Skip to content

Instantly share code, notes, and snippets.

Show Gist options
  • Star 0 You must be signed in to star a gist
  • Fork 0 You must be signed in to fork a gist
  • Save edisoncastro01/1843940423c895036bd08e2618b6e2c1 to your computer and use it in GitHub Desktop.
Save edisoncastro01/1843940423c895036bd08e2618b6e2c1 to your computer and use it in GitHub Desktop.
Created on Skills Network Labs
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center>\n",
" <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/Logos/organization_logo/organization_logo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\" />\n",
"</center>\n",
"\n",
"# Non Linear Regression Analysis\n",
"\n",
"Estimated time needed: **20** minutes\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 because, as the name implies, linear regression presumes that the data is linear. \n",
"Let's learn about non linear regressions and apply an example on 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": [
"Though Linear regression is very good to solve many problems, it cannot be used for all datasets. First recall how linear regression, could model a dataset. It models a linear relation between a dependent variable y and independent variable x. It had a simple equation, of degree 1, for example y = $2x$ + 3.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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 regressions are a relationship between independent variables $x$ and a dependent variable $y$ which result in a non-linear function modeled data. 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 $x$). \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 others. For example: $$ y = \\log(x)$$\n",
"\n",
"Or 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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEJCAYAAAB7UTvrAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAmvUlEQVR4nO3de3xdVZ338c8vtzZJ7216b0kLhVJuAqWAICI3UZGCgAMOUkAHfAYUfcYLKI84jw8zjM446ggqItiRClYQWhlBapWrQOkNWtpCQwtp2qZJr7k1t5Pf88feCYeQpIek5+xz+b5fr7zO3mtf1m8Hen5Ze+29lrk7IiIiAHlRByAiIulDSUFERLooKYiISBclBRER6aKkICIiXZQURESkS9KSgpnda2Y1Zra2h21fNTM3szFxZbeYWYWZvW5mH01WXCIi0rtkthR+BZzfvdDMpgDnApVxZbOAy4GjwmPuMrP8JMYmIiI9KEjWid39GTMr72HTfwJfBxbFlc0FHnT3FmCzmVUAc4AX+qpjzJgxXl7eUxUiItKbFStW7HT3sp62JS0p9MTMLgS2uvsrZha/aRLwYtx6VVjWp/LycpYvX35wgxQRyXJm9nZv21KWFMysBPgWcF5Pm3so63H8DTO7DrgOYOrUqQctPhERSe3TR4cC04BXzOwtYDKw0szGE7QMpsTtOxnY1tNJ3P1ud5/t7rPLynps/YiISD+lLCm4+xp3H+vu5e5eTpAITnD3amAxcLmZDTKzacAMYFmqYhMRkUAyH0l9gKCj+AgzqzKzz/W2r7u/BiwE1gFPADe4eyxZsYmISM+S+fTRFQfYXt5t/Xbg9mTFIyIiB6Y3mkVEpIuSgoiIdFFSEBHJMPc+t5k/rtmelHMrKYiIZJifP/MmS9fXJOXcSgoiIhlk3/42dtS1MGPckKScX0lBRCSDVNQ0ADBjrJKCiEjOq6ipB2DG2KFJOb+SgohIBtm4o4HBhXlMGlmclPMrKYiIZJCNNQ1MHzOE/LyexhEdOCUFEZEMUlHTkLROZlBSEBHJGI0t7Wzduz9pncygpCAikjHerA2ePDosSZ3MoKQgIpIxNu4IH0fV7SMREdlY00BhvnHIqJKk1aGkICKSISpq6pk+ZggF+cn76lZSEBHJEBtrGjgsibeOQElBRCQjNLfF2LK7icPKlBRERHLeptpGOjy5ncygpCAikhE2JnnMo05KCiIiGaCipoH8PKN8TPKePAIlBRGRjLBxRwOHjC5hUEF+UutJWlIws3vNrMbM1saVfd/MNpjZq2b2iJmNiNt2i5lVmNnrZvbRZMUlIpKJNtbUJ3V4i07JbCn8Cji/W9kS4Gh3PxZ4A7gFwMxmAZcDR4XH3GVmyU2HIiIZorktxlu7mpLenwBJTAru/gywu1vZk+7eHq6+CEwOl+cCD7p7i7tvBiqAOcmKTUQkk1TUNBDrcI6cMCzpdUXZp3At8Hi4PAnYEretKix7DzO7zsyWm9ny2traJIcoIhK99dvrAJg5IYNbCn0xs28B7cCCzqIedvOejnX3u919trvPLisrS1aIIiJpY0N1PYML8ygfXZr0ugqSXkM3ZjYPuAA42907v/irgClxu00GtqU6NhGRdLShuo4jxg1N2mxr8VLaUjCz84FvABe6e1PcpsXA5WY2yMymATOAZamMTUQkHbk767fXM3N88vsTIIktBTN7ADgTGGNmVcBtBE8bDQKWmBnAi+7+BXd/zcwWAusIbivd4O6xZMUmIpIpautb2N3YmpL+BEhiUnD3K3oo/mUf+98O3J6seEREMtH66mB4i1S1FPRGs4hIGtsQPnl0ZIpaCkoKIiJpbEN1PROGD2ZESVFK6lNSEBFJY+u31zFzfGpaCaCkICKStlrbO6ioaWBmCt5k7qSkICKSpt6sbaC9w9VSEBGRd4a3mKWWgoiIbKiupyg/j2ljkj+8RSclBRGRNLV+ex0zxg2hID91X9VKCiIiaWpDdeqGt+ikpCAikoZq6pqprW9J2UtrnZQURETS0Jqt+wA4dvKIlNarpCAikobWbN2HGRw1UbePRERy3tqt+5g+ppTSQamd9kZJQUQkDa3Zuo9jJg1Peb1KCiIiaaamvpkddS0craQgIiJrw05mtRRERIQ1VXVBJ7OSgoiIrNm6j2ljShmS4k5mUFIQEUk7a7fu49gIWgmgpCAiklZq6puprmuOpJMZkpgUzOxeM6sxs7VxZaPMbImZbQw/R8Ztu8XMKszsdTP7aLLiEhFJZ1F2MkNyWwq/As7vVnYzsNTdZwBLw3XMbBZwOXBUeMxdZpafxNhERNJSlJ3MkMSk4O7PALu7Fc8F5ofL84GL4sofdPcWd98MVABzkhWbiEi6irKTGVLfpzDO3bcDhJ9jw/JJwJa4/arCMhGRnLI2ojeZOx0wKVjgSjP7drg+1cwO9l/x1kOZ9xLPdWa23MyW19bWHuQwRESi09nJnNZJAbgLOBW4IlyvB+7sZ307zGwCQPhZE5ZXAVPi9psMbOvpBO5+t7vPdvfZZWVl/QxDRCT9rKrcC8DxU0dEFkMiSeFkd78BaAZw9z1AUT/rWwzMC5fnAYviyi83s0FmNg2YASzrZx0iIhlpZeUeCvONoyZG11JIpCejLXwSyAHMrAzoONBBZvYAcCYwxsyqgNuAO4CFZvY5oBK4DMDdXzOzhcA6oB24wd1j7/9yREQy16rKvcyaOJzBhdE9fJlIUvgx8Agw1sxuBy4Fbj3QQe5+RS+bzu5l/9uB2xOIR0Qk67THOni1ai9XzJkaaRwHTAruvsDMVhB8mRtwkbuvT3pkIiI5ZEN1Pc1tHRw/deSBd06iXpOCmY2KW60BHojf5u7d30EQEZF+WlW5B4ATIuxkhr5bCisI+hF6e1x0elIiEhHJQSsr91I2dBCTRhRHGkevScHdp6UyEBGRXLaqcg8nTB2BWU9/h6dOQu9Rm9mngNMJWgjPuvujyQxKRCSX7Gpo4a1dTVwecSczJPZG813AF4A1wFrgC2bW35fXRESkm9Vb9gJwQsSdzJBYS+HDwNHu3vmewnyCBCEiIgfByso95OdZpMNbdErkjebXgfg2zRTg1eSEIyKSe1ZV7uXICUMpLop+xoC+Hkn9A0EfwnBgvZktC9dPBv6WmvBERLJbrMN5ZcteLjlxctShAH3fPvr3lEUhIpKjNlTX0dgai3QQvHh9PZL6dCoDERHJRcs2B+8Bz5k2OuJIAok8fXSKmb1sZg1m1mpmMTOrS0VwIiLZbtnm3UweWRz5S2udEulo/gnBXAobgWLg82GZiIgMgLuzbPNu5kwbdeCdUyShl9fcvcLM8sPhrO8zM3U0i4gM0Ju1DexqbOWUNLl1BIklhSYzKwJWm9n3gO1AaXLDEhHJfi9u6uxPSJ+WQiK3jz4L5AM3Ao0E7ylcksygRERywbLNuxk7dBCHjC6JOpQuicyn8Ha4uB/45+SGIyKSGzr7E06ePjryQfDi9fXy2kJ3/7SZrSGcijOeux+b1MhERLJY5e4mquua0+rWEfTdUrgp/LwgFYGIiOSSl8L3E07JlKTg7tvNLB/4pbufk8KYRESy3kubdjOqtIjDxg6JOpR36bOjOXwEtcnMoh+6T0Qkiyx7axdzykelVX8CJPZIajOwxsyWEDx9BIC7f6m/lZrZVwhegnOCYbivAUqA3wLlwFvAp919T3/rEBFJV9v27mfL7v1c88H0m+AykaTwP+HPQWFmk4AvAbPcfb+ZLQQuB2YBS939DjO7GbgZ+MbBqldEJF08X7ETgFOmp89La50SeSR1fpLqLTazNoIWwjbgFuDMcPt84CmUFEQkCz1XsZMxQ4qYOX5o1KG8RyID4s0ws4fMbJ2Zber86W+F7r6VYFjuSoK3o/e5+5PAOHffHu6zHRjbSzzXmdlyM1teW1vb3zBERCLR0eE8X7GT0w4bQ15eevUnQGJvNN8H/BRoBz4C/Dfw6/5WaGYjgbnANGAiUGpmVyZ6vLvf7e6z3X12WVlZf8MQEYnEhup6dja0cvphY6IOpUeJJIVid18KmLu/7e7fAc4aQJ3nAJvdvdbd24DfAx8EdpjZBIDws2YAdYiIpKXnKoI7HB+akZ5/1CaSFJrNLA/YaGY3mtnF9HJrJ0GVwClmVmLBs1hnA+uBxcC8cJ95wKIB1CEikpae3biTw8YOYfzwwVGH0qNek4KZjQsXv0zQGfwl4ETgSt758n7f3P0l4CFgJcHjqHnA3cAdwLlmthE4N1wXEckazW0xlm3enba3jqDvp49eCcc9egB4w92rCN4nGDB3vw24rVtxC0GrQUQkK614ew8t7R18aEb6JoW+bh9NInhK6EPAG2b2qJn9nZmlx5xxIiIZ5tmNOynIM05Ow/cTOvWaFNw95u5/cvdrCOZQuA+4CNhsZgtSFJ+ISNZ4rqKW46eOYMighCa9jEQiHc24eyuwjqBDuI7g7WMREUnQ7sZWXttWx+mHpedTR536TApmNtXMvmZmK4HHCGZgm+vux6ckOhGRLPFcxU7c4fQ07k+AvifZ+RtBv8LvgOvcfXnKohIRyTJ/Wb+DUaVFfGDKiKhD6VNfN7ZuAZ5x9/fMuiYiIolrj3Xw1Bu1nDVzLPlpOLRFvL4m2Xk6lYGIiGSrlZV72dvUxtkzxx1454gl1NEsIiL9t3TDDgryjDMOT+/+BEhslNT3zALRU5mIiPTsL+trOHn6KIYOLow6lANKpKXwcA9lDx3sQEREslHlriY21jRwVgbcOoK+nz6aCRwFDDezT8VtGgak50hOIiJp5i8bdgBwzpEDGUc0dfp6+ugI4AJgBPDJuPJ64B+SGJOISNZYuqGGQ8tKOWR0adShJKSvp48WAYvM7FR3fyGFMYmIZIWGlnZe3LSLa07LnG7YRAbgqDCzbwLl8fu7+7XJCkpEJBs8+0YtbTHnrJmZcesIEksKi4BngT8DseSGIyKSPR5fW82o0iJmHzIy6lASlkhSKHH3byQ9EhGRLNLcFmPp+h1c+IGJFORnzithiUT6mJl9POmRiIhkkWfeqKWxNcbHjp4QdSjvSyJJ4SaCxNBsZnVmVm9mdckOTEQkkz2+tpoRJYWcemj6TqjTkwPePnL3oakIREQkW7S0x/jzuh187JjxFGbQrSNIbJgLM7Mrzez/hOtTzGxO8kMTEclMz23cSX1LOx87JrNuHUFit4/uAk4FPhOuNwB3DqRSMxthZg+Z2QYzW29mp5rZKDNbYmYbw8/M6a4XEYnzxzXVDBtcwGmHpv8AeN0lkhROdvcbgGYAd98DFA2w3h8BT7j7TOA4gmk+bwaWuvsMYGm4LiKSUVrbO1iyrppzZ42nqCCzbh1BYkmhzczyAQcwszKgo78Vmtkw4AzglxDM/+zue4G5wPxwt/nARf2tQ0QkKs+/uZO65nY+fsz4qEPpl0SSwo+BR4CxZnY78BzwLwOoczpQC9xnZqvM7B4zKwXGuft2gPAzc14BFBEJLV69jaGDC9J+LubeJPL00QIzWwGcDRhwkbuvH2CdJwBfdPeXzOxHvI9bRWZ2HXAdwNSpUwcQhojIwdXY0s4Ta6u56PiJDCrIjzqcfum1pRB2/I4ys1FADfAA8BtgR1jWX1VAlbu/FK4/RJAkdpjZhLDuCWGd7+Hud7v7bHefXVZWNoAwREQOrj+9Vs3+thgXHz856lD6ra+WwgqCfgQDpgJ7wuURQCXQr2H/3L3azLaY2RHu/jpBC2Rd+DMPuCP8XNSf84uIROWRVVuZPLI4o8Y66q6vobOnAZjZz4DF7v7HcP1jwDkDrPeLwAIzKwI2AdcQtFoWmtnnCJLOZQOsQ0QkZar3NfN8xU5u/Mhh5OVZ1OH0WyID4p3k7l/oXHH3x83suwOp1N1XA7N72HT2QM4rIhKVRau30uFw8QmZe+sIEksKO83sVuB+gttJVwK7khqViEiGeWTVVj4wZQTTxmTGDGu9SeSR1CuAMoLHUh8leFT0iiTGJCKSUdZtq2NDdT2fOmFS1KEMWCKPpO4mGClVRER68PDKKgryjAuOnRh1KAN2wKRgZocDX+W903GelbywREQyQ3NbjIdXVvHRo8YzqnSgIwBFL5E+hd8BPwPuQdNxioi8y+Nrt7O3qY0r5mTHy7SJJIV2d/9p0iMREclAD7y0hUNGl/DBDJtMpzeJdDT/wcz+0cwmdHvLWUQkp23cUc+yt3ZzxZypGf1uQrxEWgrzws+vxZU5wcB2IiI56zfLKinMNy49MbPfTYiXyNNH/RrOQkQkmzW3xXh4RdDBPGbIoKjDOWgSmY6zxMxuNbO7w/UZZnZB8kMTEUlf//Pqduqa2/nMydnRwdwpkT6F+4BW4IPhehXw/5IWkYhImnN35r/wFtPHlHLq9OzoYO6USFI41N2/B7QBuPt+gtFSRURy0vK39/Bq1T6uPX0aZtn1dZhIUmg1s2LemY7zUKAlqVGJiKSxe57dxIiSQi7J8MHvepLI00e3AU8AU8xsAXAacHUygxIRSVdv72rkyXU7+MczD6W4KDNnV+tLIk8fLTGzlcApBLeNbnL3nUmPTEQkDd33/FsU5BlXnVoedShJkUhLAeDDwOkEt5AKCUZMFRHJKfv2t7Fw+RY+edxExg0bHHU4SZHII6l3AV8A1gBrgevN7M5kByYikm4eXFZJU2uMz52eva9vJdJS+DBwtLt3djTPJ0gQIiI5o7ktxj3PbeaDh47mqInDow4naRJ5+uh1IP7tjCnAq8kJR0QkPT24rJLa+ha+dPaMqENJqkRaCqOB9Wa2LFw/CXjBzBYDuPuFyQpORCQdtLTH+NnTm5hTPopTsuxlte4SSQrfTkbFZpYPLAe2uvsF4cirvyWYzOct4NPuvicZdYuIvB+/W15FdV0z/37ZcVGHknQHvH3k7k8TfEkXhsvLgJXu/nS43l83Aevj1m8Glrr7DGBpuC4iEqnW9g5++tSbnDB1BKcdlt2tBEjs6aN/AB4Cfh4WTQYeHUilZjYZ+ATBbG6d5gLzw+X5wEUDqUNE5GB4ZFUVW/fu50tnz8i6IS16kkhH8w0EbzHXAbj7RmDsAOv9IfB1oCOubJy7bw/r2H4Q6hARGZDmthg/XlrBcZOH8+HDy6IOJyUSSQot7t7auWJmBYTjIPVHOOx2jbuv6Ofx15nZcjNbXltb298wREQO6P4X32br3v18/fyZOdFKgMSSwtNm9k2g2MzOBX4H/GEAdZ4GXGhmbwEPAmeZ2f3ADjObABB+1vR0sLvf7e6z3X12WVluZG4RSb19+9v4yV8rOOPwMk47bEzU4aRMIknhZqCW4IW164E/Arf2t0J3v8XdJ7t7OXA58Bd3vxJYzDtTf84DFvW3DhGRgfrpU2+yb38bN58/M+pQUiqRAfE6zOxR4FF3T+b9mjuAhWb2OaASuCyJdYmI9Grb3v3c9/xmLv7AJGZNHBZ1OCnVa1Kw4AbabcCNBKOjmpnFgP9y9/97MCp396eAp8LlXcDZB+O8IiID8YMlb+AO//u8w6MOJeX6un30ZYL7/ye5+2h3HwWcDJxmZl9JRXAiIqm2qnIPD62o4prTypk8siTqcFKur6RwFXCFu2/uLHD3TcCV4TYRkawS63C+veg1xg0bxBezfIyj3vSVFAp7mkwn7FcoTF5IIiLReGBZJWu27uNbn5jFkEGJTjeTXfpKCq393CYiknF2N7by/T+9zqnTR/PJYydEHU5k+kqFx5lZXQ/lBmTnlEMikrO+98QGGlva+ee5R+XMi2o96TUpuHv2zUgtItKDv1Xs5MGXt3DdGdM5fNzQqMOJVCIvr4mIZK3Glna+/vCrTBtTylfOyb1HULvLzZ4UEZHQvz2xga1797Pw+lMpLtINErUURCRnvbhpF//9wttc/cFyTiofFXU4aUFJQURyUn1zG19/6FUOGV3C1z56RNThpA3dPhKRnOPu3ProWqr2NPHb60+lpEhfhZ3UUhCRnPPQiioWrd7Gl885XLeNulFSEJGc8mZtA99e9BqnTB/FDR85LOpw0o6SgojkjOa2GDf+ZhWDC/P44d8dT35e7r6k1hvdSBORnODufOPhV9lQXce9805i/HANzNATtRREJCf84tlNLFq9jX8693A+MnNs1OGkLSUFEcl6T79Ryx2Pb+Djx4xXP8IBKCmISFarqKnni79ZyeHjhvL9S4/L6cHuEqGkICJZq3pfM1f9chlFBfn84qrZlOboHAnvh5KCiGSlffvbuPq+Zezb38avrjmJKaNyb2rN/lDaFJGs09wW4/pfL+fN2gbuvfokjp40POqQMkbKWwpmNsXM/mpm683sNTO7KSwfZWZLzGxj+Dky1bGJSOZraY9x/a9X8NLm3Xz/0uP40IyyqEPKKFHcPmoH/sndjwROAW4ws1nAzcBSd58BLA3XRUQS1tIe43/dvzJ42uhTx3DR8ZOiDinjpDwpuPt2d18ZLtcD64FJwFxgfrjbfOCiVMcmIpmrtb2DGxas5C8baviXi4/h706aGnVIGSnSjmYzKweOB14Cxrn7dggSB9Dj2yVmdp2ZLTez5bW1tSmLVUTSV0NLO9f+6mX+vL6G7849is+crITQX5ElBTMbAjwMfNnd6xI9zt3vdvfZ7j67rEz3CkVy3a6GFv7+Fy/ywqZdfP/SY/nsqeVRh5TRInn6yMwKCRLCAnf/fVi8w8wmuPt2M5sA1EQRm4hkji27m5h33zK27tnPz688kXNmjYs6pIwXxdNHBvwSWO/uP4jbtBiYFy7PAxalOjYRyRwvbdrF3DufZ2d9C/d//mQlhIMkipbCacBngTVmtjos+yZwB7DQzD4HVAKXRRCbiGSAB5dVcuuja5k6uoR7rprN9LIhUYeUNVKeFNz9OaC3wUfOTmUsIpJZmttifPexdSx4qZIPzRjDTz5zAsOLC6MOK6vojWYRyQibdzbyjwtWsn57HdefMZ2vffQICvI1Us/BpqQgImnN3fn9yq18e9FaCgvyuPfq2Zw1U/0HyaKkICJpq7a+hW8+soYl63ZwUvlIfnT58UwcURx1WFlNSUFE0o67s/iVbXxn8Ws0tsb41seP5NrTp2lO5RRQUhCRtPJmbQPfXrSW5yt2cdyUEfzHZcdy2NihUYeVM5QURCQt1De3cddTb/LLZzczqDAvHK7iELUOUkxJQUQi1Rbr4MFllfzwzxvZ1djKp46fxM0fn8nYoYOjDi0nKSmISCTaYx0sWr2N//rLRt7a1cTJ00Zx3yeO5NjJI6IOLacpKYhISrW2d7D4lW3c+dcKNu9s5MgJw/jFVbM558ixBKPgSJSUFEQkJeqa23jgpUrue/4tquuamTl+KD+78kTOmzWOPPUbpA0lBRFJqte27eP+FytZtHorTa0xTjtsNHdccgwfPrxMLYM0pKQgIgfdvqY2/vDqNh5aUcXqLXsZXJjHhcdN5KpTyzl60vCow5M+KCmIyEHR3Bbjqddr+MMr21myfget7R0cPm4It37iSC47cQrDSzRwXSZQUhCRftu3v42n36hlybodLF2/g6bWGKNLi/jMnKlccsJkjp40TLeIMoySgogkzN3ZUF3PM2/U8vQbtSzbvJv2Dmd0aREXHT+JC46ZwJxpozR6aQZTUhCRXrk7m3Y28uKmXby0aTcvbNpFbX0LAIePG8LnPzSdc2eN4wNTRujN4yyhpCAiXfbtb2Pt1n2s3rKXVZV7WFm5l92NrQCMGzaIU6eP5vQZYzhjRhnjh+uN42ykpCCSg9ydbfuaeb26jvXb61m3rY512+vYvLOxa5/pZaWcPXMsJx4ykpOnj6Z8dIn6B3KAkoJIFmtqbadydxNv7WzkzdpGNtU2UlHbQMWOehpbY137TRlVzKwJw7j0xMkcO3k4x0wazoiSoggjl6goKYhkKHdn3/42tu9rpnpfM9v27Wfb3v1U7Ql+3t7VxM6GlncdM3boIA4tG8KlJ05mxrihHDF+KDPHD2XoYD0uKoG0Swpmdj7wIyAfuMfd74g4JJGUaW3vYG9TK3ua2tjT1MquhlZ2N7awq7GVnQ0t7KxvpbahhZr6ZnbUtdDa3vGu4wvyjIkjipk0opizZpZxyOhSpo4qoXx0KdPKShkyKO3+yUuaSav/Q8wsH7gTOBeoAl42s8Xuvi7ayER6F+twmttiNLXG2N8ao6mtnabWGE0tMRpb22lsCX4aWmI0tLTR0NxOfXM7dc3t1DW3Ubc/+Nm7v42muFs63Y0sKWTMkEGMGTKIE6eOZNywwZQNHcSE4cVMGDGYCcMHM3boYD0FJAOSVkkBmANUuPsmADN7EJgLKClkGHfHHRzoCJc7usqcjs71juCzw51Y3H4dDh0dTqzD39neQdd6rCPYP9a5T7je3uHEYuFnh9Pe0UF7LPhsizntsQ7aO7xruS3WQVuH09beQWu43tLeQWv4E7/e0t5Bc1uM5vYYLW3hcltwXKLy84whgwoYMqiAYcWFDBtcwOSRJYyYVMiI4kKGFxcyorSIkSWFjCwpYlRpEaNLixhZWkShnv2XFEi3pDAJ2BK3XgWcfLAr2VBdx42/WXXA/dz9wPscsKDP4nfV4e8qjz/Wey5/1/J7z9P5BRy/r7/rOO9W7u/axz082t/Z7nHn9fjybgkgkxTl51GQbxQV5FGUn0dhfh6DCvKC9YJgeXBhPsOKCxlcmMeggvyussGF+RQX5jO4MI+SonyKiwooLsynZFA+pUUFlBTlM2RQAaVhIhhcmKcneCStpVtS6Olfy7u+YszsOuA6gKlTp/arksEF+RwxLsE5XxP499t9l97+0fd2qvjd7V3l1mM579rfus7x7mPf2d61bHFHdW3vZd+4+oNzW1cdZsG2zn06y/Msfp9gOa9rv6Csc5/8zn3NyDfIy7Nwe7Cta7+8YDkvz8g3Iz8vOGd+XtxP5/Y8oyDPKMjLIy8PCvPzutYL8oNt+XlGYUEehXFl+pIWeUe6JYUqYErc+mRgW/wO7n43cDfA7Nmz+/U3afmYUu78+xP6G6OISNZKt5uULwMzzGyamRUBlwOLI45JRCRnpFVLwd3bzexG4E8Ej6Te6+6vRRyWiEjOSKukAODufwT+GHUcIiK5KN1uH4mISISUFEREpIuSgoiIdFFSEBGRLkoKIiLSxRIZyiFdmVkt8HbUcfTDGGBn1EFEIBevOxevGXLzujPpmg9x97KeNmR0UshUZrbc3WdHHUeq5eJ15+I1Q25ed7Zcs24fiYhIFyUFERHpoqQQjbujDiAiuXjduXjNkJvXnRXXrD4FERHpopaCiIh0UVKImJl91czczMZEHUsqmNn3zWyDmb1qZo+Y2YioY0oWMzvfzF43swozuznqeJLNzKaY2V/NbL2ZvWZmN0UdU6qYWb6ZrTKzx6KOZaCUFCJkZlOAc4HKqGNJoSXA0e5+LPAGcEvE8SSFmeUDdwIfA2YBV5jZrGijSrp24J/c/UjgFOCGHLjmTjcB66MO4mBQUojWfwJfp/cpnLOOuz/p7u3h6osEs+tlozlAhbtvcvdW4EFgbsQxJZW7b3f3leFyPcGX5KRoo0o+M5sMfAK4J+pYDgYlhYiY2YXAVnd/JepYInQt8HjUQSTJJGBL3HoVOfAF2cnMyoHjgZciDiUVfkjwx11HxHEcFGk3yU42MbM/A+N72PQt4JvAeamNKDX6um53XxTu8y2C2w0LUhlbClkPZTnRIjSzIcDDwJfdvS7qeJLJzC4Aatx9hZmdGXE4B4WSQhK5+zk9lZvZMcA04BUzg+AWykozm+Pu1SkMMSl6u+5OZjYPuAA427P3megqYErc+mRgW0SxpIyZFRIkhAXu/vuo40mB04ALzezjwGBgmJnd7+5XRhxXv+k9hTRgZm8Bs909UwbT6jczOx/4AfBhd6+NOp5kMbMCgo70s4GtwMvAZ7J5znEL/sKZD+x29y9HHE7KhS2Fr7r7BRGHMiDqU5BU+wkwFFhiZqvN7GdRB5QMYWf6jcCfCDpcF2ZzQgidBnwWOCv8b7s6/AtaMohaCiIi0kUtBRER6aKkICIiXZQURESki5KCiIh0UVIQEZEuSgqSFsys4X3uf2aUI1K+33i7HXu1mU3spfyBbmVjzKzWzAYleO7ZZvbjBOr/SS/b+n1dkh2UFERS72rgPUkB+D1wrpmVxJVdCix295YDndTMCtx9ubt/6eCEKblISUHSStgCeMrMHgrnXVgQvinbOT/BBjN7DvhU3DGlZnavmb0cjmk/Nyy/2swWmdkT4bwGt8Udc6WZLQtfsPp5ONQ1ZtZgZreb2Stm9qKZjQvLp5nZC2Ed3+0W89fC8lfN7J/DsvJwXoFfhHMLPGlmxWZ2KTAbWBDWXdx5nnCcoGeAT8ad/nLgATP7pJm9FF7fn+Pi+o6Z3W1mTwL/Hd+CMrM5Zva38Ji/mdkRceed0tPv5UDXJTnA3fWjn8h/gIbw80xgH8FYQXnAC8DpBOPKbAFmEAw2txB4LDzmX4Arw+URBMNLlBL8Rb4dGA0UA2sJvpCPBP4AFIbH3AVcFS478Mlw+XvAreHy4rh9boiL9zyCuXktjPcx4AygnGDAvw+E+y2Mi/EpgmFNevo9XAY8Ei5PJBgvKR8YyTsvm34e+I9w+TvACqA47vfX+XsZBhSEy+cAD4fLPf5euv136PG6ov7/RD/J/9GAeJKOlrl7FYCZrSb4gm0ANrv7xrD8fuC6cP/zCAYl+2q4PhiYGi4vcfdd4TG/J0gw7cCJwMthI6QYqAn3byX4AoTgy/bccPk04JJw+dfAv8XVfR6wKlwfQpC4KsN4V8edqzyBa38MuMvMhgGfBh5y91g4Zv9vzWwCUARsjjtmsbvv7+Fcw4H5ZjaDINkVxm3r6feyPG57b9f1TALXIBlMSUHSUfz98xjv/H/a25gsBlzi7q+/q9Ds5B6O8XD/+e7e06xvbe7eeUx83b3Vb8C/uvvPu9Vd3sN1FHMA7r7fzJ4ALia4dfSVcNN/AT9w98XhwGvfiTussZfTfRf4q7tfHMbzVB/X0n29x+uS7Kc+BckUG4BpZnZouH5F3LY/AV+M63s4Pm7buWY2Krx3fxHwPLAUuNTMxob7jzKzQw5Q//MEX9IAf9+t7mstmEMAM5vUed4+1BMMCtibB4D/DYwjmJ0Ogr/6t4bL8w5w/k7xx1zdbVtPv5d4/bkuyQJKCpIR3L2Z4HbR/4QdzW/Hbf4uwa2RV81sbbje6TmC2z2rCe6pL3f3dcCtwJNm9irBvNETDhDCTQRzDr9M8GXbGdeTwG+AF8xsDfAQfX/hA/wK+Fn3juY4TxL0J/w2rtXyHeB3ZvYskOgQ698D/tXMnifol4j3nt9L/MZ+XpdkAY2SKlnLzK4m6EC9MepYRDKFWgoiItJFLQUREemiloKIiHRRUhARkS5KCiIi0kVJQUREuigpiIhIFyUFERHp8v8BLGjhwLZx9YIAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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 logarithmic map from input $x$'s to output variable $y$. 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 polynomial representation of the $x$'s. In general form it would be written as \n",
"\\begin{equation}\n",
"y = \\log(X)\n",
