Praktikum_Machine_Learning/Regression/Regiska Sari Putri Prasetyo_202310715132_Regresi Non Linear.ipynb

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{
"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": {
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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": 21,
"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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w/Rs3buCpp55Cz549cfbsWcybNw9Tp07F9u3bazg5ERFZsuz8Irz739Kzx17t0xStfVwkTkSmJBNCCKlDVFVISAg6d+6MVatWGZYFBQVhyJAhiIiIKLf+nDlz8PPPPyM6OtqwLDw8HOfOncOxY8eq9J4ajQYqlQpqtRouLvzhJyKyRm9+fw7bz9xEMw8n7JnaA0obzilU2xnz+9tiRoaKiopw+vRp9O/fv8zy/v374+jRoxVuc+zYsXLrDxgwAKdOnUJxcXGF22i1Wmg0mjI3IiKyXn/GZmL7mdJrj30yvD2LUB1kMWUoMzMTOp0Onp6eZZZ7enoiLS2twm3S0tIqXL+kpASZmZkVbhMREQGVSmW4+fr6muYbICIii6Mt0eHdny4CAEZ380OwXwOJE5E5WEwZukcmKzufgxCi3LKHrV/R8nvmzp0LtVptuCUlJVUzMRERWarVh6/jemYe3J2VmDWgpdRxyExspA5QVW5ublAoFOVGgdLT08uN/tzj5eVV4fo2NjZo2LBhhdsolUoolUrThCYiIosVn5mHFYdiAQDvPB0EF3tbiRORuVjMyJCdnR2Cg4Nx4MCBMssPHDiA7t27V7hNaGhoufX379+PLl26wNaWP9RERFQxIQTm/3wJRSV69Gjmhmc7+EgdiczIYsoQAMycORNr167F+vXrER0djRkzZiAxMRHh4eEASndxjRkzxrB+eHg4EhISMHPmTERHR2P9+vVYt24dZs2aJdW3QEREFmDvhTQcuZoBO4Uc7z3XptLDMcjyWcxuMgAYMWIEbt++jffeew+pqalo27Yt9u7dCz8/PwBAampqmTmHAgICsHfvXsyYMQNffvklfHx88MUXX2D48OFSfQtERFTL5RQWY9Guv+YU4iU36j6LmmdICpxniIjIury36zLW/3kD/g0dsW96L9jb8lR6S1Qn5xkiIiIyt2u3crDpWDwAYNFzbVmErATLEBEREUoPml606zJ0eoF+rT3Ru4W71JGohrAMERERAdh/+Rb+LzYTdjZyvPt0a6njUA1iGSIiIqtXWKzD+7svAwD+2TMQTRo6SpyIahLLEBERWb2vj1zHzTsF8HKxx2thTaWOQzWMZYiIiKxaSnYBVkbGAQDmPtUKjnYWNesMmQDLEBERWbWIX66goFiHx/wbcKZpK8UyREREVutUfBZ2nUuBTAYsGMyZpq0VyxAREVklvV7g/T3RAICRj/mibSOVxIlIKixDRERklXadT8G5pGzUs1NgRr8WUschCbEMERGR1Sks1mHxvhgAQHjvpvBwtpc4EUmJZYiIiKzOhj/jkZxdeir9pJ6BUschibEMERGRVcnM1eLLQ7EAgLcGtISDHa8/Zu1YhoiIyKos++0qcrUlaNvIBUM7NZI6DtUCLENERGQ1YtNz8O2JJADA20+1hlzOU+mJZYiIiKzIx79cgU4v0DfIE6FNG0odh2oJliEiIrIKJ25k4bfodCjkMsx9qpXUcagWYRkiIqI6TwiBj38pnWDxxS6+aOruJHEiqk1YhoiIqM47cPkWziRmw95Wjul9m0sdh2qZRy5DRUVFiImJQUlJiSnzEBERmVSJTo/Fv5ZOsDjh8QB4unCCRSrL6DKUn5+PiRMnwtHREW3atEFiYiIAYOrUqfj4449NHpCIiKg6dpxJRmx6Luo72uKV3k2ljkO1kNFlaO7cuTh37hwiIyNhb/9Xu+7bty+2bdtm0nBERETVUVisw79/uwoAeL1PM6gcbCVORLWRjbEb/PTTT9i2bRu6desGmeyv+Rlat26NuLg4k4YjIiKqjk1H45GqLoSPyh6jQ/2kjkO1lNEjQxkZGfDw8Ci3PC8vr0w5IiIikpK6oBgrI0v/kz6jXwvY2/KyG1Qxo8vQY489hj179hge3ytAX3/9NUJDQ02XjIiIqBrWHImDuqAYLTydMKxzY6njUC1m9G6yiIgIDBw4EJcvX0ZJSQk+//xzXLp0CceOHcPhw4fNkZGIiMgomblabPgzHgDwZv+WUPCyG1QJo0eGunfvjj///BP5+flo2rQp9u/fD09PTxw7dgzBwcHmyEhERGSUVZFxyC/SoX1jFfq39pQ6DtVyRo8MAUC7du2wadMmU2chIiKqtlR1Ab45ngCgdFSIx7PSw1SpDGk0miq/oIuLyyOHISIiqq7lB2NRVKJHV39X9GruJnUcsgBVKkP169d/aLMWQkAmk0Gn05kkGBERkbESb+fj+5NJAIBZAzgqRFVTpTJ06NAhc+cgIiKqtmW/X0WJXqBXC3d0DXCVOg5ZiCqVod69e5s7BxERUbXEpufgp7PJAIA3+7WQOA1Zkke6UOudO3ewZMkSTJw4EZMmTcLSpUuRlZVl6mzl3nP06NFQqVRQqVQYPXo0srOzK91m3LhxkMlkZW7dunUza04iIpLGZweuQi+A/q090cG3vtRxyIIYXYYOHz4Mf39/fPHFF7hz5w6ysrLwxRdfICAgwKzzDI0aNQpRUVHYt28f9u3bh6ioKIwePfqh2w0cOBCpqamG2969e82WkYiIpHE5RYO9F9IgkwEz+3NUiIxj9Kn1r7/+OkaMGIFVq1ZBoSid2lyn0+G1117D66+/josXL5o8ZHR0NPbt24fjx48jJCQEwF8zXsfExKBly5YP3FapVMLLy8vkmYiIqPb44vdrAICn2nmjlRfPaibjGD0yFBcXhzfffNNQhABAoVBg5syZZrtQ67Fjx6BSqQxFCAC6desGlUqFo0ePVrptZGQkPDw80KJFC0yePBnp6emVrq/VaqHRaMrciIio9rqUosa+S6WjQtOfbC51HLJARpehzp07Izo6utzy6OhodOzY0RSZyklLS6vw4rAeHh5IS0t74HaDBg3C1q1bcfDgQSxduhQnT57EE088Aa1W+8BtIiIiDMclqVQq+Pr6muR7ICIi8/j8t9JRoWfa+6C5p7PEacgSVWk32fnz5w33p06dimnTpiE2NtZwMPLx48fx5Zdf4uOPPzbqzRcuXIhFixZVus7JkycBoMK5Iu7NbfQgI0aMMNxv27YtunTpAj8/P+zZswfDhg2rcJu5c+di5syZhscajYaFiIiolrqYrMb+y7cgkwHTnmwmdRyyUFUqQx07doRMJoMQwrBs9uzZ5dYbNWpUmQLyMFOmTMHIkSMrXcff3x/nz5/HrVu3yj2XkZEBT8+qX3PG29sbfn5+uHbt2gPXUSqVUCqVVX5NIiKSzrK7o0KD2/ugmQdHhejRVKkM3bhxwyxv7ubmBje3h0+VHhoaCrVajRMnTqBr164AgP/9739Qq9Xo3r17ld/v9u3bSEpKgre39yNnJiKi2uHCTTV+i74FuQyYymOFqBqqVIb8/PzMnaNSQUFBGDhwICZPnozVq1cDAP75z3/imWeeKXMmWatWrRAREYGhQ4ciNzcXCxcuxPDhw+Ht7Y34+HjMmzcPbm5uGDp0qFTfChERmcjnv18FADzbwQfNPJwkTkOW7JGuWg8Aly9fRmJiIoqKisosf/bZZ6sdqiJbt27F1KlT0b9/f8P7rFixosw6MTExUKvVAErPcLtw4QI2b96M7OxseHt7IywsDNu2bYOzM4dSiYgs2fmb2fgtOh1yGfAGR4WomowuQ9evX8fQoUNx4cKFMscR3TuQ2VwXanV1dcWWLVsqXef+Y5ocHBzw66+/miULERFJ64vfYwEAz3VshKbuHBWi6jH61Ppp06YhICAAt27dgqOjIy5duoQjR46gS5cuiIyMNENEIiKiv1xMLj1WSCYDpjzBM8io+oweGTp27BgOHjwId3d3yOVyyOVy9OjRAxEREZg6dSrOnj1rjpxEREQAgBUHS0eFBrf34agQmYTRI0M6nQ5OTqU/fG5ubkhJSQFQepB1TEyMadMRERHd50qaxjDbNEeFyFSMHhlq27Ytzp8/j8DAQISEhGDx4sWws7PDmjVrEBgYaI6MREREAIDld0eFnmrrjRacbZpMxOgy9M477yAvLw8A8MEHH+CZZ55Bz5490bBhQ2zbts3kAYmIiAAgNj0Hey+kAuCoEJmW0WVowIABhvuBgYG4fPkysrKy0KBBg0ovjUFERFQdKw7GQgigf2tPBHnzyvRkOo88z9D9XF1dTfEyREREFbqekYufz5Ueo8rZpsnUqlSGhg0bho0bN8LFxeWBFzi9Z8eOHSYJRkREdM+Xh+KgF8CTrTzQtpFK6jhUx1SpDKlUKsMuMJWKP4RERFRzEm/n46eoZACcbZrMo0plaMOGDQBKZ3heuHAh3N3d4ejoaNZgREREALDqcBx0eoGezd3Q0be+1HGoDjJqniEhBJo3b47k5GRz5SEiIjJIVRdg++mbAIA3nuCoEJmHUWVILpejefPmuH37trnyEBERGaw5ch1FOj26BriiawBP1iHzMHoG6sWLF+Ott97CxYsXzZGHiIgIAJCZq8W3JxIBAFPCOK8QmY/Rp9a//PLLyM/PR4cOHWBnZwcHB4cyz2dlZZksHBERWa91/3cDhcV6dGisQs/mblLHoTrM6DK0bNkyM8QgIiL6izq/GN8cSwAATHmiOSf1JbMyugyNHTvWHDmIiIgMNh6NR662BK28nPFkKw+p41AdV60ZqAsKClBcXFxmmYsLp0gnIqJHl6stwfo/bwAAXg9rBrmco0JkXkYfQJ2Xl4cpU6bAw8MDTk5OaNCgQZkbERFRdWw9ngB1QTEC3erhqXbeUschK2B0GZo9ezYOHjyIlStXQqlUYu3atVi0aBF8fHywefNmc2QkIiIrUVisw9d/lI4KvdqnKRQcFaIaYPRusl27dmHz5s3o06cPJkyYgJ49e6JZs2bw8/PD1q1b8dJLL5kjJxERWYEfTt9EZq4Wjeo7YEinRlLHISth9MhQVlYWAgICAJQeH3TvVPoePXrgyJEjpk1HRERWo1inx1eRcQCAV3oHwlZh9K8ookdi9E9aYGAg4uPjAQCtW7fG999/D6B0xKh+/fqmzEZERFbk56gUJGcXwM3JDi928ZU6DlkRo8vQ+PHjce7cOQDA3LlzDccOzZgxA2+99ZbJAxIRUd2n1wusjIwFAEzsEQh7W4XEiciaVPmYoenTp2PSpEmYMWOGYVlYWBiuXLmCU6dOoWnTpujQoYNZQhIRUd22/3Ia4jLy4Gxvg5e7NZE6DlmZKo8M7du3Dx06dEDXrl2xZs0aaDQaAECTJk0wbNgwFiEiInokQgh8eaj0WKFx3f3hbG8rcSKyNlUuQ1euXMGRI0fQrl07zJo1Cz4+PhgzZgwPmiYiomr541omLiSr4WCrwPjHA6SOQ1bIqGOGHn/8caxbtw5paWlYvnw54uPj0adPHzRv3hwff/wxUlJSzJWTiIjqqC8PlR4r9I+uTeBaz07iNGSNHum8RUdHR4wfPx5HjhzBtWvX8OKLL2Lx4sXw9/c3cTwiIqrLTidk4X83smCrkGFyL44KkTSqNYlDXl4eDh8+jMOHDyM7OxtNmzY1VS4iIrICK+8eKzSsU2N4qxwkTkPW6pHK0JEjRzB+/Hh4eXlh2rRpaNGiBf744w9ER0ebOh8REdVR0aka/H4lHXIZEN6H/5km6VT51PqbN29i06ZN2LhxI+Li4hASEoJ///vfGDlyJJycnMyZkYiI6qBVd2ebHtTOGwFu9SROQ9asymXI398fDRs2xOjRozFx4kQEBQWZMxcREdVh8Zl52H2+9KSb1zgqRBKrchn6/vvv8eyzz8LGxuhruxIREZWx+sh16AXQp6U72viopI5DVq7KxwwNGzZM0iL04Ycfonv37nB0dKzyNdCEEFi4cCF8fHzg4OCAPn364NKlS+YNSkRElbqlKcT20zcBAK/1aSZxGqJqnk1Wk4qKivDCCy/g1VdfrfI2ixcvxmeffYYVK1bg5MmT8PLyQr9+/ZCTk2PGpEREVJm1f1xHkU6Px/wboGuAq9RxiCynDC1atAgzZsxAu3btqrS+EALLli3D22+/jWHDhqFt27bYtGkT8vPz8Z///MfMaYmIqCLZ+UXY+r9EABwVotrDYsqQsW7cuIG0tDT079/fsEypVKJ37944evToA7fTarXQaDRlbkREZBobj8Yjv0iHIG8X9GnpLnUcIgCPUIYmTJhQ4W6mvLw8TJgwwSShTCEtLQ0A4OnpWWa5p6en4bmKREREQKVSGW6+vr5mzUlEZC3ytCXYeDQeQOkZZDKZTNpARHcZXYY2bdqEgoKCcssLCgqwefNmo15r4cKFkMlkld5OnTplbMQy/v6XTQhR6V/AuXPnQq1WG25JSUnVen8iIir17YlEZOcXw7+hI55q5y11HCKDKp8eptFoIISAEAI5OTmwt7c3PKfT6bB37154eHgY9eZTpkzByJEjK13nUa935uXlBaB0hMjb+6+/dOnp6eVGi+6nVCqhVCof6T2JiKhi2hIdvv7jOgAgvHdTKOQcFaLao8plqH79+obRmhYtWpR7XiaTYdGiRUa9uZubG9zc3IzapqoCAgLg5eWFAwcOoFOnTgBKz0g7fPgwPvnkE7O8JxERVWznmWTc0mjh6aLE0M6NpI5DVEaVy9ChQ4cghMATTzyB7du3w9X1r9Mh7ezs4OfnBx8fH7OEBIDExERkZWUhMTEROp0OUVFRAIBmzZoZLgfSqlUrREREYOjQoZDJZJg+fTo++ugjNG/eHM2bN8dHH30ER0dHjBo1ymw5iYioLJ1e4KvDpZfemNwzEEobhcSJiMqqchnq3bs3gNKztHx9fSGX1+yJaPPnz8emTZsMj++N9hw6dAh9+vQBAMTExECtVhvWmT17NgoKCvDaa6/hzp07CAkJwf79++Hs7Fyj2YmIrNneC6mIv52P+o62+EfXJlLHISpHJoQQxm6UnZ2NEydOID09HXq9vsxzY8aMMVm42kCj0UClUkGtVsPFxUXqOEREFkUIgae++D9Ep2owo28LTOvbXOpIZCWM+f1t9PU1du3ahZdeegl5eXlwdnYuc2aWTCarc2WIiIgeXWRMBqJTNahnp8DY7n5SxyGqkNH7ut58803DXEPZ2dm4c+eO4ZaVlWWOjEREZKFWRsYCAEaFNEF9RzuJ0xBVzOgylJycjKlTp8LR0dEceYiIqI44cSMLJ+PvwE4hx6SegVLHIXogo8vQgAEDqj0RIhER1X1fHiodFRoe3BieLvYPWZtIOkYfM/T000/jrbfewuXLl9GuXTvY2tqWef7ZZ581WTgiIrJMF5PVOHw1A3IZ8GrvplLHIaqU0WVo8uTJAID33nuv3HMymQw6na76qYiIyKLdO1bo2Q4+aNKQh1VQ7WZ0Gfr7qfRERET3i03PwS8XSy+I/WqfZhKnIXq4as2cWFhYaKocRERUR6yKvA4hgH6tPdHSi5PcUu1ndBnS6XR4//330ahRIzg5OeH69dIL77377rtYt26dyQMSEZHlSMrKx09RyQCA18M4KkSWwegy9OGHH2Ljxo1YvHgx7Oz+mjOiXbt2WLt2rUnDERGRZfn6j+vQ6QV6NHNDR9/6UschqhKjy9DmzZuxZs0avPTSS1Ao/rrYXvv27XHlyhWThiMiIsuRnlOI704mAQBeC+MZZGQ5HmnSxWbNyg996vV6FBcXmyQUERFZnnX/dwNFJXp0alIfoYENpY5DVGVGl6E2bdrgjz/+KLf8hx9+MFxJnoiIrEt2fhG2HEsAALzep1mZ61YS1XZGn1q/YMECjB49GsnJydDr9dixYwdiYmKwefNm7N692xwZiYioltt4NB55RToEebvgySAPqeMQGcXokaHBgwdj27Zt2Lt3L2QyGebPn4/o6Gjs2rUL/fr1M0dGIiKqxXIKi7Hhz3gAwOthTTkqRBbH6JEhoPT6ZAMGDDB1FiIiskBbjidCXVCMQPd6GNTWW+o4REar1qSLRERk3QqKdFj3f6Xzzb3WpxkUco4KkeWp0shQgwYNqjzsmZWVVa1ARERkOb47mYjM3CI0buCA5zr6SB2H6JFUqQwtW7bMcP/27dv44IMPMGDAAISGhgIAjh07hl9//RXvvvuuWUISEVHtoy3RYc2R0lGh8N5NYavgzgayTDIhhDBmg+HDhyMsLAxTpkwps3zFihX47bff8NNPP5kyn+Q0Gg1UKhXUajVcXFykjkNEVGt8eyIRc3dcgKeLEoffCoO9reLhGxHVEGN+fxtd43/99VcMHDiw3PIBAwbgt99+M/bliIjIApXo9FgVGQcAmNwzkEWILJrRZahhw4bYuXNnueU//fQTGjbkjKNERNbg53MpSMzKh2s9O4wKaSJ1HKJqMfrU+kWLFmHixImIjIw0HDN0/Phx7Nu3jxdqJSKyAjq9wIpDsQCAiT0C4Gj3SLO0ENUaRv8Ejxs3DkFBQfjiiy+wY8cOCCHQunVr/PnnnwgJCTFHRiIiqkX2XEjF9Yw8qBxsMba7v9RxiKrtkep8SEgItm7dauosRERUy+n1Ast/vwagdFTISclRIbJ8j/RTrNfrERsbi/T0dOj1+jLP9erVyyTBiIio9tl3KQ3X0nPhbG/DUSGqM4wuQ8ePH8eoUaOQkJCAv5+VL5PJoNPpTBaOiIhqD71e4Iu7o0LjHw+AysFW4kREpmF0GQoPD0eXLl2wZ88eeHt784J8RERW4rfoW7iSlgMnpQ0mPO4vdRwikzG6DF27dg0//vgjmjVrZo48RERUCwkh8MXB0lGhsd39UN/RTuJERKZj9DxDISEhiI2NNUcWIiKqpQ7FpONisgaOdgpM7BEodRwikzJ6ZOiNN97Am2++ibS0NLRr1w62tmX3Gbdv395k4YiISHpCCHz+e+l/gkd384NrPY4KUd1idBkaPnw4AGDChAmGZTKZDEIIHkBNRFQHRcZk4FxSNuxt5ZjUk6NCVPcYXYZu3LhhjhxERFQLCSHw79+uAgDGhPrD3VkpcSIi0zO6DPn5+Zkjx0N9+OGH2LNnD6KiomBnZ4fs7OyHbjNu3Dhs2rSpzLKQkBAcP37cTCmJiOqWg1fScf6mGg62CvyzF0eFqG4y+gBqAPjmm2/w+OOPw8fHBwkJCQCAZcuW4b///a9Jw92vqKgIL7zwAl599VWjths4cCBSU1MNt71795opIRFR3SKEwLLfSs8gG9PdD25OHBWiusnoMrRq1SrMnDkTTz31FLKzsw3HCNWvXx/Lli0zdT6DRYsWYcaMGWjXrp1R2ymVSnh5eRlurq6uZkpIRFS3/BadjgvJajjaKfBKr6ZSxyEyG6PL0PLly/H111/j7bffhkKhMCzv0qULLly4YNJwphAZGQkPDw+0aNECkydPRnp6eqXra7VaaDSaMjciImtTOipUeqzQ2O7+PIOM6jSjy9CNGzfQqVOncsuVSiXy8vJMEspUBg0ahK1bt+LgwYNYunQpTp48iSeeeAJarfaB20REREClUhluvr6+NZiYiKh22H/5Fi6laFDPToF/8gwyquOMLkMBAQGIiooqt/yXX35B69atjXqthQsXQiaTVXo7deqUsRENRowYgaeffhpt27bF4MGD8csvv+Dq1avYs2fPA7eZO3cu1Gq14ZaUlPTI709EZIn0+r+OFRr3uD8acFSI6jijzyZ766238Prrr6OwsBBCCJw4cQLffvstIiIisHbtWqNea8qUKRg5cmSl6/j7+xsb8YG8vb3h5+eHa9euPXAdpVIJpZIHCRKR9dp/OQ3RqRo4KW0wmaNCZAWMLkPjx49HSUkJZs+ejfz8fIwaNQqNGjXC559//tBi83dubm5wc3MzNsIju337NpKSkuDt7