{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", " \n", " \"Skills\n", " \n", "

\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": [ "

Importing required libraries

\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [] }, "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": { "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": { "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": { "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": { "tags": [] }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjsAAAGzCAYAAADJ3dZzAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAABN2klEQVR4nO3deXgTdeIG8DdJ2/RO6UHaQksLVO4brCAIKFJRLmEVF5ZbHvgBQi0C4sGlUkFFdmVhF2UpigoegCIoFIVWRZT7plDoBaWUozQ90zT5/v4oCYRSaErSSdL38zx5SGYm07cRzet3vjMjE0IIEBERETkpudQBiIiIiGyJZYeIiIicGssOEREROTWWHSIiInJqLDtERETk1Fh2iIiIyKmx7BAREZFTY9khIiIip8ayQ0RERE6NZYeIiIicmouUPzw5ORnvvfceDhw4gEuXLmHTpk0YPHjwXbedOHEiVq1ahQ8//BCxsbGm5VqtFq+88gq+/PJLlJSU4IknnsCKFSvQsGHDaucwGAzIzs6Gj48PZDLZA/5WREREVBuEECgoKEBoaCjk8qrHbyQtO0VFRWjXrh3Gjh2LoUOHVrnd5s2b8eeffyI0NLTSutjYWGzZsgXr169HQEAAZsyYgf79++PAgQNQKBTVypGdnY2wsLAa/x5EREQknaysrHsOckhadvr164d+/frdc5uLFy9i6tSp2L59O5555hmzdfn5+Vi9ejU+++wz9OnTBwCwbt06hIWFYefOnYiJialWDh8fHwAVH5avr28NfhMiIiKqbRqNBmFhYabv8apIWnbux2AwYOTIkZg5cyZatWpVaf2BAweg0+nQt29f07LQ0FC0bt0ae/bsqbLsaLVaaLVa0+uCggIAgK+vL8sOERGRg7nfFBS7nqC8ePFiuLi4YNq0aXddn5OTAzc3N9SrV89suVqtRk5OTpX7jY+Ph0qlMj14CIuIiMh52W3ZOXDgAP75z38iISHB4knDQoh7vmfOnDnIz883PbKysh40LhEREdkpuy07v/76K3JzcxEeHg4XFxe4uLggIyMDM2bMQEREBAAgODgYZWVlyMvLM3tvbm4u1Gp1lftWKpWmQ1Y8dEVEROTc7LbsjBw5EkePHsXhw4dNj9DQUMycORPbt28HAHTq1Amurq5ITEw0ve/SpUs4fvw4unXrJlV0IiIisiOSTlAuLCxEamqq6XVaWhoOHz4Mf39/hIeHIyAgwGx7V1dXBAcHo1mzZgAAlUqF8ePHY8aMGQgICIC/vz9eeeUVtGnTxnR2FhEREdVtkpad/fv3o3fv3qbXcXFxAIDRo0cjISGhWvv48MMP4eLigueff950UcGEhIRqX2OHiIiInJtMCCGkDiE1jUYDlUqF/Px8zt8hIiJyENX9/rbbOTtERERE1sCyQ0RERE6NZYeIiIicGssOEREROTWWHSIiInJqLDtERERkM1nXi5F9owQGg3Qnf7PsEBERkc0sTTyDbu/+gv8mn5csA8sOERER2Uza1SIAQESAp2QZWHaIiIjIZjKuVZSdRgFekmVg2SEiIiKbyC/WIa9YBwBoxJEdIiIicjbpN0d16vso4aWU7nacLDtERERkE8ayEyHhISyAZYeIiIhsJP1qMQAgIlC6Q1gAyw4RERHZSLodTE4GWHaIiIjIRoxlJzKQZYeIiIicUMa1isNYUp6JBbDsEBERkQ3kl+hwvagMACcoExERkRMyXkwwSOLTzgGWHSIiIrIB420iIiUe1QFYdoiIiMgG7GW+DsCyQ0RERDaQbrwBqMRnYgEsO0RERGQD9nL1ZIBlh4iIiGwg/Zp9XD0ZYNkhIiIiK7v9tHOpr54MsOwQERGRlRlPOw/0VsJb4tPOAZYdIiIisjLjIaxIOziEBbDsEBERkZVlXLWPG4AasewQERGRVaXZyQ1AjVh2iIiIyKrs6YKCAMsOERERWZnpgoI8jEVERETORlOqwzXj3c55GIuIiIicTcbVikNY9nLaOcCyQ0RERFZ06zYR9jFfB2DZISIiIiuypxuAGrHsEBERkdWY7onFkR0iIiJyRqbDWBzZISIiImeUcc2+TjsHWHaIiIjISgpKdbhaaLzbOQ9jERERkZMxXjk50NsNPu6uEqe5RdKyk5ycjAEDBiA0NBQymQybN282rdPpdJg9ezbatGkDLy8vhIaGYtSoUcjOzjbbh1arxUsvvYTAwEB4eXlh4MCBuHDhQi3/JkRERHTuSiEA+7knlpGkZaeoqAjt2rXD8uXLK60rLi7GwYMH8eabb+LgwYPYuHEjzpw5g4EDB5ptFxsbi02bNmH9+vX47bffUFhYiP79+0Ov19fWr0FEREQAzuVWlJ2m9b0lTmJO0ksb9uvXD/369bvrOpVKhcTERLNlH330ER5++GFkZmYiPDwc+fn5WL16NT777DP06dMHALBu3TqEhYVh586diImJsfnvQERERBXOXamYnNwkyL7KjkPN2cnPz4dMJoOfnx8A4MCBA9DpdOjbt69pm9DQULRu3Rp79uypcj9arRYajcbsQURERA/GeBiLZaeGSktL8eqrr2L48OHw9fUFAOTk5MDNzQ316tUz21atViMnJ6fKfcXHx0OlUpkeYWFhNs1ORETk7PQGgfNXObJTYzqdDi+88AIMBgNWrFhx3+2FEJDJZFWunzNnDvLz802PrKwsa8YlIiKqcy7kFaOs3AClixwN6nlIHceM3ZcdnU6H559/HmlpaUhMTDSN6gBAcHAwysrKkJeXZ/ae3NxcqNXqKvepVCrh6+tr9iAiIqKau/1MLIW86gEHKdh12TEWnbNnz2Lnzp0ICAgwW9+pUye4urqaTWS+dOkSjh8/jm7dutV2XCIiojrrXO7NQ1h2diYWIPHZWIWFhUhNTTW9TktLw+HDh+Hv74/Q0FD87W9/w8GDB/HDDz9Ar9eb5uH4+/vDzc0NKpUK48ePx4wZMxAQEAB/f3+88soraNOmjensLCIiIrK9VONp53Y2XweQuOzs378fvXv3Nr2Oi4sDAIwePRrz58/H999/DwBo37692ft27dqFXr16AQA+/PBDuLi44Pnnn0dJSQmeeOIJJCQkQKFQ1MrvQERERLediWWHIzsyIYSQOoTUNBoNVCoV8vPzOX+HiIioBjos3IG8Yh22TuuOVqGqWvmZ1f3+tus5O0RERGT/rhVqkVesg0wGNA60v5Edlh0iIiJ6IMYrJzfw84CHm/1NI2HZISIiogdir1dONmLZISIiogdiPBOLZYeIiIic0q0zsbwkTnJ3LDtERET0QIxlxx6vsQOw7BAREdEDKNXpcSGvBIB9XmMHYNkhIiKiB3D+ShGEAFQergjwcpM6zl2x7BAREVGNmQ5h1feGTGZfNwA1YtkhIiKiGrt1JpZ9Tk4GWHaIiIjoAdj7NXYAlh0iIiJ6AMarJ7PsEBERkdPRGwTO3zZnx16x7BAREVGNZN8ogbbcADeFHA3reUgdp0osO0RERFQjqTdHdSICPeGisN9KYb/JiIiIyK6dy7X/Q1gAyw4RERHVkCOciQWw7BAREVEN2fvdzo1YdoiIiMhiQgicuczDWEREROSkLmu0yC/RQS5j2SEiIiInlHK5AAAQEegFd1eFxGnujWWHiIiILJaSowEANA/2kTjJ/bHsEBERkcVScirm6zRT+0qc5P5YdoiIiMhiKZcrRnaaBdv3fB2AZYeIiIgspDcInL15JlazYI7sEBERkZPJuFYEbbkB7q5yhPt7Sh3nvlh2iIiIyCJnbp6JFVXfBwq5TOI098eyQ0RERBY5nVNRdh5S2/+ZWADLDhEREVnIOLLjCKedAyw7REREZCHTyA7LDhERETmbUp0e6VeLAHBkh4iIiJxQam4hDAJQebiivo9S6jjVwrJDRERE1ZZy8xBWs2AfyGT2fyYWwLJDREREFnC0yckAyw4RERFZwNFOOwdYdoiIiMgCHNkhIiIip5VfrMOl/FIAQBRHdoiIiMjZnMmtGNUJVblD5eEqcZrqY9khIiKianG0iwkaSVp2kpOTMWDAAISGhkImk2Hz5s1m64UQmD9/PkJDQ+Hh4YFevXrhxIkTZttotVq89NJLCAwMhJeXFwYOHIgLFy7U4m9BRERUN5y57bRzRyJp2SkqKkK7du2wfPnyu65fsmQJli5diuXLl2Pfvn0IDg7Gk08+iYKCAtM2sbGx2LRpE9avX4/ffvsNhYWF6N+/P/R6fW39GkRERHWC6Ro7DjRfBwBcpPzh/fr1Q79+/e66TgiBZcuW4fXXX8eQIUMAAGvXroVarcYXX3yBiRMnIj8/H6tXr8Znn32GPn36AADWrVuHsLAw7Ny5EzExMbX2uxARETkzIQRSLnNkx6rS0tKQk5ODvn37mpYplUr07NkTe/bsAQAcOHAAOp3ObJvQ0FC0bt3atM3daLVaaDQaswcRERFV7bJGi/wSHRRyGZoEeUsdxyJ2W3ZycnIAAGq12my5Wq02rcvJyYGbmxvq1atX5TZ3Ex8fD5VKZXqEhYVZOT0REZFzMY7qRAR4wt1VIXEay9ht2TG6874bQoj73ovjftvMmTMH+fn5pkdWVpZVshIRETmrk9kVR0Gah/hKnMRydlt2goODAaDSCE1ubq5ptCc4OBhlZWXIy8urcpu7USqV8PX1NXsQERFR1U5k5wMAWoU63nem3ZadyMhIBAcHIzEx0bSsrKwMSUlJ6NatGwCgU6dOcHV1Ndvm0qVLOH78uGkbIiIienAnbo7stApVSZzEcpKejVVYWIjU1FTT67S0NBw+fBj+/v4IDw9HbGwsFi1ahKioKERFRWHRokXw9PTE8OHDAQAqlQrjx4/HjBkzEBAQAH9/f7zyyito06aN6ewsIiIiejCF2nKkXS0C4JgjO5KWnf3796N3796m13FxcQCA0aNHIyEhAbNmzUJJSQkmT56MvLw8REdHY8eOHfDxuXXK24cffggXFxc8//zzKCkpwRNPPIGEhAQoFI41eYqIiMhenbpUMaoT7OuOQG+lxGksJxNCCKlDSE2j0UClUiE/P5/zd4iIiO6Q8Hsa5m85iSea18fqMV2kjmNS3e9vu52zQ0RERPbh1nwdxxwQYNkhIiKiezpuLDsNHG9yMsCyQ0RERPegLdfj7M0LCnJkh4iIiJzO2cuFKDcIqDxc0cDPQ+o4NcKyQ0RERFW6/WKC97uDgb1i2SEiIqIqHb/o2JOTAZYdIiIiugfjyE5rB52cDLDsEBERURX0BoFTlxx7cjLwAGWnrKwMKSkpKC8vt2YeIiIishNpV4tQotPDw1WByEBvqePUmMVlp7i4GOPHj4enpydatWqFzMxMAMC0adPw7rvvWj0gERERScN4CKt5iA8UcsecnAzUoOzMmTMHR44cwe7du+Hu7m5a3qdPH2zYsMGq4YiIiEg6xisnt3bAO53fzuIbgW7evBkbNmzAI488YnYKWsuWLXHu3DmrhiMiIiLp3H7auSOzeGTnypUrqF+/fqXlRUVFDnv+PREREZkTQtx2TyzHHtmxuOx06dIFW7duNb02FpyPP/4YXbt2tV4yIiIikkx2filuFOvgIpfhoWDHnZwM1OAwVnx8PJ566imcPHkS5eXl+Oc//4kTJ07gjz/+QFJSki0yEhERUS07frHiEFbT+t5QuigkTvNgLB7Z6datG37//XcUFxejSZMm2LFjB9RqNf744w906tTJFhmJiIiolpkmJzvwxQSNLB7ZAYA2bdpg7dq11s5CREREduKkk0xOBqpZdjQaTbV36Ovr+B8KERFRXXfrnlh1ZGTHz8/vvmdaCSEgk8mg1+utEoyIiIikcVlTihxNKeSyOjSys2vXLlvnICIiIjtxOOsGAOAhtQ+8lDWa8WJXqvUb9OzZ09Y5iIiIyE4cuVl22jX0kzSHtdSoruXl5WH16tU4deoUZDIZWrRogbFjx8Lf39/a+YiIiKiWGUd22of7SZrDWiw+9TwpKQkRERH417/+hby8PFy/fh3/+te/EBkZyevsEBEROTiDQeDohYozsersyM6UKVMwbNgwrFy5EgpFxUWG9Ho9Jk+ejClTpuD48eNWD0lERES149yVQhRqy+HhqsBDase+crKRxSM7586dw4wZM0xFBwAUCgXi4uJ4I1AiIiIHZzyE1aaBCi4Ki2uCXbL4t+jYsSNOnTpVafmpU6fQvn17a2QiIiIiiRy5cAMA0C7M8a+vY1Stw1hHjx41PZ82bRqmT5+O1NRUPPLIIwCAvXv34t///jfeffdd26QkIiKiWmGanBxWT9ogViQTQoj7bSSXyyGTyXC/TR31ooIajQYqlQr5+fm8AjQREdVZpTo9Ws/bjnKDwG+ze6NhPU+pI91Tdb+/qzWyk5aWZrVgREREZJ9OZOej3CAQ6O2GBn4eUsexmmqVnUaNGtk6BxEREUnscFbFKeftw+5/myhHUuNrQJ88eRKZmZkoKyszWz5w4MAHDkVERES1z9munGxkcdk5f/48nn32WRw7dsxsHo+xATrinB0iIiJyvisnG1l86vn06dMRGRmJy5cvw9PTEydOnEBycjI6d+6M3bt32yAiERER2dr1ojJkXi8GALRt4CdtGCuzeGTnjz/+wC+//IKgoCDI5XLI5XJ0794d8fHxmDZtGg4dOmSLnERERGRDxkNYjQO9oPJ0lTaMlVk8sqPX6+HtXXH56MDAQGRnZwOomMSckpJi3XRERERUK25dX8dP0hy2YPHITuvWrXH06FE0btwY0dHRWLJkCdzc3LBq1So0btzYFhmJiIjIxm5dOdlP0hy2YHHZeeONN1BUVAQAePvtt9G/f3/06NEDAQEB2LBhg9UDEhERkW0JIUyHsTiyAyAmJsb0vHHjxjh58iSuX7+OevXqOdU5+URERHVF5vVi5BXr4KaQo3mIj9RxrK7G19m5nb+/vzV2Q0RERBIwztdpEeoLpYtC2jA2UK2yM2TIECQkJMDX1xdDhgy557YbN260SjAAKC8vx/z58/H5558jJycHISEhGDNmDN544w3I5RVzq4UQWLBgAVatWoW8vDxER0fj3//+N1q1amW1HERERM7sYEYeAKCDEx7CAqpZdlQqlekQlUpVe7d8X7x4Mf7zn/9g7dq1aNWqFfbv34+xY8dCpVJh+vTpAIAlS5Zg6dKlSEhIwEMPPYS3334bTz75JFJSUuDj43xDcURERNa2L72i7HSJcM4jNdW667mREAKZmZkICgqCp6ft74Tav39/qNVqrF692rRs6NCh8PT0xGeffQYhBEJDQxEbG4vZs2cDALRaLdRqNRYvXoyJEydW6+fwrudERFRXaUp1aL9gBwwC+PO1J6D2dZc6UrVV9/vbouvsCCEQFRWFixcvPnDA6ujevTt+/vlnnDlzBgBw5MgR/Pbbb3j66acBVNyNPScnB3379jW9R6lUomfPntizZ0+V+9VqtdBoNGYPIiKiuuhQ5g0YBBDu7+lQRccSFk1QlsvliIqKwrVr1xAVFWWrTCazZ89Gfn4+mjdvDoVCAb1ej3feeQd///vfAQA5OTkAALVabfY+tVqNjIyMKvcbHx+PBQsW2C44ERGRg9iXdh0A0DminsRJbMfiKygvWbIEM2fOxPHjx22Rx8yGDRuwbt06fPHFFzh48CDWrl2L999/H2vXrjXb7s5T3oUQ9zwNfs6cOcjPzzc9srKybJKfiIjI3u1Lryg7zjpfB6jBqef/+Mc/UFxcjHbt2sHNzQ0eHh5m669fv261cDNnzsSrr76KF154AQDQpk0bZGRkID4+HqNHj0ZwcDAAmM7UMsrNza002nM7pVIJpVJptZxERESOqKzcYDrtnGXnNsuWLbNBjLsrLi42nWJupFAoYDAYAACRkZEIDg5GYmIiOnToAAAoKytDUlISFi9eXGs5iYiIHNHx7Hxoyw2o5+mKJkFeUsexGYvLzujRo22R464GDBiAd955B+Hh4WjVqhUOHTqEpUuXYty4cQAqDl/FxsZi0aJFiIqKQlRUFBYtWgRPT08MHz681nISERE5ov3pxvk6/k59F4QHuoJySUkJdDqd2TJrnrr90Ucf4c0338TkyZORm5uL0NBQTJw4EXPnzjVtM2vWLJSUlGDy5Mmmiwru2LGD19ghIiK6j1vX13HeycmAhdfZAYCioiLMnj0bX331Fa5du1ZpvV6vt1q42sLr7BARUV0jhEDHtxKRV6zDxsnd0DHc8QqPTa6zA1SMpPzyyy9YsWIFlEolPvnkEyxYsAChoaH49NNPHyg0ERER1Y5zV4qQV6yDu6scrUNr7+4IUrD4MNaWLVvw6aefolevXhg3bhx69OiBpk2bolGjRvj8888xYsQIW+QkIiIiKzLO12kf5gc3F4vHPhyKxb/d9evXERkZCaBifo7xVPPu3bsjOTnZuumIiIjIJpz9fli3s7jsNG7cGOnp6QCAli1b4quvvgJQMeLj5+dnzWxERERkI/szbp2J5ewsLjtjx47FkSNHAFRcidg4d+fll1/GzJkzrR6QiIiIrCtXU4qMa8WQy4CO4X5Sx7G5as/ZiY2NxYsvvoiXX37ZtKx37944ffo09u/fjyZNmqBdu3Y2CUlERETWYzyE1TzYFz7urhKnsb1qj+z89NNPaNeuHR5++GGsWrXKdKfw8PBwDBkyhEWHiIjIQdy6H5bjnW5eE9UuO6dPn0ZycjLatGmDV155BaGhoRg1ahQnJRMRETkY43ydLpHOP18HsHDOzqOPPorVq1cjJycHH330EdLT09GrVy9ERUXh3XffRXZ2tq1yEhERkRVoSnU4mV1xdKZzI5adKnl6emLs2LFITk7G2bNn8fzzz2PJkiWIiIiwcjwiIiKypr/OX4dBAJGBXghWuUsdp1Y80FWEioqKkJSUhKSkJNy4cQNNmjSxVi4iIiKygT3nKm711K1JgMRJak+Nyk5ycjLGjh2L4OBgTJ8+HQ899BB+/fVXnDp1ytr5iIiIyIr2nLsKAOjWJFDiJLWn2qeeX7hwAWvXrkVCQgLOnTuH6OhofPjhh3jhhRfg7e1ty4xERERkBVcLtTidUwAAeKRx3ZivA1hQdiIiIhAQEICRI0di/PjxaNGihS1zERERkZX9cfMQVosQXwR4KyVOU3uqXXa++uorDBw4EC4uFt87lIiIiOxAXZyvA1hQdoYMGWLLHERERGRjxvk6jzatW2XHue/pTkRERACAC3nFyLhWDIVcVifudH47lh0iIqI6wHgIq11DVZ24H9btWHaIiIjqgD9M83XqzinnRhaXnXHjxqGgoKDS8qKiIowbN84qoYiIiMh6hBD4PdV4fZ26NV8HqEHZWbt2LUpKSiotLykpwaeffmqVUERERGQ9564UIbdACzcXOTo2qht3Or9dtc/G0mg0EEJACIGCggK4u9+6n4Zer8e2bdtQv359m4QkIiKimjOehdW5UT24uyokTlP7ql12/Pz8IJPJIJPJ8NBDD1VaL5PJsGDBAquGIyIioge3J7Vivs6jTevefB3AgrKza9cuCCHw+OOP49tvv4W//63T1tzc3NCoUSOEhobaJCQRERHVjN4g8Mf5irLTtQ7O1wEsKDs9e/YEAKSlpSEsLAxyOU/kIiIisnenLmmQX6KDt9IFbRuopI4jCYvv/dCoUSPcuHEDf/31F3Jzc2EwGMzWjxo1ymrhiIiI6MEYz8KKjvSHi6JuDlRYXHa2bNmCESNGoKioCD4+PpDJZKZ1MpmMZYeIiMiOJJ+9AgDoVkfn6wA1OPV8xowZpmvt3LhxA3l5eabH9evXbZGRiIiIaqBIW46/0iq+m3s3C5I4jXQsLjsXL17EtGnT4OnpaYs8REREZCW/p16FTi8Q7u+JyEAvqeNIxuKyExMTg/3799siCxEREVnR7jMVh7B6NQsym3ZS11g8Z+eZZ57BzJkzcfLkSbRp0wauruY3Exs4cKDVwhEREVHNCCGw+3QuAKB3s7p90V+Ly86ECRMAAAsXLqy0TiaTQa/XP3gqIiIieiBncwuRnV8KNxc5HmlcN6+vY2Rx2bnzVHMiIiKyP7tTKkZ1ujYOgIdb3btFxO0e6IT70tJSa+UgIiIiK9p1+tZ8nbrO4rKj1+vx1ltvoUGDBvD29sb58+cBAG+++SZWr15t9YBERERkmYJSHfZnGE85r9vzdYAalJ133nkHCQkJWLJkCdzc3EzL27Rpg08++cSq4YiIiMhyv6deg04vEBHgiYg6fMq5kcVl59NPP8WqVaswYsQIKBS3jgG2bdsWp0+ftmo4IiIislzSmYr5Or04qgOghhcVbNq0aaXlBoMBOp3OKqGIiIioZoQQnK9zB4vLTqtWrfDrr79WWv7111+jQ4cOVglFRERENZNyuQA5mlIoecq5icVlZ968eZg6dSoWL14Mg8GAjRs3YsKECVi0aBHmzp1r9YAXL17EP/7xDwQEBMDT0xPt27fHgQMHTOuFEJg/fz5CQ0Ph4eGBXr164cSJE1bPQURE5Ah2p9y88WeTALi71u1Tzo0sLjsDBgzAhg0bsG3bNshkMsydOxenTp3Cli1b8OSTT1o1XF5eHh599FG4urrixx9/xMmTJ/HBBx/Az8/PtM2SJUuwdOlSLF++HPv27UNwcDCefPJJFBQUWDULERGRI9h1mvN17iQTQgipQ1Tl1Vdfxe+//37Xw2ZAxahOaGgoYmNjMXv2bACAVquFWq3G4sWLMXHixGr9HI1GA5VKhfz8fPj6+lotPxERUW3SlOrQcWEiyg0CyTN7IzzAuW/aXd3v7we6qKCtff/99+jcuTOee+451K9fHx06dMDHH39sWp+WloacnBz07dvXtEypVKJnz57Ys2dPlfvVarXQaDRmDyIiIke363Quyg0CTYK8nL7oWKJat4uoV69ete+Wev369QcKdLvz589j5cqViIuLw2uvvYa//voL06ZNg1KpxKhRo5CTkwMAUKvVZu9Tq9XIyMiocr/x8fFYsGCB1XISERHZgx0nLgMAYloFS5zEvlSr7Cxbtsz0/Nq1a3j77bcRExODrl27AgD++OMPbN++HW+++aZVwxkMBnTu3BmLFi0CAHTo0AEnTpzAypUrMWrUKNN2dxYxIcQ9y9mcOXMQFxdneq3RaBAWFmbV7ERERLWpVKfHrpv3w2LZMVetsjN69GjT86FDh2LhwoWYOnWqadm0adOwfPly7Ny5Ey+//LLVwoWEhKBly5Zmy1q0aIFvv/0WABAcXPEPMycnByEhIaZtcnNzK4323E6pVEKpVFotJxERkdR+O3sVxWV6hKjc0bahSuo4dsXiOTvbt2/HU089VWl5TEwMdu7caZVQRo8++ihSUlLMlp05cwaNGjUCAERGRiI4OBiJiYmm9WVlZUhKSkK3bt2smoWIiMiebT9RMbWjb0t1taee1BUWl52AgABs2rSp0vLNmzcjIMC6Fy96+eWXsXfvXixatAipqan44osvsGrVKkyZMgVAxeGr2NhYLFq0CJs2bcLx48cxZswYeHp6Yvjw4VbNQkREZK/K9QbsPMX5OlWp1mGs2y1YsADjx4/H7t27TXN29u7di59++snqNwLt0qULNm3ahDlz5mDhwoWIjIzEsmXLMGLECNM2s2bNQklJCSZPnoy8vDxER0djx44d8PHxsWoWIiIie7UvPQ95xTr4ebri4Uh/qePYnRpdZ+fPP//Ev/71L5w6dQpCCLRs2RLTpk1DdHS0LTLaHK+zQ0REjmz+9yeQsCcdf+vUEO8/107qOLWmut/fFo/sAEB0dDQ+//zzGocjIiIi6xBCIPEkD2HdS43KjsFgQGpqKnJzc2EwGMzWPfbYY1YJRkRERPd3/KIGF2+UwNNNgR5RgVLHsUsWl529e/di+PDhyMjIwJ1HwGQyGfR6vdXCERER0b0Zz8Lq+VAQb/xZBYvLzqRJk9C5c2ds3boVISEhPL2NiIhIQj/dLDs8hFU1i8vO2bNn8c0336Bp06a2yENERETVdO5KIVJzC+Eil6F3c97lvCoWX2cnOjoaqamptshCREREFjAewuraJAAqD1eJ09gvi0d2XnrpJcyYMQM5OTlo06YNXF3NP9y2bdtaLRwRERFVbduxSwB4COt+LC47Q4cOBQCMGzfOtEwmk5luvskJykRERLZ37kohjl/UwEUuw9NtQu7/hjrM4rKTlpZmixxERERkge8PZwMAekQFwt/LTeI09s3ismO8CScRERFJQwiB749UlJ2B7UMlTmP/LJ6gDACfffYZHn30UYSGhiIjIwMAsGzZMnz33XdWDUdERESVHbuYj7SrRXB3lePJlpyvcz8Wl52VK1ciLi4OTz/9NG7cuGGao+Pn54dly5ZZOx8RERHd4bubh7D6tFDDW1mjmyHUKRaXnY8++ggff/wxXn/9dSgUt67U2LlzZxw7dsyq4YiIiMic3iDww9GKsjOofQOJ0zgGi8tOWloaOnToUGm5UqlEUVGRVUIRERHR3f2Zdg2XNVr4urvgsYd4L6zqsLjsREZG4vDhw5WW//jjj2jZsqU1MhEREVEVjGdhPd0mBEoX3gurOiw+0Ddz5kxMmTIFpaWlEELgr7/+wpdffon4+Hh88skntshIREREALTletOFBHkWVvVZXHbGjh2L8vJyzJo1C8XFxRg+fDgaNGiAf/7zn3jhhRdskZGIiIgAJJ+5Ck1pOer7KBEdGSB1HIdRoyncEyZMwIQJE3D16lUYDAbUr8+bjxEREdnad4cvAgAGtAuFQi6TOI3jqPH5arm5uUhJSYFMJoNMJkNQUJA1cxEREdFtirTl2HnqMgBgEA9hWcTiCcoajQYjR45EaGgoevbsicceewyhoaH4xz/+gfz8fFtkJCIiqvO2HruEUp0BkYFeaNNAJXUch2Jx2XnxxRfx559/YuvWrbhx4wby8/Pxww8/YP/+/ZgwYYItMhIREdV5X+3LAgD8rVNDyGQ8hGUJiw9jbd26Fdu3b0f37t1Ny2JiYvDxxx/jqaeesmo4IiIiAlJzC7E/Iw9yWUXZIctYPLITEBAAlary8JlKpUK9evWsEoqIiIhu+Xp/xahO72b1ofZ1lziN47G47LzxxhuIi4vDpUuXTMtycnIwc+ZMvPnmm1YNR0REVNfp9AZ8e/ACAOD5LmESp3FMFh/GWrlyJVJTU9GoUSOEh4cDADIzM6FUKnHlyhX897//NW178OBB6yUlIiKqg345nYurhWUI9Fbi8ea81EtNWFx2Bg8ebIMYREREdDfGiclDOzaAq8LiAzKEGpSdefPm2SIHERER3eGyphS7UnIBAM915iGsmqpRRbxx4wY++eQTzJkzB9evXwdQccjq4sWLVg1HRERUl31z4AIMAujcqB6a1veWOo7Dsnhk5+jRo+jTpw9UKhXS09MxYcIE+Pv7Y9OmTcjIyMCnn35qi5xERER1isEg8NXNs7CGcWLyA7F4ZCcuLg5jxozB2bNn4e5+6/S3fv36ITk52arhiIiI6qo/064j41oxvJUueKZtiNRxHJrFZWffvn2YOHFipeUNGjRATk6OVUIRERHVdcZRnQHtQuDpVuNbWRJqUHbc3d2h0WgqLU9JSeHNQImIiKzgaqEWW49WXM9uWJdwidM4PovLzqBBg7Bw4ULodDoAgEwmQ2ZmJl599VUMHTrU6gGJiIjqmi//zESZ3oB2YX5oH+YndRyHZ3HZef/993HlyhXUr18fJSUl6NmzJ5o2bQofHx+88847tshIRERUZ+j0Bqz7MwMAMLZbhLRhnITFBwF9fX3x22+/4ZdffsHBgwdhMBjQsWNH9OnTxxb5iIiI6pSfjufgskaLQG8lnm7DicnWUOMZT48//jgef/xxa2YhIiKq89buSQcAjIgOh5sLr5hsDRaVHYPBgISEBGzcuBHp6emQyWSIjIzE3/72N4wcORIymcxWOYmIiJzesQv52J+RBxe5DCOiOTHZWqpdGYUQGDhwIF588UVcvHgRbdq0QatWrZCRkYExY8bg2WeftWVOIiIip5dwc1TnmbYhqO/rfu+NqdqqPbKTkJCA5ORk/Pzzz+jdu7fZul9++QWDBw/Gp59+ilGjRlk9JBERkbO7WqjFliPZAIDRnJhsVdUe2fnyyy/x2muvVSo6QMX8nVdffRWff/65VcPdKT4+HjKZDLGxsaZlQgjMnz8foaGh8PDwQK9evXDixAmb5iAiIrK29X/dPN28oQodeLq5VVW77Bw9ehRPPfVUlev79euHI0eOWCXU3ezbtw+rVq1C27ZtzZYvWbIES5cuxfLly7Fv3z4EBwfjySefREFBgc2yEBERWZNOb8C6vZkAKkZ1OAfWuqpddq5fvw61Wl3lerVajby8PKuEulNhYSFGjBiBjz/+GPXq1TMtF0Jg2bJleP311zFkyBC0bt0aa9euRXFxMb744gubZCEiIrK2bccuIUdTikBvN94HywaqXXb0ej1cXKqe4qNQKFBeXm6VUHeaMmUKnnnmmUrX8klLS0NOTg769u1rWqZUKtGzZ0/s2bOnyv1ptVpoNBqzBxERkRSEEFi5+xwAYOQjEVC6KCRO5HyqPUFZCIExY8ZAqVTedb1Wq7VaqNutX78eBw8exL59+yqtM9549M4RJ7VajYyMjCr3GR8fjwULFlg3KBERUQ3sSsnF6ZwCeLkpMLpbI6njOKVql53Ro0ffdxtrn4mVlZWF6dOnY8eOHXB3r/oUvDuPbQoh7nm8c86cOYiLizO91mg0CAsLe/DAREREFlqxq2JUZ3h0OPw83SRO45yqXXbWrFljyxx3deDAAeTm5qJTp06mZXq9HsnJyVi+fDlSUlIAVIzwhITcOsaZm5t7z/lFSqWyyhEqIiKi2vJX2nXsz8iDm0KOF3s0ljqO07Lr61A/8cQTOHbsGA4fPmx6dO7cGSNGjMDhw4fRuHFjBAcHIzEx0fSesrIyJCUloVu3bhImJyIiur8Vu1MBAEM7NYSaFxG0mRrfG6s2+Pj4oHXr1mbLvLy8EBAQYFoeGxuLRYsWISoqClFRUVi0aBE8PT0xfPhwKSITERFVy4nsfOxOuQK5DJjUk6M6tmTXZac6Zs2ahZKSEkyePBl5eXmIjo7Gjh074OPjI3U0IiKiKhnPwHqmbSgaBXhJnMa5yYQQQuoQUtNoNFCpVMjPz4evr6/UcYiIyMmlXy3C4x/shkEA26b1QMtQfvfURHW/v+16zg4REZEz+m/yORgE0LtZEItOLWDZISIiqkVZ14vxzYELAIDJvZtKnKZuYNkhIiKqRct2noVOL9AjKhBdIvyljlMnsOwQERHVktTcAmw6VDGq80rfZhKnqTtYdoiIiGrJ0sQzMAggppUa7cL8pI5TZ7DsEBER1YJjF/Kx7VgOZDJgBkd1ahXLDhERUS14f0fFLY4Gt2+Ah9S8FlxtYtkhIiKysb/SriPpzBW4yGWI7RMldZw6h2WHiIjIhoQQeG/7aQDAsC5hvFqyBFh2iIiIbGh3yhXsS8+D0kWOlx7nqI4UWHaIiIhsRKc34O2tJwEAo7tFIFjFO5tLgWWHiIjIRj77IwPnrhQhwMsNU3i1ZMmw7BAREdnAtUItPtx5BgDwSkwzqDxcJU5Ud7HsEBER2cDSxDMoKC1HyxBfPN85TOo4dRrLDhERkZWduqTBl39lAgDmDWgJhVwmcaK6jWWHiIjIioQQWLjlJAwCeKZNCKIbB0gdqc5j2SEiIrKi7Sdy8Mf5a1C6yPFqv+ZSxyGw7BAREVlNSZkeb289BQCY+FhjhPl7SpyIAJYdIiIiq/lw5xlcyCtBqModk3o1kToO3cSyQ0REZAXHL+bjk1/PAwDefrY1PN1cJE5ERiw7RERED6hcb8Dsb4/CIIAB7ULxeHO11JHoNiw7RERED2j1b2k4ka2BysMVc/u3lDoO3YFlh4iI6AFkXCvC0sSKKyW//kwLBPkoJU5Ed2LZISIiqiEhBF7bdAzacgO6NQnAc50aSh2J7oJlh4iIqIa+3n8Bv6dWXFNn0bNtIJPxSsn2iGWHiIioBjKvFWPBlhMAgJeffAgRgV4SJ6KqsOwQERFZqFxvQOyGQygq0+PhCH9M6NFY6kh0Dyw7REREFlqx+xwOZt6Aj9IFHzzfjjf6tHMsO0RERBY4lJmHf/58FgCwcHAr3hLCAbDsEBERVVORthwvbzgMvUFgQLtQDG7fQOpIVA0sO0RERNW0cMtJpF8rRqjKHW8Pas2zrxwEyw4REVE1bD50ERv2Z0EmAz54vj1Unq5SR6JqYtkhIiK6j1OXNHh141EAwNTeTdG1SYDEicgSLDtERET3kF+iw/+tO4BSnQE9ogIR2+chqSORhVh2iIiIqmAwCMz46gjSrxWjgZ8H/vVCB55m7oBYdoiIiKqwMukcdp66DDeFHCv/0RH1vNykjkQ1wLJDRER0F7+evYIPdqQAABYOaoW2Df2kDUQ1xrJDRER0h7OXCzD584MwCGBY5zC88HC41JHoAbDsEBER3eZKgRZjE/ahoLQcnRvVw4JBraSORA/IrstOfHw8unTpAh8fH9SvXx+DBw9GSkqK2TZCCMyfPx+hoaHw8PBAr169cOLECYkSExGRIysp0+PFT/fjQl4JGgV4YtWoznB3VUgdix6QXZedpKQkTJkyBXv37kViYiLKy8vRt29fFBUVmbZZsmQJli5diuXLl2Pfvn0IDg7Gk08+iYKCAgmTExGRozEYBF7ecBhHsm7Az9MVa8Z0gT8nJDsFmRBCSB2iuq5cuYL69esjKSkJjz32GIQQCA0NRWxsLGbPng0A0Gq1UKvVWLx4MSZOnFit/Wo0GqhUKuTn58PX19eWvwIREdmpRdtOYVXyebgp5Fj3YjQejvSXOhLdR3W/v+16ZOdO+fn5AAB//4q/gGlpacjJyUHfvn1N2yiVSvTs2RN79uypcj9arRYajcbsQUREddeq5HNYlXweAPDec21ZdJyMw5QdIQTi4uLQvXt3tG7dGgCQk5MDAFCr1WbbqtVq07q7iY+Ph0qlMj3CwsJsF5yIiOzaZ3szsGjbaQDAzJhmGMQ7mTsdhyk7U6dOxdGjR/Hll19WWnfnXWeFEPe8E+2cOXOQn59vemRlZVk9LxER2b9vD1zAm5uPAwAm92qCKb2bSpyIbMFF6gDV8dJLL+H7779HcnIyGjZsaFoeHBwMoGKEJyQkxLQ8Nze30mjP7ZRKJZRKpe0CExGR3fvx2CXM/OYIAGBMtwjMjGkmcSKyFbse2RFCYOrUqdi4cSN++eUXREZGmq2PjIxEcHAwEhMTTcvKysqQlJSEbt261XZcIiJyELtO52La+kMwCOC5Tg0xt3/Lex4RIMdm1yM7U6ZMwRdffIHvvvsOPj4+pnk4KpUKHh4ekMlkiI2NxaJFixAVFYWoqCgsWrQInp6eGD58uMTpiYjIHv10PAcvfXkQOr1A/7YheHdoW8h5c0+nZtdlZ+XKlQCAXr16mS1fs2YNxowZAwCYNWsWSkpKMHnyZOTl5SE6Oho7duyAj49PLaclIiJ7t+nQBbzy9VHoDQJPtwnGh8Pa8y7mdYBDXWfHVnidHSIi5/f5nxl4Y/NxCAEM7dgQi4e2gYvCrmdz0H1U9/vbrkd2iIiIrOHj5PN4Z9spAMCoro0wf0ArHrqqQ1h2iIjIaRkMAu/+dNp0wcD/69UEs2KacTJyHcOyQ0RETqmkTI+XNxzGTycqTm6ZGdOM19Gpo1h2iIjI6eQWlGLC2v04ciEfbgo53nuuLa+MXIex7BARkVM5c7kAY9fsw8UbJfDzdMWqkZ15r6s6jmWHiIicxrZjlzDz6yMoKtMjIsATa8Y+jMhAL6ljkcRYdoiIyOHp9AYs/vE0PvktDQDwSGN/rBzRCfW83CRORvaAZYeIiBxabkEppn5+CH+lXwcATHysMWbGNOM1dMiEZYeIiBzWntSriN1wGLkFWngrXfD+c23xVOuQ+7+R6hSWHSIicjjacj3e356Cj3+tOGz1kNob//lHJzQO8pY4Gdkjlh0iInIop3M0iF1/GKdzCgAAw6PD8cYzLeDpxq80ujv+zSAiIoegNwis+T0NS7anoKzcgAAvNywe2hZ9WqqljkZ2jmWHiIjs3slsDeZsPIojF/IBAI83r4/FQ9siyEcpcTJyBCw7RERkt0p1evzz57P4OPk8yg0CPu4ueO3pFnihSxjvb0XVxrJDRER2KenMFcz77jjSrxUDAJ5qFYwFg1pB7esucTJyNCw7RERkV85fKcQ7W0/h59O5AAC1rxILB7VGTKtgiZORo2LZISIiu6Ap1eGjn88iYU86dHoBF7kMo7tFYHqfKPi6u0odjxwYyw4REUmqVKfHur0ZWLH7HK4XlQEAejcLwhv9W6IJr5tDVsCyQ0REkigrN+Cr/Vn46JezuKzRAgCaBHnhzf4t0atZfYnTkTNh2SEiolpVVm7A5kMXsXxXKjKvV0w+buDngelPRGFIxwa8pxVZHcsOERHViiJtOb78KxOf/JqGHE0pACDQW4mpvZvg79HhULooJE5Izoplh4iIbOpKgRbr9mZg7R/puFGsAwDU91FiQo/GGPFIOG/zQDbHv2FERGQTh7NuYO2edPxwNBs6vQAARAR4YmLPJhjSsQFHcqjWsOwQEZHVFJeVY+vRS1j3ZyaOZN0wLe8Q7odxj0bi6TYhUMh55WOqXSw7RET0QIQQOJx1A1/tz8KWI5dQqC0HALgp5OjfLgRjukWgbUM/aUNSncayQ0RENZJ1vRjfH8nGd4cv4szlQtPyRgGeeL5zGIZ1CUOgN2/USdJj2SEiomrLLSjFj8dy8N3hiziYecO0XOkix9NtQvB85zBER/pDzkNVZEdYdoiI6J4yrhVh+4kcbD9xGQcz8yAq5hpDJgO6Ng7AoPaheKp1CFQevKUD2SeWHSIiMqPTG3AwIw+7z1zBrtO5OJ1TYLa+fZgfBrQLRf+2IbwDOTkElh0iIkLmtWLsOXcVyWev4NezV1FQWm5ap5DL8Ehjf8S0CsaTLdUIUXlImJTIciw7RER1UPaNEuxLv47fU69iz7lruJBXYra+nqcrej4UhF7N6qNXsyD4ebpJlJTowbHsEBE5uXK9AWdzC3EgIw/70q9jf3oeLt4wLzcuchnah/nh0aaB6NUsCG0b+vF6OOQ0WHaIiJyIEAKZ14tx/KIGRy7cwOGsGzh2IR8lOr3Zdgq5DC1DfNG1SQC6NQlAlwh/eCn5lUDOiX+ziYgcVKlOj7OXC3E6R4OTlzQ4ka3BqWwNCrTllbb1VrqgXZgKXSL80SXCH+3D/FhuqM7g33QiIjtXpC3H+StFOHelEOeuFOLs5UKkXC5AxrUiGETl7d0UcjQL9kG7MBXah9VD+zAVGgd689o3VGex7BAR2YGCUh0u5JUg41oxMq4VIf1aEdKuFiH9ajFyNKVVvq+epyuaBfugebAvWjdQoVWoL5rW94arQl6L6YnsG8sOEZGNGQwCV4u0yMkvRfaNEmTfuPlnfgmyrpcgK68YN4p199xHoLcbGgd5o0mQN5oEeaF5sC8eCvZGkLcSMhlHbIjuhWWHiKiGtOV6XC8qw7XCMlwp1OKKRosrhVrkakqRW6BFjqYUl/Mrnpff7XjTHep5uiLc3xONArwQEeiFiICK502CvHjqN9EDYNkhojpPCIGiMj00JTrkl+hwo1iH/JIy3CjW4UaJDnnFZcgrKsP1oorn14vKcLVQa3bhvfuRyYBAbyUa+HmggZ8HQlTuCPHzQFg9D4T5eyLM3xPenDBMZBNO82/WihUr8N577+HSpUto1aoVli1bhh49ekgdi4hsxGAQKNHpKx5lehSVlaNIq0fxzT+LtOUoKitHobYchaXlKNKWo0BbjoLSchSU6lB487mmRAdNaTn01Rh5uRsXuQz+Xm4I9Faivq8SQd5KBPlUPIJ93aFWuSPY1x1BPkrOoyGSiFOUnQ0bNiA2NhYrVqzAo48+iv/+97/o168fTp48ifDwcKnjETkVIQR0egGd3oByvUCZ3oBygwG6cgGdwQCdvuJ5md6AsnIDyvQG6G7+WVZe8dDqDdDq9CjTG6DVGaAtN0Bbroe23IBSnR5a3c0/b74uLdejuEyP0jK9qeCU6gxW/91cFTL4urvCz9MVfp5u8PNwhcrDFfW83ODv5YZ6nm7w96pYF+itRKC3G3zdXXmWE5Gdkwkhava/M3YkOjoaHTt2xMqVK03LWrRogcGDByM+Pv6+79doNFCpVMjPz4evr6/VcuUVlaGorPIwt7U+8Tv3I1B5x5W3udt+RDW2qby2qn3fvtyYybjsXuvutt/bt7m1f3GXnyVM2whx63cSt20jULHBnctuvc/4/Oafty83vadinUFU/V6DoWKZQQjTcoO47TUqRiWMy3Bz21vbAHqDMC0TouK53lDxXH/be/UGAb0QMBjuvdz4Wm8wf5Sb/Wm49VpvXF6xrNxYbm6utzcergp4uingpXQx+9Nb6QJvpQu8bv7p7e4CH/eK577urvBxd4Gvhyt83StKjburnJN9iRxIdb+/HX5kp6ysDAcOHMCrr75qtrxv377Ys2fPXd+j1Wqh1WpNrzUajU2yvbcjBV/8mWmTfRPZExe5DC4KGdwUcri5yOGmkMPltueuLnIoFXK4usigdFHATSGH0lVu+tPdRQGlq7xinYsc7i5yuLsqbj7kULoq4OmqgIebAh43l3u4VRQcdxcFR1aI6J4cvuxcvXoVer0earXabLlarUZOTs5d3xMfH48FCxbYPJurXAZ31+odo5fh/v+xvtv/cN656G7/V1ppSU33c4/3Gbe/229x632ySvuR3baN7Lb1t+/n9izGp3dub9yXWY47lstue59Zhpvr5PJb62Q3d3zrPbdtd3OBcZ1cJjPbr0wmg/zm+op1spvbVWwjlxu3uW07+e2vZTdfV1zSX34zrEIug0IuM/1Mhey27W4+V8hvLVcY3y+XweXmfoz7cJHLbz1XVLzH5bbXxvXG58Yy46owPjcWmor3cTSEiOyZw5cdozv/YyuEqPI/wHPmzEFcXJzptUajQVhYmNUzLRjUGgsGtbb6fomIiKj6HL7sBAYGQqFQVBrFyc3NrTTaY6RUKqFUKmsjHhEREUnM4c+DdHNzQ6dOnZCYmGi2PDExEd26dZMoFREREdkLhx/ZAYC4uDiMHDkSnTt3RteuXbFq1SpkZmZi0qRJUkcjIiIiiTlF2Rk2bBiuXbuGhQsX4tKlS2jdujW2bduGRo0aSR2NiIiIJOYU19l5ULa6zg4RERHZTnW/vx1+zg4RERHRvbDsEBERkVNj2SEiIiKnxrJDRERETo1lh4iIiJwayw4RERE5NZYdIiIicmosO0REROTUWHaIiIjIqTnF7SIelPEi0hqNRuIkREREVF3G7+373QyCZQdAQUEBACAsLEziJERERGSpgoICqFSqKtfz3lgADAYDsrOz4ePjA5lMJnUcyWk0GoSFhSErK4v3CrMxfta1h5917eFnXXvq+mcthEBBQQFCQ0Mhl1c9M4cjOwDkcjkaNmwodQy74+vrWyf/5ZECP+vaw8+69vCzrj11+bO+14iOEScoExERkVNj2SEiIiKnxrJDlSiVSsybNw9KpVLqKE6Pn3Xt4Wdde/hZ1x5+1tXDCcpERETk1DiyQ0RERE6NZYeIiIicGssOEREROTWWHSIiInJqLDtULVqtFu3bt4dMJsPhw4eljuN00tPTMX78eERGRsLDwwNNmjTBvHnzUFZWJnU0p7FixQpERkbC3d0dnTp1wq+//ip1JKcTHx+PLl26wMfHB/Xr18fgwYORkpIidaw6IT4+HjKZDLGxsVJHsUssO1Qts2bNQmhoqNQxnNbp06dhMBjw3//+FydOnMCHH36I//znP3jttdekjuYUNmzYgNjYWLz++us4dOgQevTogX79+iEzM1PqaE4lKSkJU6ZMwd69e5GYmIjy8nL07dsXRUVFUkdzavv27cOqVavQtm1bqaPYLZ56Tvf1448/Ii4uDt9++y1atWqFQ4cOoX379lLHcnrvvfceVq5cifPnz0sdxeFFR0ejY8eOWLlypWlZixYtMHjwYMTHx0uYzLlduXIF9evXR1JSEh577DGp4zilwsJCdOzYEStWrMDbb7+N9u3bY9myZVLHsjsc2aF7unz5MiZMmIDPPvsMnp6eUsepU/Lz8+Hv7y91DIdXVlaGAwcOoG/fvmbL+/btiz179kiUqm7Iz88HAP49tqEpU6bgmWeeQZ8+faSOYtd4I1CqkhACY8aMwaRJk9C5c2ekp6dLHanOOHfuHD766CN88MEHUkdxeFevXoVer4darTZbrlarkZOTI1Eq5yeEQFxcHLp3747WrVtLHccprV+/HgcPHsS+ffukjmL3OLJTB82fPx8ymeyej/379+Ojjz6CRqPBnDlzpI7ssKr7Wd8uOzsbTz31FJ577jm8+OKLEiV3PjKZzOy1EKLSMrKeqVOn4ujRo/jyyy+ljuKUsrKyMH36dKxbtw7u7u5Sx7F7nLNTB129ehVXr1695zYRERF44YUXsGXLFrMvBL1eD4VCgREjRmDt2rW2jurwqvtZG/9jlZ2djd69eyM6OhoJCQmQy/n/Iw+qrKwMnp6e+Prrr/Hss8+alk+fPh2HDx9GUlKShOmc00svvYTNmzcjOTkZkZGRUsdxSps3b8azzz4LhUJhWqbX6yGTySCXy6HVas3W1XUsO1SlzMxMaDQa0+vs7GzExMTgm2++QXR0NBo2bChhOudz8eJF9O7dG506dcK6dev4Hyorio6ORqdOnbBixQrTspYtW2LQoEGcoGxFQgi89NJL2LRpE3bv3o2oqCipIzmtgoICZGRkmC0bO3YsmjdvjtmzZ/PQ4R04Z4eqFB4ebvba29sbANCkSRMWHSvLzs5Gr169EB4ejvfffx9XrlwxrQsODpYwmXOIi4vDyJEj0blzZ3Tt2hWrVq1CZmYmJk2aJHU0pzJlyhR88cUX+O677+Dj42OaE6VSqeDh4SFxOufi4+NTqdB4eXkhICCARecuWHaI7MCOHTuQmpqK1NTUSkWSg68PbtiwYbh27RoWLlyIS5cuoXXr1ti2bRsaNWokdTSnYjy1v1evXmbL16xZgzFjxtR+IKKbeBiLiIiInBpnPxIREZFTY9khIiIip8ayQ0RERE6NZYeIiIicGssOEREROTWWHSIiInJqLDtERETk1Fh2iIiIyKmx7BARgIq7gm/evFnqGNUyf/58tG/fXuoYVterVy/ExsZWe/vdu3dDJpPhxo0bVW6TkJAAPz+/B85G5MhYdogc3JgxYzB48GCpYzi86pSCDz74ACqVCsXFxZXWlZaWws/PD0uXLq1xho0bN+Ktt96q8fuJ6O5YdoiIqmnUqFEoKSnBt99+W2ndt99+i+LiYowcOdLi/ep0OgCAv78/fHx8HjgnEZlj2SFyMr169cK0adMwa9Ys+Pv7Izg4GPPnzzfb5uzZs3jsscfg7u6Oli1bIjExsdJ+Ll68iGHDhqFevXoICAjAoEGDkJ6eblpvHFFasGAB6tevD19fX0ycOBFlZWWmbYQQWLJkCRo3bgwPDw+0a9cO33zzjWm98TDMzz//jM6dO8PT0xPdunVDSkqKWZZ3330XarUaPj4+GD9+PEpLSyvlXbNmDVq0aAF3d3c0b94cK1asMK1LT0+HTCbDxo0b0bt3b3h6eqJdu3b4448/TDnGjh2L/Px8yGQyyGSySp8ZAAQFBWHAgAH43//+V2nd//73PwwcOBBBQUGYPXs2HnroIXh6eqJx48Z48803TYUGuHUY7n//+x8aN24MpVIJIUSlw1jr1q1D586d4ePjg+DgYAwfPhy5ubmVfvbvv/+Odu3awd3dHdHR0Th27FilbW63ZcsWdOrUCe7u7mjcuDEWLFiA8vLye76HyKEJInJoo0ePFoMGDTK97tmzp/D19RXz588XZ86cEWvXrhUymUzs2LFDCCGEXq8XrVu3Fr169RKHDh0SSUlJokOHDgKA2LRpkxBCiKKiIhEVFSXGjRsnjh49Kk6ePCmGDx8umjVrJrRarennent7i2HDhonjx4+LH374QQQFBYnXXnvNlOW1114TzZs3Fz/99JM4d+6cWLNmjVAqlWL37t1CCCF27dolAIjo6Gixe/duceLECdGjRw/RrVs30z42bNgg3NzcxMcffyxOnz4tXn/9deHj4yPatWtn2mbVqlUiJCREfPvtt+L8+fPi22+/Ff7+/iIhIUEIIURaWpoAIJo3by5++OEHkZKSIv72t7+JRo0aCZ1OJ7RarVi2bJnw9fUVly5dEpcuXRIFBQV3/by3bt0qZDKZOH/+vGlZWlqakMlkYtu2bUIIId566y3x+++/i7S0NPH9998LtVotFi9ebNp+3rx5wsvLS8TExIiDBw+KI0eOCIPBIHr27CmmT59u2m716tVi27Zt4ty5c+KPP/4QjzzyiOjXr59pvfHza9GihdixY4c4evSo6N+/v4iIiBBlZWVCCCHWrFkjVCqV6T0//fST8PX1FQkJCeLcuXNix44dIiIiQsyfP//uf8GInADLDpGDu1vZ6d69u9k2Xbp0EbNnzxZCCLF9+3ahUChEVlaWaf2PP/5oVnZWr14tmjVrJgwGg2kbrVYrPDw8xPbt200/19/fXxQVFZm2WblypfD29hZ6vV4UFhYKd3d3sWfPHrMs48ePF3//+9+FELe+rHfu3Glav3XrVgFAlJSUCCGE6Nq1q5g0aZLZPqKjo83KTlhYmPjiiy/MtnnrrbdE165dhRC3ys4nn3xiWn/ixAkBQJw6dUoIUbkUVKW8vFw0aNBAzJ0717Rs7ty5okGDBqK8vPyu71myZIno1KmT6fW8efOEq6uryM3NNdvuzrJzp7/++ksAMBUx4+e3fv160zbXrl0THh4eYsOGDXf9vXr06CEWLVpktt/PPvtMhISE3PsXJ3JgLhINKBGRDbVt29bsdUhIiOnwx6lTpxAeHo6GDRua1nft2tVs+wMHDiA1NbXS/JHS0lKcO3fO9Lpdu3bw9PQ0209hYSGysrKQm5uL0tJSPPnkk2b7KCsrQ4cOHarMGxISAgDIzc1FeHg4Tp06hUmTJplt37VrV+zatQsAcOXKFWRlZWH8+PGYMGGCaZvy8nKoVKpq/ZzmzZujuhQKBUaPHo2EhATMmzcPMpkMa9euxZgxY6BQKAAA33zzDZYtW4bU1FQUFhaivLwcvr6+Zvtp1KgRgoKC7vmzDh06hPnz5+Pw4cO4fv06DAYDACAzMxMtW7Y0+zyM/P390axZM5w6dequ+zxw4AD27duHd955x7RMr9ejtLQUxcXFZv88iZwFyw6RE3J1dTV7LZPJTF+UQohK28tkMrPXBoMBnTp1wueff15p2/t9Qd/587Zu3YoGDRqYrVcqlVXmNWYxvv9+jNt9/PHHiI6ONltnLB/W+Dm3GzduHOLj4/HLL78AqCgfY8eOBQDs3bsXL7zwAhYsWICYmBioVCqsX78eH3zwgdk+vLy87vkzioqK0LdvX/Tt2xfr1q1DUFAQMjMzERMTYzYvqip3/jM1MhgMWLBgAYYMGVJpnbu7+333S+SIWHaI6piWLVsiMzMT2dnZCA0NBQDTRF2jjh07YsOGDaaJx1U5cuQISkpK4OHhAaDii97b2xsNGzZEvXr1oFQqkZmZiZ49e9Y4b4sWLbB3716MGjXKtGzv3r2m52q1Gg0aNMD58+cxYsSIGv8cNzc36PX6am3bpEkT9OzZE2vWrDFNLG7SpAmAisnCjRo1wuuvv27aPiMjw+I8p0+fxtWrV/Huu+8iLCwMALB///67brt3716Eh4cDAPLy8nDmzJkqR6s6duyIlJQUNG3a1OJMRI6KZYeojunTpw+aNWuGUaNG4YMPPoBGozH7YgaAESNG4L333sOgQYOwcOFCNGzYEJmZmdi4cSNmzpxpOgRWVlaG8ePH44033kBGRgbmzZuHqVOnQi6Xw8fHB6+88gpefvllGAwGdO/eHRqNBnv27IG3tzdGjx5drbzTp0/H6NGj0blzZ3Tv3h2ff/45Tpw4gcaNG5u2mT9/PqZNmwZfX1/069cPWq0W+/fvR15eHuLi4qr1cyIiIlBYWIiff/7ZdHjuXod0bj9s9sknn5iWN23aFJmZmVi/fj26dOmCrVu3YtOmTdXKcLvw8HC4ubnho48+wqRJk3D8+PEqr8GzcOFCBAQEQK1W4/XXX0dgYGCV116aO3cu+vfvj7CwMDz33HOQy+U4evQojh07hrffftvinESOgKeeE9UxcrkcmzZtglarxcMPP4wXX3zRbP4GAHh6eiI5ORnh4eEYMmQIWrRogXHjxqGkpMRspOeJJ55AVFQUHnvsMTz//PMYMGCA2Snbb731FubOnYv4+Hi0aNECMTEx2LJlCyIjI6udd9iwYZg7dy5mz56NTp06ISMjA//3f/9nts2LL76ITz75BAkJCWjTpg169uyJhIQEi35Ot27dMGnSJAwbNgxBQUFYsmTJPbcfOnQolEollEql2SGhQYMG4eWXX8bUqVPRvn177NmzB2+++Wa1cxgFBQUhISEBX3/9NVq2bIl3330X77///l23fffddzF9+nR06tQJly5dwvfffw83N7e7bhsTE4MffvgBiYmJ6NKlCx555BEsXboUjRo1sjgjkaOQibsdwCciuo8xY8bgxo0bDnOLCSKquziyQ0RERE6NZYeIiIicGg9jERERkVPjyA4RERE5NZYdIiIicmosO0REROTUWHaIiIjIqbHsEBERkVNj2SEiIiKnxrJDRERETo1lh4iIiJza/wNdhxie1akKtAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = np.arange(-5.0, 5.0, 0.1)\n", "\n", "##You can adjust the slope and intercept to verify the changes in the graph\n", "\n", "Y= np.exp(X)\n", "\n", "plt.plot(X,Y) \n", "plt.ylabel('Dependent Variable')\n", "plt.xlabel('Independent Variable')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Logarithmic\n", "\n", "The response $y$ is a results of applying the logarithmic map from the input $x$ to the output $y$. It is one of the simplest form of __log()__: i.e. $$ y = \\log(x)$$\n", "\n", "Please consider that instead of $x$, we can use $X$, which can be a polynomial representation of the $x$ values. In general form it would be written as \n", "\\begin{equation}\n", "y = \\log(X)\n", "\\end{equation}\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "tags": [] }, "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": [ "
" ] }, "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": { "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": [ "\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": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2025-10-20 08:55:15 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": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
YearValue
019605.918412e+10
119614.955705e+10
219624.668518e+10
319635.009730e+10
419645.906225e+10
519656.970915e+10
619667.587943e+10
719677.205703e+10
819686.999350e+10
919697.871882e+10
\n", "
" ], "text/plain": [ " Year Value\n", "0 1960 5.918412e+10\n", "1 1961 4.955705e+10\n", "2 1962 4.668518e+10\n", "3 1963 5.009730e+10\n", "4 1964 5.906225e+10\n", "5 1965 6.970915e+10\n", "6 1966 7.587943e+10\n", "7 1967 7.205703e+10\n", "8 1968 6.999350e+10\n", "9 1969 7.871882e+10" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "\n", "#downloading dataset\n", "!wget -nv -O china_gdp.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv\n", " \n", "df = pd.read_csv(\"china_gdp.csv\")\n", "df.head(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Did you know?__ When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: [Sign up now for free](http://cocl.us/ML0101EN-IBM-Offer-CC)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the Dataset ###\n", "This is what the datapoints look like. It kind of looks like an either logistic or exponential function. The growth starts off slow, then from 2005 on forward, the growth is very significant. And finally, it decelerates slightly in the 2010s.\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAArMAAAHPCAYAAABA71I8AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAAA4m0lEQVR4nO3de3SU1b3/8c+TCSQSzdAghISJSapSqfEGHBE0NVhNxUqh0Uq1C+q10CNC5NgqlePtWNObCi3ihaqtPYLUMNr2HA41LkHCxQs0WVWxyiVIiBMQlARBEzPZvz/ml5EhE5hJZvLMk3m/1pqVNXu+88yebNGPm/3sbRljjAAAAAAHSrG7AwAAAEB3EWYBAADgWIRZAAAAOBZhFgAAAI5FmAUAAIBjEWYBAADgWIRZAAAAOBZhFgAAAI5FmAUAAIBjEWYBAADgWEkdZtesWaOJEycqNzdXlmXpxRdfjOr9n3/+ua699lqdccYZSk1N1eTJkzvVrF27Vueff74GDRqk4447Tqeddpoefvjh2HwBAACAJJdqdwfsdPDgQZ111lm67rrrdMUVV0T9fr/fr+OOO06zZs3S8uXLw9ZkZGRo5syZOvPMM5WRkaG1a9dq+vTpysjI0I9+9KOefgUAAICkZhljjN2dSASWZemFF14ImV1tbW3VvHnz9Oyzz2r//v0qKirSL3/5S5WUlHR6/7XXXqv9+/dHNLtbVlamjIwM/elPf4rdFwAAAEhCSb3M4Fiuu+46rVu3Ts8995z++c9/6nvf+54uvfRSbdmypdvXrKmp0fr163XhhRfGsKcAAADJKamXGRzNtm3btHTpUu3atUu5ubmSpNtuu00rV67U008/rQceeCCq63k8Hn300Udqa2vTPffcoxtvvDEe3QYAAEgqhNku/OMf/5AxRsOHDw9pb2lp0aBBg6K+XnV1tT799FO99tpruuOOO3TKKafo6quvjlV3AQAAkhJhtgvt7e1yuVzatGmTXC5XyGvHH3981NcrLCyUJJ1xxhnavXu37rnnHsIsAABADxFmu3DOOefI7/drz549Ki4ujum1jTFqaWmJ6TUBAACSUVKH2U8//VRbt24NPq+rq1Ntba2ysrI0fPhw/eAHP9C0adP04IMP6pxzztHevXv1yiuv6IwzztBll10mSdq8ebNaW1v18ccf68CBA6qtrZUknX322ZKkRx55RCeddJJOO+00SYF9Z3/zm9/olltu6dXvCgAA0Bcl9dZcq1ev1vjx4zu1//CHP9Qf/vAHffHFF7r//vv1zDPPqKGhQYMGDdLYsWN177336owzzpAkFRQU6IMPPuh0jY5f6+9+9zs9/vjjqqurU2pqqk4++WTddNNNmj59ulJS2EwCAACgJ5I6zAIAAMDZmBoEAACAYxFmAQAA4FhJdwNYe3u7PvzwQ51wwgmyLMvu7gAAAOAIxhgdOHBAubm5x7zHKOnC7Icffqi8vDy7uwEAAIBjqK+vl8fjOWpN0oXZE044QVLgl5OZmWlzbwAAAHCk5uZm5eXlBXPb0SRdmO1YWpCZmUmYBQAASGCRLAnlBjAAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4VtKdAAYAAIAo+P1SdbXk80k5OVJxseRy2d2rIMIsAAAAwvN6pdmzpV27vmzzeKQFC6SyMvv6dRiWGQAAAKAzr1e68srQICtJDQ2Bdq/Xnn4dgTALAACAUH5/YEbWmM6vdbSVlwfqbEaYBQAAQKjq6s4zsoczRqqvD9TZjDALAACAUD5fbOviiDALAACAUDk5sa2LI8IsAAAAQhUXB3YtsKzwr1uWlJcXqLMZYRYAAAChXK7A9ltS50Db8Xz+/ITYb5YwCwAAgM7KyqTKSmnYsNB2jyfQniD7zHJoAgAAAMIrK5MmTeIEMAAAADiUyyWVlNjdiy6xzAAAAACOZWuYXbNmjSZOnKjc3FxZlqUXX3zxmO959dVXNWrUKKWnp+urX/2qHnvssfh