9OnU7/DcnpdFJRUeGWUCIiv+Tf36RwIq+M6FArd13U3uw4IuJBXC43PXr0YMOGDacdX7JkCf3793dLKBGRcykqr2Del4cBeGhkFwL8tDmmiPzI5angM2fOZMKECaSlpeF0Ovnkk084ePAgixYtYsWKFXWRUUSkhgVfHSW3xE6HFkH8emBrs+OIiIdx+crN9ddfz/Lly1m7di1BQUHMnDmT/fv3s3z5cq666qq6yCgiUi2zqJwFG44B8GhCV3y8L2hFCxFphFy+cgNwySWX8Pnnn7s7i4jIL3p13SHKKhz0i2tGQs8Ys+OIiAfSrzwi0mAczSrm/a1Vm2NO1eaYInIWtbpyEx4eXus3kdzc3AsKJCJyNn9ZcxCH0+DKblEM7RBpdhwR8VC1Kjdz586t/ntOTg7PPPMMCQkJDBs2DIDNmzezZs0aZsyYUTcpRaTJ25GSx6ffpeNlgcdGdzM7joh4MJd3Bb/pppsYMWIE999/f43j8+bNY+3atSxdutStAd1Nu4KLNDyGYTDu79+wNTmXWwa15oWb+5odSUTqmSs/v10ec7NmzRpGjRp12vFRo0axdu1aVz+diMgvWrs/k63JuVh9vHhYm2OKyC9wudxERkaybNmy044vW7aMyEjdAxcR96p0OHl+ddXWLpOGt6dlmDbHFJFzc3kq+JNPPsnkyZNZv3498fHxAGzZsoXVq1ezYMECtwcUkaZtyfYTHM4splmgL/de1tHsOCLSALhcbiZOnEj37t159dVX+eSTTwDo3r07GzdurC47IiLuUGZ38Ne1VZtj3j+iE2EBviYnEpGG4LwW8YuPj+ff//63u7OIiNTw5oajZBTaaB0ewJ3D2podR0QaiPMqN06nk8OHD5OZmYnT6azx3KWXXuqWYCLStGUV2Zj/3yMATEnoitVHm2OKSO24XG6++eYbbr/9do4fP87PZ5FbLBYcDofbwolI0/XKuiRK7A76tA7juj6tzI4jIg2Iy+Xm3nvvZdCgQaxcuZKWLVtq+XMRcbvDmT9us/D4mO54eel9RkRqz+Vyc+jQIZYsWUKnTp3qIo+ICM+vPoDDaTCyu7ZZEBHXubzOTXx8PIcPH3ZriNdff5127drh7+9PfHw8W7durdV5H3zwARaLhRtuuMGteUTEPFuP5fL5vgy8vSxM1TYLInIeXL5y88ADD/CnP/2J9PR0evfuja9vzamZffr0cenzLV68mMTERObPn098fDxz584lISGBgwcPEhUVddbzkpOTeeSRR7jkkktc/RZExEMZhsHsVfsBuHVwHJ2iQkxOJCINkct7S3l5nX6xx2KxYBjGeQ0ojo+PZ/DgwcybNw+omokVFxfHAw88wNSpU894jsPh4NJLL2XSpEls2LCB/Pz8Wu9ppb2lRDzX8t0neeD9nQT5ebN+yghahFjNjiQiHsKVn98uX7k5duzYeQf7Obvdzvbt25k2bVr1MS8vL0aOHMnmzZvPet5TTz1FVFQUd999Nxs2bDjn17DZbNhstuqPCwsLLzy4iLhdeYWjepuF313WUcVGRM6by+WmbVv3LaSVnZ2Nw+EgOjq6xvHo6GgOHDhwxnM2btzIW2+9xa5du2r1NebMmcOTTz55wVlFpG4t3JTMibwyYkL9mXxJe7PjiEgD5vKAYoB//etfXHzxxbRq1Yrjx48DMHfu3DNuqOlORUVF3HnnnSxYsIDmzZvX6pxp06ZRUFBQ/UhNTa3TjCLiupxiG69/UTVRYUpCVwL9zmt9URER4DzKzRtvvEFiYiJjxowhPz+/eoxNs2bNmDt3rkufq3nz5nh7e5ORkVHjeEZGBjExMae9/siRIyQnJ3Pdddfh4+ODj48PixYt4v/+7//w8fHhyJEjp51jtVoJDQ2t8RARzzJ37SGKbJX0ig3lV/1jzY4jIg2cy+XmtddeY8GCBTzxxBN4e/+4HPqgQYPYu3evS5/Lz8+PgQMHsm7duupjTqeTdevWMWzYsNNe361bN/bu3cuuXbuqH2PHjmXEiBHs2rWLuLg4V78dETHZoYwi3tuaAsD0a3powT4RuWDnNaC4f//+px23Wq2UlJS4HCAxMZEJEyYwaNAghgwZwty5cykpKeGuu+4CYPz48cTGxjJnzhz8/f3p1atXjfObNWsGcNpxEWkYnl21H4fT4Ooe0VqwT0TcwuVy0759e3bt2nXawOLVq1fTvXt3lwOMGzeOrKwsZs6cSXp6Ov369WP16tXVg4xTUlLOOP1cRBq+r5Ky+PJgFj5eFqaNcf39Q0TkTFwuN4mJidx3332Ul5djGAZbt27l/fffZ86cObz55pvnFeL+++/n/vvvP+Nz69evP+e5CxcuPK+vKSLmcjgNZq+sWrBv/LB2tG8eZHIiEWksXC43kydPJiAggOnTp1NaWsrtt99Oq1ateOWVV7j11lvrIqOINEIffJvCwYwiwgJ8efBK7VUnIu5zXvMt77jjDu644w5KS0spLi4+5zYJIiI/V1BWwUufJQHw0MjONAv0MzmRiDQm572YRGZmJgcPHgSqtl9o0aKF20KJSOP26rpD5JbY6RQVzG+Gum9hUBEROI+p4D8spNeqVSsuu+wyLrvsMlq1asVvfvMbCgoK6iKjiDQiR7KKeWdTMgAzru2Br7cmDIiIe7n8rjJ58mS2bNnCypUryc/PJz8/nxUrVrBt2zZ+97vf1UVGEWlEnlmxj0qnwZXdorisi674ioj7uXxbasWKFaxZs4bhw4dXH0tISGDBggWMGjXKreFEpHH58mAmXx7MwtfbwhPXaOq3iNQNl6/cREZGEhYWdtrxsLAwwsPD3RJKRBqfCoeTZ1bsA2DiRe3o0CLY5EQi0li5XG6mT59OYmIi6enp1cfS09OZMmUKM2bMcGs4EWk8/rX5OEeySogM8uOBKzubHUdEGjGXb0u98cYbHD58mDZt2tCmTRugahVhq9VKVlYWf//736tfu2PHDvclFZEGK7vYxl/XVk39fiShK6H+viYnEpHGzOVyc8MNN9RFDhFpxF5YfYCi8qpdv28ZpA1uRaRuuVxuZs2aVRc5RKSR2pmSx4fbTgDw5NheeGvXbxGpY+e1wER+fj5vvvkm06ZNIzc3F6i6BZWWlubWcCLSsDmdBrP+73sAbhrQmoFtNelAROqey1du9uzZw8iRIwkLCyM5OZl77rmHiIgIPvnkE1JSUli0aFFd5BSRBujDbansOVFAiNWHx0Z3NTuOiDQRLl+5SUxMZOLEiRw6dAh/f//q42PGjOGrr75yazgRabjyS+08v/oAAA9d1YWoEP9fOENExD1cLjfffvvtGVcijo2NrTE9XESatpc/TyKvtIIu0cGMH6b9o0Sk/rhcbqxWK4WFhacdT0pK0uaZIgLA9ycLePeb4wD8eWxP7R8lIvXK5XecsWPH8tRTT1FRUQFU7QiekpLCY489xk033eT2gCLSsDidBtOXfofTgGv6tOSijs3NjiQiTYzL5eall16iuLiYqKgoysrKuOyyy+jUqRMhISHMnj27LjKKSAPywbep7EzJJ8jPmxnX9DA7jog0QS7PlgoLC+Pzzz9n48aN7Nmzh+LiYgYMGMDIkSPrIp+INCDZxbbqQcSJV3clJkyDiEWk/rlcbn4wfPjwGjuDi4jMWXWAgrIKerQMZYIGEYuISVwqN06nk4ULF/LJJ5+QnJyMxWKhffv23Hzzzdx5551YLFp5VKSp2nI0h493nMBigdm/6oWPBhGLiElq/e5jGAZjx45l8uTJpKWl0bt3b3r27Mnx48eZOHEiv/rVr+oyp4h4MHulk+lLvwPgtiFt6N9GKxGLiHlqfeVm4cKFfPXVV6xbt44RI0bUeO6LL77ghhtuYNGiRYwfP97tIUXEs7218RiHMouJDPLjsYRuZscRkSau1ldu3n//fR5//PHTig3AFVdcwdSpU/n3v//t1nAi4vlSckp5ZV0SAI+P6U5YoK/JiUSkqat1udmzZw+jRo066/OjR49m9+7dbgklIg2DYRg8sXQv5RVOhnWI5MYBsWZHEhGpfbnJzc0lOjr6rM9HR0eTl5fnllAi0jD8Z2caGw5lY/XxYs6NvTWpQEQ8Qq3LjcPhwMfn7EN0vL29qaysdEsoEfF8OcU2nl6xD4A/juxMu+ZBJicSEalS6wHFhmEwceJErFbrGZ+32WxuCyUinu/pFfvIK62ge8tQ7rmkg9lxRESq1brcTJgw4Rdfo5lSIk3Df5OyWLrrJF4WeO7G3toYU0Q8Sq3LzT//+c+6zCEiDUSpvZIn/rMXgIkXtadvXDOTE4mI1KRft0TEJS+uSeJEXhmxzQL409VdzI4jInIalRsRqbVvk3P556ZjQNUWC0HW896eTkSkzqjciEitlNkdTPloN4YBtwxqzeVdo8yOJCJyRio3IlIrL352kOScUmJC/Xnimh5mxxEROSuVGxH5RduSc3n766rbUXNu6k1YgLZYEBHPpXIjIudUXuFgypI9GAb8emBrRuh2lIh4OJUbETmnlz47yLHsEqJDrUy/VrejRMTzqdyIyFltOZrDmxv/dzvqRt2OEpGGQeVGRM6oqLyCxA93V9+OuqLb2TfOFRHxJCo3InJGTy7fR1p+GXERAcwa29PsOCIitaZyIyKnWf3dKZZsP4GXBV6+pR/BWqxPRBoQlRsRqSGzqJxpn1TtHXXvZR0Z3C7C5EQiIq5RuRGRaoZh8OiSPeSVVtCjZSgPjdTeUSLS8KjciEi1d7eksP5gFn4+Xsy9tR9+PnqLEJGGR+9cIgLAgfRCnlmxD4Cpo7rRJTrE5EQiIudH5UZEKLM7uP+9ndgqnYzo2oK7Lm5ndiQRkfOmciMiPLXiew5nFhMVYuXFX/fFYrGYHUlE5Lyp3Ig0cSv2nOT9ralYLDB3XD8ig61mRxIRuSAqNyJNWGpuKdM+rpr2fd/lnbioU3OTE4mIXDiVG5Emyl7p5MEPdlJkq2Rg23AeGtnZ7EgiIm6hciPSRM35dD87U/IJ9ffhlVv74eOttwMRaRz0bibSBK3Yc5J/fp0MwEu39KN1eKC5gURE3EjlRqSJOZxZxGNL9gDw+8s7clUP7fYtIo2Lyo1IE1Jiq+Ted3dQYncwrEMkf7pK2yuISOOjciPSRBiGwdRP9lavZ/Pqbf01zkZEGiW9s4k0EQs3JbN890l8vCz87Y4BtAjRejYi0jip3Ig0AZsOZ/PMyv0ATB3djUHtIkxOJCJSdzyi3Lz++uu0a9cOf39/4uPj2bp161lfu2DBAi655BLCw8MJDw9n5MiR53y9SFOXklPKH97bgcNp8Kv+sdw9vL3ZkURE6pTp5Wbx4sUkJiYya9YsduzYQd++fUlISCAzM/OMr1+/fj233XYbX375JZs3byYuLo6rr76atLS0ek4u4vmKbZVMXvQt+aUV9G0dxpwbe2vfKBFp9CyGYRhmBoiPj2fw4MHMmzcPAKfTSVxcHA888ABTp079xfMdDgfh4eHMmzeP8ePH/+LrCwsLCQsLo6CggNDQ0AvOL+KpnE6D3727nc/3ZRAVYuX/7h9OTJi/2bFERM6LKz+/Tb1yY7fb2b59OyNHjqw+5uXlxciRI9m8eXOtPkdpaSkVFRVERJx5DIHNZqOwsLDGQ6QpmLs2ic/3ZeDn7cX8Oweq2IhIk2FqucnOzsbhcBAdXXMRsejoaNLT02v1OR577DFatWpVoyD91Jw5cwgLC6t+xMXFXXBuEU+3bFcar35xGIBnb+zNgDbhJicSEak/po+5uRDPPfccH3zwAf/5z3/w9z/zb6XTpk2joKCg+pGamlrPKUXq15ajOUz5qGoF4t9e2oGbB7Y2OZGISP3yMfOLN2/eHG9vbzIyMmocz8jIICYm5pznvvjiizz33HOsXbuWPn36nPV1VqsVq1XreUjTcCSrmN/+azt2h5PRvWKYOqqb2ZFEROqdqVdu/Pz8GDhwIOvWras+5nQ6WbduHcOGDTvreS+88AJPP/00q1evZtCgQfURVcTjZRfbmPjPrRSUVdC/TTP+Oq4fXl6aGSUiTY+pV24AEhMTmTBhAoMGDWLIkCHMnTuXkpIS7rrrLgDGjx9PbGwsc+bMAeD5559n5syZvPfee7Rr1656bE5wcDDBwcGmfR8iZiqzO5j8zjZSc8toExHIm+MH4e/rbXYsERFTmF5uxo0bR1ZWFjNnziQ9PZ1+/fqxevXq6kHGKSkpeHn9eIHpjTfewG63c/PNN9f4PLNmzeLPf/5zfUYX8QiVDid//GAnu1LzaRboy8K7BhMZrFuxItJ0mb7OTX3TOjfSmBiGwaNL9vDR9hP4+Xjx7t3xDGmvrRVEpPFpMOvciMj5MwyDZ1ft56PtJ/CywGu39VexERFB5UakwXrjv0dYsOEYAM/f1IeEnueeYSgi0lSo3Ig0QO9tSeGF1QcBmH5Nd349SItTioj8QOVGpIFZtiuNJ5buBeC+ER2ZfEkHkxOJiHgWlRuRBmT57pM8vHgXhgG3x7fhkau7mh1JRMTjqNyINBAr95ziocW7cBowblAcz1zfC4tFi/SJiPycyo1IA/Dp3lM8+MFOHE6Dmwe2Zs6NvbX6sIjIWajciHi41d+l88D7VcXmxv6xPH9THxUbEZFzMH2FYhE5u2W70kj8cDcOp8EN/Vrxl1/3xVvFRkTknFRuRDzUe1tSeGLpXgwDbuwfyws391GxERGpBZUbEQ/0j6+O8OyqAwDcObQtT47tqVtRIiK1pHIj4kEMw+Cvnyfx6heHAfj95R15NKGrZkWJiLhA5UbEQ1Q6nPx5+fe8+00KAI+O6sofLu9kcioRkYZH5UbEA5TaK3ngvZ2sO5CJxQJPje3JncPamR1LRKRBUrkRMVlWkY3J73zL7hMFWH28eOXW/ozqpU0wRUTOl8qNiImOZBUz8Z9bSc0tIzzQlzcnDGZg23CzY4mINGgqNyIm2Xgom/ve20FBWQVtIgJZeNdgOrQINjuWiEiDp3IjUs8Mw+CfXycze9V+HE6DfnHNeHPCIJoHW82OJiLSKKjciNQjW6WD6f/5jo+2nwDgxgGxPPur3vj7epucTESk8VC5EaknmYXl3Pvudnak5ONlgcfHdOfu4e21ho2IiJup3IjUg02Hs3nwg51kF9sJ9fdh3u0DuLRLC7NjiYg0Sio3InXI4TSY98Vh5q5LwjCgW0wIb/xmIO2bB5kdTUSk0VK5Eakj2cU2HvpgFxsPZwMwblAcfx7bkwA/ja8REalLKjcideCrpCwe+Wg3mUU2Any9eeaGXtw0sLXZsUREmgSVGxE3Kq9w8NynB1i4KRmATlHB/O2OAXSJDjE3mIhIE6JyI+Im36UV8NDiXRzOLAZg/LC2TBvdXbehRETqmcqNyAWyVzr5+3+P8OoXh6hwGLQIsfKXm/twedcos6OJiDRJKjciF2B3aj6PfbyHA+lFAIzqGcOzN/YmIsjP5GQiIk2Xyo3IeSi1V/LyZ0m8/fUxnAZEBPkx89oeXN+vlRblExExmcqNiIu+OJDBrP/7ntTcMgCu79eKmdf2IFJ7Q4mIeASVG5FaOp5TwlPL97HuQCYArcL8eeZXvbiiW7TJyURE5KdUbkR+QZndwd/WH+bvXx3FXunEx8vC3Ze054ErOhNs1T8hERFPo3dmkbNwOA0+3nGClz9LIr2wHIBLOjdn1nU96RQVbHI6ERE5G5UbkZ8xDIP1SVk8t+oABzOqZkHFNgtgxrXdSegZowHDIiIeTuVG5Ce2H8/jpc8OsulIDgCh/j48cEVn7hzWFn9fLcYnItIQqNyIADtT8vjr2kN8lZQFgJ+3FxMvbscfLu9Is0CtWSMi0pCo3EiTtiMlj1fXHWL9wapS4+1l4eYBrbn/ik7ERQSanE5ERM6Hyo00OU6nwfqkTOb/9yhbj+UCVaXmpgGx3D+iM20iVWpERBoylRtpMmyVDpbvPsU/vjpCUkbV5pa+3hZu6BfL/Vd0om1kkMkJRUTEHVRupNE7VVDGe1tSeH9rCtnFdgCCrT7cEd+Guy5uT0yYv8kJRUTEnVRupFEyDINvjubyr2+SWfN9Bg6nAUBMqD8TLmrHHUPbEOrva3JKERGpCyo30qikF5Tz8Y4TfLgtleM5pdXH49tHMOGidlzVIxpfby8TE4qISF1TuZEGr7zCwdr9GXyyI431BzP530Uagq0+jO3XivHD2tItJtTckCIiUm9UbqRBqnQ42XQkh6W70vjs+wyKbZXVzw1uF84tg+K4pk9LAv30v7iISFOjd35pMOyVTjYfzWH1d+l8vi+9enAwVG2PcH2/Vtw0sDUdW2jfJxGRpkzlRjxaUXkFGw9l8/m+DNbuz6Cw/McrNOGBvlzbpxXX92vFwLbh2vNJREQAlRvxMIZhcCy7hC8PZvHFgQy2HsulwmFUP9882I+re8YwulcMQztEanCwiIicRuVGTJdbYufrw9lsPJTNxsPZpOWX1Xi+ffMgRnSNYlSvGAa2DcfbS1doRETk7FRupN7lltjZeiyHb47msuVYLgfSCzF+vDiDr7eFwe0iuKJbFFd0i6KDxtCIiIgLVG6kTjmdBkezi9lxPJ8dKXlsP57Hoczi017XNTqE4Z2bM7xzc+LbR2iWk4iInDf9BBG3MQyD9MJy9pwoYO+JAvakFbA7NZ+CsorTXtslOpj49pHEd4hgSPsIokK0BYKIiLiHyo2cl0qHk6PZJew7Wcj+U4XsO1X150+nZ//A39eLPq2bMaBNOAPaNGNQuwgigvxMSC0iIk2Byo2ck73SSUpuCYczSziUUURSZjFJ6UUczS6uMYvpB95eFrpGh9CndRi9W4fRJ7YZ3VqGaFaTiIjUG5UbocLhJC2vjOO5pRzPKeF4TinHsks4mlVMal5Z9aaTPxfk5023lqH0aBlK95ahdG8ZQveWofj7etfzdyAiIvIjlZsmoLzCQXpBOScLyjiVX86JvDJO5JWSmlfKibwyThWUn7XAQFWJ6dAimM7RwXSJDqFLdDCdo0KIbRaAl6Zli4iIh1G5acAqHE5yiu1kFdnIKi4nq8hGeoGNjKJyMgrKSS8sJ6Ow/IzjYH7O6uNF28hA2kQE0S4ykHbNg+jQIoiOLYKJCrFq9V8REWkwVG48hGEYFNsqyS+toKCsgrxSO7kldvJK7OSWVlT9WWInu9hGTomdnGIbeaWnz0I6mwBfb1o286dVWACtw394BFb/GRVi1VUYERFpFFRu3OSHqyjFtgqKbQ5KbJUUlVdSbKukuLyCovJKiv53rLC8gsKyCgrLK6v+LKsgv6zinLeGzsbHy0LzYCstQqw0D/YjJsyfqBB/YsL8iQ61Eh1aVWiaBfrq6ouIiDQJHlFuXn/9df7yl7+Qnp5O3759ee211xgyZMhZX//RRx8xY8YMkpOT6dy5M88//zxjxoypx8Sn2348j1v/8c0Ffx4/Hy/CA31pFuBHRFDVIzzIl/BAPyKD/IgMthIZ7EfzYCuRQX6EB/rpiouIiMhPmF5uFi9eTGJiIvPnzyc+Pp65c+eSkJDAwYMHiYqKOu31mzZt4rbbbmPOnDlce+21vPfee9xwww3s2LGDXr16mfAdVAm2+uDjZSHY34cgPx+CrT5Vf7f6EOLvQ6h/1bEQf19C/X0IDfAl1N+36s8AH5oF+NEs0FczjURERC6QxTAM1++FuFF8fDyDBw9m3rx5ADidTuLi4njggQeYOnXqaa8fN24cJSUlrFixovrY0KFD6devH/Pnzz/t9TabDZvNVv1xYWEhcXFxFBQUEBoa6rbv44f/jLr1IyIi4n6FhYWEhYXV6ue3qSur2e12tm/fzsiRI6uPeXl5MXLkQHwU2QAAEZNJREFUSDZv3nzGczZv3lzj9QAJCQlnff2c/2/v3oOiKt84gH8PGJeNBcUEQcHQSMkLm6AImGBZOTGmXZnSBEIbC9TExvuFfmk4IWVqmUmClaaNoo46qXgBs6Q00kZCEwxlVBArEVAX2n1+fzSe3EDDSxw5fD8z+8ee99lzvvsOwuN7zp5NSYGbm5v68PHxuX1v4CqKorCxISIiugNo2tycO3cOFosFnp6eNts9PT1RVlbW4GvKyspuqH7q1KmorKxUH6WlpbcnPBEREd2RNL/m5r/m6OgIR0dHrWMQERFRE9F05eaee+6Bvb09ysvLbbaXl5ejffv2Db6mffv2N1RPRERELYumzY2DgwOCgoKwc+dOdZvVasXOnTsRGhra4GtCQ0Nt6gEgOzv7mvVERETUsmh+WiopKQkxMTEIDg5G3759sWDBAtTU1CAuLg4AMHLkSHTo0AEpKSkAgPHjxyMiIgJpaWmIiorC6tWrceDAAXz88cdavg0iIiK6Q2je3ERHR6OiogKzZs1CWVkZTCYTtm7dql40fPLkSdjZ/b3AFBYWhlWrVmHGjBmYNm0a/P39sWHDBk3vcUNERER3Ds3vc9PUbuRz8kRERHRnaDb3uSEiIiK63djcEBERka6wuSEiIiJdYXNDREREusLmhoiIiHSFzQ0RERHpiub3uWlqVz75fuHCBY2TEBERUWNd+bvdmDvYtLjmpqqqCgDg4+OjcRIiIiK6UVVVVXBzc7tuTYu7iZ/VasXp06dhNBqhKIrWcTR34cIF+Pj4oLS0lDc1/I9xrpsW57vpcK6bTkueaxFBVVUVvL29bb65oCEtbuXGzs4OHTt21DrGHcfV1bXF/UPRCue6aXG+mw7nuum01Ln+txWbK3hBMREREekKmxsiIiLSFfvk5ORkrUOQtuzt7REZGYlWrVrcWcomx7luWpzvpsO5bjqc63/X4i4oJiIiIn3jaSkiIiLSFTY3REREpCtsboiIiEhX2NwQERGRrrC5oQaZzWaYTCYoioKDBw9qHUd3SkpKEB8fDz8/Pzg7O6NLly6YPXs2amtrtY6mCx988AHuvfdeODk5ISQkBN9//73WkXQnJSUFffr0gdFohIeHB4YNG4ajR49qHatFmDdvHhRFweuvv651lDsWmxtq0KRJk+Dt7a11DN06cuQIrFYrli5dioKCArz33nv46KOPMG3aNK2jNXtr1qxBUlISZs+ejfz8fAQGBuLxxx/H2bNntY6mK7m5uUhISEBeXh6ys7NRV1eHxx57DDU1NVpH07X9+/dj6dKl6NWrl9ZR7mj8KDjV89VXXyEpKQnr1q1D9+7d8eOPP8JkMmkdS/dSU1OxZMkSHD9+XOsozVpISAj69OmDxYsXA/jr++R8fHwwduxYTJkyReN0+lVRUQEPDw/k5uZiwIABWsfRperqavTu3Rsffvgh5syZA5PJhAULFmgd647ElRuyUV5ejtGjR+Ozzz6DwWDQOk6LUllZCXd3d61jNGu1tbX44YcfMGjQIHWbnZ0dBg0ahH379mmYTP8qKysBgD/D/6GEhARERUXZ/HxTw3h7Q1KJCGJjYzFmzBgEBwejpKRE60gtRlFRERYtWoT58+drHaVZO3fuHCwWCzw9PW22e3p64siRIxql0j+r1YrXX38d4eHh6NGjh9ZxdGn16tXIz8/H/v37tY7SLHDlpgWYMmUKFEW57uPIkSNYtGgRqqqqMHXqVK0jN1uNneurnTp1CoMHD8Zzzz2H0aNHa5Sc6OYlJCTg8OHDWL16tdZRdKm0tBTjx4/HypUr4eTkpHWcZoHX3LQAFRUV+O23365b07lzZzz//PPYtGkTFEVRt1ssFtjb22P48OFYsWLFfx212WvsXDs4OAAATp8+jcjISPTr1w+ZmZmws+P/N25FbW0tDAYD1q5di2HDhqnbY2JicP78eWzcuFHDdPqUmJiIjRs3Ys+ePfDz89M6ji5t2LABTz31FOzt7dVtFosFiqLAzs4OZrPZZozY3NBVTp48iQsXLqjPT58+jccffxxr165FSEgIOnbsqGE6/Tl16hQGDhyIoKAgfP755/zldJuEhISgb9++WLRoEYC/Tpn4+voiMTGRFxTfRiKCsWPHYv369cjJyYG/v7/WkXSrqqoKJ06csNkWFxeHbt26YfLkyTwV2ABec0MqX19fm+cuLi4AgC5durCxuc1OnTqFyMhIdOrUCfPnz0dFRYU61r59ew2TNX9JSUmIiYlBcHAw+vbtiwULFqCmpgZxcXFaR9OVhIQErFq1Chs3boTRaERZWRkAwM3NDc7Ozhqn0xej0Vivgbn77rvRtm1bNjbXwOaGSAPZ2dkoKipCUVFRvcaRi6m3Jjo6GhUVFZg1axbKyspgMpmwdevWehcZ061ZsmQJACAyMtJme0ZGBmJjY5s+ENFVeFqKiIiIdIVXLxIREZGusLkhIiIiXWFzQ0RERLrC5oaIiIh0hc0NERER6QqbGyIiItIVNjdERESkK2xuiIiISFfY3BC1MIqiYMOGDVrHaJTk5GSYTCatY/wnRowYgWeffbbR9UVFRVAUBYcPH75mzY4dO6AoCqqrq29HRKJmi80NUTMRGxtr803XdHMyMzPRunXr69akpaWhTZs2uHz5cr2xixcvwtXVFQsXLrylHB988AHS09NvaR9E1DA2N0RE//DSSy+hpqYGWVlZ9cbWrl2L2tpajBgx4qb2bbFYYLVa4ebm9q9NFhHdHDY3RM1UZGQkxo0bh0mTJsHd3R3t27dHcnKyTc2xY8cwYMAAODk54YEHHkB2dna9/ZSWluL5559H69at4e7ujqFDh6KkpEQdv7Ji9Oabb6Jdu3ZwdXXFmDFjUFtbq9ZYrVakpKTAz88Pzs7OCAwMxNq1a9XxnJwcKIqCnTt3Ijg4GAaDAWFhYTh69KhNlnnz5sHT0xNGoxHx8fENrpykp6cjICAATk5O6NatGz788EN1rKSkBIqiICsrCwMHDoTBYEBgYCD27dun5oiLi0NlZSUURYGiKPXmDAA8PDwwZMgQLF++vN7Y8uXLMWzYMLi7uwMAUlNT0aNHDxgMBvj4+CAxMRE1NTU2ee+55x5s2LABAQEBcHR0xOnTp+udltqyZQvCw8PRunVrtG3bFkOGDMHx48frHb+goAD9+vWDk5MTevbsib1799arudqePXsQHh4OZ2dn+Pr6YsKECbh48eJ1X0PU7AkRNQsxMTEydOhQ9XlERIS4urpKcnKy/PLLL7JixQpRFEW2b98uIiIWi0V69OghjzzyiBw8eFByc3PlwQcfFACyfv16ERGpra2VgIAAefnll+Wnn36Sn3/+WV588UXp2rWrmM1m9bguLi4SHR0thw8fls2bN0u7du1k2rRpapY5c+ZIt27dZOvWrVJcXCwZGRni6OgoOTk5IiKye/duASAhISGSk5MjBQUF8tBDD0lYWJi6jzVr1oijo6Okp6fLkSNHZPr06WI0GiUwMFCt+fzzz8XLy0vWrVsnx48fl3Xr1om7u7tkZmaKiMivv/4qAKRbt26yefNmOXr0qDz77LPSqVMnqaurE7PZLAsWLBBXV1c5c+aMnDlzRqqqqhqc7y1btoiiKFJSUqJuKy4utpljEZF3331Xdu/eLb/++qvs2LFD/P39ZezYser4smXLxMHBQcLDw2Xfvn1SWFgoFy9elOHDh8szzzyj1n355ZeSlZUlx44dk/z8fHniiSfEZDKJxWIREZFjx44JAPH19ZWsrCz5+eefJS4uTtzc3OT3338XEZHs7GwBoL6no0ePyt133y3vv/++HDt2TPbu3SuBgYEyatSof/lpI2re2NwQNRMNNTf9+/e3qenTp49MnjxZRES2bdsmrVq1klOnTqnjX331lU1z89lnn0nXrl3FarWqNWazWZydnWXbtm3qcd3d3aWmpkatWbJkibi4uIjFYpHLly+LwWCQb7/91iZLfHy8vPDCCyLyd3OzY8cOdXzLli0CQC5duiQiIqGhofLaa6/Z7CMkJMSmuenSpYusWrXKpuatt96S0NBQEfm7uUlPT1fHCwoKBIAUFhaKiEhGRoa4ubn9c3rr+fPPP6VDhw4ye/ZsddvMmTPF19dXbTga8sUXX4inp6f6fNmyZQJADh8+bFP3z+bmn86cOWOT+0pzM3/+fLXGbDaLl5eXpKWliUj95iYmJqbenO7evVvs7e3V5pVIj3haiqgZ69Wrl81zLy8vnD17FgBQWFgIHx8feHt7q+OhoaE29YcOHUJRURGMRiNcXFzg4uICd3d3XL58GcXFxWpdYGAgDAaDzX6qq6tRWlqKoqIiXLx4EY8++qi6DxcXF3z66ac2+/hnXi8vLwCwyRsSEmJTf3XempoaFBcXIz4+3uY4c+bMuaHjNJa9vT1iYmKQmZkJEYHVasWKFSsQFxcHO7u/f3Vu374dDz/8MLy9veHi4oK4uDiUl5fDbDarNc7Ozujevft1j/fLL78gOjoafn5+MBqNuO+++wAAJ0+evOacODg4ICgoCIWFhQ3u89ChQ0hPT7eZr6ioKFgsFpw4ceKG5oOoOWmldQAiunl33XWXzXNFUWC1Whv9+urqagQFBWHlypX1xtq1a9fofQB/XTPSoUMHmzFHR8dr5lUUBQAanffKcZYtW1avCbK3t79tx7nayy+/jJSUFOzatQtWqxWlpaWIi4tTx4uLizFkyBAkJiYiJSUFbdq0QW5uLl555RXU1dWp7//qxvBaoqKi4O/vj08++QReXl6oq6tDYGCgzbVNN6q6uhoJCQl47bXX6o35+vre9H6J7nRsboh0KiAgAKWlpThz5oy6epGXl2dT07t3b6xZswYeHh5wdXW95r4OHTqES5cuwdnZWd2Pi4sLfHx84O7uDkdHR5w8eRIRERG3lPe7777DyJEj1W1X5/X09IS3tzeOHz+O4cOH3/RxHBwcYLFYGlXbpUsXREREYPny5RARDBo0CJ06dVLHDxw4AEVRkJaWpm5btWrVDWcqLy9HUVERPv30U3VlJicnp8HavLw8hIWFAQDq6uqQn5+PiRMnNljbu3dvFBQUqKtARC0FmxsinRo0aBDuv/9+xMTEIDU1FRcuXMD06dNtaoYPH47U1FQMHToU//vf/9CxY0ecOHECWVlZmDRpEjp27AgAqK2tRXx8PGbMmIGSkhLMnj0biYmJsLOzg9FoxBtvvIEJEybAarWif//+qKysxDfffANXV1fExMQ0Ku/48eMRGxuL4OBghIeHY+XKlSgoKEDnzp3VmjfffBPjxo2Dm5sbBg8eDLPZjAMHDuCPP/5AUlJSo45z7733orq6Gjt37lRPt11vZSU+Ph6jR48G8Nc9cq523333wWw2Y/HixXjiiSfw9ddf4+OPP25Ujqu1bdsWbdq0wdKlS+Hh4YGSkhJMnjy5wdqFCxeic+fO6Nq1K9LS0lBdXY3Y2NgGa6dOnYp+/fph3LhxiI+Ph8FgQEFBAXbt2nXL9+khupPxmhsinbKzs8P69etx6dIl9O3bF6NGjcLcuXNtagwGA/bs2QNfX188/fTTCAgIUD+CffVKziOPPAJ/f38MGDAA0dHRePLJJ20+Qv3WW29h5syZSElJQUBAAAYPHowtW7bAz8+v0Xmjo6Mxc+ZMTJo0CUFBQThx4gReffVVm5pRo0YhPT0dGRkZ6NmzJyIiIpCZmXlDxwkLC8OYMWMQHR2Ndu3a4Z133rlu/TPPPANHR0cYDIZ6N1EMCgpCamoq5s6dix49emDNmjVISUlpdJYrWrVqhdWrV+O7775D9+7dMXHiRKSmpjZYO2/ePLz99tswmUzIy8vDpk2b1I+l/5PJZEJubi4KCwsRHh6O3r17Izk5ud7pQyK9UUREtA5BRHeu2NhYnD9/vtl8ZQMREVduiIiISFfY3BAREZGu8LQUERER6QpXboiIiEhX2NwQERGRrrC5ISIiIl1hc0NERES6wuaGiIiIdIXNDREREekKmxsiIiLSFTY3REREpCv/B64arO7389dIAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"Y = 1.0 / (1.0 + np.exp(-X))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"The formula for the logistic function is the following:\n",
"\n",
"$$ \\hat{Y} = \\frac1{1+e^{-\\beta_1(X-\\beta_2)}}$$\n",
"\n",
"$\\beta_1$: Controls the curve's steepness,\n",
"\n",
"$\\beta_2$: Slides the curve on the x-axis.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building The Model ###\n",
"Now, let's build our regression model and initialize its parameters. \n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def sigmoid(x, Beta_1, Beta_2):\n",
" y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))\n",
" return y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets look at a sample sigmoid line that might fit with the data:\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7310825dde10>]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGsCAYAAAAPJKchAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAAgAElEQVR4nOzdd3hUZfrG8e9kQhJaQgmENAi9CITQAiIruCiWRTCiCEoV1F0LyLqrrAqyFlzbwk9xVUQQkaIY2SKCiqKg1EAoKjVACklIgHTSZs7vj5FgJIEEkpzMzP25rrnYnDln5gmsmTvved/ntRiGYSAiIiJiEg+zCxARERH3pjAiIiIiplIYEREREVMpjIiIiIipFEZERETEVAojIiIiYiqFERERETGVwoiIiIiYSmFERERETKUwIiIiIqZyqjDy3XffMWzYMIKCgrBYLKxevbpS1+fn5zNhwgS6deuGp6cnI0aMuOCcTZs2MWDAAJo2bUrdunXp1KkT//znP6vqWxAREZHf8DS7gMrIzc0lPDycSZMmERUVVenrbTYbdevW5ZFHHuGTTz4p85z69evz0EMP0b17d+rXr8+mTZu4//77qV+/Pvfdd9+VfgsiIiLyGxZn3SjPYrHw6aeflhrdKCgo4Mknn2T58uVkZGTQtWtX/vGPfzBo0KALrp8wYQIZGRkVGl2Jioqifv36fPDBB1X5LYiIiAhOdpvmUh566CE2b97MihUr2LNnD3fccQc33ngjhw4duuzX3LVrFz/88APXXnttFVYqIiIi5zjVbZqLiY+PZ9GiRcTHxxMUFATAY489xtq1a1m0aBEvvPBCpV4vJCSEtLQ0iouLeeaZZ5g8eXJ1lC0iIuL2XCaM7N27F5vNRocOHUodLygooGnTppV+vY0bN5KTk8OWLVt44oknaNeuHaNHj66qckVEROQXLhNGcnJysFqtxMTEYLVaSz3XoEGDSr9e69atAejWrRupqak888wzCiMiIiLVwGXCSEREBDabjZMnTzJw4MAqfW273U5BQUGVvqaIiIg4OFUYycnJ4fDhwyVfHz16lNjYWJo0aUKHDh24++67GTduHK+++ioRERGkpaWxfv16unfvzi233ALATz/9RGFhIadPnyY7O5vY2FgAevToAcD8+fNp2bIlnTp1Ahy9TV555RUeeeSRGv5uRURE3INTLe3dsGEDgwcPvuD4+PHjWbx4MUVFRTz33HMsWbKEpKQk/P396devH7Nnz6Zbt24AhIWFcfz48Qte49xfw+uvv87bb7/N0aNH8fT0pG3btkyZMoX7778fDw+XWnwkIiJSKzhVGBERERHXo1/1RURExFQKIyIiImIqp5jAarfbOXHiBA0bNsRisZhdjoiIiFSAYRhkZ2cTFBR00XmXThFGTpw4QWhoqNlliIiIyGVISEggJCSk3OedIow0bNgQcHwzvr6+JlcjIiIiFZGVlUVoaGjJ53h5nCKMnLs14+vrqzAiIiLiZC41xUITWEVERMRUCiMiIiJiKoURERERMVWlw8h3333HsGHDCAoKwmKxsHr16gpf+/333+Pp6VmyD4yIiIhIpcNIbm4u4eHhzJ8/v1LXZWRkMG7cOH7/+99X9i1FRETEhVV6Nc1NN93ETTfdVOk3euCBBxgzZgxWq7VSoykiIiLi2mpkzsiiRYuIi4tj1qxZFTq/oKCArKysUg8RERFxTdUeRg4dOsQTTzzB0qVL8fSs2EDMnDlz8PPzK3mo+6qIiIjrqtYwYrPZGDNmDLNnz6ZDhw4Vvm7GjBlkZmaWPBISEqqxShERETFTtXZgzc7OZseOHezatYuHHnoIcGx6ZxgGnp6efPHFF1x33XUXXOft7Y23t3d1liYiIiK1RLWGEV9fX/bu3Vvq2JtvvsnXX3/NqlWraN26dXW+vYiIiDiBSoeRnJwcDh8+XPL10aNHiY2NpUmTJrRs2ZIZM2aQlJTEkiVL8PDwoGvXrqWub968OT4+PhccFxEREfdU6TkjO3bsICIigoiICACmT59OREQEM2fOBCA5OZn4+PiqrVJERESqXGZeESu2xXPfkh0U2eym1WExDMMw7d0rKCsrCz8/PzIzM7Vrr4iIyBU4W2jjq59T+XfsCb49eJIimyMGLJrYh8Edm1fpe1X087ta54yIiIiI+YpsdjYeSuM/sSf44qdU8gptJc91atGQW3sE0SXQvF/2FUZERERckGEYxCZksComkTV7kzmTV1TyXGiTugwPD+bWHkF0CGhoYpUOCiMiIiIuJC27gE93JfLxjkQOncwpOe7fwJs/dA9keI8geoQ2wmKxmFhlaQojIiIiTq7IZufr/Sf5eEci3xw4ic3umAfiU8eDm7oGEtUzmP5tmuJprZFdYCpNYURERMRJHT6Zw4pt8Xy6K4lTuYUlxyNaNuKOXqH8ITwQX586JlZYMQojIiIiTqTIZueLH1NZuuU4m+NOlRxv1tCbqIhg7ugdQrvm5s8DqQyFERERESeQnHmW5VvjWbE9gZPZBQB4WOC6TgGM7hvKtR2a1drbMJeiMCIiIlJL2e0Gmw6ns3TLcb76OZVfpoLg38Cb0X1DuatvS4Ib1TW3yCqgMCIiIlLLnC208cnORN7bdJS49NyS4/3aNOGefq24oUsLvDydcxSkLAojIiIitURqVj5LNh/jw63xZPzSF6Shtye39wrh7siWtK8FPUGqg8KIiIiIyX48kcnCTUf57+4TJe3ZWzapx6QBYYzsHUoDb9f+uHbt705ERKSWMgyDbw6c5N2NR/nhyPlVMX3CGnPvNW24vksAVo/a05isOimMiIiI1CCb3WDN3mTmf3OY/SnZAFg9LNzcLZB7r2lNj9BGJldY8xRGREREakCRzc6nu5J4a8ORkkmp9b2sjIlsyYQBrV1iVczlUhgRERGpRvlFNj7akcDb38aRlHEWgEb16jDx6taMv7oVjep5mVyh+RRGREREqkFuQTFLtxxnwcajpOc4mpQ1a+jNlIGtGRPZyuUnpVaG/iZERESqUH6RjaVbjvOvDUdK9osJblSXB65twx29Q/GpYzW5wtpHYURERKQKFBbbWbkjgTe+PkRqlmMkJKxpPR4c3I4REcHUcdJW7TVBYUREROQKFP8yMXXe+kMknnHMCQluVJepv29PVM9gp90vpiYpjIiIiFwGu93gf3uTmfvlwZLVMc0aevPwde0Y1ScUb0/djqkohREREZFK2nQonefX/MzPyVkANK5Xhz8OasvYfmHU9VIIqSyFERERkQo6mJrNC2t+ZsOBNMCxb8yU37Vh4oAwGvrUMbk656UwIiIicgkns/P555eHWLk9HrsBnh4WxvZvxSPXtadxffUJuVIKIyIiIuU4W2jj3Y1xvPXtEXILbQDceFULHr+pE63965tcnetQGBEREfkNu90gelcSr6w7QEpWPgDhoY146pbO9AlrYnJ1rkdhRERE5Ff2JGbw9L9/ZHdCBuBYpvv4TZ0Y1j0Qi8U9dtGtaQojIiIiwOncQl5et58V2xMwDGjg7cnD17Vj/NVh6ppazRRGRETErdnsBsu2xfPKugNkni0CICoimCdu6kRzXx+Tq3MPCiMiIuK2Yo6f5unVP/LTL/1COrVoyLMjumpeSA1TGBEREbeTll3Ai5/v55OdiQD4+njy2NCOjOnbUu3bTaAwIiIibsMwDD7ekcjza34uuSUzqncof7mxI/4NvE2uzn0pjIiIiFs4mp7L36L3sjnuFABXBfny3IiuRLRsbHJlojAiIiIurchm553v4pi3/hCFxXZ86ngw/foOTBrQWrdkagmFERERcVm74s8wI3ov+1OyARjY3p/nR3SjZdN6Jlcmv6YwIiIiLienoJhX1h3g/c3HMAzHrrpP/6ELt0UEq3FZLaQwIiIiLuWHw+n8ZdUekjLOAnBbRDBP3dKZppqgWmspjIiIiEvIKyzmH5/v5/3NxwEIaVyX52/rxrUdmplcmVyKwoiIiDi9HcdO89jHuzl2Kg+AuyNb8rebO1PfWx9zzqDS04i/++47hg0bRlBQEBaLhdWrV1/0/OjoaK6//nqaNWuGr68v/fv3Z926dZddsIiIyDn5RTZeWPMzd7y9mWOn8gj082HJpL48f1s3BREnUukwkpubS3h4OPPnz6/Q+d999x3XX389a9asISYmhsGDBzNs2DB27dpV6WJFRETO2ZOYwR9e38Q738VhGDCyVwhrp/2O3+m2jNOxGIZhXPbFFguffvopI0aMqNR1V111FaNGjWLmzJkVOj8rKws/Pz8yMzPx9fW9nFJFRMRFFNnsvL7+EPM3HMFmN/Bv4M2cqG5c3yXA7NLkNyr6+V3jY1h2u53s7GyaNCl/E6KCggIKCgpKvs7KyqqJ0kREpJY7lp7L1BW72J2YCcAfugfy7PCuNK7vZXJlciVqPIy88sor5OTkcOedd5Z7zpw5c5g9e3YNViUiIrWZYRhE70xi5r/3kVtow9fHkxeiuvGH7kFmlyZVoEb74C5btozZs2fz0Ucf0bx583LPmzFjBpmZmSWPhISEGqxSRERqk6z8IqauiOXPH+8mt9BG39ZNWDvtdwoiLqTGRkZWrFjB5MmT+fjjjxkyZMhFz/X29sbbW81pRETcXczxM0xdsYvEM2exelh4dEh7/jioHVYPdVF1JTUSRpYvX86kSZNYsWIFt9xyS028pYiIODGb3WD+N4eZt/4QNrtBSOO6zLsrgl6ttMOuK6p0GMnJyeHw4cMlXx89epTY2FiaNGlCy5YtmTFjBklJSSxZsgRw3JoZP3488+bNIzIykpSUFADq1q2Ln59fFX0bIiLiKk5knGXaili2HTsNwPAeQTw7oiu+PnVMrkyqS6WX9m7YsIHBgwdfcHz8+PEsXryYCRMmcOzYMTZs2ADAoEGD+Pbbb8s9vyK0tFdExD18c+Akj66MJSOviPpeVp4d0ZWoniFmlyWXqaKf31fUZ6SmKIyIiLg2m93gn18e5I1vHCPv3YL9eGNMBK2a1je5MrkStbbPiIiIyK+dzM5n6vJYNsedAmBsv1Y89YfOeHtaTa5MaorCiIiImGZL3CkeXr6LtOwC6nlZmRPVjeE9gs0uS2qYwoiIiNQ4u93g7e/ieHndfuwGtG/egH/d05N2zRuaXZqYQGFERERqVEZeIX/+aDfr958EICoimOdu60o9L30kuSv9y4uISI356UQW932wg8QzZ/Hy9GD2rVdxV59QLBY1MXNnCiMiIlIj/rP7BH9dtZv8Ijstm9Tjzbt70jVY/aZEYURERKqZzW7w0rr9vP1tHAC/69CM1++KwK+empiJg8KIiIhUm8y8Ih5esYvvDqYB8MC1bfnL0I7aW0ZKURgREZFqcSAlm/s+2MHxU3n41PHgpZHh3BqunXblQgojIiJS5dbuS2b6R7vJK7QR0rgu74ztTZcgddCWsimMiIhIlbHbDf751UFe/9rR1v3qtk15Y0xPmtT3Mrkyqc0URkREpErkFRYzbUUsX/yUCsC917Rmxk2d8LR6mFyZ1HYKIyIicsVSMvOZvGQ7+5Ky8LJ6MCeqG7f30m67UjEKIyIickX2JWVy7/vbSc0qoGl9L94e24veYU3MLkuciMKIiIhctnU/pjBtRSxni2y0b96A9yb0IbRJPbPLEiejMCIiIpVmGAbvfBfHi2v3YxgwsL0/8+/uia+PGplJ5SmMiIhIpRQW23lq9V4+2pEIwNh+rZg1rIsmqsplUxgREZEKy8gr5IGlMWyJO42HBWb+oQsTBrQ2uyxxcgojIiJSIQmn8xi/aBtxabk08Pbk9TERDO7Y3OyyxAUojIiIyCXtS8pkwqLtpOcUEOTnw6KJfenYoqHZZYmLUBgREZGL2nDgJH/6cCd5hTY6B/qyeGIfAnx9zC5LXIjCiIiIlOujHQnMiN6LzW5wTTt//nVPTxpqxYxUMYURERG5gGEY/N/6w/zzq4MAREUE8+Lt3fHy1IoZqXoKIyIiUkqxzc7T/97H8m0JAPxpUFv+MrQjFovF5MrEVSmMiIhIibzCYh5atouv95/EwwKzh3dlbL9WZpclLk5hREREADidW8jERdvYnZiJTx0PXh/dk+u7BJhdlrgBhREREeFExlnuWbiVuLRcGterw8IJfejZsrHZZYmbUBgREXFzh0/mMG7hVk5k5hPk58MHkyNp26yB2WWJG1EYERFxY3sSM5iwaDuncwtp26w+H9wbSVCjumaXJW5GYURExE39cDidKUt2kFtoIzzEj0UT+9KkvpfZZUlNstlg40ZITobAQBg4EKzWGi9DYURExA2t3ZfCI8t3UWizM6BdU94e25sG3vpIcCvR0TB1KiQmnj8WEgLz5kFUVI2Wou41IiJu5qPtCfzpwxgKbXZuvKoF703ooyDibqKjYeTI0kEEICnJcTw6ukbLURgREXEjb397hL9+sge7AaN6hzL/7p54e9b8sLyYyGZzjIgYxoXPnTs2bZrjvBqiMCIi4gYMw+DldfuZ8/l+AO6/tg0v3t4Nq4e6qrqdjRsvHBH5NcOAhATHeTVE43IiIi7OMAz+/r+fWPT9MQAev7ETfxzU1tyixDzJyVV7XhVQGBERcWF2u8GTq/exfFs8AM8Ov4qx/cPMLUrMFRhYtedVAd2mERFxUcU2O499vJvl2+LxsMBLI7sriIhj+W5ICJS38aHFAqGhjvNqiMKIiIgLKiy288iKXUTvSsLqYWHuXRHc2TvU7LKkNrBaHct34cJAcu7ruXNrtN9IpcPId999x7BhwwgKCsJisbB69epLXrNhwwZ69uyJt7c37dq1Y/HixZdTq4iIVEB+kY0HlsawZm8KXlYP3ry7J7eGB5ldltQmUVGwahUEB5c+HhLiOF7b+4zk5uYSHh7O/PnzK3T+0aNHueWWWxg8eDCxsbFMmzaNyZMns27dukoXKyIiF5dXWMzk93fw9f6TeHt6sGB8b4Ze1cLssqQ2ioqCY8fgm29g2TLHn0eP1ngQAbAYRlkLjSt4scXCp59+yogRI8o95/HHH+ezzz5j3759JcfuuusuMjIyWLt2bYXeJysrCz8/PzIzM/H19b3cckVEXFp2fhGTFm9n+7Ez1POysnB8H/q3bWp2WeLGKvr5Xe1zRjZv3syQIUNKHRs6dCibN28u95qCggKysrJKPUREpHyZZ4u4Z+E2th87Q0MfTz64N1JBRJxGtYeRlJQUAgICSh0LCAggKyuLs2fPlnnNnDlz8PPzK3mEhmrSlYhIeTLzihi7cCu7EzJoVK8Oy6f0o1erxmaXJVJhtXI1zYwZM8jMzCx5JCQkmF2SiEitlJlXxD0Lt7InMZPG9eqwbHI/ugb7mV2WSKVUe9OzFi1akJqaWupYamoqvr6+1K1bt8xrvL298fb2ru7SREScWkZeIfcs3Mq+pCya1Pfiw8mRdA7UvDpxPtU+MtK/f3/Wr19f6tiXX35J//79q/utRURc1pncQsYscASRpvW9WD6ln4KIOK1Kh5GcnBxiY2OJjY0FHEt3Y2NjiY93tBqeMWMG48aNKzn/gQceIC4ujr/+9a/s37+fN998k48++ohHH320ir4FERH3cjq3kDHvbuWn5Cz8G3ix/L5+dGzR0OyyRC5bpcPIjh07iIiIICIiAoDp06cTERHBzJkzAUhOTi4JJgCtW7fms88+48svvyQ8PJxXX32Vd999l6FDh1bRtyAi4j5O5RQwZsEWfk7Owr+BN8un9KNDgIKIOLcr6jNSU9RnREQE0nMKuHvBVg6kZtOsoTfLp0TSrrmCiNReFf381q69IiJO4NSvgkjzht4sv68fbZs1MLsskSqhMCIiUsudyS3k7ncVROQy2GywcSMkJ0NgoGMn3hrcAK+iFEZERGqxc31E9qf8cmtGQUQqKjoapk6FxMTzx0JCHDv2mrD/zMXUyqZnIiICWflFjHtvKz+ecCzfXTY5UkFEKiY6GkaOLB1EAJKSHMejo82pqxwKIyIitVBOQTET3tvG7l86q344JZL2WjUjFWGzOUZEylqfcu7YtGmO82oJhRERkVomt6CYiYu2sTM+A7+6dVg6OZJOLbSSUCpo48YLR0R+zTAgIcFxXi2hMCIiUoucLbRx7/vbS3bfXXpvJFcFaa8ZqYTk5Ko9rwYojIiI1BL5RTamLNnBlrjTNPD2ZMmkvnQLURCRSgoMrNrzaoDCiIhILVBQbOP+D2LYdDidel5WFk/sQ0TLxmaXJc5o4EDHqhmLpeznLRYIDXWcV0sojIiImKzIZufBD3fx7cE0fOp48N6EPvQOa2J2WeKsrFbH8l24MJCc+3ru3FrVb0RhRETERDa7wfSPdvPVz6l4eXqwcHwf+rVpanZZ4uyiomDVKggOLn08JMRxvJb1GVHTMxERk9jtBjOi9/Df3SeoY7Xw1j09GdDO3+yyxFVERcHw4erAKiIiZTMMg7//7yc+2pGIhwXm3RXBdZ0CzC5LXI3VCoMGmV3FJek2jYhIDTMMg5fWHWDxD8cAeHlkODd3qz0rG0RqmsKIiEgNm//NYf614QgAz43oyu29QkyuSMRcCiMiIjVo4aajvPLFQQCevLkz9/RrZXJFIuZTGBERqSHLtsbz7P9+AuDRIR2Y8rs2JlckUjsojIiI1IDVu5J4cvVeAO7/XRse+X07kysSqT0URkREqtmXP6Xy5493Yxgwrn8rnripE5byumOKuCGFERGRavTD4XQeXLYTm90gqmcwzwy7SkFE5DcURkREqsmu+DNMXrKDwmI7N3QJ4KXbu+PhoSAi8lsKIyIi1eBASjYTFm0nr9DGNe38eX1MBJ5W/cgVKYv+yxARqWLHT+Vyz8KtZJ4tIqJlI94e2wtvz9rXgluktlAYERGpQimZ+dz97lbSsgvo1KIhiyb0ob63dt4QuRiFERGRKnI6t5B7Fm4l8cxZWjWtx5J7+9KonpfZZYnUegojIiJVIDu/iAmLtnH4ZA4tfH1Yem8kzRv6mF2WiFPQ2KGIyBXKL7Ix+f0d7EnMpEl9L5ZO7ktok3pmlyWuzmaDjRshORkCA2HgQMcuvU5IYURE5AoU2+w8tGwnW4+epoG3J+9P7Eu75g3NLktcXXQ0TJ0KiYnnj4WEwLx5EBVlXl2XSbdpREQuk91u8Pgne/nq55N4e3rw7vjedAvxM7sscXXR0TByZOkgApCU5DgeHW1OXVdAYURE5DIYhsHza37mk52JWD0svDGmJ/3aNDW7LHF1NptjRMQwLnzu3LFp0xznORGFERGRy/DmhiMs3HQUgJdu7871XQJMrkjcwsaNF46I/JphQEKC4zwnojAiIlJJH249zsvrDgDw1C2dub1XiMkVidtITq7a82oJhRERkUr4bE8yT63eB8CDg9syeWAbkysStxIYWLXn1RIKIyIiFbTxUBrTVu7CMGBMZEseu6Gj2SWJuxk40LFqprydny0WCA11nOdEFEZERCpgV/wZ7v8ghiKbwS3dAnl2eFcs5X0giFQXq9WxfBcuDCTnvp471+n6jSiMiIhcwqHUbCYuduzAO7C9P6+NCsfqoSAiJomKglWrIDi49PGQEMdxJ+wzoqZnIiIXkZRxlnHvbSMjr4jw0Ea8dY924JVaICoKhg9XB1YREVd3OreQcQu3kpyZT7vmDVisHXilNrFaYdAgs6uoEpd1m2b+/PmEhYXh4+NDZGQk27Ztu+j5c+fOpWPHjtStW5fQ0FAeffRR8vPzL6tgEZGakFtQzMTF2zmSlkugnw9LJvWlcX3twCtSHSodRlauXMn06dOZNWsWO3fuJDw8nKFDh3Ly5Mkyz1+2bBlPPPEEs2bN4ueff2bhwoWsXLmSv/3tb1dcvIhIdSgstvPA0hh2J2TQqF4dPri3L0GN6ppdlojLqnQYee2115gyZQoTJ06kS5cuvPXWW9SrV4/33nuvzPN/+OEHBgwYwJgxYwgLC+OGG25g9OjRlxxNERExg91u8OePd7PxUDp161hZNKGPNr4TqWaVCiOFhYXExMQwZMiQ8y/g4cGQIUPYvHlzmddcffXVxMTElISPuLg41qxZw80331zu+xQUFJCVlVXqISJS3QzDYPZ/f+S/u0/g6WHhrbG9iGjZ2OyyRFxepWZipaenY7PZCAgovQdDQEAA+/fvL/OaMWPGkJ6ezjXXXINhGBQXF/PAAw9c9DbNnDlzmD17dmVKExG5Ym98fZj3Nx8H4NU7w7m2QzOTKxJxD9XeZ2TDhg288MILvPnmm+zcuZPo6Gg+++wznn322XKvmTFjBpmZmSWPhISE6i5TRNzch1uP8+qXBwGYNawLw3sEX+IKEakqlRoZ8ff3x2q1kpqaWup4amoqLVq0KPOap59+mrFjxzJ58mQAunXrRm5uLvfddx9PPvkkHh4X5iFvb2+8vb0rU5qIyGX7fO/5/WYevq4dEwe0NrkiEfdSqZERLy8vevXqxfr160uO2e121q9fT//+/cu8Ji8v74LAYf2lKYthGJWtV0SkSv1wJJ2pK2IxDBjdtyXTr+9gdkkibqfS3XumT5/O+PHj6d27N3379mXu3Lnk5uYyceJEAMaNG0dwcDBz5swBYNiwYbz22mtEREQQGRnJ4cOHefrppxk2bFhJKBERMcO+pEzuWxJDoc3O0KsCeG6E9psRMUOlw8ioUaNIS0tj5syZpKSk0KNHD9auXVsyqTU+Pr7USMhTTz2FxWLhqaeeIikpiWbNmjFs2DCef/75qvsuREQq6fipXCYs2k5OQTH92jRh3l0R2m9GxCQWwwnulWRlZeHn50dmZia+vr5mlyMiTu5kdj4j/7WZ+NN5dA70ZeX9/fD1qWN2WSIup6Kf39q1V0TcSnZ+ERPe20786TxCm9Tl/Yl9FERETKYdn0TEbeQX2bhvSQw/JWfh38CLDyZF0tzXx+yyRMpms7nMrryXojAiIm7BZjd4dGUsm+NO0cDbk8UT+xLmX9/sskTKFh0NU6dCYuL5YyEhMG8eREWZV1c10W0aEXF5hmEw89/7+HxfCl5WD94Z24uuwX5mlyVStuhoGDmydBABSEpyHI+ONqeuaqQwIiIub976Q3y4NR6LBebe1YOr2/mbXZJI2Ww2x4hIWWtLzh2bNs1xngtRGBERl7Z0y3Hmfu4GWCwAACAASURBVHUIgL8P78rN3QJNrkjkIjZuvHBE5NcMAxISHOe5EIUREXFZa/Ym8/S/HW3eH/l9e8b2a2VyRSKXkJxctec5CYUREXFJPxxJZ9ovbd7HRLbk0SHtzS5J5NICKzhyV9HznITCiIi4nF+3eb+pawueHa427+IkBg50rJop7/+vFguEhjrOcyEKIyLiUn7b5v2fo3qozbs4D6vVsXwXLgwk576eO9fl+o0ojIiIy0jLLmDswm2k5xTQOdCXd8b1xqeOa/3QFjcQFQWrVkFwcOnjISGO4y7YZ0RNz0TEJWTnFzFh0TbiT+fRskk93p+kNu/ixKKiYPhwdWAVEXEW59q8/3jC0eZ9yaS+NG+oNu/i5KxWGDTI7CpqhG7TiIhTs9kNpn+kNu8izkxhRESclmEYzPrPPtbsVZt3EWemMCIiTmvuV4dYusXR5v2fo9TmXcRZKYyIiFNasvkY89afb/N+S3fXagIl4k4URkTE6fxvzwlm/edHAKYNUZt3EWenMCIiTmXToXQeXelo8z62Xyum/l5t3kWcncKIiDiN3QkZ3PfBDopsBrd0D+SZW69Sm3cRF6AwIiJO4UhaDhMXbyev0MY17fx57c5wtXkXcREKIyJS66Vk5jNu4TZO5xbSPcSPt8b2wtvTNTtRirgjhRERqdUy8goZ995WkjLO0sa/Posm9KGBt5pHi7gShRERqbXyCou59/0dHEzNIcDXm/cn9aVpA2+zyxKRKqYwIiK1UmGxnT8u3UnM8TP4+niyZFIkoU3qmV2WiFQDhRERqXXsdoPHPt7NtwfT8KnjwaKJfejYoqHZZYlINVEYEZFaxTAMnvnvj/xn9wk8PSy8dU8verVqYnZZIlKNFEZEpFaZ+9Uhlmw+jsUCr94ZzqCOzc0uSUSqmcKIiNQai78/en6/mVuvYniPYJMrEpGaoDAiIrXC6l1JPPPfnwCYfn0HxvYPM7cgEakxCiMiYrpv9p/ksY93AzDh6jAevq6dyRWJSE1SGBERU20/dpoHlsZQbDe4LSKYmX/oov1mRNyMwoiImOanE1lMWrydgmI713Vqzksju+Oh/WZE3I7CiIiY4mh6LuPe20p2fjF9whozf0xP6lj1I0nEHem/fBGpcScyznLPu1tJzynkqiBfFk7oQ10vbXwn4q4URkSkRqXnFHDPwvMb370/qS++PnXMLktETKQwIiI1Jiu/iPHvbSMuLZfgRnVZOjkSf218J+L2tA+3iNSIs4U27l28nR9PZOHfwIsP7u1LUKO6ZpclYh6bDTZuhORkCAyEgQPB6p63KxVGRKTaFRbbeWBpDNuPnaGhjyfvT+pLm2YNzC5LxDzR0TB1KiQmnj8WEgLz5kFUlHl1meSybtPMnz+fsLAwfHx8iIyMZNu2bRc9PyMjgwcffJDAwEC8vb3p0KEDa9asuayCRcS52OwGj34Uy7cH06hbx8qiCX24KsjP7LJEzBMdDSNHlg4iAElJjuPR0ebUZaJKh5GVK1cyffp0Zs2axc6dOwkPD2fo0KGcPHmyzPMLCwu5/vrrOXbsGKtWreLAgQMsWLCA4GDtOSHi6gzD4MlP9/LZnmTqWC28NbYXvcO0A6+4MZvNMSJiGBc+d+7YtGmO89yIxTDK+hspX2RkJH369OGNN94AwG63ExoaysMPP8wTTzxxwflvvfUWL7/8Mvv376dOncubMZ+VlYWfnx+ZmZn4+vpe1muISM0yDIMX1vzMgo1H8bDAG2N6cnO3QLPLEjHXhg0wePClz/vmGxg0qLqrqXYV/fyu1MhIYWEhMTExDBky5PwLeHgwZMgQNm/eXOY1//nPf+jfvz8PPvggAQEBdO3alRdeeAHbRVJfQUEBWVlZpR4i4lzmfnWIBRuPAvBiVHcFERFwTFatyvNcRKXCSHp6OjabjYCAgFLHAwICSElJKfOauLg4Vq1ahc1mY82aNTz99NO8+uqrPPfcc+W+z5w5c/Dz8yt5hIaGVqZMETHZ298eYd76QwA8M6wLd/bRf8MigGPVTFWe5yKqvc+I3W6nefPmvPPOO/Tq1YtRo0bx5JNP8tZbb5V7zYwZM8jMzCx5JCQkVHeZIlJFlmw+xpzP9wPw1xs7MmFAa3MLEqlNBg50rJopbzNIiwVCQx3nuZFKLe319/fHarWSmppa6nhqaiotWrQo85rAwEDq1KmD9Vdrpzt37kxKSgqFhYV4eXldcI23tzfe3mqEJOJsPt6RwMx//wjAQ4Pb8adB7UyuSKSWsVody3dHjnQEj19P2zwXUObOdbt+I5UaGfHy8qJXr16sX7++5Jjdbmf9+vX079+/zGsGDBjA4cOHsdvtJccOHjxIYGBgmUFERJzTf3ef4PFP9gAwaUBr/nxDB5MrEqmloqJg1Sr47arSkBDHcfUZubTp06ezYMEC3n//fX7++Wf++Mc/kpuby8SJEwEYN24cM2bMKDn/j3/8I6dPn2bq1KkcPHiQzz77jBdeeIEHH3yw6r4LETHVVz+l8ujKWOwGjO7bkqf/0BlLecPQIuIIHMeOOVbNLFvm+PPoUbcMInAZHVhHjRpFWloaM2fOJCUlhR49erB27dqSSa3x8fF4eJzPOKGhoaxbt45HH32U7t27ExwczNSpU3n88cer7rsQEdNsOpTOnz7cSbHdYESPIJ4b0VVBRKQirFaXWL5bFSrdZ8QM6jMiUjttP3aacQu3cbbIxo1XteCNMRF4WrX/pog4