859 lines
311 KiB
Plaintext
859 lines
311 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<p style=\"text-align:center\">\n",
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" <a href=\"https://skills.network\" target=\"_blank\">\n",
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" <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",
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" </a>\n",
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"</p>\n",
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"\n",
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"\n",
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"# Non Linear Regression Analysis\n",
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"\n",
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"\n",
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"Estimated time needed: **20** minutes\n",
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" \n",
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"\n",
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"## Objectives\n",
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"\n",
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"After completing this lab you will be able to:\n",
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"\n",
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"* Differentiate between linear and non-linear regression\n",
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"* Use non-linear regression model in Python\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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",
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"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"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<h2 id=\"importing_libraries\">Importing required libraries</h2>\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"metadata": {},
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"outputs": [
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{
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"data": {
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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": 19,
|
||
"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": 20,
|
||
"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": 21,
|
||
"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": 22,
|
||
"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": 23,
|
||
"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": 24,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"2025-10-20 16:22:45 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": 24,
|
||
"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": 25,
|
||
"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": 26,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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lUnvz8PDQ689BRGQojlzPwnv7rwMAlo7qhH5tnURORCQO0QcU/3XkviAI9x3Nf+3aNcyZMwdLlixBTEwM9u/fj9u3b2P27Nn3ff6FCxeisLBQe0tNTdVrfiIiQxCfVYw5Oy5AEIAXenvipT5eYkciEo1oI8ycnJxgZmZW5yhNVlZWnaM594SFhaF///5YsGABAKBr166wsbHBwIEDsXLlSrRs2bLOY2QyGWQymf5/ACIiA1FYWoVZ26JRVFGN3t4OWD6al3xT8ybakRtLS0sEBAQgKiqq1vaoqCj069ev3seUlpZCKq0d2czMDEDNER8iouZGrRHw2ncXtFdGrX+pJyzNRT8oTyQqUX8DQkNDsWnTJmzevBlxcXGYP38+UlJStKeZFi5ciMmTJ2v3HzVqFHbt2oUNGzYgMTERJ0+exJw5c9C7d2+4u7uL9WMQEYlm7aGbOH4zG3ILKTZODoCTLY9UE4k68cGECROQm5uLFStWICMjA/7+/oiMjISXV8254oyMjFpz3kydOhVFRUX49NNP8frrr8Pe3h7Dhg3De++9J9aPQEQkmsPX72Ld4XgAwHvPdUVnd6XIiYgMg0RoZudzVCoVlEolCgsLoVAoxI5DRPRIUvNK8fQnJ6Aqr8bkvl5YMcZf7EhEjUqXz2+emCUiMjLlVWr8c3sMVOXV6O5hj0VP+4kdicigsNwQERmZ5Xuv4kqaCi2sLbB+Yk/IzM3EjkRkUFhuiIiMyA8xd7DjbCokEuCTF3rA3d5K7EhEBoflhojISMRnFWPxnisAgPnD22NgO2eRExEZJpYbIiIjUF6lxqvfnkdZlRoD2jrh1aFtxY5EZLBYboiIjEBYZByuZxbB0cYSH47vBqmUMxAT3Q/LDRGRgTt4NRNbTycDANaM7wYXhVzkRESGjeWGiMiApReUYcEPlwAAswb6YEgHF5ETERk+lhsiIgNVrdZg3nexKCyrQtfWSiwI6Sh2JCKjwHJDRGSgPj+WgLNJebCVmWPdCz24ICZRA/E3hYjIAF2+U4i1h24BAJaP7gwvRxuRExEZD5YbIiIDU16lxryIC6jWCHiqixvG9WwldiQio8JyQ0RkYFb9ch0J2SVwsZPh32O7QCLhZd9EumC5ISIyIMdvZiP8VBIA4P2/d0MLG0txAxEZIZYbIiIDUVBaiQU/XAQATO7rhcHtubwC0aNguSEiMhCLf7yKu6oK+DrbYOFIP7HjEBktlhsiIgPwy+UM7L2YDjOpBB+N7w4rSzOxIxEZLZYbIiKR5ZVUYvGPNat9/3NwG3TzsBc3EJGRY7khIhLZ0p+uIqe4Eu1dbfHaE1ztm+hxsdwQEYlo/5U/Tkd98PdukJnzdBTR42K5ISISSX5JJf61p+Z01D8G+aJra3txAxGZCJYbIiKRLNtbczqqnYst5g5vJ3YcIpPBckNEJIKoa3fxY2w6pJKayfp4OopIf1huiIiaWFF5FRb/fjpq1kBfdOfVUUR6xXJDRNTEVu+/gUxVOTwdrDFveHux4xCZHJYbIqImFJOch2/+lwwACBvXhZP1ETUClhsioiZSUa3G2zsvQxCAvwW0Rv+2TmJHIjJJLDdERE3k86OJuJVVDEcbSyx6imtHETWWRy43lZWVuHHjBqqrq/WZh4jIJMVnFeGzI/EAgCWjOqGFjaXIiYhMl87lprS0FDNmzIC1tTU6d+6MlJQUAMCcOXOwatUqvQckIjJ2Go2Ad3ZdQaVagyEdnDG6m7vYkYhMms7lZuHChbh48SKOHj0KuVyu3T58+HBEREToNRwRkSn44fwdnE3Kg5WFGVaO9YdEIhE7EpFJM9f1AXv27EFERAT69OlT6xe0U6dOSEhI0Gs4IiJjl19SibDIOADAvOHt0LqFtciJiEyfzkdusrOz4eLiUmd7SUkJ/zVCRPQX7+2/jvzSKnRwtcP0AT5ixyFqFnQuN7169cK+ffu0398rNF9++SX69u2rv2REREYuJjkP351LBQCsfNYfFma8QJWoKeh8WiosLAwjRozAtWvXUF1djY8//hhXr17F6dOncezYscbISERkdKrVGizaXbPEwvjA1ujl7SByIqLmQ+d/RvTr1w8nT55EaWkp2rRpg4MHD8LV1RWnT59GQEBAY2QkIjI64aeScD2zCPbWFnh7JOe0IWpKOh+5AYAuXbpg69at+s5CRGQSMgrL8FHUTQDAwpEd4cA5bYiaVIPKjUqlavATKhSKRw5DRGQKVu6LQ0mlGgFeLfD3AA+x4xA1Ow0qN/b29g+9EkoQBEgkEqjVar0EIyIyRqfic7DvUgakEuDdMf6QSnkVKVFTa1C5OXLkSGPnICIyelVqDZb+dBUAMKmPFzq580g2kRgaVG4GDx7c2DmIiIzettPJuJVVDAcbS4Q+2UHsOETN1iMNKM7Pz8dXX32FuLg4SCQS+Pn5Ydq0aXBw4KWORNQ8ZRWVY+3vg4jfDOkApbWFyImImi+dLwU/duwYvL298cknnyA/Px95eXn45JNP4OPjw3luiKjZeu+XGyiqqEa31kqMD+QgYiIx6Xzk5pVXXsGECROwYcMGmJmZAQDUajVefvllvPLKK7hy5YreQxIRGbKY5DzsPH8HALCcg4iJRKfzkZuEhAS8/vrr2mIDAGZmZggNDeXCmUTU7Kg1gnYQ8YRAD3T3sBc3EBHpXm569uyJuLi4Otvj4uLQvXt3fWQiIjIa30en4kqaCnZycywYwUHERIagQaelLl26pP16zpw5mDt3LuLj49GnTx8AwJkzZ/DZZ59h1apVjZOSiMgAqcqr8P6BGwCAecPbw8lWJnIiIgIAiSAIwsN2kkqlkEgkeNiuxjCJn0qlglKpRGFhIWdTJqLH8p/IOGw8nghfZxscmDeIq34TNSJdPr8bdOTm9u3beglGRGQqbueUYMvJmr8bFz/TicWGyIA0qNx4eXk1dg4iIqPy733XUKUWMKSDM4Z2cBE7DhH9ySNN4gcA165dQ0pKCiorK2ttHz169GOHIiIyZMdvZuNQXBbMpRL86+lOYschor/QudwkJibi2WefxeXLl2uNw7m3sKahj7khInocVWoN3v35GgBgcl9vtHWxFTkREf2VzieJ586dCx8fH9y9exfW1ta4evUqjh8/jsDAQBw9erQRIhIRGY7tZ2rWj2phbYG5T7QTOw4R1UPnIzenT5/G4cOH4ezsDKlUCqlUigEDBiAsLAxz5szBhQsXGiMnEZHoCkursPbXWwCA0GCuH0VkqHQ+cqNWq2FrW3MY1snJCenp6QBqBh3fuHFDv+mIiAzIp0duoaC0Cu1cbPFCL64fRWSodD5y4+/vj0uXLsHX1xdBQUFYvXo1LC0tsXHjRvj6+jZGRiIi0SXnliD8VBIAYNHTfjDnpd9EBkvncvOvf/0LJSUlAICVK1fimWeewcCBA+Ho6IiIiAi9ByQiMgSrfrmOKrWAQe2dMYSXfhMZNJ3/6RESEoJx48YBAHx9fXHt2jXk5OQgKysLw4YN0znA+vXr4ePjA7lcjoCAAJw4ceKB+1dUVGDRokXw8vKCTCZDmzZtsHnzZp1fl4iooc7ezsMvVzIhlQCLnvITOw4RPcQjz3PzZw4ODo/0uIiICMybNw/r169H//798cUXX2DkyJG4du0aPD09633M+PHjcffuXXz11Vdo27YtsrKyUF1d/TjxiYjuS6MRsHJfzaXfz/f2RAc3O5ETEdHDNGhtqXHjxiE8PBwKhUJ71OZ+du3a1eAXDwoKQs+ePbFhwwbtNj8/P4wdOxZhYWF19t+/fz+ef/55JCYmPnKh4tpSRKSL3RfuYH7ERdjKzHHkjSFwtuPimERi0OXzu0GnpZRKpXaSPqVS+cBbQ1VWViImJgbBwcG1tgcHB+PUqVP1Puann35CYGAgVq9ejVatWqF9+/Z44403UFZWdt/XqaiogEqlqnUjImqIsko1Vu+vuQr05aFtWGyIjESDTktt2bIFACAIApYtWwZnZ2dYW1s/1gvn5ORArVbD1dW11nZXV1dkZmbW+5jExET89ttvkMvl2L17N3JycvDyyy8jLy/vvuNuwsLCsHz58sfKSkTN0+aTt5FRWI5W9laY3t9H7DhE1EA6DSgWBAHt2rVDWlqa3gLcOyL059f467Z7NBoNJBIJtm/fjt69e+Opp57Chx9+iPDw8PsevVm4cCEKCwu1t9TUVL1lJyLTlVNcgQ1HEwAAC0I6QG5hJnIiImooncqNVCpFu3btkJub+9gv7OTkBDMzszpHabKysuoczbmnZcuWaNWqVa3TX35+fhAEAXfu3Kn3MTKZDAqFotaNiOhhPvn1FoorquHfSoHR3dzFjkNEOtD5UvDVq1djwYIFuHLlymO9sKWlJQICAhAVFVVre1RUFPr161fvY/r374/09HQUFxdrt928eRNSqRStW7d+rDxERPckZhfj2/+lAADeecoPUmn9R5OJyDDpXG5eeuklnD17Ft26dYOVlRUcHBxq3XQRGhqKTZs2YfPmzYiLi8P8+fORkpKC2bNnA6g5pTR58mTt/i+++CIcHR0xbdo0XLt2DcePH8eCBQswffp0WFlZ6fqjEBHV673911GtEfBERxf0a+Mkdhwi0pHO89ysXbtWby8+YcIE5ObmYsWKFcjIyIC/vz8iIyPh5eUFAMjIyEBKSop2f1tbW0RFReG1115DYGAgHB0dMX78eKxcuVJvmYioeTt7Ow8Hrt6FVAK8PbKj2HGI6BE0aJ4bU8J5bojofgRBwLPrTyE2tQAv9PZE2LguYkciot/p8vn9WDMUl5WVoaqqqtY2FgYiMlb7LmcgNrUA1pZmmP9kO7HjENEj0nnMTUlJCV599VW4uLjA1tYWLVq0qHUjIjJGldUa7YR9/zfIFy52cpETEdGj0rncvPnmmzh8+DDWr18PmUyGTZs2Yfny5XB3d8e2bdsaIyMRUaP79n/JSMkrhZOtDLMG+oodh4geg86npfbu3Ytt27ZhyJAhmD59OgYOHIi2bdvCy8sL27dvx8SJExsjJxFRoykqr8Inh+MBAPOGt4ONTC9rChORSHQ+cpOXlwcfn5ppyBUKBfLy8gAAAwYMwPHjx/WbjoioCWw8noi8kkr4OtlgQi8PseMQ0WPSudz4+voiKSkJANCpUyf897//BVBzRMfe3l6f2YiIGl2WqhybTtwGALw5ogMszHT+a5GIDIzOv8XTpk3DxYsXAdRMsndv7M38+fOxYMECvQckImpMHx26hbIqNXp62iOks5vYcYhIDxp8YnnevHmYOXMm5s+fr902dOhQXL9+HdHR0WjTpg26devWKCGJiBpDfFYx/htds5juwqf87rtoLxEZlwYfudm/fz+6deuG3r17Y+PGjVCpVAAAT09PjBs3jsWGiIzO6v3XodYIGO7nil7eui0fQ0SGq8Hl5vr16zh+/Di6dOmCN954A+7u7pg8eTIHERORUYpJzsPBazXLLLw1ooPYcYhIj3Qac9O/f3989dVXyMzMxLp165CUlIQhQ4agXbt2WLVqFdLT0xsrJxGR3giCgLDI6wCAvwd4oJ2rnciJiEifHumyAGtra0ybNg3Hjx/HrVu3MH78eKxevRre3t56jkdEpH+/xmUhOjkfMnMp5j/ZXuw4RKRnj3XNY0lJCY4dO4Zjx46hoKAAbdq00VcuIqJGodYIWH2g5qjNtP4+cFNymQUiU/NI5eb48eOYNm0a3NzcMHfuXLRv3x4nTpxAXFycvvMREenVrvN3cPNuMZRWFvjnYP6DjMgUNfhS8Dt37mDr1q0IDw9HQkICgoKC8NFHH+H555+Hra1tY2YkItKL8io1Poy6CQB4ZWgbKK0tRE5ERI2hweXG29sbjo6OmDRpEmbMmAE/P7/GzEVEpHfbTicho7AcLZVyTO7rLXYcImokDS43//3vfzF69GiYm3NBOSIyPoVlVfjsSAIAYP6T7SG3MBM5ERE1lgY3lXHjxjVmDiKiRvX5sQQUllWhvastnuvZWuw4RNSIuEIcEZm8u6pybDlZszjmgpCOMJNymQUiU8ZyQ0Qmb+2hWyiv0iDQqwWG+7mIHYeIGhnLDRGZtITsPxbHfGtkRy6OSdQM6Fxupk+fjqKiojrbS0pKMH36dL2EIiLSlzUHb0CtEfBERxcujknUTOhcbrZu3YqysrI628vKyrBt2za9hCIi0oeLqQWIvJwJiQRYwMUxiZqNBl8tpVKpIAgCBEFAUVER5PI/pixXq9WIjIyEiwvPZRORYRAEAe/tr1lm4dkerdDRTSFyIiJqKg0uN/b29pBIJJBIJGjfvu5CcxKJBMuXL9drOCKiR3XiVg5OJeTC0kyKUC6OSdSsNLjcHDlyBIIgYNiwYdi5cyccHP44d21paQkvLy+4u7s3SkgiIl1oNH8ctXmpjxdat7AWORERNaUGl5vBgwcDAG7fvg0PDw9IpbzQiogM08+XM3A1XQVbmTleHdZW7DhE1MR0XkvBy8sLBQUFOHv2LLKysqDRaGrdP3nyZL2FIyLSVWW1BmsO3gAA/N8gXzjYWIqciIiams7lZu/evZg4cSJKSkpgZ2dXa84IiUTCckNEooo4l4Lk3FI42cowY4CP2HGISAQ6n1t6/fXXtXPdFBQUID8/X3vLy8trjIxERA1SUlGNj3+NBwDMeaItbGRc6JeoOdK53KSlpWHOnDmwtuYAPSIyLJt/u42c4gp4Oljj+V6eYschIpHoXG5CQkIQHR3dGFmIiB5ZXkklvjieCAB4Pbg9LM150QNRc6XzMdunn34aCxYswLVr19ClSxdYWFjUun/06NF6C0dE1FCfHYlHcUU1OrsrMKorp6Ugas4kgiAIujzgQZeASyQSqNXqxw7VmFQqFZRKJQoLC6FQcMZSIlNwJ78Uwz44hkq1Blun98bg9s5iRyIiPdPl81vnIzd/vfSbiEhsH0XdQqVag76+jhjUzknsOEQkssc6KV1eXq6vHEREj+RGZhF2XbgDAHhrZMda01MQUfOkc7lRq9V499130apVK9ja2iIxsWYA3+LFi/HVV1/pPSAR0YO8f+A6BAEY6e+G7h72YschIgOgc7n597//jfDwcKxevRqWln/M/NmlSxds2rRJr+GIiB7kXFIeDsVlwUwqwRshHcSOQ0QGQudys23bNmzcuBETJ06EmZmZdnvXrl1x/fp1vYYjIrofQRCw6peav3Mm9PJAG2dbkRMRkaF4pEn82ratuxCdRqNBVVWVXkIRET1M1LW7iEnOh9xCirlPtBM7DhEZEJ3LTefOnXHixIk627///nv06NFDL6GIiB6kWq3B6gM1i2POGOADV4Vc5EREZEh0vhR86dKlmDRpEtLS0qDRaLBr1y7cuHED27Ztw88//9wYGYmIatl1Pg3xWcWwt7bAPwa3ETsOERkYnY/cjBo1ChEREYiMjIREIsGSJUsQFxeHvXv34sknn2yMjEREWuVVanwYdRMA8OrQtlDILR7yCCJqbh5pydyQkBCEhIToOwsR0UOFn0pCpqocreyt8FIfL7HjEJEB4spyRGQ0Ckorsf5IPABg/pPtIbcwe8gjiKg5atCRmxYtWjR41s+8vLzHCkREdD+fHYmHqrwaHd3s8GyPVmLHISID1aBys3btWu3Xubm5WLlyJUJCQtC3b18AwOnTp3HgwAEsXry4UUISEd3JL8XWU8kAgLdHdoSZlMssEFH9dF4V/LnnnsPQoUPx6quv1tr+6aef4tChQ9izZ48+8+kdVwUnMk6hEbHYdSEN/do4YvvMIK4hRdTM6PL5rfOYmwMHDmDEiBF1toeEhODQoUO6Ph0R0UNdTS/E7tg0AMDCkX4sNkT0QDqXG0dHR+zevbvO9j179sDR0VEvoYiI/mzVLzWLY47q5o4urZVixyEiA6fzpeDLly/HjBkzcPToUe2YmzNnzmD//v1cOJOI9O63Wzk4cSsHFmYSLAjm4phE9HA6l5upU6fCz88Pn3zyCXbt2gVBENCpUyecPHkSQUFBjZGRiJopjUbAqv1xAICJQV7wdLQWORERGYNHmsQvKCgI27dv13cWIqJafryYhitpKtjKzPHasLoL9hIR1eeRyo1Go0F8fDyysrKg0Whq3Tdo0CC9BCOi5q28So0PDtQss/DPIW3gaCsTORERGQudy82ZM2fw4osvIjk5GX+9ilwikUCtVustHBE1X+GnkpBWUIaWSjlmDPAROw4RGRGdy83s2bMRGBiIffv2oWXLlrwkk4j0Lr+kEp/9vszC68EduMwCEelE53Jz69Yt/PDDD2jblue/iahxfHL4ForKq+HXUsFlFohIZzrPcxMUFIT4+Hi9BVi/fj18fHwgl8sREBCAEydONOhxJ0+ehLm5Obp37663LEQkvuTcEnxzpmaZhXee4jILRKQ7nY/cvPbaa3j99deRmZmJLl26wMLCotb9Xbt2bfBzRUREYN68eVi/fj369++PL774AiNHjsS1a9fg6el538cVFhZi8uTJeOKJJ3D37l1dfwQiMmCr999AlVrA4PbOGNjOWew4RGSEdF5bSiqte7BHIpFAEASdBxQHBQWhZ8+e2LBhg3abn58fxo4di7CwsPs+7vnnn0e7du1gZmaGPXv2IDY2tsGvybWliAzX+ZR8jFt/ClIJEDl3IDq68XeUiGro8vmt85Gb27dvP3KwP6usrERMTAzefvvtWtuDg4Nx6tSp+z5uy5YtSEhIwDfffIOVK1c+9HUqKipQUVGh/V6lUj16aCJqNIIgYOXP1wAAfwtozWJDRI9M53Lj5eWllxfOycmBWq2Gq6trre2urq7IzMys9zG3bt3C22+/jRMnTsDcvGHRw8LCsHz58sfOS0SNa9/lDJxPKYCVhRle5zILRPQYdB5QDABff/01+vfvD3d3dyQn1wz8W7t2LX788Uedn+uvl5LfO731V2q1Gi+++CKWL1+O9u3bN/j5Fy5ciMLCQu0tNTVV54xE1LjKq9R4b/91AMDswW3gqpCLnIiIjJnO5WbDhg0IDQ3FU089hYKCAu0YG3t7e6xdu7bBz+Pk5AQzM7M6R2mysrLqHM0BgKKiIkRHR+PVV1+Fubk5zM3NsWLFCly8eBHm5uY4fPhwva8jk8mgUChq3YjIsGw9lYTUvDK4KeSYNYgT9hHR49G53Kxbtw5ffvklFi1aBDOzPybWCgwMxOXLlxv8PJaWlggICEBUVFSt7VFRUejXr1+d/RUKBS5fvozY2Fjtbfbs2ejQoQNiY2O5aCeRkcotrsCnh2uml1gQ0gHWlo+0KgwRkdYjDSju0aNHne0ymQwlJSU6PVdoaCgmTZqEwMBA9O3bFxs3bkRKSgpmz54NoOaUUlpaGrZt2wapVAp/f/9aj3dxcYFcLq+znYiMx9pDt1BUUQ3/Vpywj4j0Q+dy4+Pjg9jY2DoDi3/55Rd06tRJp+eaMGECcnNzsWLFCmRkZMDf3x+RkZHa587IyEBKSoquEYnISNy6W4Rvz9b8ji96qhOknLCPiPRA53lutmzZgsWLF2PNmjWYMWMGNm3ahISEBISFhWHTpk14/vnnGyurXnCeGyLDMW3LWRy5kY3gTq7YODlQ7DhEZMAadZ6badOmobq6Gm+++SZKS0vx4osvolWrVvj4448NvtgQkeE4djMbR25kw1wqwcKn/MSOQ0Qm5JFG7s2aNQuzZs1CTk4ONBoNXFxc9J2LiExYlVqDd3+fsG9KP2/4ONmInIiITMkjX5aQlZWFGzduQCKRQCKRwNmZa8AQUcN8cyYZ8VnFcLCxxJwn2okdh4hMjM6XgqtUKkyaNAnu7u4YPHgwBg0aBHd3d7z00ksoLCxsjIxEZELySirxUdRNAMAbwR2gtLJ4yCOIiHSjc7mZOXMm/ve//2Hfvn0oKChAYWEhfv75Z0RHR2PWrFmNkZGITMhHUTehKq+GX0sFJvTyEDsOEZkgnU9L7du3DwcOHMCAAQO020JCQvDll19ixIgReg1HRKbleqYK2/9Xs2TLkmc6wYyXfhNRI9D5yI2joyOUSmWd7UqlEi1atNBLKCIyPYIg4N2fr0EjACP93dC3jaPYkYjIROlcbv71r38hNDQUGRkZ2m2ZmZlYsGABFi9erNdwRGQ6oq7dxcn4XFiaS/EOL/0mokak82mpDRs2ID4+Hl5eXvD09AQApKSkQCaTITs7G1988YV23/Pnz+svKREZrfIqNd7dV3Pp96yBPvBwsBY5ERGZMp3LzdixYxshBhGZso3HE7Wrfr88pK3YcYjIxOlcbpYuXdoYOYjIRKXmleKzIzWrfi962g82Mq76TUSNS+cxNwBQUFCATZs2YeHChcjLywNQcwoqLS1Nr+GIyPj9e18cKqo16OPrgGe6thQ7DhE1Azr/E+rSpUsYPnw4lEolkpKSMGvWLDg4OGD37t1ITk7Gtm3bGiMnERmhE7eysf9qJsykEiwb3RkSCS/9JqLGp/ORm9DQUEydOhW3bt2CXC7Xbh85ciSOHz+u13BEZLwqqzVY9tNVAMDkvl7o6PbgVXyJiPRF53Jz7tw5/OMf/6izvVWrVsjMzNRLKCIyfuGnbiMhuwROtpaYN7y92HGIqBnRudzI5XKoVKo622/cuMHFM4kIAHBXVY6PD90CALw5oiPXjyKiJqVzuRkzZgxWrFiBqqoqAIBEIkFKSgrefvttPPfcc3oPSETGZ8XP11BSqUZ3D3v8rWdrseMQUTOjc7n54IMPkJ2dDRcXF5SVlWHw4MFo27Yt7Ozs8O9//7sxMhKRETl+Mxv7LmVAKgFWjvWHlOtHEVET0/lqKYVCgd9++w2HDx/G+fPnodFo0LNnTwwfPrwx8hGRESmvUmPJj1cAAFP6ecO/Vd116IiIGtsjz6Y1bNgwDBs2TJ9ZiMjIbTiagKTcUrgqZAh9koOIiUgcOpUbjUaD8PBw7Nq1C0lJSZBIJPDx8cHf/vY3TJo0iXNYEDVjt3NKsOFoAgBgyTOdYSfnIGIiEkeDx9wIgoDRo0dj5syZSEtLQ5cuXdC5c2ckJydj6tSpePbZZxszJxEZMEEQsOTHK6hUazCovTOe6uImdiQiasYafOQmPDwcx48fx6+//oqhQ4fWuu/w4cMYO3Ystm3bhsmTJ+s9JBEZtp8vZeDErRxYmkuxgjMRE5HIGnzkZseOHXjnnXfqFBugZvzN22+/je3bt+s1HBEZvsLSKqz4+RoA4JUhbeHtZCNyIiJq7hpcbi5duoQRI0bc9/6RI0fi4sWLeglFRMZj1f44ZBdVoI2zDWYP8RU7DhFRw8tNXl4eXF1d73u/q6sr8vPz9RKKiIzDmcRc7DibCgBY9VxXyMzNRE5ERKRDuVGr1TA3v/8QHTMzM1RXV+slFBEZvvIqNd7ZdRkA8GKQJ3p5O4iciIioRoMHFAuCgKlTp0Imk9V7f0VFhd5CEZHh+/RwPBJzSuBiJ8PbIzuKHYeISKvB5WbKlCkP3YdXShE1D9czVfj8WM2cNivGdIaCc9oQkQFpcLnZsmVLY+YgIiOh1gh4e+dlVGsEBHdyxQj/lmJHIiKqReeFM4moedt6KgmxqQWwk5ljxRh/seMQEdXBckNEDZaUU4LVB64DAN5+qiPclHKRExER1cVyQ0QNotEIePOHSyiv0qBfG0e82NtT7EhERPViuSGiBtl6Oglnk/JgbWmG957ryiUWiMhgsdwQ0UMl5ZTgvf01p6MWPuUHDwdrkRMREd0fyw0RPZBGI+DNnX+cjprI01FEZOBYbojogb4+k4yzt/84HSWV8nQUERk2lhsiuq/E7GKs+uX301EjO/J0FBEZBZYbIqpXlVqD+RGxKKtSo39bR0wM8hI7EhFRg7DcEFG9PjsSj4t3CqGQm+ODv3fj6SgiMhosN0RUR2xqAdYdjgcAvDvWHy2VViInIiJqOJYbIqqltLIa8yNiodYIGN3NHWO6txI7EhGRTlhuiKiW/0TG4XZOCdwUcrzLtaOIyAix3BCR1pHrWfjmTAoAYM34blBaW4iciIhIdyw3RAQAuKsqx+vfXwQATO/vg/5tnURORET0aFhuiAhqjYD5EbHIK6lEp5YKvDWyg9iRiIgeGcsNEeHzYwk4lZALa0szrHuxB2TmZmJHIiJ6ZCw3RM1cTHIePoy6CQBYMcYfbZxtRU5ERPR4WG6ImrHC0irM2VFz2ffY7u54ricv+yYi48dyQ9RMCYKAt3ddQlpBGbwcrbHy2S6QSDgLMREZP5YbomZq88kk/HIlExZmEqx7oQdsZeZiRyIi0guWG6JmKDopD2GRcQCAfz3dCV1b24sbiIhIj1huiJqZ7KIKvPLteVRrBIzq5o7JfbnaNxGZFpYbomakWq3BnB0XcFdVgbYutlg1juNsiMj0sNwQNSNrom7idGLNfDafv9QTNhxnQ0QmiOWGqJk4eDUTG44mAADee64r2rrYiZyIiKhxsNwQNQM37xZhfkQsAGBqP2+M6uYubiAiokYkerlZv349fHx8IJfLERAQgBMnTtx33127duHJJ5+Es7MzFAoF+vbtiwMHDjRhWiLjk19SiZlbo1FSqUYfXwcsetpP7EhERI1K1HITERGBefPmYdGiRbhw4QIGDhyIkSNHIiUlpd79jx8/jieffBKRkZGIiYnB0KFDMWrUKFy4cKGJkxMZh2q1Bq/uOI+UvFK0bmGF9RMDYGEm+r9piIgalUQQBEGsFw8KCkLPnj2xYcMG7TY/Pz+MHTsWYWFhDXqOzp07Y8KECViyZEmD9lepVFAqlSgsLIRCoXik3ETGYtlPVxF+KgnWlmbY9XI/dHTj//NEZJx0+fwW7Z9wlZWViImJQXBwcK3twcHBOHXqVIOeQ6PRoKioCA4ODvfdp6KiAiqVqtaNqDn477lUhJ9KAgB8OL47iw0RNRuilZucnByo1Wq4urrW2u7q6orMzMwGPceaNWtQUlKC8ePH33efsLAwKJVK7c3Dw+OxchMZgzOJuVi05zIAYP7w9hjh7yZyIiKipiP6yfe/TiAmCEKDJhXbsWMHli1bhoiICLi4uNx3v4ULF6KwsFB7S01NfezMRIYsPqsI/7ctGlVqAU93aYnXhrUVOxIRUZMSbQYvJycnmJmZ1TlKk5WVVedozl9FRERgxowZ+P777zF8+PAH7iuTySCTyR47L5ExyC6qwNQt56Aqr0ZPT3usGd8NUilnICai5kW0IzeWlpYICAhAVFRUre1RUVHo16/ffR+3Y8cOTJ06Fd9++y2efvrpxo5JZDTKKtWYuS0ad/LL4OVojS8nB0JuYSZ2LCKiJifq3OuhoaGYNGkSAgMD0bdvX2zcuBEpKSmYPXs2gJpTSmlpadi2bRuAmmIzefJkfPzxx+jTp4/2qI+VlRWUSqVoPweR2NQaAXO/u4CLqQVoYW2B8Gm94WjLI5ZE1DyJWm4mTJiA3NxcrFixAhkZGfD390dkZCS8vGpWKc7IyKg1580XX3yB6upqvPLKK3jllVe026dMmYLw8PCmjk9kEARBwIq9V3Hw2l1Ymkvx5eRA+DjZiB2LiEg0os5zIwbOc0OmZu2hm1h76BYAYN0LPbi0AhGZJKOY54aIHt/WU0naYrN8dGcWGyIisNwQGa0fY9Ow9KerAIB5w9thSj9vcQMRERkIlhsiI3TkehZe/+9FADWrfM99op3IiYiIDAfLDZGROZ2Qi39uj0G1RsDY7u5Y8kynBk18SUTUXLDcEBmRM4m5mB5+DuVVGjzR0QXv/52T9BER/RXLDZGROHs7D9PDz6GsSo3B7Z3x2cSesDDjrzAR0V/xb0YiIxCdlIepW86itFKNge2c8MWkAM4+TER0Hyw3RAYuJjkfUzbXFJsBbZ24rAIR0UOIOkMxET3YqYQczNwajdJKNfq1cWSxISJqAJYbIgN16NpdvPzteVRWazCgrRM2Tg6AlSWLDRHRw7DcEBmgny6mIzQiFtUaAU92csW6F3rwiA0RUQOx3BAZmB1nU/DO7ssQBODZHq2w+m9deVUUEZEOWG6IDIQgCFh/NAHvH7gBAHipjydWjPbnPDZERDpiuSEyANVqDRb/eAU7zqYCAP45pA3eDOnAmYeJiB4Byw2RyEoqqvHqt+dx5EY2pBJg2ejOmNzXW+xYRERGi+WGSERZReWYHn4OV9JUkFtI8cnzPRDc2U3sWERERo3lhkgkV9ML8X/bYpBWUAYHG0t8NSUQPTxbiB2LiMjosdwQieDnS+l44/uLKK/SwMfJBlum9oK3k43YsYiITALLDVET0mgEfBh1E58eiQcADGrvjHXP94DS2kLkZEREpoPlhqiJFJVXYX7ERRyKuwsA+L9BvnhrREeY8VJvIiK9YrkhagJX0wvxyvbzSMothaW5FKvGdcG4nq3FjkVEZJJYbogakSAI2HE2Fcv2XkVltQat7K3w2cSe6O5hL3Y0IiKTxXJD1EhKKqrxzu7L+DE2HQDwREcXrBnfDfbWliInIyIybSw3RI3g0p0CzIuIRWJ2CcykEiwI6YD/G+jLpRSIiJoAyw2RHlWrNfj8WALWHrqFao0AV4UM617oid4+DmJHIyJqNlhuiPQkJbcU8/8bi5jkfADAU13c8O+xXdDChqehiIiaEssN0WPSaATsOJeC/+yLQ0mlGrYycywf3RnjerbiwpdERCJguSF6DInZxXh712WcvZ0HAOjt7YA147vBw8Fa5GRERM0Xyw3RI6hSa/DliUSsPXQLldUaWFmYYUFIB0zp581J+YiIRMZyQ6SjmOQ8LN5zFdcyVACAge2c8J9nu/BoDRGRgWC5IWqg7KIKrPrlOnaevwMAUFpZYPEznfAcx9YQERkUlhuih6hSa/D16WR8FHUTRRXVAIAJgR5YMKIDnGxlIqcjIqK/Yrkhug9BEBB17S5W7b+OxOwSAEDX1kosH90ZPTxbiJyOiIjuh+WGqB7nU/IRFhmHc0k1c9Y42FhiQUgHjA/04IBhIiIDx3JD9Cc37xbho6ib+OVKJgBAbiHFzAG++MdgX9jJLUROR0REDcFyQwTg1t0ifPzrLey7nAFBAKQS4G8BrRH6ZAe4KeVixyMiIh2w3FCzdutuEdYdjsfeS+kQhJptI/3dMG94e3RwsxM3HBERPRKWG2p2BEFAdHI+vjiWgENxWdrtIzq7Yc4T7dDJXSFiOiIielwsN9RsqDU1Vz9tPJ6A8ykFAACJBAjp5IbXnmiLzu5KcQMSEZFesNyQycsvqUREdCq+Pp2MtIIyAICluRTP9WyNWQN94OtsK3JCIiLSJ5YbMkmCIOByWiG+OZOMH2PTUVGtAQDYW1vgxd6emNrfGy52HChMRGSKWG7IpBSUVmL3hTREnEvF9cwi7fbO7gpM6eeN0d3cIbcwEzEhERE1NpYbMnpVag1+u5WDnefv4ODVu6hU1xylsTSXYqS/Gyb39UJPzxZc/4mIqJlguSGjJAgCYpLz8WNsOvZdzkBeSaX2vk4tFZjQywNjurvD3tpSxJRERCQGlhsyGmqNgPMp+fjlciYOXM3UDg4GACdbSzzT1R1/C2gN/1a86omIqDljuSGDVl6lxumEXByKu4sDV+8ip7hCe5+NpRlC/N0wtnsr9GvjCHMzqYhJiYjIULDckMFJLyjDkRtZOByXhZMJOSiv0mjvs5Ob40k/V4zwd8Og9s4cHExERHWw3JDoisqrcCYxD7/dysaJ+BwkZpfUur+lUo6hHV0Q0tkNfX0dYWnOIzRERHR/LDfU5FTlVYhJyseZ27n4X2IeLqcVQq0RtPdLJUB3D3sM6+iCYR1d4dfSjlc6ERFRg7HcUKMSBAGpeWU4n5KvvV1LV+FPXQYA4O1ojf5tnTCwnRP6+jpBaW0hTmAiIjJ6LDekVznFFbh8pxCX7hTicloBYlMLaw0Cvsfb0Rq9fRwQ5OOIIF8HtG5hLUJaIiIyRSw39Eg0GgFJuSWIyyhCXIYKcRkqXMtQIaOwvM6+FmYSdHZXoqdnC/T0skeglwPclFz6gIiIGgfLDT1QtVqDO/llSMguxs27xbh1twg3s4oQn1Vc6yqmeyQSoI2zLbq2UqJLayW6tlais7uSVzUREVGTYbkhqDUCMgrLkJxb+vutBLdzSpCYU4Lk3BJUqYV6Hyczl6KDmx06tVTA7/dbJ3cFbGX834qIiMTDT6FmoEqtQWZhOTIKy5FeUIa0gjLcyS9Fal7Nn2kFZfctMAAgt5DC29EG7Vzt0N7FtuZPV1t4Olhz4jwiIjI4LDdGTK0RkFtSgeyiP25ZRRXILCxHpqocWaqaQpNdXAHh/t0FQM24GA8Ha3g5WMPL0QbejtbwdbaFr7MN3JVWkEp5KTYRERkHlhsDIQgCSivVKCirQkFpJQpKq5BXUomC0krklVQhv7QSuSWVyC2uQG5xJXJLKpBXUlnnkur7sTSXoqVSDnelFdztreDhYIXWLazRuoUVWrewQkulFcxYYIiIyASw3OiJWiMgt7gCRRXVKKmoRnF5NYor/rgVlVdDVV6FovLfvy6rgqq8CoVlVVCVVaOwrPKBp4buRyoBHG1lcLaVwclOBlc7GdyUcrgo5HBTyOGqkMHd3gqONpacCI+IiJoF0cvN+vXr8f777yMjIwOdO3fG2rVrMXDgwPvuf+zYMYSGhuLq1atwd3fHm2++idmzZzdh4vplFJZhwHtHHvt5LMwksLe2hL2VBRxsLOFgYwl7a0s42FjA0UYGR1vLP/78/WsecSEiIvqDqOUmIiIC8+bNw/r169G/f3988cUXGDlyJK5duwZPT886+9++fRtPPfUUZs2ahW+++QYnT57Eyy+/DGdnZzz33HMi/AR/sJWZQyqp+dNWZg5buTlsfv/aTm4OO5kFbOW/fy23gNLKAgq5ORRWFlDILWBvXXOzsjDjERYiIqLHIBGEhw01bTxBQUHo2bMnNmzYoN3m5+eHsWPHIiwsrM7+b731Fn766SfExcVpt82ePRsXL17E6dOn632NiooKVFT8MUOuSqWCh4cHCgsLoVAo9Paz3HsbWUyIiIj0T6VSQalUNujzW7TreCsrKxETE4Pg4OBa24ODg3Hq1Kl6H3P69Ok6+4eEhCA6OhpVVVX1PiYsLAxKpVJ78/Dw0M8P8BcSiYTFhoiIyACIVm5ycnKgVqvh6upaa7urqysyMzPrfUxmZma9+1dXVyMnJ6fexyxcuBCFhYXaW2pqqn5+ACIiIjJIog8o/uvRDkEQHngEpL7969t+j0wmg0wme8yUREREZCxEO3Lj5OQEMzOzOkdpsrKy6hyducfNza3e/c3NzeHo6NhoWYmIiMh4iFZuLC0tERAQgKioqFrbo6Ki0K9fv3of07dv3zr7Hzx4EIGBgbCwsGi0rERERGQ8RF0YKDQ0FJs2bcLmzZsRFxeH+fPnIyUlRTtvzcKFCzF58mTt/rNnz0ZycjJCQ0MRFxeHzZs346uvvsIbb7wh1o9AREREBkbUMTcTJkxAbm4uVqxYgYyMDPj7+yMyMhJeXl4AgIyMDKSkpGj39/HxQWRkJObPn4/PPvsM7u7u+OSTT0Sf44aIiIgMh6jz3IhBl+vkiYiIyDAYxTw3RERERI2B5YaIiIhMCssNERERmRSWGyIiIjIpLDdERERkUlhuiIiIyKSIvrZUU7t35btKpRI5CRERETXUvc/thsxg0+zKTVFREQDAw8ND5CRERESkq6KiIiiVygfu0+wm8dNoNEhPT4ednd0DVx9vLlQqFTw8PJCamspJDZsA3++mw/e66fC9bjrN+b0WBAFFRUVwd3eHVPrgUTXN7siNVCpF69atxY5hcBQKRbP7RRET3++mw/e66fC9bjrN9b1+2BGbezigmIiIiEwKyw0RERGZFJabZk4mk2Hp0qWQyWRiR2kW+H43Hb7XTYfvddPhe90wzW5AMREREZk2HrkhIiIik8JyQ0RERCaF5YaIiIhMCssNERERmRSWG6pXRUUFunfvDolEgtjYWLHjmJykpCTMmDEDPj4+sLKyQps2bbB06VJUVlaKHc0krF+/Hj4+PpDL5QgICMCJEyfEjmRywsLC0KtXL9jZ2cHFxQVjx47FjRs3xI7VLISFhUEikWDevHliRzFYLDdUrzfffBPu7u5ixzBZ169fh0ajwRdffIGrV6/io48+wueff4533nlH7GhGLyIiAvPmzcOiRYtw4cIFDBw4ECNHjkRKSorY0UzKsWPH8Morr+DMmTOIiopCdXU1goODUVJSInY0k3bu3Dls3LgRXbt2FTuKQeOl4FTHL7/8gtDQUOzcuROdO3fGhQsX0L17d7Fjmbz3338fGzZsQGJiothRjFpQUBB69uyJDRs2aLf5+flh7NixCAsLEzGZacvOzoaLiwuOHTuGQYMGiR3HJBUXF6Nnz55Yv349Vq5cie7du2Pt2rVixzJIPHJDtdy9exezZs3C119/DWtra7HjNCuFhYVwcHAQO4ZRq6ysRExMDIKDg2ttDw4OxqlTp0RK1TwUFhYCAP8fbkSvvPIKnn76aQwfPlzsKAav2S2cSfcnCAKmTp2K2bNnIzAwEElJSWJHajYSEhKwbt06rFmzRuwoRi0nJwdqtRqurq61tru6uiIzM1OkVKZPEASEhoZiwIAB8Pf3FzuOSfruu+9w/vx5nDt3TuwoRoFHbpqBZcuWQSKRPPAWHR2NdevWQaVSYeHChWJHNloNfa//LD09HSNGjMDf//53zJw5U6TkpkUikdT6XhCEOttIf1599VVcunQJO3bsEDuKSUpNTcXcuXPxzTffQC6Xix3HKHDMTTOQk5ODnJycB+7j7e2N559/Hnv37q31IaBWq2FmZoaJEydi69atjR3V6DX0vb73F1R6ejqGDh2KoKAghIeHQyrlvzceR2VlJaytrfH999/j2Wef1W6fO3cuYmNjcezYMRHTmabXXnsNe/bswfHjx+Hj4yN2HJO0Z88ePPvsszAzM9NuU6vVkEgkkEqlqKioqHUfsdzQn6SkpEClUmm/T09PR0hICH744QcEBQWhdevWIqYzPWlpaRg6dCgCAgLwzTff8C8nPQkKCkJAQADWr1+v3dapUyeMGTOGA4r1SBAEvPbaa9i9ezeOHj2Kdu3aiR3JZBUVFSE5ObnWtmnTpqFjx4546623eCqwHhxzQ1qenp61vre1tQUAtGnThsVGz9LT0zFkyBB4enrigw8+QHZ2tvY+Nzc3EZMZv9DQUEyaNAmBgYHo27cvNm7ciJSUFMyePVvsaCbllVdewbfffosff/wRdnZ22jFNSqUSVlZWIqczLXZ2dnUKjI2NDRwdHVls7oPlhkgEBw8eRHx8POLj4+sURx5MfTwTJkxAbm4uVqxYgYyMDPj7+yMyMhJeXl5iRzMp9y61HzJkSK3tW7ZswdSpU5s+ENGf8LQUERERmRSOXiQiIiKTwnJDREREJoXlhoiIiEwKyw0RERGZFJYbIiIiMiksN0RERGRSWG6IiIjIpLDcEBERkUlhuSFqhiQSCfbs2SN2jAZZtmwZunfvLnYMvRsyZAjmzZvX4P2PHj0KiUSCgoKC++4THh4Oe3v7x85GZOxYboiMyNSpUzF27FixYxi9hpSANWvWQKlUorS0tM595eXlsLe3x4cffvjIGXbt2oV33333kR9PRPfHckNEVI/JkyejrKwMO3furHPfzp07UVpaikmTJun8vFVVVQAABwcH2NnZPXZOIqqL5YbIiA0ZMgRz5szBm2++CQcHB7i5uWHZsmW19rl16xYGDRoEuVyOTp06ISoqqs7zpKWlYcKECWjRogUcHR0xZswYJCUlae+/d8Ro+fLlcHFxgUKhwD/+8Q9UVlZq9xEEAatXr4avry+srKzQrVs3/PDDD9r7751W+fXXXxEYGAhra2v069cPN27cqJVl1apVcHV1hZ2dHWbMmIHy8vI6ebds2QI/Pz/I5XJ07NgR69ev196XlJQEiUSCXbt2YejQobC2tka3bt1w+vRpbY5p06ahsLAQEokEEomkznsGAM7Ozhg1ahQ2b95c577Nmzdj9OjRcHZ2xltvvYX27dvD2toavr6+WLx4sbbAAH+cVtu8eTN8fX0hk8kgCEKd01LffPMNAgMDYWdnBzc3N7z44ovIysqq89onT55Et27dIJfLERQUhMuXL9fZ58/27t2LgIAAyOVy+Pr6Yvny5aiurn7gY4iMnkBERmPKlCnCmDFjtN8PHjxYUCgUwrJly4SbN28KW7duFSQSiXDw4EFBEARBrVYL/v7+wpAhQ4QLFy4Ix44dE3r06CEAEHbv3i0IgiCUlJQI7dq1E6ZPny5cunRJuHbtmvDiiy8KHTp0ECoqKrSva2trK0yYMEG4cuWK8PPPPwvOzs7CO++8o83yzjvvCB07dhT2798vJCQkCFu2bBFkMplw9OhRQRAE4ciRIwIAISgoSDh69Khw9epVYeDAgUK/fv20zxERESFYWloKX375pXD9+nVh0aJFgp2dndCtWzftPhs3bhRatmwp7Ny5U0hMTBR27twpODg4COHh4YIgCMLt27cFAELHjh2Fn3/+Wbhx44bwt7/9TfDy8hKqqqqEiooKYe3atYJCoRAyMjKEjIwMoaioqN73e9++fYJEIhESExO1227fvi1IJBIhMjJSEARBePfdd4WTJ08Kt2/fFn766SfB1dVVeO+997T7L126VLCxsRFCQkKE8+fPCxcvXhQ0Go0wePBgYe7cudr9vvrqKyEyMlJISEgQTp8+LfTp00cYOXKk9v5775+fn59w8OBB4dKlS8IzzzwjeHt7C5WVlYIgCMKWLVsEpVKpfcz+/fsFhUIhhIeHCwkJCcLBgwcFb29vYdmyZfX/D0ZkIlhuiIxIfeVmwIABtfbp1auX8NZbbwmCIAgHDhwQzMzMhNTUVO39v/zyS61y89VXXwkdOnQQNBqNdp+KigrByspKOHDggPZ1HRwchJKSEu0+GzZsEGxtbQW1Wi0UFxcLcrlcOHXqVK0sM2bMEF544QVBEP74cD506JD2/n379gkAhLKyMkEQBKFv377C7Nmzaz1HUFBQrXLj4eEhfPvtt7X2effdd4W+ffsKgvBHudm0aZP2/qtXrwoAhLi4OEEQ6paA+6murhZatWolLFmyRLttyZIlQqtWrYTq6up6H7N69WohICBA+/3SpUsFCwsLISsrq9Z+fy03f3X27FkBgLZ43Xv/vvvuO+0+ubm5gpWVlRAREVHvzzVw4EDhP//5T63n/frrr4WWLVs++AcnMnLmIh0wIiI96dq1a63vW7ZsqT2dERcXB09PT7Ru3Vp7f9++fWvtHxMTg/j4+DrjP8rLy5GQkKD9vlu3brC2tq71PMXFxUhNTUVWVhbKy8vx5JNP1nqOyspK9OjR4755W7ZsCQDIysqCp6cn4uLiMHv27Fr79+3bF0eOHAEAZGdnIzU1FTNmzMCsWbO0+1RXV0OpVDbodTp27IiGMjMzw5QpUxAeHo6lS5dCIpFg69atmDp1KszMzAAAP/zwA9auXYv4+HgUFxejuroaCoWi1vN4eXnB2dn5ga914cIFLFu2DLGxscjLy4NGowEApKSkoFOnTrXej3scHBzQoUMHxMXF1fucMTExOHfuHP79739rt6nVapSXl6O0tLTWf08iU8JyQ2TkLCwsan0vkUi0H4yCINTZXyKR1Ppeo9EgICAA27dvr7Pvwz6Q//p6+/btQ6tWrWrdL5PJ7pv3XpZ7j3+Ye/t9+eWXCAoKqnXfvbKhj9f5s+nTpyMsLAyHDx8GUFM2pk2bBgA4c+YMnn/+eSxfvhwhISFQKpX47rvvsGbNmlrPYWNj88DXKCkpQXBwMIKDg/HNN9/A2dkZKSkpCAkJqTWu6X7++t/0Ho1Gg+XLl2PcuHF17pPL5Q99XiJjxXJDZMI6deqElJQUpKenw93dHQC0A2vv6dmzJyIiIrQDhe/n4sWLKCsrg5WVFYCaD3ZbW1u0bt0aLVq0gEwmQ0pKCgYPHvzIef38/HDmzBlMnjxZu+3MmTPar11dXdGqVSskJiZi4sSJj/w6lpaWUKvVDdq3TZs2GDx4MLZs2aIdCNymTRsANYN7vby8sGjRIu3+ycnJOue5fv06cnJysGrVKnh4eAAAoqOj6933zJkz8PT0BADk5+fj5s2b9z0a1bNnT9y4cQNt27bVORORMWO5ITJhw4cPR4cOHTB58mSsWbMGKpWq1gcxAEycOBHvv/8+xowZgxUrVqB169ZISUnBrl27sGDBAu0prcrKSsyYMQP/+te/kJycjKVLl+LVV1+FVCqFnZ0d3njjDcyfPx8ajQYDBgyASqXCqVOnYGtriylTpjQo79y5czFlyhQEBgZiwIAB2L59O65evQpfX1/tPsuWLcOcOXOgUCgwcuRIVFRUIDo6Gvn5+QgNDW3Q63h7e6O4uBi//vqr9nTbg07R/Pk02KZNm7Tb27Zti5SUFHz33Xfo1asX9u3bh927dzcow595enrC0tIS69atw+zZs3HlypX7zoGzYsUKODo6wtXVFYsWLYKTk9N95z5asmQJnnnmGXh4eODvf/87pFIpLl26hMuXL2PlypU65yQyFrwUnMiESaVS7N69GxUVFejduzdmzpxZa/wFAFhbW+P48ePw9PTEuHHj4Ofnh+nTp6OsrKzWkZwnnngC7dq1w6BBgzB+/HiMGjWq1iXU7777LpYsWYKwsDD4+fkhJCQEe/fuhY+PT4PzTpgwAUuWLMFbb72FgIAAJCcn45///GetfWbOnIlNmzYhPDwcXbp0weDBgxEeHq7T6/Tr1w+zZ8/GhAkT4OzsjNWrVz9w/+eeew4ymQwymazWKZ4xY8Zg/vz5ePXVV9G9e3ecOnUKixcvbnCOe5ydnREeHo7vv/8enTp1wqpVq/DBBx/Uu++qVaswd+5cBAQEICMjAz/99BMsLS3r3TckJAQ///wzoqKi0KtXL/Tp0wcffvghvLy8dM5IZEwkQn0n5YmI/mTq1KkoKCgwmiUbiKh545EbIiIiMiksN0RERGRSeFqKiIiITAqP3BAREZFJYbkhIiIik8JyQ0RERCaF5YaIiIhMCssNERERmRSWGyIiIjIpLDdERERkUlhuiIiIyKT8P7Gd3MhYXCfAAAAAAElFTkSuQmCC\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": 27,
|
||
"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": 28,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"[<matplotlib.lines.Line2D at 0x7485709d92d0>]"
|
||
]
|
||
},
|
||
"execution_count": 28,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\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": 29,
|
||
"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": 30,
|
||
"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": 31,
|
||
"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": 32,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Mean absolute error: 0.03\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
|
||
}
|