3FAAAAAnJ1jB78OBBnXXWWVq4cGFE9XV1dbrssstUXFysmpoa/exnP9OsWbO0fPnyOPcUAAAAicjWNbMTJkzQhAkTIq5/7LHHdNJJJ2n+/PmSpBEjRmjjxo36zW9+oyuuuCJOvQQAAECictSa2Q0bNqi0tDSk7Vvf+pY2btyoL774Iux7Wlpa1NzcHPIAAABA3+CoMNvY2Kjs7OyQtuzsbLW1tWnv3r1h31NRUSG32x185OXl9UZXAQAA0AscFWYlyTriFApjTNj2DnPnzlVTU1PwUV9fH/c+AgAAoHc4ap/ZoUOHqrGxMaRtz549Sk1N1aBBg8K+Jy0tTWlpab3RPQAAAPQyR83Mjh07VlVVVSFtL730kkaPHq1+/frZ1CsAAADYxdYw++mnn6q2tla1tbWSAltv1dbWaufOnZICSwSmTZsWrJ8xY4Y++OADzZkzR++++66eeuopPfnkk7rtttvs6D4AAABsZusyg40bN2r8+PHB53PmzJEk/fCHP9Qf/vAH+Xy+YLCVpMLCQq1YsUK33nqrHnnkEeXm5uq3v/0t23IBAAAkKct03EGVJJqbm+V2u9XU1KTMzEy7uwMAAIAjRJPXHLVmFgAAADgcYRYAAACORZgFAACAYxFmAQAA4FiEWQAAADgWYRYAAACO5ajjbAEAABAjfr9UXS35fFJOjlRcLLlcdvcqaoRZAACAZOP1SrNnS7t2fdnm8UgLFkhlZfb1qxtYZgAAAJBMvF7pyitDg6wkNTQE2r1ee/rVTYRZAACAZOH3B2Zkwx0A29FWXh6ocwjCLAAAQLKoru48I3s4Y6T6+kCdQxBmAQAAkoXPF9u6BECYBQAASBY5ObGtSwCEWQAAgGRRXBzYtcCywr9uWVJeXqDOIQizAAAAycLlCmy/JXUOtB3P58931H6zhFkAAIBkUlYmVVZKw4aFtns8gXaH7TPLoQkAAADJpqxMmjSJE8AAAADgUC6XVFJidy96jGUGAAAAcCzCLAAAAByLMAsAAADHIswCAADAsQizAAAAcCzCLAAAAByLMAsAAADHIswCAADAsQizAAAAcCzCLAAAAByLMAsAAADHIswCAADAsQizAAAAcCzCLAAAAByLMAsAAADHIswCAADAsQizAAAAcCzCLAAAAByLMAsAAADHIswCAADAsQizAAAAcCzCLAAAAByLMAsAAADHSrW7AwAAAIgRv1+qrpZ8PiknRyoullwuu3sVV4RZAACAvsDrlWbPlnbt+rLN45EWLJDKyuzrV5yxzAAAAMDpvF7pyitDg6wkNTQE2r1ee/rVCwizAAAATub3B2Zkjen8WkdbeXmgrg8izAIAADhZdXXnGdnDGSPV1wfq+iDCLAAAgJP5fLGtcxjCLAAAgJPl5MS2zmEIswAAAE5WXBzYtcCywr9uWVJeXqCuDyLMAgAAOJnLFdh+S+ocaDuez5/fZ/ebJcwCAAA4XVmZVFkpDRsW2u7xBNr78D6zHJoAAADQF5SVSZMmcQIYAAAAHMrlkkpK7O5Fr2KZAQAAAByLMAsAAADHIswCAADAsQizAAAAcCzbw+yiRYtUWFio9PR0jRo1StXHODf42Wef1VlnnaUBAwYoJydH1113nfbt29dLvQUAAEAisTXMLlu2TOXl5brzzjtVU1Oj4uJiTZgwQTt37gxbv3btWk2bNk033HCD3nnnHT3//PN68803deONN/ZyzwEAAJAIbA2zDz30kG644QbdeOONGjFihObPn6+8vDw9+uijYetfe+01FRQUaNasWSosLNQFF1yg6dOna+PGjb3ccwAAACQC28Jsa2urNm3apNLS0pD20tJSrV+/Pux7xo0bp127dmnFihUyxmj37t2qrKzUt7/97S4/p6WlRc3NzSEPAAAA9A22hdm9e/fK7/crOzs7pD07O1uNjY1h3zNu3Dg9++yzmjJlivr376+hQ4dq4MCB+t3vftfl51RUVMjtdgcfeXl5Mf0eAAAAsI/tN4BZlhXy3BjTqa3D5s2bNWvWLN11113atGmTVq5cqbq6Os2YMaPL68+dO1dNTU3BR319fUz7DwAAAPvYdpztiSeeKJfL1WkWds+ePZ1maztUVFTo/PPP109+8hNJ0plnnqmMjAwVFxfr/vvvV05OTqf3pKWlKS0tLfZfAAAAALazbWa2f//+GjVqlKqqqkLaq6qqNG7cuLDvOXTokFJSQrvscrkkBWZ0AQAAkFxsXWYwZ84c/f73v9dTTz2ld999V7feeqt27twZXDYwd+5cTZs2LVg/ceJEeb1ePfroo9q+fbvWrVunWbNm6dxzz1Vubq5dXwMAAAA2sW2ZgSRNmTJF+/bt03333Sefz6eioiKtWLFC+fn5kiSfzxey5+y1116rAwcOaOHChfqP//gPDRw4UBdddJF++ctf2vUVAAAAYCPLJNnfzzc3N8vtdqupqUmZmZl2dwcAAABHiCav2b6bAQAAANBdhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYtm7NBQAAgAj4/VJ1teTzSTk5UnGx9P8Pjkp2hFkAAIBE5vVKs2dLu3Z92ebxSAsWSGVl9vUrQbDMAAAAIFF5vdKVV4YGWUlqaAi0e7329CuBEGYBAAASkd8fmJENd75VR1t5eaAuiRFmAQAAElF1decZ2cMZI9XXB+qSGGEWAAAgEfl8sa3rowizAAAAiSgnJ7Z1fRRhFgAAIBEVFwd2LbCs8K9blpSXF6hLYoRZAACARORyBbbfkjoH2o7n8+cn/X6zhFkAAIBEVVYmVVZKw4aFtns8gXb2meXQBAAAgIRWViZNmsQJYF0gzAIAACQ6l0sqKbG7FwmJZQYAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHCvV7g4AAAAkJb9fqq6WfD4pJ0cqLpZcLrt75TiEWQAAgN7m9UqzZ0u7dn3Z5vFICxZIZWX29cuBbF9msGjRIhUWFio9PV2jRo1SdXX1UetbWlp05513Kj8/X2lpaTr55JP11FNP9VJvAQAAesjrla68MjTISlJDQ6Dd67WnXw5l68zssmXLVF5erkWLFun888/X448/rgkTJmjz5s066aSTwr7nqquu0u7du/Xkk0/qlFNO0Z49e9TW1tbLPQcAAOgGvz8wI2tM59eMkSxLKi+XJk1iyUGELGPC/TZ7x5gxYzRy5Eg9+uijwbYRI0Zo8uTJqqio6FS/cuVKff/739f27duVlZXVrc9sbm6W2+1WU1OTMjMzu913AACAqK1eLY0ff+y6VaukkpJ49yZhRZPXbFtm0Nraqk2bNqm0tDSkvbS0VOvXrw/7nr/+9a8aPXq0fvWrX2nYsGEaPny4brvtNn322Wddfk5LS4uam5tDHgAAALbw+WJbB/uWGezdu1d+v1/Z2dkh7dnZ2WpsbAz7nu3bt2vt2rVKT0/XCy+8oL179+rf//3f9fHHH3e5braiokL33ntvzPsPAAAQtZyc2NbB/hvALMsKeW6M6dTWob29XZZl6dlnn9W5556ryy67TA899JD+8Ic/dDk7O3fuXDU1NQUf9fX1Mf8OAAAAESkuDuxa0EXWkWVJeXmBOkTEtjB74oknyuVydZqF3bNnT6fZ2g45OTkaNmyY3G53sG3EiBEyxmjXkXcE/n9paWnKzMwMeQAAANjC5QpsvyV1DrQdz+fP5+avKNgWZvv3769Ro0apqqoqpL2qqkrjxo0L+57zzz9fH374oT799NNg2/vvv6+UlBR5PJ649hcAACAmysqkykpp2LDQdo8n0M4+s1GxdTeDZcuWaerUqXrsscc0duxYPfHEE1q8eLHeeecd5efna+7cuWpoaNAzzzwjSfr00081YsQInXfeebr33nu1d+9e3Xjjjbrwwgu1ePHiiD6T3QwAAEBC4ASwLkWT12zdZ3bKlCnat2+f7rvvPvl8PhUVFWnFihXKz8+XJPl8Pu3cuTNYf/zxx6uqqkq33HKLRo8erUGDBumqq67S/fffb9dXAAAA6B6XK6m334oVW2dm7cDMLAAAQGJzxD6zAAAAQE8RZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjhX1CWAffPCBXnrpJX3xxRe68MILdfrpp8ejXwAAAMAxRRVm16xZo8suu0yHDh0KvDk1VX/84x919dVXx6VzAAAAwNFEtczgP//zPzV+/Hjt2rVL+/bt0/XXX6+f/vSn8eobAAAAcFSWMcZEWpyVlaU1a9aoqKhIknTw4EFlZmZq7969+spXvhK3TsZSNGf9AgAAoPdFk9eimpndv3+/hgwZEnyekZGhAQMGaP/+/d3qKAAAANATUd8AtnnzZjU2NgafG2P07rvv6sCBA8G2M888Mza9AwAAAI4iqmUGKSkpsixL4d7S0W5Zlvx+f0w7GUssMwAAAEhs0eS1qGZm6+rqetQxAAAAIJaiCrP5+fnx6gcAAAAQtajXzErSli1b9Je//EU7duyQZVkqLCzU5MmT9dWvfjXW/QMAAAC6FHWYraio0F133aX29nYNGTJExhh99NFHuuOOO/TAAw/otttui0c/AQAAgE6i2ppr1apVmjdvnu68807t3btXPp9PjY2NwTB7xx13aM2aNfHqKwAAABAiqt0MpkyZooEDB+rxxx8P+/qPfvQjHThwQEuXLo1ZB2ON3QwAAEBc+f1SdbXk80k5OVJxseRy2d0rR4nboQlvvPGGpk6d2uXrU6dO1WuvvRbNJQEAAPoOr1cqKJDGj5euuSbws6Ag0I64iCrM7t69WwUFBV2+XlhYGHKgAgAAQNLweqUrr5R27Qptb2gItBNo4yKqMPv555+rf//+Xb7er18/tba29rhTAAAAjuL3S7NnS+FWb3a0lZcH6hBTUe9m8Pvf/17HH3982NcOP9IWAAAgaVRXd56RPZwxUn19oK6kpNe6lQyiCrMnnXSSFi9efMwaAACApOLzxbYOEYsqzO7YsSNO3QAAAHCwnJzY1iFiUYXZzz//XC+//LIuv/xySdLcuXPV0tLy5cVSU3XfffcpPT09tr0EAABIZMXFkscTuNkr3LpZywq8Xlzc+33r46IKs3/84x/1P//zP8Ewu3DhQp1++uk67rjjJEn/+te/NHToUM2ZMyf2PQUAAEhULpe0YEFg1wLLCg20lhX4OX8++83GQVS7GTz77LO6/vrrQ9qWLFmiVatWadWqVfr1r3+t559/PqYdBAAAcISyMqmyUho2LLTd4wm0l5XZ068+LqqZ2ffff1/Dhw8PPk9PT1dKypd5+Nxzz9XNN98cu94BAAA4SVmZNGkSJ4D1oqjCbFNTk1JTv3zLRx99FPJ6e3t7yBpaAACApONysf1WL4pqmYHH49Hbb7/d5ev//Oc/5fF4etwpAAAAIBJRhdnLLrtMd911lz7//PNOr3322We699579e1vfztmnQMAAACOxjIm3P4R4e3evVtnn322+vfvr5kzZ2r48OGyLEv/+te/tHDhQrW1tammpkbZ2dnx7HOPNDc3y+12q6mpSZmZmXZ3BwAAAEeIJq9FtWY2Oztb69ev149//GPdcccd6sjBlmXpkksu0aJFixI6yAIAAKBviSrMSlJhYaFWrlypjz/+WFu3bpUknXLKKcrKyop55wAAAICjiTrMdsjKytK5554by74AAAAkLr+fLbcSULfDLAAAQNLweqXZs6Vdu75s83gCp35xGIKtotrNAAAAIOl4vYFjag8PspLU0BBo93rt6RckEWYBAAC65vcHZmTDbf7U0VZeHqiDLQizAAAAXamu7jwjezhjpPr6QB1sQZgFAADois8X2zrEHGEWAACgKzk5sa1DzBFmAQAAulJcHNi1wLLCv25ZUl5eoA62IMwCAAB0xeUKbL8ldQ60Hc/nz2e/WRsRZgEAAI6mrEyqrJSGDQtt93gC7ewzaysOTQAAADiWsjJp0iROAEtAhFkAAIBIuFxSSYndvcARWGYAAAAAxyLMAgAAwLEIswAAAHAswiwAAAAcizALAAAAxyLMAgAAwLEIswAAAHAswiwAAAAcy/Ywu2jRIhUWFio9PV2jRo1SdXV1RO9bt26dUlNTdfbZZ8e3gwAAAEhYtobZZcuWqby8XHfeeadqampUXFysCRMmaOfOnUd9X1NTk6ZNm6ZvfvObvdRTAAAAJCLLGGPs+vAxY8Zo5MiRevTRR4NtI0aM0OTJk1VRUdHl+77//e/r1FNPlcvl0osvvqja2tqIP7O5uVlut1tNTU3KzMzsSfcBAAAQB9HkNdtmZltbW7Vp0yaVlpaGtJeWlmr9+vVdvu/pp5/Wtm3bdPfdd0f0OS0tLWpubg55AAAAoG+wLczu3btXfr9f2dnZIe3Z2dlqbGwM+54tW7bojjvu0LPPPqvU1NSIPqeiokJutzv4yMvL63HfAQAAkBhsvwHMsqyQ58aYTm2S5Pf7dc011+jee+/V8OHDI77+3Llz1dTUFHzU19f3uM8AAABIDJFNb8bBiSeeKJfL1WkWds+ePZ1mayXpwIED2rhxo2pqajRz5kxJUnt7u4wxSk1N1UsvvaSLLrqo0/vS0tKUlpYWny8BAAAAW9k2M9u/f3+NGjVKVVVVIe1VVVUaN25cp/rMzEy99dZbqq2tDT5mzJihr33ta6qtrdWYMWN6q+sAAABIELbNzErSnDlzNHXqVI0ePVpjx47VE088oZ07d2rGjBmSAksEGhoa9MwzzyglJUVFRUUh7x8yZIjS09M7tQMAACA52Bpmp0yZon379um+++6Tz+dTUVGRVqxYofz8fEmSz+c75p6zAAAASF627jNrB/aZBQAASGyO2GcWAAAA6CnCLAAAAByLMAsAAADHIswCAADAsWzdzQAAAMBWfr9UXS35fFJOjlRcLLlcdvcKUSDMAgCA5OT1SrNnS7t2fdnm8UgLFkhlZfb1C1FhmQEAAEg+Xq905ZWhQVaSGhoC7V6vPf1C1AizAAAgufj9gRnZcFvtd7SVlwfqkPAIswAAILlUV3eekT2cMVJ9faAOCY8wCwAAkovPF9s62IowCwAAkktOTmzrYCvCLAAASC7FxYFdCywr/OuWJeXlBeqQ8AizAAAgubhcge23pM6BtuP5/PnsN+sQhFkAAJB8ysqkykpp2LDQdo8n0M4+s47BoQkAACA5lZVJkyZxApjDEWYBAEDycrmkkhK7e4EeYJkBAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxUu3uAAAAQMz5/VJ1teTzSTk5UnGx5HLZ3SvEAWEWAAD0LV6vNHu2tGvXl20ej7RggVRWZl+/EBcsMwAAAH2H1ytdeWVokJWkhoZAu9drT78QN4RZAADQN/j9gRlZYzq/1tFWXh6oQ59BmAUAAH1DdXXnGdnDGSPV1wfq0GcQZgEAQN/g88W2Do5AmAUAAH1DTk5s6+AIhFkAANA3FBcHdi2wrPCvW5aUlxeoQ59BmAUAAH2DyxXYfkvqHGg7ns+fz36zfQxhFgAA9B1lZVJlpTRsWGi7xxNoZ5/ZPodDEwAAQN9SViZNmsQJYEmCMAsAAPoel0sqKbG7F+gFLDMAAACAYxFmAQAA4FiEWQAAADgWYRYAAACOxQ1gAADAGfx+dihAJ4RZAACQ+LxeafZsadeuL9s8nsAhCewdm9RYZgAAABKb1ytdeWVokJWkhoZAu9drT7+QEAizAAAgcfn9gRlZYzq/1tFWXh6oQ1IizAIAgMRVXd15RvZwxkj19YE6JCXCLAAASFw+X2zr0OcQZgEAQOLKyYltHfocwiwAAEhcxcWBXQssK/zrliXl5QXqkJQIswAAIHG5XIHtt6TOgbbj+fz57DebxAizAAAgsZWVSZWV0rBhoe0eT6CdfWaTmu1hdtGiRSosLFR6erpGjRql6qPcjej1enXJJZdo8ODByszM1NixY/X3v/+9F3sLAABsUVYm7dghrVolLVkS+FlXR5CFvWF22bJlKi8v15133qmamhoVFxdrwoQJ2rlzZ9j6NWvW6JJLLtGKFSu0adMmjR8/XhMnTlRNTU0v9xwAAMSM3y+tXi0tXRr42dWesS6XVFIiXX114CdLCyDJMibcLsS9Y8yYMRo5cqQeffTRYNuIESM0efJkVVRURHSN008/XVOmTNFdd90VUX1zc7PcbreampqUmZnZrX4DAIAY4ZhahBFNXrNtZra1tVWbNm1SaWlpSHtpaanWr18f0TXa29t14MABZWVldVnT0tKi5ubmkAcAAEgAHFOLGLAtzO7du1d+v1/Z2dkh7dnZ2WpsbIzoGg8++KAOHjyoq666qsuaiooKud3u4CMvL69H/QYAADHAMbWIEdtvALOO2GbDGNOpLZylS5fqnnvu0bJlyzRkyJAu6+bOnaumpqbgo76+vsd9BgAAPcQxtYiRVLs++MQTT5TL5eo0C7tnz55Os7VHWrZsmW644QY9//zzuvjii49am5aWprS0tB73FwAAxBDH1CJGbJuZ7d+/v0aNGqWqqqqQ9qqqKo0bN67L9y1dulTXXnutlixZom9/+9vx7iYAAIgHjqlFjNg2MytJc+bM0dSpUzV69GiNHTtWTzzxhHbu3KkZM2ZICiwRaGho0DPPPCMpEGSnTZumBQsW6LzzzgvO6h533HFyu922fQ8AABCljmNqGxrCr5u1rMDrHFOLY7B1zeyUKVM0f/583XfffTr77LO1Zs0arVixQvn5+ZIkn88Xsufs448/rra2Nt18883KyckJPmbPnm3XVwAAAN3BMbWIEVv3mbUD+8wCAJBAwu0zm5cXCLLsM5u0oslrti4zAAAAfZTfH9iJwOcLrHstLg4/y1pWJk2aFFktEAZhFgAAxFa0p3p1HFMLdIPt+8wCAIA+hFO90MsIswAAIDY41Qs2IMwCAIDY4FQv2IAwCwAAYoNTvWADbgADAACRO9ouBZzqBRswMwsAACLj9UoFBdL48dI11wR+FhR8eVNXx6leRx6C0MGyAnvIcqoXYogwCwAAji2SXQo41Qs2IMwCAICji2aXgrIyqbJSGjYstM7jCbRzqhdijDWzAADg6KLZpaCkhFO90KsIswAA4Og3dnVnlwJO9UIvIcwCAJDsjnX8LLsUIIGxZhYAgGQWyY1d7FKABEaYBQAgWUV6Y5fELgVIWIRZAAD6Kr9fWr1aWro08NPvD309mhu72KUACYo1swAA9EXHWgcrRX9jF7sUIAERZgEA6Gs61sEeuXygYx1sx0xqd27sYpcCJBiWGQAA0JdEc8ABN3ahDyDMAgDgNEdbCxvNOliOn0UfQJgFAMBJvF6poEAaP1665prAz4KCQLvUvXWw3NgFB2PNLAAAieBoJ3B1iGQtbHfWwXJjFxzMMibcopq+q7m5WW63W01NTcrMzLS7OwAARLbzgN8fmIHtagmBZQXes3WrdPLJgYAb7j/xHXV1dYRVJKxo8hrLDAAAiKdj7fUayQlcUuRrYdevZx0skgphFgCAeDnW+tZodh6IZi0s62CRRFgzCwBAPESyvjUrK/KdB6JdC8s6WCQJwiwAALF2rBlXywrMuFZURHY9n0+66qrAzOqx1sIevicsBxwgCbDMAACAaB1rHWyk61s/+iiyz8vJYU9YoAuEWQAAonGsdbBS5OtbBw+O7gQu1sICnRBmAQCIVKQ7D0S6vnXYsOhnW8vKpB07pFWrpCVLAj/r6giySFrsMwsAQCQi3ee1ri7wvKAg8r1ew+0zm5cXCLKEVCShaPIaN4ABANDhaKdwRboOtro6cNPVggWB2VrLCg204WZc2XkA6DbCLAAA0rFP4Ypmn1fpy/Wt4a4ZbsaVnQeAbiHMAgAQyZ6w0e7zKjHjCvQC1swCAJJbpGtht26VTj458nWwALotmrzGbgYAgOQW6VrY9evZ5xVIQIRZAEByi2YtLPu8AgmHNbMAgL7taDsUSNGvhWUdLJBQCLMAgL7rWDsUSIEg6vEcey1sxylcEjsPAAmEZQYAgL4p0tO6XC7WwgIORpgFAPQ9fn9gRjbcTGtHW3l5oE5iLSzgYCwzAAAklmOtcY2kLtrTuiTWwgIORZgFACSOSNa4RlIX7WldHVgLCzgOYRYAEH+RzLZGcgpXWVn8TusC4EicAAYACBXpX/NHWhvJbGu0p3BxWhfQp3ECGAAkKr9fWr1aWro08LPjBqRE+WyvNxAqx4+Xrrkm8LOg4Ms7/6OtjXRHgUjXuC5axGldAEIQZgGgt0QTFGMdemMZPCOtjWZHgUjXuG7bFlkdp3UBSYNlBgDQUz1ZD9oxS3h4uIr0JqhYfvakSZH9NX9dXeB5JLVPPy1dfHH4msOtWhX4OX78sWsffli69dbIrtlxI1c0yyYAJIRo8hphFgC60tvrQevqpL/8JbahN9LPjkfwnDdPuv/+Y9ctWSJddVWgn8da48paWCApsGYWQN8QzV+1R1obaZ0d60FXr478r+Xj8dmR8PkiXxIQqZycyE/h6t+ftbAAQhBmgb4kHjcX2XXNWN+IFG2dHetBV6+OfeiNR/CMdDurkpLALOmRobODZUl5eYEZbynyNa6shQVwOJNkmpqajCTT1NRkd1eQ7NrajFm1ypglSwI/29p6Vrt8uTEejzGBOBN4eDyB9t64ZqTfJ5JrLl9ujGWF1kiBNsvqXm2kdW1tnft3ZH1enjEvv9x1zeGPVasCj0hq582LbV00n/3yy4HvHe53dPj3bmv78ncUSW3H7/3I2nBjGe0/S9H8GQLgKNHkNcIsEAk7g2esw188rhnp94nkmpGGycND1bFqW1oiv2asg+eSJZGHv0gDcjw+O9rgGW3tkb//vLyu/0cLQNIjzB4FYbaH4jFjkujXtDN4xjr8xeOaTpjxfPjhyK+5ZElsA+WqVaG/96OFv1iH3mg++2j/DHcVPKOpZRYVQBQIs0fR62E21kHNzpAYzexbLMOfnde0M3jGI/zF+podfzUdyfeJx4xnpMFz5szIrxmPv5Y/2j9zR4a/WIbeaD+7Qzz+PQMAUSDMHkWvhtlYBzU7Q2Ks1yU64Zp2B894hD87127GY8YzHjOzibAeNFahtzufDQAJgDB7FL0WZmMd1JxwQ0w06xKdcE27g2c8wl+srxmPIB2PG5E6xjzSmcxEWA8aq9ALAA7kqDD7yCOPmIKCApOWlmZGjhxp1qxZc9T61atXm5EjR5q0tDRTWFhoHn300ag+r1fCbKxDld0hMR6zX064pt3BMx7hL9bX7M4SB7tuRIp2JtMp60GZbQXQBzkmzD733HOmX79+ZvHixWbz5s1m9uzZJiMjw3zwwQdh67dv324GDBhgZs+ebTZv3mwWL15s+vXrZyorKyP+zF4Js7EOVXaHxHisS3TCNe0OnvEIf7G+ZrRrN+2+ESnamUyCIgDYwjFh9txzzzUzZswIaTvttNPMHXfcEbb+pz/9qTnttNNC2qZPn27OO++8iD+zV8JsrEOV3SHRCbOo8bim3cHTmPiEv1hfM1FmPNmbFAD6DEeE2ZaWFuNyuYzX6w1pnzVrlvnGN74R9j3FxcVm1qxZIW1er9ekpqaa1tbWsO/5/PPPTVNTU/BRX18f8S+n2/razGw81iU65Zp2B89oa3uyM0VPrsmMJwAghhwRZhsaGowks27dupD2n//852b48OFh33Pqqaean//85yFt69atM5LMhx9+GPY9d999t5HU6dEra2ZjFarsDnTGxGddopOuafe+m/EIf7G+JgEVABAjjgqz69evD2m///77zde+9rWw7zn11FPNAw88ENK2du1aI8n4fL6w77FlZtaY2IcquwNdR32s1yU65Zp2B08AAJKII8Jsby0zOJLt+8z2JFTZHeiMccbhDvG6JgAA6BXR5DXLGGNkkzFjxmjUqFFatGhRsO3rX/+6Jk2apIqKik71t99+u/72t79p8+bNwbYf//jHqq2t1YYNGyL6zObmZrndbjU1NSkzM7PnX+JY/H6pulry+aScHKm4WHK54l8Xr2sCAADEWTR5zdYwu2zZMk2dOlWPPfaYxo4dqyeeeEKLFy/WO++8o/z8fM2dO1cNDQ165plnJEl1dXUqKirS9OnTddNNN2nDhg2aMWOGli5dqiuuuCKiz+z1MAsAAICoRJPXUnupT2FNmTJF+/bt03333Sefz6eioiKtWLFC+fn5kiSfz6edO3cG6wsLC7VixQrdeuuteuSRR5Sbm6vf/va3EQdZAAAA9C22zszagZlZAACAxBZNXkvppT4BAAAAMUeYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4lq0ngNmh44yI5uZmm3sCAACAcDpyWiRneyVdmD1w4IAkKS8vz+aeAAAA4GgOHDggt9t91JqkO862vb1dH374oU444QRZltUrn9nc3Ky8vDzV19dzhG4CYnwSG+OT+BijxMb4JDbGJzxjjA4cOKDc3FylpBx9VWzSzcympKTI4/HY8tmZmZn8g5rAGJ/ExvgkPsYosTE+iY3x6exYM7IduAEMAAAAjkWYBQAAgGMRZntBWlqa7r77bqWlpdndFYTB+CQ2xifxMUaJjfFJbIxPzyXdDWAAAADoO5iZBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYjcCaNWs0ceJE5ebmyrIsvfjiiyGv7969W9dee61yc3M1YMAAXXrppdqyZUun62zYsEEXXXSRMjIyNHDgQJWUlOizzz4Lvv7JJ59o6tSpcrvdcrvdmjp1qvbv3x/nb9c39HSMduzYIcuywj6ef/75YB1j1D2x+DPU2NioqVOnaujQocrIyNDIkSNVWVkZUsP4dF8sxmjbtm367ne/q8GDByszM1NXXXWVdu/eHVLDGEWvoqJC//Zv/6YTTjhBQ4YM0eTJk/Xee++F1BhjdM899yg3N1fHHXecSkpK9M4774TUtLS06JZbbtGJJ56ojIwMfec739GuXbtCahif7onVGD3xxBMqKSlRZmamLMsK+7tnjDojzEbg4MGDOuuss7Rw4cJOrxljNHnyZG3fvl1/+ctfVFNTo/z8fF188cU6ePBgsG7Dhg269NJLVVpaqjfeeENvvvmmZs6cGXJE2zXXXKPa2lqtXLlSK1euVG1traZOndor39HpejpGeXl58vl8IY97771XGRkZmjBhQvBajFH3xOLP0NSpU/Xee+/pr3/9q9566y2VlZVpypQpqqmpCdYwPt3X0zE6ePCgSktLZVmWXnnlFa1bt06tra2aOHGi2tvbg9dijKL36quv6uabb9Zrr72mqqoqtbW1qbS0NOTPx69+9Ss99NBDWrhwod58800NHTpUl1xyiQ4cOBCsKS8v1wsvvKDnnntOa9eu1aeffqrLL79cfr8/WMP4dE+sxujQoUO69NJL9bOf/azLz2KMwjCIiiTzwgsvBJ+/9957RpJ5++23g21tbW0mKyvLLF68ONg2ZswYM2/evC6vu3nzZiPJvPbaa8G2DRs2GEnmX//6V2y/RB/X3TE60tlnn22uv/764HPGKDa6Oz4ZGRnmmWeeCblWVlaW+f3vf2+MYXxiqTtj9Pe//92kpKSYpqamYM3HH39sJJmqqipjDGMUK3v27DGSzKuvvmqMMaa9vd0MHTrU/OIXvwjWfP7558btdpvHHnvMGGPM/v37Tb9+/cxzzz0XrGloaDApKSlm5cqVxhjGJ5a6M0aHW7VqlZFkPvnkk5B2xig8ZmZ7qKWlRZKUnp4ebHO5XOrfv7/Wrl0rSdqzZ49ef/11DRkyROPGjVN2drYuvPDC4OtSYObW7XZrzJgxwbbzzjtPbrdb69ev76Vv0zdFMkZH2rRpk2pra3XDDTcE2xij+Ih0fC644AItW7ZMH3/8sdrb2/Xcc8+ppaVFJSUlkhifeIpkjFpaWmRZVsjG7+np6UpJSQnWMEax0dTUJEnKysqSJNXV1amxsVGlpaXBmrS0NF144YXB3+umTZv0xRdfhNTk5uaqqKgoWMP4xE53xigSjFF4hNkeOu2005Sfn6+5c+fqk08+UWtrq37xi1+osbFRPp9PkrR9+3ZJ0j333KObbrpJK1eu1MiRI/XNb34zuOassbFRQ4YM6XT9IUOGqLGxsfe+UB8UyRgd6cknn9SIESM0bty4YBtjFB+Rjs+yZcvU1tamQYMGKS0tTdOnT9cLL7ygk08+WRLjE0+RjNF5552njIwM3X777Tp06JAOHjyon/zkJ2pvbw/WMEY9Z4zRnDlzdMEFF6ioqEiSgr+77OzskNrs7Ozga42Njerfv7++8pWvHLWG8em57o5RJBij8AizPdSvXz8tX75c77//vrKysjRgwACtXr1aEyZMkMvlkqTgerHp06fruuuu0znnnKOHH35YX/va1/TUU08Fr2VZVqfrG2PCtiNykYzR4T777DMtWbIkZFa2A2MUe5GOz7x58/TJJ5/o5Zdf1saNGzVnzhx973vf01tvvRWsYXziI5IxGjx4sJ5//nn97W9/0/HHHy+3262mpiaNHDkyZBwZo56ZOXOm/vnPf2rp0qWdXjvydxjJ7/XIGsan52I9Rse6Rnev05ek2t2BvmDUqFGqra1VU1OTWltbNXjwYI0ZM0ajR4+WJOXk5EiSvv71r4e8b8SIEdq5c6ckaejQoZ3u+pWkjz76qNP/ySF6xxqjw1VWVurQoUOaNm1aSDtjFD/HGp9t27Zp4cKFevvtt3X66adLks466yxVV1frkUce0WOPPcb4xFkkf4ZKS0u1bds27d27V6mpqRo4cKCGDh2qwsJCSfwZ6qlbbrlFf/3rX7VmzRp5PJ5g+9ChQyUFZu06/nsjBZa4dfxehw4dqtbWVn3yySchs7N79uwJ/g0U49NzPRmjSDBG4TEzG0Nut1uDBw/Wli1btHHjRk2aNEmSVFBQoNzc3E7bdLz//vvKz8+XJI0dO1ZNTU164403gq+//vrrampqCvmrbvRMV2N0uCeffFLf+c53NHjw4JB2xij+uhqfQ4cOSVLI7h9SYN1mx998MD69I5I/QyeeeKIGDhyoV155RXv27NF3vvMdSYxRdxljNHPmTHm9Xr3yyivB/znoUFhYqKFDh6qqqirY1traqldffTX4ex01apT69esXUuPz+fT2228Haxif7ovFGEWCMeqCLbedOcyBAwdMTU2NqampMZLMQw89ZGpqaswHH3xgjDHmz3/+s1m1apXZtm2befHFF01+fr4pKysLucbDDz9sMjMzzfPPP2+2bNli5s2bZ9LT083WrVuDNZdeeqk588wzzYYNG8yGDRvMGWecYS6//PJe/a5OFYsxMsaYLVu2GMuyzP/93/+F/RzGqHt6Oj6tra3mlFNOMcXFxeb11183W7duNb/5zW+MZVnmf//3f4N1jE/3xeLP0FNPPWU2bNhgtm7dav70pz+ZrKwsM2fOnJAaxih6P/7xj43b7TarV682Pp8v+Dh06FCw5he/+IVxu93G6/Wat956y1x99dUmJyfHNDc3B2tmzJhhPB6Pefnll80//vEPc9FFF5mzzjrLtLW1BWsYn+6J1Rj5fD5TU1NjFi9ebCSZNWvWmJqaGrNv375gDWPUGWE2Ah1bZBz5+OEPf2iMMWbBggXG4/GYfv36mZNOOsnMmzfPtLS0dLpORUWF8Xg8ZsCAAWbs2LGmuro65PV9+/aZH/zgB+aEE04wJ5xwgvnBD37QaVsOhBerMZo7d67xeDzG7/eH/RzGqHtiMT7vv/++KSsrM0OGDDEDBgwwZ555Zqetuhif7ovFGN1+++0mOzvb9OvXz5x66qnmwQcfNO3t7SE1jFH0wo2LJPP0008Ha9rb283dd99thg4datLS0sw3vvEN89Zbb4Vc57PPPjMzZ840WVlZ5rjjjjOXX3652blzZ0gN49M9sRqju++++5jXYYw6s4wxJl6zvgAAAEA8sWYWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWABKIMUYXX3yxvvWtb3V6bdGiRXK73dq5c6cNPQOAxESYBYAEYlmWnn76ab3++ut6/PHHg+11dXW6/fbbtWDBAp100kkx/cwvvvgiptcDgN5EmAWABJOXl6cFCxbotttuU11dnYwxuuGGG/TNb35T5557ri677DIdf/zxys7O1tSpU7V3797ge1euXKkLLrhAAwcO1KBBg3T55Zdr27Ztwdd37Nghy7L05z//WSUlJUpPT9d///d/2/E1ASAmLGOMsbsTAIDOJk+erP379+uKK67Qf/3Xf+nNN9/U6NGjddNNN2natGn67LPPdPvtt6utrU2vvPKKJGn58uWyLEtnnHGGDh48qLvuuks7duxQbW2tUlJStGPHDhUWFqqgoEAPPvigzjnnHKWlpSk3N9fmbwsA3UOYBYAEtWfPHhUVFWnfvn2qrKxUTU2NXn/9df39738P1uzatUt5eXl67733NHz48E7X+OijjzRkyBC99dZbKioqCobZ+fPna/bs2b35dQAgLlhmAAAJasiQIfrRj36kESNG6Lvf/a42bdqkVatW6fjjjw8+TjvtNEkKLiXYtm2brrnmGn31q19VZmamCgsLJanTTWOjR4/u3S8DAHGSancHAABdS01NVWpq4F/V7e3tmjhxon75y192qsvJyZEkTZw4UXl5eVq8eLFyc3PV3t6uoqIitba2htRnZGTEv/MA0AsIswDgECNHjtTy5ctVUFAQDLiH27dvn9599109/vjjKi4uliStXbu2t7sJAL2KZQYA4BA333yzPv74Y1199dV64403tH37dr300ku6/vrr5ff79ZWvfEWDBg3SE088oa1bt+qVV17RnDlz7O42AMQVYRYAHCI3N1fr1q2T3+/Xt771LRUVFWn27Nlyu91KSUlRSkqKnnvuOW3atElFRUW69dZb9etf/9rubgNAXLGbAQAAAByLmVkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBY/w99KbzwXu7KKQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "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": { "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": { "tags": [] }, "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": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": { "tags": [] }, "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": { "tags": [] }, "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": { "tags": [] }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(1960, 2015, 55)\n", "x = x/max(x)\n", "plt.figure(figsize=(8,5))\n", "y = sigmoid(x, *popt)\n", "plt.plot(xdata, ydata, 'ro', label='data')\n", "plt.plot(x,y, linewidth=3.0, label='fit')\n", "plt.legend(loc='best')\n", "plt.ylabel('GDP')\n", "plt.xlabel('Year')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Practice\n", "Can you calculate what is the accuracy of our model?\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean absolute error: 0.03\n", "Residual sum of squares (MSE): 0.00\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/sklearn/utils/validation.py:37: DeprecationWarning: distutils Version classes are deprecated. Use packaging.version instead.\n", " LARGE_SPARSE_SUPPORTED = LooseVersion(scipy_version) >= '0.14.0'\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "R2-score: 0.98\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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Click here for the solution\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", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Want to learn more?

\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: SPSS Modeler\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 Watson Studio\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", "Joseph Santarcangelo\n", "\n", "\n", "##

© IBM Corporation 2020. All rights reserved.

\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 }