"\\end{equation}\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEJCAYAAACKWmBmAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAArBUlEQVR4nO3dd5xU5dn/8c+1DVh6lbqAilRFdAXUxBIbEkvUaOz1EX0Sf9HkSR5bYoymGE3V2HhQYy+JYkUBo8YKAoqA9M5Sl74sbL9+f5xDnODsMMDOnJ3d7/v1mtecNnO+syxz7Tn3Ofdt7o6IiEhtsqIOICIi9ZsKhYiIJKRCISIiCalQiIhIQioUIiKSkAqFiIgkFGmhMLNHzWydmc2qZb2Z2b1mttDMZpjZYenOKCLS2EV9RPE3YESC9acCfcLHKODBNGQSEZEYOVHu3N3fN7NeCTY5E3jCg7sCJ5lZGzPr4u6rE71vhw4dvFevRG8rIiKxpk2btt7dO8ZbF2mhSEI3YEXMfFG4LGGh6NWrF1OnTk1lLhGRBsXMltW2LupTT7tjcZbF7XPEzEaZ2VQzm1pcXJziWCIijUd9LxRFQI+Y+e7Aqngbuvtody9098KOHeMePYmIyF6o74XiVeDS8Oqn4cCW3bVPiIhI3Yq0jcLMngWOAzqYWRHwCyAXwN0fAsYBI4GFwHbgimiSiog0XlFf9XTBbtY78IM0xRERkTjq+6knERGJmAqFiIgkpEIhIpLhNm+v4JXpK3nwvUUpef/6fsOdiIjEsWLjdt6ctZq3Z69j6rKN1Dh0ad2Uq7/Zm5zsuj0GUKEQEckQqzbv4NUvVvHGjNXMXLkFgP5dWvGD4w/k+H6dGNy9DdlZ8e5T3jcqFCIi9dj2iiremLGalz5byaQlG3CHwT3acMvIfowY2IWC9vkpz6BCISJSD81ZvZVnJi/n5c9XUlJeRa/2+dxwwkF8Z0hXerZvntYsKhQiIvVEdY3zztx1PPLhYiYt3kheThbfPrgL5x/Rg6G922FW96eVkqFCISISsYqqGl76rIiH/rWIpRu207V1U24+tR/fO6IHbfLzoo6nQiEiEpXyqmqenbych99fzOotZRzcrTV/vXAIIwZ2rvMrl/aFCoWISJpV1zgvfVbEn99ewMrNOxjaqx13nXMIx/TpENnppURUKERE0uhf84v51euzWbBuG4d0b83vzjmEb/TpEHWshFQoRETSYMn6Un71+mz+OXcdvdrn8+BFhzFiUOd6eQSxKxUKEZEUKq+q5v53F/HgewtpkpPNzaf24/Kje9EkJzvqaElToRARSZHJizdw89iZLC4u5TuHduWWb/enU8umUcfaYyoUIiJ1rKyymrvenMvfPl5K97bNePzKoRx7UOYO0axCISJSh75YsZkfvzCdRcWlXH5UL/53RF/y8zL7qzbSC3XNbISZzTOzhWZ2U5z1x5nZFjObHj5uiyKniMju1NQ4D763iLMf/JjtFdU8ddUwbj9jYMYXCYjwiMLMsoH7gZOAImCKmb3q7rN32fQDdz8t7QFFRJK0qbSCH78wnXfnFfPtg7vwm7MPpnWz3Khj1ZkoS91QYKG7LwYws+eAM4FdC4WISL01fcVmvv/UNNZvq+DOMwdy8fCeGXHJ656I8tRTN2BFzHxRuGxXR5rZF2b2ppkNTE80EZHde+mzIs57+BOysowX//soLjmyV4MrEhDtEUW8n6bvMv8Z0NPdt5nZSOBloE/cNzMbBYwCKCgoqMOYIiL/qbrGufutuTz8/mKG79+OBy46nHbNo++8L1WiPKIoAnrEzHcHVsVu4O5b3X1bOD0OyDWzuPe6u/tody9098KOHTP3MjQRqd92VFRzzZPTePj9xVwyvCdPXjWsQRcJiPaIYgrQx8x6AyuB84ELYzcws87AWnd3MxtKUNg2pD2piAiwsbSCqx6fwvQVm/nlGQO57KheUUdKi8gKhbtXmdl1wHggG3jU3b80s2vD9Q8B3wX+28yqgB3A+e6+6+kpEZGUW7FxO5c++imrNu/gwYsOZ8SgzlFHShtriN+7hYWFPnXq1KhjiEgDsXDdNi4aM4myyhoeuayQwl7too5U58xsmrsXxluX+XeCiIik0JzVW7l4zGTMjBeuOZK+nVtGHSnt6s8QSiIi9cyMos2cP3oSudlZPH/N8EZZJEBHFCIicc1auYWLx0ymVbNcnr16OD3a5UcdKTIqFCIiu5i3poRLHplMy6a5PDdqON3bNt4iATr1JCLyHxYVb+OiMZPJzc7i6f8a1uiLBKhQiIj82+otO7hkzGTcnWeuHkavDs2jjlQv6NSTiAiwZXsllz86ha1lVTw3ajgHdmqcDdfx6IhCRBq9sspqrn5iKovXb2P0JYczqFvrqCPVKzqiEJFGrabG+dHz05mybCP3nj+Eow6M251co6YjChFp1O6ZMI83Z63h1pH9OX1w16jj1EsqFCLSaP1jWhEPvreIi4YVcNU3ekcdp95SoRCRRunTJRu5+aUZHH1ge24/Y2CDHHCorqhQiEijs3LzDq59aho92uXzwIWHk5utr8JE9NMRkUalrLKaa5+cRmVVDWMuLaR1fm7Ukeo9XfUkIo2Gu/Pzl2cxc+UW/u/SQvbv2CLqSBlBRxQi0mg8PXk5f59WxA+/dSAnDdgv6jgZQ4VCRBqFGUWb+eVrX3Jc345cf+JBUcfJKJEWCjMbYWbzzGyhmd0UZ72Z2b3h+hlmdlgUOUUks20tq+S6Zz6nY4sm/Om8Q8nO0hVOeyKyQmFm2cD9wKnAAOACMxuwy2anAn3CxyjgwbSGFJGM5+7c/OJMVm7ewX0XDqFt87yoI2WcKI8ohgIL3X2xu1cAzwFn7rLNmcATHpgEtDGzLukOKiKZ66nJy3lj5mp+cnJfDu/Z8Ma6TocoC0U3YEXMfFG4bE+3ERGJa96aEu58fTbHHNSRa47ZP+o4GSvKQhHvJKHvxTbBhmajzGyqmU0tLi7e53AiktnKKqu5/rnPadU0hz+eN5gstUvstSgLRRHQI2a+O7BqL7YBwN1Hu3uhuxd27NixToOKSOb5/fh5zF1Twj3fHUyHFk2ijpPRoiwUU4A+ZtbbzPKA84FXd9nmVeDS8Oqn4cAWd1+d7qAiklk+XLCeMR8u4ZLhPTm+X6eo42S8yO7MdvcqM7sOGA9kA4+6+5dmdm24/iFgHDASWAhsB66IKq+IZIYt2yv5n79P54COzbllZP+o4zQIkXbh4e7jCIpB7LKHYqYd+EG6c4lI5vrla1+yflsFYy49gmZ52VHHaRB0Z7aINBgTZ6/lpc9X8oPjDuDg7hrOtK6oUIhIg7CptIJbxs6kX+eWXPetPlHHaVB2WyjChuSLzey2cL7AzIamPpqISPJuf+1LNpVW8IfzBpOXo7+B61