VEufERGRc2ITMpi4aDtni2wM6tiM/xutICIil0c/OUSk0vYmZjJ24VZyCorp16YJb93TCy9P/TgRkcujnx4iUik/nsjknoVbyc4vpm9YE96b0AefOu61DFFEqpbCiIhU2IGUbO55dyuZZ4vo2bIR703sQz2vSs+DFxEpRWFERCrk8Mls7n53C2fyiggP8WPxpL408FYQEZErpzAiIpcUl5bD6AVbSc8ppGuwL0smReLrc3m7cIuI/JbCiIhc1PFTuYxZsJW07AI6tWjIB5Mi8aunICIiVUdhRETKlXA6j9HvbCElK58OAQ34cHIkjetrGwcRqVoKIyJSpqSMs4xesIUTmfm0bVafDyf3o2kDbWApIlVPs89E5AIJp/MYvWALiWfO0tq/Psum9KNZQwUREakeCiMiUkrC6TzuemcLSRlnCWtaj2VTIgnw9TG7LBFxYQojIlIi/pRjRCQpwzEisnxKP1r4KYiIVJrNBhs3QnIyBAbCwIGOjfGkTAojIgI4Vs2MfscxR6SNf32W39dPIyIilyM6GqZOhcTE88dCQmDePIiKMq+uWkwTWEWEY+m53HUuiDSrzwoFEZHLEx0NI0eWDiIASUmO49HR5tRVyymMiLi5o78EkeRfVs2suK8fzRVERCrPZnOMiBjGhc+dOzZtmuM8KUVhRMSNxaXlcNc7m0nJyqd98wasuK8/zRsqiIhclo0bLxwR+TXDgIQEx3lSiuaMiLipI2k5jH5nCyezC35paKbluyJXJDm5as9zIwojIm7oQEo2d7+7lfScAjoGNOTDKZH4q6GZyJUJDKza89yIbtOIuJm9iZmMemcz6TkFdA70ZZmCiEjVGDjQsWrGYin7eYsFQkMd50kpCiMibiTm+GnGLNhCRl4R4aGNWDFFLd5FqozV6li+CxcGknNfz52rfiNlUBgRcRM/HEln7MJtZBcU0zesCUvv7avdd0WqWlQUrFoFwcGlj4eEOI6rz0iZNGdExA1sOHCS+z+IoaDYzsD2/rwztjd1vfTbmUi1iIqC4cPVgbUSFEZEXNzafSk8vHwnRTaDIZ2b88aYnvjU0Q9FkWpltcKgQWZX4TQURkRc2L9jk5j+0W5sdoNbugUy964e1LHq7qzIFdPeM1VKYUTERX20PYHHo/dgGBDVM5iXbu+Op4KIyJXT3jNVTj+ZRFzQuxvj+OsnjiByd2RLXhkZriAiUhW090y10E8nERdiGAYvrd3Pc5/9DMB9v2vDcyO64uFRTt8DEak47T1TbRRGRFyEzW7wt0/38eaGIwA8fmMn/nZzZyzlNWASkcrR3jPVRnNGRFxAQbGN6St389neZDws8Pxt3Rjdt6XZZYm4Fu09U20URkScXG5BMQ8sjWHjoXS8rB7MvasHN3fT3hciVU57z1Qb3aYRcWJncgu5+92tbDyUTj0vK+9N6KMgIlJdtPdMtVEYEXFSKZn53Pn2ZmITMmhUrw7LpvTjmvb+Zpcl4rq090y1URgRcUJxaTnc/q8fOHQyhxa+Pnx8f396hDYyuywR16e9Z6qF5oyIOJmY42eY/P52zuQV0dq/Ph/c25eQxvXMLkvEfWjvmSqnMCLiRNb9mMIjy3dRUGwnPMSPhRP64N/A2+yyRNyP9p6pUgojIk7ig83HmPWfH7Eb8PtOzXl9TAT1vPSfsIg4P/0kE6nl7HaDl9Yd4K1vHc3MRvdtybPDr1J7dxFxGQojIrVYYbGdv67azerYEwD8+foOPHRdO3VVFRGXclm/Ws2fP5+wsDB8fHyIjIxk27ZtFbpuxYoVWCwWRowYcTlvK+JWsvKLmLh4G6tjT+DpYeHlkd15+PftFURExOVUOoysXLmS6dOnM2vWLHbu3El4eDhDhw7l5MmTF73u2LFjPPbYYwxUMxiRS0rJzOfOtzbz/eFT1PeysnBCH+7oHWp2WSIi1aLSYeS1115jypQpTJw4kS5duvDWW29Rr1493nvvvXKvsdls3H333cyePZs2bdpcUcEirm5fUiYj5n/P/pRsmjX0ZuX9/bm2QzOzyxIRqTaVCiOFhYXExMQwZMiQ8y/g4cGQIUPYvHlzudf9/e9/p3nz5tx7770Vep+CggKysrJKPUTcwRc/pnDHW5tJycqnXfMGRP/xaroG+5ldlohItarUBNb09HRsNhsBAQGljgcEBLB///4yr9m0aRMLFy4kNja2wu8zZ84cZs+eXZnSRJyaYRgs2BjHnM/3YxgwsL0/b4zpiV/dOmaXJiJS7ap1bWB2djZjx45lwYIF+PtXfM+MGTNmkJmZWfJISEioxipFzFVYbOeJT/bywhpHELmnX0sWTeijICIibqNSIyP+/v5YrVZSU1NLHU9NTaVFixYXnH/kyBGOHTvGsGHDSo7Z7XbHG3t6cuDAAdq2bXvBdd7e3nh7q6ukuL6MvEIeWBrDlrjTeFhg5h+6MP7qMK2YERG3UqmRES8vL3r16sX69etLjtntdtavX0///v0vOL9Tp07s3buX2NjYksett97K4MGDiY2NJTRUqwPEfcWl5XDbmz+wJe60Y8XM+D5MGNBaQURE3E6lm55Nnz6d8ePH07t3b/r27cvcuXPJzc1l4sSJAIwbN47g4GDmzJmDj48PXbt2LXV9o0aOnUV/e1zEnWw+cooHlsaQebaI4EZ1WTihN51a+JpdloiIKSodRkaNGkVaWhozZ84kJSWFHj16sHbt2pJJrfHx8Xh4qE21SFkMw2DpluPM/u9PFNsNeoQ2YsG43jRrqNuSIuK+LIZhGGYXcSlZWVn4+fmRmZmJr69+exTnVFBsY+bqH1m5wzEhe1h4EC+P7I5PHW07LlLr2GywcSMkJ0NgIAwc6NipVyqlop/f2ptGpAakZuXzwNIYdsVn4GGBx2/sxH2/a6P5ISK1UXQ0TJ0KiYnnj4WEwLx5EBVlXl0uTGFEpJrFHD/DA0tjSMsuwNfHk9fH9FRHVZHaKjoaRo6E3940SEpyHF+1SoGkGmhyh0g1WrEtnrve2UxadgEdAxry34evURARqa1sNseISFmzF84dmzbNcZ5UKYURkWpQWGzn6dX7eCJ6L0U2gxuvakH0n66mVdP6ZpcmIuXZuLH0rZnfMgxISHCcJ1VKt2lEqtjJ7Hwe+nAX246dxmKBP1/fgQcHt9P8EJHaLjm5as+TClMYEalCW+JO8fDyXaRlF9DQ25N5o3twXaeAS18oIuYLDKza86TCFEZEqoDdbvCvb4/w6hcHsBvQMaAhb97Tk7bNGphdmohU1MCBjlUzSUllzxuxWBzPDxxY87W5OM0ZEblCGXmFTF6yg5fXOYLI7T1DWP3gAAUREWdjtTqW74IjePzaua/nzlW/kWqgMCJyBXYnZHDL/23i6/0n8fb04B+3d+OVO7pT10s/rEScUlSUY/lucHDp4yEhWtZbjXSbRuQyGIbBks3Hee6znyiyGYQ1rcebd/eiS5A6BIs4vagoGD5cHVhrkMKISCXlFBTzxCd7+N8ex4z6m7q24B8ju+PrU8fkykSkylitMGiQ2VW4DYURkUrYk5jB1BWxHE3PxdPDwoybOzNpQJiW7YqIXAGFEZEKsNsN3tkYxyvrDlBsNwjy8+H1MT3p1aqx2aWJiDg9hRGRS0jNymf6R7F8f/gUADd3a8Gc27rjV0+3ZUREqoLCiMhFfPlTKn9dtZszeUXUrWPlmVu7cGfvUN2WERGpQgojImXIL7Lx/Gc/88GW4wBcFeTL/42OUO8QEZFqoDAi8hv7U7J4ZPkuDqbmADBlYGseG9oRb08t6xMRqQ4KIyK/sNkNFm6K45UvDlJYbMe/gTev3hnOtR2amV2aiIhLUxgRAY6l5/LYx7vZcfwMAIM7NuPlO8Lxb+BtcmUiIq5PYUTcmt1u8MGW47z4+X7OFtlo4O3J03/orEmqIq7MZlN31VpGYUTcVuKZPP66ag8/HHEs2e3fpikv39GdkMb1TK5MRKpNdDRMnQqJieePhYQ4NsjTvjOmURgRt2MYBh/tSODZ//1MTkExPnU8mHFTZ8b2a4WHh0ZDRFxWdDSMHAmGUfp4UpLjuDbCM43FMH77r1L7ZGVl4efnR2ZmJr6+2ohMLl9KZj4zovfwzYE0AHq1aswrd4TT2r++yZWJSLWy2SAsrPSIyK9ZLI4RkqNHdcumClX081sjI+IW7HaDD7ce5x9rD5BTUIyXpweP3dCBe69pg1WjISKub+PG8oMIOEZLEhIc52mDvBqnMCIu72BqNjOi9xLzy0qZHqGNeGlkdzoENDS5MhGpMcnJVXueVCmFEXFZBcU25n99mH99e4Qim0F9Lyt/vbET9/RrpdEQEXcTGFi150mVUhgRl7Tt6GmeiN5DXFouAEM6N+fvw7sS1KiuyZWJiCkGDnTMCUlKunACK5yfMzJwYM3XJgoj4loyzxbx4uf7Wb4tHoBmDb2ZfetV3NS1hfqGiLgzq9WxfHfkSEfw+HUgOfezYe5cTV41iYfZBYhUBbvdYFVMIr9/dUNJEBndN5SvHr2Wm7sFKoiIiGPZ7qpVEBxc+nhIiJb1mkwjI+L09iVlMus/P5ZMUG3TrD4v3NaNfm2amlyZiNQ6UVEwfLg6sNYyCiPitDLyCnnliwMs2xqP3YB6XlYe+X17Jg1ojZenBv1E3Nal2r1brVq+W8sojIjTsdkdHVRfWrufM3lFANwaHsTfbu5MCz8fk6sTEVOp3btTUhgRpxKbkMHMf+9jT2ImAB0DGvLMrVfRv61uyYi4PbV7d1pqBy9OIfFMHq+sO8Dq2BMANPT25NHrOzC2fyvqWHVLRsTtqd17raR28OISsvKLePObI7z3/VEKi+0A3N4zhMdv6kjzhrolIyK/ULt3p6YwIrVSkc3O8m3xzP3qEKdzCwHo16YJT93Sha7BfiZXJyK1jtq9OzWFEalVDMPgy59SefHz/cSlO7qntm1Wn7/d3JnrOjVXvxARKZvavTs1hRGpNXbFn+HFz/ez9ehpAJrW92La9R0Y3ScUT80LEZGLUbt3p3ZZP+Hnz59PWFgYPj4+REZGsm3btnLPXbBgAQMHDqRx48Y0btyYIUOGXPR8cT8/nsjk3sXbue3NH9h69DTenh48OLgtG/4yiLH9WimIiEhpNhts2ADLlzv+tNnOt3uH8+3dz1G791qv0j/lV65cyfTp05k1axY7d+4kPDycoUOHcvLkyTLP37BhA6NHj+abb75h8+bNhIaGcsMNN5CUlHTFxYtzO3wymwc/3Mkt/7eJ9ftP4mGBO3qF8PVjg/jL0E409KljdokiUttERztWzQweDGPGOP4MC3McV7t3p1Xppb2RkZH06dOHN954AwC73U5oaCgPP/wwTzzxxCWvt9lsNG7cmDfeeINx48ZV6D21tNe1xJ/KY+76g6zelYTdcPzSMqx7ENOGtKdNswZmlycitVV5fUTOjXycCxyX6sAqNaZalvYWFhYSExPDjBkzSo55eHgwZMgQNm/eXKHXyMvLo6ioiCZNmpR7TkFBAQUFBSVfZ2VlVaZMqaVOZJzl9a8P8/GOBIrtjh8mN3QJYPoNHejUQiFTRC7CZnN0Vi3r92fjl99qpk1z7Dujdu9Op1JhJD09HZvNRkBAQKnjAQEB7N+/v0Kv8fjjjxMUFMSQIUPKPWfOnDnMnj27MqVJLXb8VC7/2nCET3YmUmRz/CD5XYdm/Pn6DoSHNjK5OhFxCuoj4tJqdDXNiy++yIoVK9iwYQM+PuU3rJoxYwbTp08v+TorK4vQ0NCaKFGq0MHUbOZ/c5j/7j7BLwMhRLZuwp9v6Ejf1uWPjImIXEB9RFxapcKIv78/VquV1NTUUsdTU1Np0aLFRa995ZVXePHFF/nqq6/o3r37Rc/19vbG29u7MqVJLbInMYM3vj7MFz+d///JoI7NeGhwO3qHKYSIyGVQHxGXVqkw4uXlRa9evVi/fj0jRowAHBNY169fz0MPPVTudS+99BLPP/8869ato3fv3ldWsdRKhmGw7ehp3vjmMBsPpQOOW7g3XtWCBwe3U9dUEamY8iafqo+IS6v0bZrp06czfvx4evfuTd++fZk7dy65ublMnDgRgHHjxhEcHMycOXMA+Mc//sHMmTNZtmwZYWFhpKSkANCgQQMaNNDKCWdXZLPz+b4UFm6MY/cvO+laPSwMDw/iT4Pb0q55Q5MrFBGnER3tmKT667khISGO/iFRUY4/R450BI9fBxL1EXF6lQ4jo0aNIi0tjZkzZ5KSkkKPHj1Yu3ZtyaTW+Ph4PDzOty/517/+RWFhISNHjiz1OrNmzeKZZ565surFNJlni1i5PZ7F3x/jRGY+AF6eHozsFcIDv2tLy6b1TK5QRJxKect2k5Icx88t2121quzAMneu+og4sUr3GTGD+ozUHvGn8njv+6N8vCOB3EIbAP4NvBjbL4y7+7XEv4Hm+ohIJdlsjsZl5a2WOXcL5uhRx8iH+og4jWrpMyLuyTAMth49zeLvj/HFTyklK2M6BjTk3oGtuTU8CJ86+kEgIpepsst21UfE5SiMSLmy8ouIjknkw63xHDqZU3L82g7NmDywNde089cuuiJSOWWNamjZrttTGJEL7EvK5MOtx1m96wRnixy3Yup5WRneI5iJA8LoEKBJqSJyGcqboDplSsWu17Jdl6U5IwJAfpGNNXuT+WDLcXbFZ5Qc7xDQgHv6teK2iGBtXCcil+9i+8oYBjRtCqdPX3zZ7rk5I+I0NGdELskwDPYlZfFxTAL/jj1B5tkiAOpYLdzYNZB7IlvSt3UT3YoRkYor6zYMXHpfmXO0bNctKYy4oVM5BXy6K4lVMYnsT8kuOR7cqC5jIltyZ+9QmjXUqhgRqaSL3Ya51ATVU6dg9mxYsEDLdt2QwoibKLbZ2XAgjY9jElj/88mSXXO9PD0YelUL7uwdwtVt/bF6aBRERC7DxfqEzJpVsddo3x6OHdOyXTekMOLCDMMgNiGD/+w+wX93J5OeU1DyXHiIHyN7h3Jr9yD86mkuiIhUQHn9PWy2i9+GqajAQC3bdVMKIy7oUGo2/449wX92nyD+dF7J8ab1vbgtIpg7eofSsYVWxIhIJVysVXuTJhe/DXMp2lfG7SmMuIjEM3n8d3cy/45NKjUPpJ6Xleu7BDC8RxAD2zejjtXjIq8iIlKGS7Vqnzq14q+lCapSBoURJ3b8VC5r96Xw+b4UYhPOL8etY7VwbYfm3NojiCGdm1PPS//MIlIBl7sS5sMPK/b6mqAq5dCnlBMxDIODqTms3ZfC2h9T+Dk5q+Q5iwX6tW7K8B5B3Ni1BY3qeZlYqYjUShfb0+VKVsKkpUGzZpCefvE+IU8+6Xhogqr8hsJILWe3G+xJymTdjyms25dCXHpuyXNWDwv92zRlaNcWDO0SQHNfHxMrFZFa7WJzPuDKV8LcfbfjtSpyG0YTVOU3FEZqoez8IjYdSufr/Sf55sBJ0nMKS57zsnowsL0/N3ZtwZDOATSurxEQEeHSox7lhY3bb3d0P73SlTDDhzves6zAo9swcglqB19LHEvP5ev9J/l6/0m2Hj1Fke38P0sDb0+u7dCMoV1bMLhjM7VlF5HSLjbqMXw4hIVd2WqXi/ltq/aLhSJxO2oHX8vlFhSzJe4UGw+l892hNOLScks9H9a0Hr/vHMB1nZrTJ6wJXp5aBSMiZbjUSpdnnqm6IFKRWzDqEyKXQWGkhtjsBnuTMtl0KI3vDqWzK/5MqdEPTw8LfVs34bpOzbmuU3PaNGtgYrUiUutc7kqXc3NCrpRWwkg1UhipJoZhcCQthy1xp/nhSDrfHz5VshHdOaFN6jKwfTMGtvNnQHt/fHX7RUTKciUrXU6fvrL31koYqQEKI1XEMAwOn8xhS9wptsSdZuvRU6UmngI09PHk6rZNHQGkvT+tmtY3qVoRcRpVsedLkyZw5kz5y26bNDkfWrQSRkygMHKZim129qdks+PYabYdO83WuNOcyi0dPrw9PejZsjH92jTlmvb+hIf44akOqCJSlsu5DVNRU6c65o6UN+fjnXfOn6fbMGIChZEKyswrYmfCGXYeP8OOY2eITcjgbJGt1Dk+dTzo1aox/Vo3JbJNU8JD/fD21BCmiFzC5d6GuZRf32Lp2vXSYWP4cN2GEVNoaW8Zim12DqbmsCcxg92JGcQcP8PB1JwLzmvo40nPlo3p3aox/ds2pXtII616EZHKKe82zG9HMS6lvFGPVavOhw0tu5UapqW9KqslPQAAEipJREFUFWQYBsdP5bE7MYPdCZnsScxg34lM8ovsF5wb1rQevVo1oVerxvRq1Zj2zRvg4WExoWoRcQk2W9XchqnoShctu5Vayq3DyIMf7mTT4fQLVrkANPT2pFuIH91DGtGzZSN6tmqMfwNvE6oUEadX3ojExo1VdxtGK13Eibl1GMk4W0jm2SK8PD3oEuhLj9BGdP8lgLTxr69RDxG5chfrjlpQUPHX0Z4v4sLcOow8dkNHZtzkQYeAhprrISJVryLdUStCDcfExWkCq4jIxVRk0md5y3IvtieMxQLBwY7/nZRUfg+Qc/u+gG7DiNPRBFYRkYq41G635d1iOTcicSXdURMTHaMeF+sBotsw4gY0MiIizutyRy0qEjag/CW34Fgye7FzKvqjddky8Pa+sI7QUN2GEadX0c9vhRERuTyXCgJV0dOiukYtLhU2DAOaNoVTp8qu69e3WK50R9xvvnGMeKgHiLgghRERuTJXEgQqEhSu5D3gykctLhY2asKv54ModIiLUhgRkfJd6rfwKwkCjz0Gr7xy8aBwqcBysfeoyVGLqlKR7qgiLkhhRKQ6VPeth4q+x5W8RkVGNa5kRMFqdbx/Wc6NBrz2Gtx5Z+0dtahKZS3L1XwQcRMV/vw2nEBmZqYBGJmZmWaXImYqLjaMb74xjGXLHH8WF1fu+St9jU8+MYyQEMNwfFw6HiEhjuNV9RoVeY8reY1PPjEMi6X0c+A4ZrEYxkcfXXhtdTyaNav+96jOh8Xi+HsKCSn77/PcOaGhjn//ivx/U8QFVfTzW2FEqsaVBoVLPV/bP8Sr4jX+8pdLv8eVvAYYRtOmF/+AdfaQUJVho2nT83+vl/r3uNg5Im5MYeRSqvu3aHd6jysNChV5vrZ/iIeGGsbH/9/e3QdFVb1xAP/u4rK44ILoshuyUI5GJiliQUv5Ujmow2hKMzCOI6ZmVDCNWWY2pPRPmL1Qk5TWaFYzDEKFZSYOBb5v+BIUqCGihikvlfISKG/7/P5w9v68AnKVu3th9/nM3D8493jOnsdz9z733Lu7uXfeBkDk4XHrPuxX4nfahrtsUlctpCYbN8fcbO47yb25DmNuipORW3H0VbQ79dHfRKGv/VJuGwyUkzivKvw/lrdKAvobJzlXLaQkEnIk/Iy5KU5GeiNlud3RJ1hX6aO/iUJf+/m2gTKbwdC/FQX7vOltv33eDJRVC04kGHMYhyYjGzdupJCQENJqtRQZGUnFxcW3rJ+Tk0OhoaGk1WopLCyMdu3adVv9yZaMdHbe+uQp11W0M67UB0IfnCi41nbz7ab+JAJS9vOqBWMuz2HJSHZ2Nnl6etLWrVvpxIkTtHz5cvLz86O6uroe6x86dIg8PDxow4YNdPLkSUpNTSWNRkNlZWWS+5QtGSkqUv4NnzfX2+RKzPq6vdHXcxBS2pCy4kAkTyJwJ88a8aoFYy7FYclIZGQkJScnC393dXVRYGAgpaen91g/Pj6eYmNjRWVRUVGUlJQkuU/ZkpGsLOVPXLzd/nar2wbAwDiJy3Hroa/bG1Keg5DahpQHLp2RCHCywZhLc0gy0tbWRh4eHpSXlycqT0xMpLlz5/b4b8xmM2VkZIjK1q5dSxMmTOi1n2vXrlFjY6OwXbhwQdJg+sQrI/Jv/UkUpCQBUm4bDJSTuBy3HuR4DoJXHBhjA4RDkpGLFy8SADp8+LCofNWqVRQZGdnjv9FoNJSVlSUqy8zMpICAgF77WbduHQHotsn2zIgjr6KlnGBdpQ85EgUpSQDR4DmJO+P2hlxtMMaYgw3qZMRhKyNE0q9eHX2CdZU+7DHt78OMctw2GCgncU4EGGOMiAb5bZqbOeV7RuS+inanPoic8+VtjDHGBhWp528VEdHt/OhNVFQUIiMj8dFHHwEAbDYbgoODkZKSgtdee61b/YSEBLS2tmLnzp1CWXR0NCZMmIBNmzZJ6tMhP5Tn6B8jc7c+GGOMsZs47Fd7t2/fjsWLF2Pz5s2IjIzEBx98gJycHPzxxx8wGo1ITEzEqFGjkJ6eDgA4fPgwpk2bhvXr1yM2NhbZ2dl466238OuvvyIsLEzWwTDGGGNs4JB6/h5yuw0nJCTg77//xtq1a1FbW4vw8HDk5+fDaDQCAKqrq6FWq4X60dHRyMrKQmpqKl5//XWMHTsWO3bskJyIMMYYY8y13fbKiBJ4ZYQxxhgbfKSev9W97mGMMcYYcwJORhhjjDGmKE5GGGOMMaYoTkYYY4wxpihORhhjjDGmKE5GGGOMMaYoTkYYY4wxpqjb/tIzJdi/CqWpqUnhV8IYY4wxqezn7b6+0mxQJCPNzc0AALPZrPArYYwxxtjtam5uhq+vb6/7B8U3sNpsNly6dAnDhg2DSqWSrd2mpiaYzWZcuHCBv9lVBhxP+XAs5cXxlA/HUl6uHk8iQnNzMwIDA0U/FXOzQbEyolarERQU5LD29Xq9S04CpXA85cOxlBfHUz4cS3m5cjxvtSJixw+wMsYYY0xRnIwwxhhjTFEeaWlpaUq/CCV5eHhg+vTpGDJkUNyxGvA4nvLhWMqL4ykfjqW8OJ6D5AFWxhhjjLkuvk3DGGOMMUVxMsIYY4wxRXEywhhjjDFFcTLCGGOMMUUN+mRk//79mDNnDgIDA6FSqbBjxw7R/rq6Ojz99NMIDAyETqfDrFmzUFlZ2a0dq9WKxx9/HN7e3tDr9Zg6dSquXr0q7L98+TIWLlwIvV4PPz8/LFu2DP/995/Dx+ds/Y3n+fPnoVKpetxyc3OFetXV1YiNjYVOp0NAQABWrVqFzs5Op43TGeSYm7W1tVi0aBFMJhO8vb0RERGBb775RlSH5+Z1UuJZVVWF+fPnw2AwQK/XIz4+HnV1daI67hDP9PR0PPTQQxg2bBgCAgIwb948VFRUiOpcu3YNycnJGDFiBHx8fPDUU091i5WU43jv3r2IiIiAVqvFmDFjsG3bNkcPz6nkiuWLL76IyZMnQ6vVIjw8vMe+fv/9d0yZMgVeXl4wm83YsGGDw8blbIM+GWlpacHEiRORmZnZbR8RYd68eTh79iy+++47lJSUICQkBDNmzEBLS4tQz2q1YtasWYiJicGRI0dw9OhRpKSkiL66duHChThx4gQKCgrwww8/YP/+/Xj22WedMkZn6m88zWYzampqRNubb74JHx8fzJ49GwDQ1dWF2NhYtLe34/Dhw/jiiy+wbds2rF271qljdTQ55mZiYiIqKirw/fffo6ysDHFxcYiPj0dJSYlQh+emtHi2tLQgJiYGKpUKhYWFOHToENrb2zFnzhzYbDahLXeI5759+5CcnIxffvkFBQUF6OjoQExMjGjuvfTSS9i5cydyc3Oxb98+XLp0CXFxccJ+KcfxuXPnEBsbi8ceewylpaVYsWIFnnnmGezZs8ep43UkOWJpt3TpUiQkJPTYT1NTE2JiYhASEoLjx4/jnXfeQVpaGj799FOHjc2pyIUAoLy8POHviooKAkDl5eVCWVdXFxkMBvrss8+EsqioKEpNTe213ZMnTxIAOnr0qFC2e/duUqlUdPHiRZlHMXDcaTxvFh4eTkuXLhX+/vHHH0mtVlNtba1Q9sknn5Ber6e2tjaZRzEw3Gksvb296csvvxS15e/vL9ThuXmdlHju2bOH1Go1NTY2CnUaGhpIpVJRQUEBEblvPOvr6wkA7du3j4iux0Wj0VBubq5Q59SpUwSArFYrEUk7jl999VUaP368qK+EhASaOXOmo4ekmDuJ5Y3WrVtHEydO7Fb+8ccf0/Dhw0XvkatXr6bQ0FAHjML5Bv3KyK20tbUBALy8vIQytVoNrVaLgwcPAgDq6+tRXFyMgIAAREdHw2g0Ytq0acJ+4PrKiZ+fHx588EGhbMaMGVCr1SguLnbSaJQnJZ43O378OEpLS7Fs2TKhzGq14oEHHoDRaBTKZs6ciaamJpw4ccJBr35gkRrL6OhobN++HZcvX4bNZkN2djauXbuG6dOnA+C5aSclnm1tbVCpVNBqtUIdLy8vqNVqoY67xrOxsREA4O/vD+D6cdvR0YEZM2YIde677z4EBwfDarUCkHYcW61WURv2OvY2XNGdxFIKq9WKqVOnwtPTUyibOXMmKioqcOXKFZlevXJcOhmx/4evWbMGV65cQXt7O95++2389ddfqKmpAQCcPXsWAJCWlobly5cjPz8fEREReOKJJ4T7zbW1tQgICBC1PWTIEPj7+6O2tta5g1KQlHjebMuWLRg3bhyio6OFstraWtEbGADhb3eJp9RY5uTkoKOjAyNGjIBWq0VSUhLy8vIwZswYADw37aTE8+GHH4a3tzdWr16N1tZWtLS04JVXXkFXV5dQxx3jabPZsGLFCjzyyCMICwsDcD0Onp6e8PPzE9U1Go1CHKQcx73VaWpqEj2T5yruNJZSuPr7pksnIxqNBt9++y1Onz4Nf39/6HQ6FBUVYfbs2cLzIPZ7xUlJSViyZAkmTZqEjIwMhIaGYuvWrUq+/AFHSjxvdPXqVWRlZYlWRdh1UmP5xhtvoKGhAT/99BOOHTuGlStXIj4+HmVlZQq++oFHSjwNBgNyc3Oxc+dO+Pj4wNfXFw0NDYiIiLjlT5u7uuTkZJSXlyM7O1vplzLocSzvnMt/Ef7kyZNRWlqKxsZGtLe3w2AwICoqSliGveuuuwAA999/v+jfjRs3DtXV1QAAk8mE+vp60f7Ozk5cvnwZJpPJCaMYOPqK542+/vprtLa2IjExUVRuMplw5MgRUZn9yXJ3imdfsayqqsLGjRtRXl6O8ePHAwAmTpyIAwcOIDMzE5s2beK5eQMpczMmJgZVVVX4559/MGTIEPj5+cFkMmH06NEA3O9YT0lJER7SDQoKEspNJhPa29vR0NAguqKvq6sT4iDlODaZTN0+NVJXVwe9Xo+hQ4c6ZExK6U8spegtlvZ9g53bXA74+vrCYDCgsrISx44dw5NPPgkAuPvuuxEYGNjto1inT59GSEgIAMBisaChoQHHjx8X9hcWFsJmsyEqKsp5gxhAeovnjbZs2YK5c+fCYDCIyi0WC8rKykRv+gUFBdDr9d2SQnfQWyxbW1sBoNtVu4eHh7Cix3OzOylzc+TIkfDz80NhYSHq6+sxd+5cAO4TTyJCSkoK8vLyUFhYiHvuuUe0f/LkydBoNPj555+FsoqKClRXV8NisQCQdhxbLBZRG/Y69jZcgRyxlMJisWD//v3o6OgQygoKChAaGorhw4f3fyBKU/oJ2v5qbm6mkpISKikpIQD0/vvvU0lJCf35559ERJSTk0NFRUVUVVVFO3bsoJCQEIqLixO1kZGRQXq9nnJzc6myspJSU1PJy8uLzpw5I9SZNWsWTZo0iYqLi+ngwYM0duxYWrBggVPH6gxyxJOIqLKyklQqFe3evbvbvs7OTgoLC6OYmBgqLS2l/Px8MhgMtGbNGoePz5n6G8v29nYaM2YMTZkyhYqLi+nMmTP07rvvkkqlol27dgn1eG5Kn5tbt24lq9VKZ86coa+++or8/f1p5cqVojruEM/nn3+efH19ae/evVRTUyNsra2tQp3nnnuOgoODqbCwkI4dO0YWi4UsFouwX8pxfPbsWdLpdLRq1So6deoUZWZmkoeHB+Xn5zt1vI4kRyyJrr9nlpSUUFJSEt17773CXLd/eqahoYGMRiMtWrSIysvLKTs7m3Q6HW3evNmp43WUQZ+MFBUVEYBu2+LFi4mI6MMPP6SgoCDSaDQUHBxMqampPX58ND09nYKCgkin05HFYqEDBw6I9v/777+0YMEC8vHxIb1eT0uWLKHm5mZnDNGp5IrnmjVryGw2U1dXV4/9nD9/nmbPnk1Dhw6lkSNH0ssvv0wdHR2OHJrTyRHL06dPU1xcHAUEBJBOp6MJEyZ0+6gvz83FRCQtnqtXryaj0UgajYbGjh1L7733HtlsNlEdd4hnT3EEQJ9//rlQ5+rVq/TCCy/Q8OHDSafT0fz586mmpkbUjpTjuKioiMLDw8nT05NGjx4t6sMVyBXLadOm9djOuXPnhDq//fYbPfroo6TVamnUqFG0fv16J43S8VRERA5bdmGMMcYY64PbPDPCGGOMsYGJkxHGGGOMKYqTEcYYY4wpipMRxhhjjCmKkxHGGGOMKYqTEcYYY4wpipMRxhhjjCmKkxHGGGOMKYqTEcYYY4wpipMRxhhjjCmKkxHGGGOMKYqTEcYYY4wp6n8CQ0Qq1ie87gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"beta_1 = 0.10\n",
"beta_2 = 1990.0\n",
"\n",
"#logistic function\n",
"Y_pred = sigmoid(x_data, beta_1 , beta_2)\n",
"\n",
"#plot initial prediction against datapoints\n",
"plt.plot(x_data, Y_pred*15000000000000.)\n",
"plt.plot(x_data, y_data, 'ro')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our task here is to find the best parameters for our model. Lets first normalize our x and y:\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# Lets normalize our data\n",
"xdata =x_data/max(x_data)\n",
"ydata =y_data/max(y_data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### How we find the best parameters for our fit line?\n",
"we can use __curve_fit__ which uses non-linear least squares to fit our sigmoid function, to data. Optimize values for the parameters so that the sum of the squared residuals of sigmoid(xdata, *popt) - ydata is minimized.\n",
"\n",
"popt are our optimized parameters.\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" beta_1 = 690.451712, beta_2 = 0.997207\n"
]
}
],
"source": [
"from scipy.optimize import curve_fit\n",
"popt, pcov = curve_fit(sigmoid, xdata, ydata)\n",
"#print the final parameters\n",
"print(\" beta_1 = %f, beta_2 = %f\" % (popt[0], popt[1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we plot our resulting regression model.\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 800x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(1960, 2015, 55)\n",
"x = x/max(x)\n",
"plt.figure(figsize=(8,5))\n",
"y = sigmoid(x, *popt)\n",
"plt.plot(xdata, ydata, 'ro', label='data')\n",
"plt.plot(x,y, linewidth=3.0, label='fit')\n",
"plt.legend(loc='best')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Practice\n",
"Can you calculate what is the accuracy of our model?\n"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean absolute error: 0.04\n",
"Residual sum of squares (MSE): 0.00\n",
"R2-score: 0.97\n"
]
}
],
"source": [
"# split data into train/test\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"# build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(test_y,y_hat) )\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python \n",
"# split data into train/test\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"# build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(test_y,y_hat) )\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Want to learn more?</h2>\n",
"\n",
"IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems by your enterprise as a whole. A free trial is available through this course, available here: <a href=\"https://www.ibm.com/analytics/spss-statistics-software?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">SPSS Modeler</a>\n",
"\n",
"Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at <a href=\"https://www.ibm.com/cloud/watson-studio?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">Watson Studio</a>\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Thank you for completing this lab!\n",
"\n",
"\n",
"## Author\n",
"\n",
"Saeed Aghabozorgi\n",
"\n",
"\n",
"### Other Contributors\n",
"\n",
"<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
"\n",
"\n",
"## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n",
"\n",
"<!--## Change Log\n",
"\n",
"\n",
"| Date (YYYY-MM-DD) | Version | Changed By | Change Description |\n",
"|---|---|---|---|\n",
"| 2020-11-03 | 2.1 | Lakshmi | Made changes in URL |\n",
"| 2020-08-27 | 2.0 | Lavanya | Moved lab to course repo in GitLab |\n",
"| | | | |\n",
"| | | | | --!>\n",
"\n",
"\n",
"\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python",
"language": "python",
"name": "conda-env-python-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.12"
},
"prev_pub_hash": "f873d3177bf529d2d648c46bab1627042a257e5ec6ce42ca68028520459f817e"
},
"nbformat": 4,
"nbformat_minor": 4
}