V1j70lEZEl0eoHPDpQeKzT+cX9eg4yswiOdWj958mQkJCQgPT0daWlpSEpKwsSJE02drYzExERERUUhMTEROp0OUVFRiIqKQm5urmGdVq1aYefOnQCA3NxczJo1C8eOHUN8fDwiIyMxePBguLm5YejQoWbNSkRkqXadS8HVW7lwsbfhbNNkNYweGbonPT0dMTExhmN73N3dTZmrnPnz55eZQPHeQdyHDh1Cnz59AAAxMTFQq9UAAIVCgQsXLmDz5s3Izs6Gt7c3wsLCsG3bNjg7O5s1KxGRJSrW6Q1nkL3SuylUDrYP2YKobpAJIYQxG2g0Grz++uv49ttvodfrAZQWjxEjRuDLL7+ESqUyS1CpaDQaqFQqqNVquLi4SB2HiMhsvjuRiH/tuICG9exwZHYY6ikf+f/LRJIz5ve30bvJJk2ahP/973/Ys2cPsrOzoVarsXv3bpw6dQqTJ09+5NBERCQdbYkOX/xeenLJq32asgiRVTH6p33Pnj349ddf0aNHD8OyAQMG4Ouvv8bAgQNNGo6IiGrGt/9LRIq6EF4u9ni5mzTXoCSSitEjQw0bNqxwV5hKpUKDBg1MEoqIiGpOflEJVhyKAwC88WQz2NsqHrIFUd1idBl65513MHPmTKSmphqWpaWl4a233sK7775r0nBERGR+m44mIDNXC19XB7wQzFn3yfoYvZts1apViI2NhZ+fH5o0aQKg9LR3pVKJjIwMrF692rDumTNnTJeUiIhMTl1QjNVHSkeFpj/ZAnY2jzTjCpFFM7oMDRkyxAwxiIhICqsPxyE7vxjNPJwwpFMjqeMQScLoMrRgwQJz5CAiohp2S1OI9X/eAADMHtASCrlM4kRE0nik8dDs7GysXbsWc+fORVZWFoDSXWLJyckmDUdEROaz7LdrKCzWI9ivAfq19pQ6DpFkjB4ZOn/+PPr27QuVSoX4+HhMnjwZrq6u2LlzJxISErB582Zz5CQiIhOKy8jF96eSAAD/GtQKMhlHhch6GT0yNHPmTIwbNw7Xrl2Dvb29YfmgQYNw5MgRk4YjIiLzWPJrDHR6gb5BHnjM31XqOESSMroMnTx5Eq+88kq55Y0aNUJaWppJQhERkfmcTbyDXy6mQSYD3hrQSuo4RJIzugzZ29tDo9GUWx4TE2P2i7USEVH1CCHwyb4rAIDhnRujpRcvXE1kdBl67rnn8N5776G4uBgAIJPJkJiYiH/9618YPny4yQMSEZHpHL6agePXs2BnI8eMfi2kjkNUKxhdhpYsWYKMjAx4eHigoKAAvXv3RrNmzeDs7IwPP/zQHBmJiMgEdHqBiL2lo0JjuvmhUX0HiRMR1Q5Gn03m4uKC//u//8PBgwdx5swZ6PV6dO7cGX379jVHPiIiMpHvTyUh5lYOVA62mPJEM6njENUaRpehe5544gk88cQTpsxCRERmkqstwdL9VwEAU59sjvqOdhInIqo9jCpDer0eGzduxI4dOxAfHw+ZTIaAgAA8//zzGD16NOepICKqpb6KjENmrhb+DR0xupuf1HGIapUqHzMkhMCzzz6LSZMmITk5Ge3atUObNm2QkJCAcePGYejQoebMSUREjygluwBf/3EdAPCvQUG8GCvR31R5ZGjjxo04cuQIfv/9d4SFhZV57uDBgxgyZAg2b96MMWPGmDwkERE9uiW/xkBbokdXf1cMaMPLbhD9XZX/e/Dtt99i3rx55YoQUHr80L/+9S9s3brVpOGIiKh6LtxUY8fZ0utGvvNMEA9nIKpAlcvQ+fPnMXDgwAc+P2jQIJw7d84koYiIqPqEEPhgz2UAwJCOPmjfuL60gYhqqSqXoaysLHh6Pnh41dPTE3fu3DFJKCIiqr59F9PwvxtZUNrI8dZAXnaD6EGqXIZ0Oh1sbB58iJFCoUBJSYlJQhERUfUUFOnwwZ5oAMArvZtygkWiSlT5AGohBMaNGwelUlnh81qt1mShiIioelYfiUNydgF8VPZ4tXdTqeMQ1WpVLkNjx4596Do8k4yISHo37+RjVWQcAGDe00FwsFNInIiodqtyGdqwYYM5cxARkYlE7L0CbYkeIQGueLqdt9RxiGo9zrxFRFSHHI3LxJ4LqZDLgAWD2/BUeqIqYBkiIqojSnR6vLer9FT6l0L80NrHReJERJaBZYiIqI74z4lEXEkrvSr9zH4tpI5DZDFYhoiI6oD0nEJ8+msMAGBW/xZoUI9XpSeqKpYhIqI64MM90cgpLEG7RiqMCuFV6YmMwTJERGTh/ozNxH+jUiCTAR8ObQuFnAdNExmDZYiIyIJpS3R496eLAIAx3fx4/TGiR2ARZSg+Ph4TJ05EQEAAHBwc0LRpUyxYsABFRUWVbieEwMKFC+Hj4wMHBwf06dMHly5dqqHURETmt/rwdVzPzIO7sxJvDmgpdRwii2QRZejKlSvQ6/VYvXo1Ll26hH//+9/46quvMG/evEq3W7x4MT777DOsWLECJ0+ehJeXF/r164ecnJwaSk5EZD4Jt/Ow4lAsAODdZ1rDxd5W4kRElkkmhBBSh3gUn376KVatWoXr169X+LwQAj4+Ppg+fTrmzJkDoPT6aZ6envjkk0/wyiuvVOl9NBoNVCoV1Go1XFw4ZwcR1Q5CCIzbcBKHr2agRzM3fDOxKydYJLqPMb+/LWJkqCJqtRqurq4PfP7GjRtIS0tD//79DcuUSiV69+6No0ePPnA7rVYLjUZT5kZEVNv8fC4Fh69mwM5GjveHtGURIqoGiyxDcXFxWL58OcLDwx+4TlpaGgDA09OzzHJPT0/DcxWJiIiASqUy3Hx9fU0TmojIRG7narHo7kzTU8KaIcCtnsSJiCybpGVo4cKFkMlkld5OnTpVZpuUlBQMHDgQL7zwAiZNmvTQ9/j7/5aEEJX+D2ru3LlQq9WGW1JS0qN9c0REZrJo12Vk5RWhlZczwns3lToOkcWr8lXrzWHKlCkYOXJkpev4+/sb7qekpCAsLAyhoaFYs2ZNpdt5eXkBKB0h8vb+66rN6enp5UaL7qdUKqFUKquQnoio5v12+RZ+PpcCuQxY/Hx72NlY5AA/Ua0iaRlyc3ODm5tbldZNTk5GWFgYgoODsWHDBsjllf8DEBAQAC8vLxw4cACdOnUCABQVFeHw4cP45JNPqp2diKimaQqL8c7dOYUm9wzknEJEJmIR/6VISUlBnz594OvriyVLliAjIwNpaWnljv1p1aoVdu7cCaB099j06dPx0UcfYefOnbh48SLGjRsHR0dHjBo1Sopvg4ioWiL2XkGaphD+DR0xvS8vxEpkKpKODFXV/v37ERsbi9jYWDRu3LjMc/fPDBATEwO1Wm14PHv2bBQUFOC1117DnTt3EBISgv3798PZ2bnGshMRmcLRuEx8eyIRAPDx8PZwsFNInIio7rDYeYZqCucZIiKp5WpLMOjzI0jKKsBLIU3w4dB2UkciqvWsYp4hIiJr8cHuy0jKKkCj+g7416BWUschqnNYhoiIarHfLt/CdyeTIJMBS1/sAGdecoPI5FiGiIhqqdu5Wvxrx3kAwKQeAegW2FDiRER1E8sQEVEtJITA2zsvIjO3CC08nfBmf16RnshcWIaIiGqhnWeTse9SGmzkMnz2YkfY2/LsMSJzYRkiIqplkrMLsOC/lwAA0/s2R9tGKokTEdVtLENERLVIiU6Pqd+eRY62BJ2a1Oe1x4hqAMsQEVEtsuy3azidcAfOSht8MbITbBT8Z5rI3Pi3jIiolvgzNhNfRsYCKJ1l2tfVUeJERNaBZYiIqBbIzNVi+rYoCAH8o2sTPN3eW+pIRFaDZYiISGJ6vcCb359DRo4WLTydMP+Z1lJHIrIqLENERBL7+o/rOHw1A/a2cqwY1ZkXYSWqYSxDREQSOn79Nhb/GgMAWDC4DVp4OkuciMj6sAwREUkkTV2IKf85A51eYGinRhj5mK/UkYisEssQEZEEtCU6vLr1NDJzixDk7YKPhraDTCaTOhaRVWIZIiKSwPu7L+NsYjZc7G3w1cs8TohISixDREQ17MfTN7HleCJkMuDzkZ3g17Ce1JGIrBrLEBFRDbpwU423d14AAEx7sjnCWnlInIiIWIaIiGpImroQkzafhLZEjydaeWDqE82ljkREYBkiIqoR+UUlmLjpJG5ptGju4YRlIztCLucB00S1AcsQEZGZ6fUC07+LwqUUDVzr2WH9uMfgYm8rdSwiuotliIjIzD7dH4P9l2/BTiHHmtHBvAArUS3DMkREZEY/nErCqsg4AMAnz7dDF39XiRMR0d+xDBERmUlkTDrm7ig9c2xKWDMM7dRY4kREVBGWISIiMzibeAevbjmDEr3A4A4+mNmvhdSRiOgBWIaIiEwsNj0XEzaeREGxDj2bu2HpCx145hhRLcYyRERkQmnqQoxdfwJ38ovRvrEKq14Ohp0N/6klqs34N5SIyETU+cUYu/4EkrMLEOBWDxvGPQYnpY3UsYjoIViGiIhMQFNYjDHr/4eYWznwcFZi84SuaOiklDoWEVUByxARUTXlakswbv0JnLupRn1HW2ye2JVzCRFZEJYhIqJqyNOWYPyGEziTmA2Vgy22TAxBKy8XqWMRkRFYhoiIHlFBkQ4TN53Eyfg7cLa3wZaJIWjbSCV1LCIykkWUofj4eEycOBEBAQFwcHBA06ZNsWDBAhQVFVW63bhx4yCTycrcunXrVkOpiaguyy8qwaTNJ3H8ehaclDbYPKEr2jVmESKyRBZxmsOVK1eg1+uxevVqNGvWDBcvXsTkyZORl5eHJUuWVLrtwIEDsWHDBsNjOzs7c8clojpOXVCMCRtP4nTCHdSzU2DThMfQqUkDqWMR0SOyiDI0cOBADBw40PA4MDAQMTExWLVq1UPLkFKphJeXl7kjEpGVyMzVYvS6E4hO1cDF3gYbJ3RFZxYhIotmEbvJKqJWq+Hq+vALHkZGRsLDwwMtWrTA5MmTkZ6eXun6Wq0WGo2mzI2ICACSswvw4lfHEJ2qgZuTEtteCWURIqoDLLIMxcXFYfny5QgPD690vUGDBmHr1q04ePAgli5dipMnT+KJJ56AVqt94DYRERFQqVSGm6+vr6njE5EFisvIxQurjuJ6Zh4a1XfAD+GhCPLmWWNEdYFMCCGkevOFCxdi0aJFla5z8uRJdOnSxfA4JSUFvXv3Ru/evbF27Vqj3i81NRV+fn747rvvMGzYsArX0Wq1ZcqSRqOBr68v1Go1XFz4Dx+RNTpxIwv//OYUsvOLEeheD1smhsCnvoPUsYioEhqNBiqVqkq/vyU9ZmjKlCkYOXJkpev4+/sb7qekpCAsLAyhoaFYs2aN0e/n7e0NPz8/XLt27YHrKJVKKJWcNZaISv03Khlv/XAeRTo9OvjWx7qxXeDGmaWJ6hRJy5Cbmxvc3NyqtG5ycjLCwsIQHByMDRs2QC43fg/f7du3kZSUBG9vb6O3JSLrIoTAysg4fPprDABgQBtPLBvRCQ52ComTEZGpWcQxQykpKejTpw98fX2xZMkSZGRkIC0tDWlpaWXWa9WqFXbu3AkAyM3NxaxZs3Ds2DHEx8cjMjISgwcPhpubG4YOHSrFt0FEFqKoRI9/bb9gKEKTegRg5UvBLEJEdZRFnFq/f/9+xMbGIjY2Fo0bNy7z3P2HPMXExECtVgMAFAoFLly4gM2bNyM7Oxve3t4ICwvDtm3b4OzsXKP5ichy3NIU4tUtp3EmMRtyGbDw2TYYE+ovdSwiMiNJD6C2BMYcgEVElu1UfBZe3XoGGTlaONvb4It/dEJYSw+pYxHRI7CYA6iJiGoDIQS2HE/Aol2XUaIXaOnpjNWjg+HvVk/qaERUA1iGiMiq5WpLMP+ni9hxNhkA8HR7bywe3h71lPznkcha8G87EVmtCzfVeOPbM4i/nQ+5DJgzsBX+2SsQMplM6mhEVINYhojI6uj1Auv/vIFP9l1BsU7AR2WPz//RCY/5P/wSP0RU97AMEZFVuaUpxOwfz+Pw1QwAwMA2Xvh4eDvUd7STOBkRSYVliIisghACO84kY9GuS9AUlkBpI8f8wa0xqmsT7hYjsnIsQ0RU56WpCzFv5wUcvJIOAGjfWIUlL3RAC0/OOUZELENEVIfp9QLfn0rCh3ujkVNYAjuFHNP7Ncc/ewbCRmERE/ATUQ1gGSKiOulSihrv/nQRZxKzAQAd7o4GNedoEBH9DcsQEdUpmsJifLb/KjYfi4deAPXsFJjetwXGP+7P0SAiqhDLEBHVCTq9wPbTN/Hp/hhk5GgBlE6g+O7TreGlspc4HRHVZixDRGTRhBA4fDUDH/9yBVfScgAAAW718N5zbdCzubvE6YjIErAMEZHFupisxse/XMH/xWYCAFQOtnjjiWYYHeoHpY1C4nREZClYhojI4lxO0eDz36/i10u3AAB2CjnGdvfDlLDmUDnaSpyOiCwNyxARWYzoVA0+/+0a9l1KAwDIZMCzHXwwq39L+Lo6SpyOiCwVyxAR1WpCCJy4kYU1R67j97uTJspkwDPtfTDtyWZo5sFT5YmoeliGiKhW0ukF9l1Mw5ojcTh3Uw2gtAQ93c4b055szvmCiMhkWIaIqFa5navF96du4j8nEpCUVQAAUNrI8XxwY0zsEYBAdyeJExJRXcMyRESSE0LgTGI2thxPwJ7zqSjS6QEADRxtMTrUH2NC/eDmpJQ4JRHVVSxDRCSZdE0hdp5Nxo+nb+Jaeq5heYfGKrzUzQ+D2/vAwY6nyBORebEMEVGNyi8qwcEr6dh++iYOX82AXpQuV9rI8WwHH7zczQ8dfOtLmpGIrAvLEBGZXWGxDpEx6dh9PhW/R6ejoFhneK6LXwM8H9wYT7X3hos95wgioprHMkREZqHOL0bk1XQcuHwLh66kI6/orwLk6+qAZzv4YHjnxjwgmogkxzJERCYhhEBcRh4OX83A79G3cOJGFkru7QMD0Ki+A55u742n23mjfWMVZDKZhGmJiP7CMkREjyw7vwhH427jyNUM/HEtE8nZBWWeb+HphL5BnujX2hMdfeuzABFRrcQyRERVlp1fhP/dyMLx67dx/HoWrqRpIP4a/IGdQo7HAhogrKUH+rX2hF/DetKFJSKqIpYhIqqQXi9wPTMXpxPu4HTCHZxJzEbsfae/39PMwwk9m7uhVwt3dAtoyFPhicjisAwREfR6gaQ7+Th/U42LyWrD1xxtSbl1m3k4oVugK7oFNkTXAFd4ONtLkJiIyHRYhoisjLqgGLHpObiSloPoVA2iU3MQk5aD3AqKj72tHB0a10ewXwN0btIAnZrUR0POBE1EdQzLEFEdpNcLpKgLcCMzD/GZeYjLyENsei6upefglkZb4TZ2CjmCvJ3RrrEK7Rqp0K5RfTT3dIKtQl7D6YmIahbLEJGFyiksRnJ2AZLvFCAxKx+JWflIuvs14XY+tCX6B27rrbJHc09nBHk7I8jLBUHeLgh0r8fiQ0RWiWWIqJYRQkBdUIz0HC1uaQqRpr57u3s/ObsAKdkF0BSW3611P1uFDE1cHRHg5oRA93po5uGE5h5OaOrhxJmeiYjuwzJEZGZCCOQX6XAnvwh38oqRlV+E7Pwi3M4tQmauFrdzi3A7T4uM3CJk5miRkaM1XLX9Yeo72qJRfQc0cXVEE1dH+N796tfQEY3qO8CGIz1ERA9lMWXo2WefRVRUFNLT09GgQQP07dsXn3zyCXx8fB64jRACixYtwpo1a3Dnzh2EhITgyy+/RJs2bWowOVm6Ep0eeVodcotKkKctQa62BDmFJcgtLEGuthg5hSXQFBRDY/haDHVBMbLzi5FdUAx1fnGVy8396jvawsNZCS+VA7xclPBysYenyh4+9R3QuL4DfOo7oJ7SYv4KExHVWhbzL2lYWBjmzZsHb29vJCcnY9asWXj++edx9OjRB26zePFifPbZZ9i4cSNatGiBDz74AP369UNMTAycnZ1rMD2Zkl4vUKTTQ1uiR1GJHkW60q/aEl3p45LS5wqLddDeXV5YXPr4r6+lt4JiHfKL/rqfp9WhoEiHvKIS5BfpkKctqfTYG2PYKeRwrWeHBvXs4FrPFg0c7eDmpISbkx0aOinhWs8OHs5KuN+9KW04Xw8RUU2QCXH//LGW4+eff8aQIUOg1Wpha1v++AchBHx8fDB9+nTMmTMHAKDVauHp6YlPPvkEr7zySpXeR6PRQKVSQa1Ww8XFxWT5c+6OHtz79IUABASEAPRCQNxbdt99vRBl1vv7NqWXgSr9qteXfv3786WvIaDX/7VM3PecXgjo9H+9hu7uMr3+vuV31ynRC8M6urvP6+6uW6L/ax2d7t5jPUr0AiV3H5fo9Xfvl34t1guU6PQo1pU+Lrr7tVhXWniKdXoU60pfVwq2ChnqKW3gpLSBs70tnJU2cLa3gZO9DVzsbeHicO+rLVzsbdHA0RYqR1vUd7RDfQdbONopeDkKIqIaYszvb4sZGbpfVlYWtm7diu7du1dYhADgxo0bSEtLQ//+/Q3LlEolevfujaNHjz6wDGm1Wmi1f516rNFoTBv+rs3HEvDprzFmeW1rY6uQQWmjgNJGDqWNHHY2cihtFLC3Lf2qtC1drrRVwMG2dLm9jQL2tgo42CngaFe6vPS+DRzvLrt330lpA0elgiM1RER1lEWVoTlz5mDFihXIz89Ht27dsHv37geum5aWBgDw9PQss9zT0xMJCQkP3C4iIgKLFi0yTeBKlP4Cl0MmA2SQ3f0KyGQV35ffvY+768pld5fdt578/q+A4f79y+Xye+vJIJcBigc8L5fJoJDLDO9Tel8GuVwGhQx3v95dLpfBRl56XyGTQaEo/Vq6TA4bRem2toq7yxRy2N5d31Yhv/tVBpu769oq5LBV3L0vLy03tneXl97/a5mdQs7RFiIiqhZJd5MtXLjwocXj5MmT6NKlCwAgMzMTWVlZSEhIwKJFi6BSqbB79+4KfxkePXoUjz/+OFJSUuDt7W1YPnnyZCQlJWHfvn0Vvl9FI0O+vr4m301GRERE5mMxu8mmTJmCkSNHVrqOv7+/4b6bmxvc3NzQokULBAUFwdfXF8ePH0doaGi57by8vACUjhDdX4bS09PLjRbdT6lUQqnk5QaIiIishaRl6F65eRT3BrTuH8W5X0BAALy8vHDgwAF06tQJAFBUVITDhw/jk08+ebTAREREVOdYxIxsJ06cwIoVKxAVFYWEhAQcOnQIo0aNQtOmTcuMCrVq1Qo7d+4EUHoczfTp0/HRRx9h586duHjxIsaNGwdHR0eMGjVKqm+FiIiIahmLOIDawcEBO3bswIIFC5CXlwdvb28MHDgQ3333XZldWjExMVCr1YbHs2fPRkFBAV577TXDpIv79+/nHENERERkYLHzDNUUc80zREREROZjzO9vi9hNRkRERGQuLENERERk1ViGiIiIyKqxDBEREZFVYxkiIiIiq8YyRERERFaNZYiIiIisGssQERERWTWWISIiIrJqFnE5Dindm6Bbo9FInISIiIiq6t7v7apcaINl6CFycnIAAL6+vhInISIiImPl5ORApVJVug6vTfYQer0eKSkpcHZ2hkwmkzqO5DQaDXx9fZGUlMRrtZkZP+uaw8+65vCzrjnW/lkLIZCTkwMfHx/I5ZUfFcSRoYeQy+Vo3Lix1DFqHRcXF6v8yyUFftY1h591zeFnXXOs+bN+2IjQPTyAmoiIiKwayxARERFZNZYhMopSqcSCBQugVCqljlLn8bOuOfysaw4/65rDz7rqeAA1ERERWTWODBEREZFVYxkiIiIiq8YyRERERFaNZYiIiIisGssQVZtWq0XHjh0hk8kQFRUldZw6Jz4+HhMnTkRAQAAcHBzQtGlTLFiwAEVFRVJHqzNWrlyJgIAA2NvbIzg4GH/88YfUkeqciIgIPPbYY3B2doaHhweGDBmCmJgYqWNZhYiICMhkMkyfPl3qKLUWyxBV2+zZs+Hj4yN1jDrrypUr0Ov1WL16NS5duoR///vf+OqrrzBv3jypo9UJ27Ztw/Tp0/H222/j7Nmz6NmzJwYNGoTExESpo9Uphw8fxuuvv47jx4/jwIEDKCkpQf/+/ZGXlyd1tDrt5MmTWLNmDdq3by91lFqNp9ZTtfzyyy+YOXMmtm/fjjZt2uDs2bPo2LGj1LHqvE8//RSrVq3C9evXpY5i8UJCQtC5c2esWrXKsCwoKAhDhgxBRESEhMnqtoyMDHh4eODw4cPo1auX1HHqpNzcXHTu3BkrV67EBx98gI4dO2LZsmVSx6qVODJEj+zWrVuYPHkyvvnmGzg6Okodx6qo1Wq4urpKHcPiFRUV4fTp0+jfv3+Z5f3798fRo0clSmUd1Go1APDn2Ixef/11PP300+jbt6/UUWo9XqiVHokQAuPGjUN4eDi6dOmC+Ph4qSNZjbi4OCxfvhxLly6VOorFy8zMhE6ng6enZ5nlnp6eSEtLkyhV3SeEwMyZM9GjRw+0bdtW6jh10nfffYczZ87g5MmTUkexCBwZojIWLlwImUxW6e3UqVNYvnw5NBoN5s6dK3Vki1XVz/p+KSkpGDhwIF544QVMmjRJouR1j0wmK/NYCFFuGZnOlClTcP78eXz77bdSR6mTkpKSMG3aNGzZsgX29vZSx7EIPGaIysjMzERmZmal6/j7+2PkyJHYtWtXmV8YOp0OCoUCL730EjZt2mTuqBavqp/1vX/MUlJSEBYWhpCQEGzcuBFyOf8vU11FRUVwdHTEDz/8gKFDhxqWT5s2DVFRUTh8+LCE6eqmN954Az/99BOOHDmCgIAAqePUST/99BOGDh0KhUJhWKbT6SCTySCXy6HVass8RyxD9IgSExOh0WgMj1NSUjBgwAD8+OOPCAkJQePGjSVMV/ckJycjLCwMwcHB2LJlC/8hM6GQkBAEBwdj5cqVhmWtW7fGc889xwOoTUgIgTfeeAM7d+5EZGQkmjdvLnWkOisnJwcJCQlllo0fPx6tWrXCnDlzuGuyAjxmiB5JkyZNyjx2cnICADRt2pRFyMRSUlLQp08fNGnSBEuWLEFGRobhOS8vLwmT1Q0zZ87E6NGj0aVLF4SGhmLNmjVITExEeHi41NHqlNdffx3/+c9/8N///hfOzs6GY7JUKhUcHBwkTle3ODs7lys89erVQ8OGDVmEHoBliKiW279/P2JjYxEbG1uuaHJgt/pGjBiB27dv47333kNqairatm2LvXv3ws/PT+podcq9qQv69OlTZvmGDRswbty4mg9EdB/uJiMiIiKrxiMwiYiIyKqxDBEREZFVYxkiIiIiq8YyRERERFaNZYiIiIisGssQERERWTWWISIiIrJqLENE9FAymQw//fST1DGqZOHChejYsaPUMUyuT58+mD59epXXj4yMhEwmQ3Z29gPX2bhxI+rXr1/tbESWjmWIqA4bN24chgwZInUMi1eV0rB06VKoVCrk5+eXe66wsBD169fHZ5999sgZduzYgffff/+RtyeiB2MZIiIygTFjxqCgoADbt28v99z27duRn5+P0aNHG/26xcXFAABXV1c4OztXOycRlccyRGRF+vTpg6lTp2L27NlwdXWFl5cXFi5cWGada9euoVevXrC3t0fr1q1x4MCBcq+TnJyMESNGoEGDBmjYsCGee+45xMfHG56/NyK1aNEieHh4wMXFBa+88gqKiooM6wghsHjxYgQGBsLBwQEdOnTAjz/+aHj+3m6e33//HV26dIGjoyO6d++OmJiYMlk+/vhjeHp6wtnZGRMnTkRhYWG5vBs2bEBQUBDs7e3RqlWrMleoj4+Ph0wmw44dOxAWFgZHR0d06NABx44dM+QYP3481Go1ZDIZZDJZuc8MANzd3TF48GCsX7++3HPr16/Hs88+C3d3d8yZMwctWrSAo6MjAgMD8e677xoKD/DXbr7169cjMDAQSqUSQohyu8m2bNmCLl26wNnZGV5eXhg1ahTS09PLvfeff/6JDh06wN7eHiEhIbhw4UK5de63a9cuBAcHw97eHoGBgVi0aBFKSkoq3YbI4gkiqrPGjh0rnnvuOcPj3r17CxcXF7Fw4UJx9epVsWnTJiGTycT+/fuFEELodDrRtm1b0adPH3H27Flx+PBh0alTJwFA7Ny5UwghRF5enmjevLmYMGGCOH/+vLh8+bIYNWqUaNmypdBqtYb3dXJyEiNGjBAXL14Uu3fvFu7u7mLevHmGLPPmzROtWrUS+/btE3FxcWLDhg1CqVSKyMhIIYQQhw4dEgBESEiIiIyMFJcuXRI9e/YU3bt3N7zGtm3bhJ2dnfj666/FlStXxNtvvy2cnZ1Fhw4dDOusWbNGeHt7i+3bt4vr16+L7du3C1dXV7Fx40YhhBA3btwQAESrVq3E7t27RUxMjHj++eeFn5+fKC4uFlqtVixbtky4uLiI1NRUkZqaKnJycir8vPfs2SNkMpm4fv26YdmNGzeETCYTe/fuFUII8f7774s///xT3LhxQ/z888/C09NTfPLJJ4b1FyxYIOrVqycGDBggzpw5I86dOyf0er3o3bu3mDZtmmG9devWib1794q4uDhx7Ngx0a1bNzFo0CDD8/c+v6CgILF//35x/vx58cwzzwh/f39RVFQkhBBiw4YNQqVSGbbZt2+fcHFxERs3bhRxcXFi//79wt/fXyxcuLDiHzCiOoJliKgOq6gM9ejRo8w6jz32mJgzZ44QQohff/1VKBQKkZSUZHj+l19+KVOG1q1bJ1q2bCn0er1hHa1WKxwcHMSvv/5qeF9XV1eRl5dnWGfVqlXCyclJ6HQ6kZubK+zt7cXRo0fLZJk4caL4xz/+IYT465f5b7/9Znh+z549AoAoKCgQQggRGhoqwsPDy7xGSEhImTLk6+sr/vOf/5RZ5/333xehoaFCiL/K0Nq1aw3PX7p0SQAQ0dHRQojypeFBSkpKRKNGjcT8+fMNy+bPny8aNWokSkpKKtxm8eLFIjg42PB4wYIFwtbWVqSnp5dZ7+9l6O9OnDghABiK2r3P77vvvjOsc/v2beHg4CC2bdtW4ffVs2dP8dFHH5V53W+++UZ4e3tX/o0TWTgbiQakiEgi7du3L/PY29vbsHslOjoaTZo0QePGjQ3Ph4aGlln/9OnTiI2NLXf8SmFhIeLi4gyPO3ToAEdHxzKvk5ubi6SkJKSnp6OwsBD9+vUr8xpFRUXo1KnTA/N6e3sDANLT09GkSRNER0cjPDy8zPqhoaE4dOgQACAjIwNJSUmYOHEiJk+ebFinpKQEKpWqSu/TqlUrVJVCocDYsWOxceNGLFiwADKZDJs2bcK4ceOgUCgAAD/++COWLVuG2NhY5ObmoqSkBC4uLmVex8/PD+7u7pW+19mzZ7Fw4UJERUUhKysLer0eAJCYmIjWrVuX+TzucXV1RcuWLREdHV3ha54+fRonT57Ehx9+aFim0+lQWFiI/Pz8Mn+eRHUJyxCRlbG1tS3zWCaTGX6RCiHKrS+Tyco81uv1CA4OxtatW8ut+7Bf4H9/vz179qBRo0ZlnlcqlQ/Mey/Lve0f5t56X3/9NUJCQso8d6+cmOJ97jdhwgRERETg4MGDAErLyfjx4wEAx48fx8iRI7Fo0SIMGDAAKpUK3333HZYuXVrmNerVq1fpe+Tl5aF///7o378/tmzZAnd3dyQmJmLAgAFljst6kL//md6j1+uxaNEiDBs2rNxz9vb2D31dIkvFMkREBq1bt0ZiYiJSUlLg4+MDAIYDie/p3Lkztm3bZjgw+kHOnTuHgoICODg4ACgtAk5OTmjcuDEaNGgApVKJxMRE9O7d+5HzBgUF4fjx4xgzZoxh2fHjxw33PT090ahRI1y/fh0vvfTSI7+PnZ0ddDpdldZt2rQpevfujQ0bNhgOfG7atCmA0oOZ/fz88PbbbxvWT0hIMDrPlStXkJmZiY8//hi+vr4AgFOnTlW47vHjx9GkSRMAwJ07d3D16tUHjnZ17twZMTExaNasmdGZiCwZyxARGfTt2xctW7bEmDFjsHTpUmg0mjK/uAHgpZdewqeffornnnsO7733Hho3bozExETs2LEDb731lmEXW1FRESZOnIh33nkHCQkJWLBgAaZMmQK5XA5nZ2fMmjULM2bMgF6vR48ePaDRaHD06FE4OTlh7NixVco7bdo0jB07Fl26dEGPHj2wdetWXLp0CYGBgYZ1Fi5ciKlTp8LFxQWDBg2CVqvFqVOncOfOHcycObNK7+Pv74/c3Fz8/vvvht1/le0yun+33Nq1aw3LmzVrhsTERHz33Xd47LHHsGfPHuzcubNKGe7XpEkT2NnZYfny5QgPD8fFixcfOAfRe++9h4YNG8LT0xNvv/023NzcHjj31Pz58/HMM8/A19cXL7zwAuRyOc6fP48LFy7ggw8+MDonkaXgqfVEZCCXy7Fz505otVp07doVkyZNKnP8CAA4OjriyJEjaNKkCYYNG4agoCBMmDABBQUFZUaKnnzySTRv3hy9evXCiy++iMGDB5c5Jf3999/H/PnzERERgaCgIAwYMAC7du1CQEBAlfOOGDEC8+fPx5w5cxAcHIyEhAS8+uqrZdaZNGkS1q5di40bN6Jdu3bo3bs3Nm7caNT7dO/eHeHh4RgxYgTc3d2xePHiStcfPnw4lEollEplmV1Ozz33HGbMmIEpU6agY8eOOHr0KN59990q57jH3d0dGzduxA8//IDWrVvj448/xpIlSypc9+OPP8a0adMQHByM1NRU/Pzzz7Czs6tw3QEDBmD37t04cOAAHnvsMXTr1g2fffYZ/Pz8jM5IZElkoqKDBIiIqmHcuHHIzs62mEt4EJF148gQERERWTWWISIiIrJq3E1GREREVo0jQ0RERGTVWIaIiIjIqrEMERERkVVjGSIiIiKrxjJEREREVo1liIiIiKwayxARERFZNZYhIiIismosQ0RERGTV/h8pmysEXefrrwAAAABJRU5ErkJggg==\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 06:32:43 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": 19,
"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": 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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",
"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 0x7749e1c55550>]"
]
},
"execution_count": 12,
"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": 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": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean Absolute Error (MAE): 0.03\n",
"Mean Squared Error (MSE): 0.00\n",
"Root Mean Squared Error (RMSE): 0.04\n",
"R2-score: 0.51\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.metrics import r2_score, mean_squared_error, mean_absolute_error\n",
"from scipy.optimize import curve_fit\n",
"\n",
"# Misal fungsi sigmoid\n",
"def sigmoid(x, beta1, beta2):\n",
" return 1 / (1 + np.exp(-beta1*(x-beta2)))\n",
"\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 metrics\n",
"mae = mean_absolute_error(test_y, y_hat)\n",
"mse = mean_squared_error(test_y, y_hat)\n",
"rmse = np.sqrt(mse)\n",
"r2 = r2_score(test_y, y_hat)\n",
"\n",
"print(\"Mean Absolute Error (MAE): %.2f\" % mae)\n",
"print(\"Mean Squared Error (MSE): %.2f\" % mse)\n",
"print(\"Root Mean Squared Error (RMSE): %.2f\" % rmse)\n",
"print(\"R2-score: %.2f\" % r2)\n",
"\n",
"# Optional: plot actual vs predicted\n",
"plt.scatter(test_x, test_y, label='Actual', color='blue')\n",
"plt.scatter(test_x, y_hat, label='Predicted', color='red')\n",
"plt.xlabel('X')\n",
"plt.ylabel('Y')\n",
"plt.title('Sigmoid Regression: Actual vs Predicted')\n",
"plt.legend()\n",
"plt.show()\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"
]
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"<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"
]
},
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"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"
]
}
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