IyP80HgCOBC8L5EoKuN0RE6oW3Z6/llemruO5bBzKwq0451bVkGrOHufthZvY5gLtvCi9nFRGJXElZJT97eRb9Orfk+8cdGHWcBimZQlEZduDnAGbWEahJaSoRkSTd/dY81paU8dAlh+uUU4ok81O9FxgLdDKzXwMfAr9JaSoRkSRMXbqRJyct44qjenNojzZRx2mwdntE4e5Pm9k04ASCvpe+4+5zUp5MRCSB8qpqbnxxBt3aNON/TtZARKlUa6Ews9j+eNcBz8auc/eNqQwmIpLIQ+8tZlFxKY9fOZTmTSK9d7jBS/TTnUbQLlFbD67qs1dEIrF0fSn3v7eQ0wd35diD1AloqtVaKNy9dzqDiIgkw935+SuzaJKdxc+/rb6c0iGp4zUzOxv4BsGRxAfu/nIqQ4mI1Ob1Gav5YMF6fnnGQDq1ahp1nEYhmTuzHwCuBWYCs4BrzUw33IlI2m0tq+SO12dzcLfWXDy8Z9RxGo1kjiiOBQaFPbliZo8TFA0RkbT688QFrN9WziOXFZKtEevSJpn7KOYBBTHzPYAZqYkjIhLfvDUlPP7JUi4cWsAh3dtEHadRSXR57GsEbRKtgTlm9mk4Pwz4OD3xRESCBuzbXplFy6Y5/OTkvlHHaXQSnXr6fap2Gt6j8TzQC1gKnOfum+Jst5SgE8JqoMrdC1OVSUTqr9dmrGbyko38+qxBtG2urubSLdHlsf9K4X5vAv7p7neZ2U3h/I21bHu8u69PYRYRqcdKy6v49RuzGdStFecfUbD7F0idS+aqp+FmNsXMtplZhZlVm9nWfdzvmcDj4fTjwHf28f1EpIG6/92FrN1azh1nDlIDdkSSacz+K8FYFAuAZsB/hcv2xX7uvhogfO5Uy3YOTDCzaWY2ah/3KSIZZvmG7Yz5YAlnH9aNwwraRh2n0Urqhjt3X2hm2e5eDTxmZrttzDazt4HOcVbdugf5jnb3VWbWCZhoZnPd/f1a9jcKGAVQUKDDU5GG4NfjZpOTbdw4ol/UURq1ZArF9nCgoulmdjewGmi+uxe5+4m1rTOztWbWxd1Xm1kXgk4H473HqvB5nZmNBYYCcQuFu48GRgMUFhb67vKJSP320cL1jP9yLT89pS/76Q7sSCVz6ukSIBu4DigluI/inH3c76vAZeH0ZcAru25gZs3NrOXOaeBkgjvDRaSBq6qu4Y7XZtO9bTOu+oa6nYtaMuNRLAsndwC/rKP93gW8YGZXAcuBcwHMrCswxt1HAvsBY81sZ85n3P2tOtq/iNRjz366nHlrS3jo4sNompsddZxGL9ENdy+4+3lmNpNwGNRY7n7I3u7U3TcQDIS06/JVwMhwejEweG/3ISKZacuOSv44cT7DerfjlIHxmjkl3RIdUVwfPp+WjiAiIhBcDrt5RyU/P20A4RkFiViiG+5Wm1k28EiihmkRkbqybEMpj320hHMO686gbq2jjiOhhI3Z4eWw281M/2IiknJ3vTmXnKwsfnqK+nOqT5K5PLYMmGlmEwmuegLA3X+YslQi0uh8umQjb85aw49OPEiXw9YzyRSKN8KHiEhK1NQ4v35jNp1bNeXqY3Q5bH2TzOWxj+9uGxGRffHajFV8UbSF3587mPy8pDqMkDTa7b+ImfUBfgsMAP59POju+6cwl4g0EmWV1dz91jwGdGnFWUO6RR1H4kjmzuzHgAeBKuB44AngyVSGEpHG44lPlrJy8w5u/XZ/9Q5bTyVTKJq5+z8Bc/dl7n478K3UxhKRxmBTaQX3vbOQ4/t25OgDO0QdR2qR1FVPZpYFLDCz64CV1N4tuIhI0u57ZyGl5VXcPLJ/1FEkgVqPKMxsv3DyBiAf+CFwOHAxX3XoJyKyV5Zv2M6Tk5ZyXmEPDtqvZdRxJIFERxRfhP08PQvMd/ci4Ir0xBKRhu7u8cHNdT866aCoo8huJGqj6Ab8HvgmMN/MXjaz75lZs/REE5GGavqKzbw+YzVXf7O3bq7LALUWCnevdvfx7n4FwRgUjxGMbb3EzJ5OUz4RaWDcnd+Om0P75nmMOvaAqONIEpK56gl3rwBmA3OArQT3VIiI7LF35q5j8pKN3HBiH1o00c11mSBhoTCzAjP7qZl9BrxOMNLdme4+JC3pRKRBqaqu4a4359K7Q3POH6qx7TNFooGLPiZop/g7MMrdp6YtlYg0SC9+VsSCddt48KLDyM1O6oSG1AOJ/qVuBnq5+0/qukiY2blm9qWZ1ZhZYYLtRpjZPDNbaGY31WUGEUmvHRXV/HHifIYUtGHEII1cl0kSNWb/y92/NgRqHZkFnA28X9sG4aBJ9wOnErSJXGBmahsRyVCPfrSEtVvLufnU/hq5LsNE0pLk7nOA3f2yDAUWhmNnY2bPAWcSNKqLSAbZWFrBQ+8t4sT++zG0d7uo48ge2u1JQjP7Wufw8ZalQDdgRcx8UbhMRDLMfe8soLSiihtHaOS6TJRMa9KLcZb9Y3cvMrO3zWxWnMeZSWaLd7hR66kwMxtlZlPNbGpxcXGSuxCRVFu+YTtPTVrGeYU96KOuOjJSoque+gEDgdZmdnbMqlbEjEtRG3c/cR+zFRHc6LdTd2BVgv2NBkYDFBYWpqptRUT20D0T5pGdZeqqI4MlaqPoC5wGtAFOj1leAlydwkw7TQH6hKe5VgLnAxemYb8iUkdmFG3mtS9Wcd3xB6qrjgxWa6Fw91eAV8zsSHf/pC53amZnAfcBHYE3zGy6u59iZl2BMe4+0t2rwm7NxxPc6Peou39ZlzlEJHWCrjrm0q55HtccqwExM1kyVz0tNLNbgF6x27v7lXu7U3cfC4yNs3wVMDJmfhwwbm/3IyLReW9+MZ8s3sDtpw+gZdPcqOPIPkimULwCfAC8DVSnNo6INATVNc7v3pxLz/b5XDisZ9RxZB8lUyjy3f3GlCcRkQbjpc+KmLumhPsuGEJejrrqyHTJ/Au+bmYjd7+ZiAiUVVbzhwnzGdyjDacd0iXqOFIHkikU1xMUizIz22pmJWa2NdXBRCQzPfrREtZsLeOWU/upq44GYrenntxdd8iISFI2llbw4LtBVx3D9m8fdRypI8l04WFmdrGZ/Tyc72FmQ1MfTUQyzc6uOm46VV11NCTJnHp6ADiSr25220bQq6uIyL8tXV/KU5OW8b0jenBgJ52IaEiSueppmLsfZmafA7j7JjPLS3EuEckwd4+fS252lrrqaICSOaKoDMeGcAAz6wjUpDSViGSUacs2Mm7mGq455gA6tVRXHQ1NMoXiXoK7qDuZ2a+BD4HfpDSViGQMd+dXb8yhU8smXH1MOkYgkHRL5qqnp81sGnACQdff39k58JCIyLiZa/h8+WbuPucQ8vMiGQtNUixRN+Oxw1CtA56NXefuG1MZTETqv/Kqan731lz6dW7JOYd3jzqOpEii8j+NoF3CgAJgUzjdBlgO6BhTpJF74uNlLN+4nSeuHEp2lm6ua6hqbaNw997uvj9BN9+nu3sHd29PMEbFS+kKKCL104Zt5dz7zgKO79uRYw7qGHUcSaFkGrOPCLv7BsDd3wSOTV0kEckEf/nnArZXVHPLyP5RR5EUS6blab2Z/Qx4iuBU1MXAhpSmEpF6bcHaEp6evJwLhxZoHOxGIJkjigsIRqIbC7wMdAqXiUgj9Ztxc8jPzeaGE/tEHUXSIJnLYzcS9CBbZ8zsXOB2oD8w1N2n1rLdUoIxuquBKncvrMscIrLn3pu3jnfnFXPzqf1o36JJ1HEkDXZbKMzsIOAnfH0o1G/tw35nAWcDDyex7fHuvn4f9iUidaSyuoY7X59Nr/b5XH50r6jjSJok00bxd+AhYAx1NBTqzhv21Fe9SGZ58pNlLCouZcylhTTJyY46jqRJMoWiyt0fTHmS+ByYYGYOPOzuoyPKIdLobdhWzp/ens83+3TghP6doo4jaZRMoXjNzL5P0JhdvnPh7u7MNrO3gc5xVt3q7q8kme9od19lZp2AiWY2193fr2V/o4BRAAUFBUm+vYgk648T57O9oprbThugswGNTDKF4rLw+acxyxzYP9GL3P3EvQ0V8x6rwud1ZjYWGArELRTh0cZogMLCQt/XfYvIV2av2sqzny7n0iN76XLYRiiZq54i6arDzJoDWe5eEk6fDNwRRRaRxszdue2VWbTJz+NHJ2qsicYomaFQ883sZ2Y2OpzvY2an7ctOzewsMysiGDnvDTMbHy7vamY77wLfD/jQzL4APgXecPe39mW/IrLnXp6+kqnLNnHjiL60zs+NOo5EIJlTT48RdBB4VDhfRHAl1Ot7u1N3H0vQ5rHr8lXAyHB6MTB4b/chIvuupKyS34yby+AebTj38B5Rx5GIJHNn9gHufjdQCeDuOwh6kRWRBu4vby9g/bZy7jhjIFnqHbbRSqZQVJhZM74aCvUAYq5+EpGGaf7aEv728VLOP6IHg3u0iTqORCiZU0+/AN4CepjZ08DRwOWpDCUi0aqpcW4dO5MWTXP46Sn9oo4jEUvmqqeJZvYZMJzglNP16lJDpGH7x2dFTFm6id+dczDtmudFHUciluwAt8cC3yA4/ZRLnIZoEWkYNpVW8Ntxcyjs2VYN2AIkd3nsA8C1wEyCzvyuMbP7Ux1MRKJx15tzKSmr4ldnDVIDtgDJHVEcCwxy952N2Y8TFA0RaWCmLN3I81NXcM0x+9Ovc6uo40g9kcxVT/OA2M6TegAzUhNHRKJSVlnNjS/OoFubZlyvAYkkRjJHFO2BOWb2aTh/BPCJmb0K4O5npCqciKTP/e8uZHFxKY9fOZT8vGSbL6UxSOa34baUpxCRSM1ds5UH31vE2UO6cexBHaOOI/VMMpfH/svMegJ93P3t8Oa7HHcvSX08EUm16hrnxhdn0rpZLj8/bUDUcaQeSuaqp6uBf/DVsKXdgZdTmElE0uixj5bwxYrN3Hb6ANrqngmJI5nG7B8Q3I29FcDdFwAa3kqkAVhUvI17xs/jxP77ccbgrlHHkXoqmUJR7u4VO2fMLIew3ycRyVzVNc5P/v4FTXOz+c1ZgzRqndQqmULxLzO7BWhmZicRdDH+WmpjiUiqjflgMZ8v38wdZw6kU6umUceReiyZQnETUExwk901wDjgZ6kMJSKptWBtCX+YOJ9TBuqUk+xeMlc91ZjZy8DL7l6c+kgikkoVVTXc8Px0mudl86vvHKxTTrJbtR5RWOB2M1sPzAXmmVmxme3zfRVmdo+ZzTWzGWY21sza1LLdCDObZ2YLzeymfd2viMAfJ87ny1Vb+d05h9CxZZOo40gGSHTq6QaCq52OcPf27t4OGAYcbWY/2sf9TiToP+oQYD5w864bmFk2cD9wKjAAuMDMdJG3yD6YtHgDD7+/iAuG9uDkgZ2jjiMZIlGhuBS4wN2X7FwQjmN9cbhur7n7BHevCmcnEdybsauhwEJ3XxxedfUccOa+7FekMduyo5IfPz+dnu3y+dm39TeXJC9RociNN0BR2E6RW4cZrgTejLO8G7AiZr4oXCYie8jdueWlmawtKefP5w+heRP15STJS/TbUrGX6wAws7eBeMe2t7r7K+E2twJVwNPx3iLOslrv3zCzUcAogIKCgto2E2mUnpq8nDdmrubGEf04VONfyx5KVCgGm9nWOMsN2O1F1+5+YqL1ZnYZcBpwws6xLnZRRNCl+U7dgVUJ9jcaGA1QWFioGwJFQl+u2sKdr8/muL4dueaY/aOOIxmo1kLh7tmp2qmZjQBuBI519+21bDYF6GNmvYGVwPnAhanKJNIQbSuv4rpnPqdtfi5/OHewRqyTvZLMDXep8FegJTDRzKab2UMAZtbVzMYBhI3d1wHjgTnAC+7+ZUR5RTKOu3PjizNYtqGUe88fQvsWuhRW9k4kLVrufmAty1cBI2PmxxHcCS4ie2jMB0t4Y0bQLjFs//ZRx5EMFtURhYik0McL1/PbN+dw6qDOXHus2iVk36hQiDQwKzfv4LpnP+eAji2459zB6qJD9pkKhUgDsr2iilFPTKWyqoaHLjmcFrpfQuqAfotEGoiaGueG56YzZ/VWHrnsCA7o2CLqSNJA6IhCpIG4e/w8Jsxey8++PYDj+2kQSqk7KhQiDcALU1fw0L8WcdGwAq44ulfUcaSBUaEQyXDvzlvHzS/N5BsHduD2Mwaq8VrqnAqFSAabvmIz33/qM/p1bsmDFx9Gbrb+S0vd02+VSIZaXLyNK/82hQ4t83jsiiNo2bQuO3UW+YoKhUgGKtq0nUse+RQDnrhyGJ1a7rafTpG9pstjRTLMmi1lXDRmMlvLKnn26uH07tA86kjSwOmIQiSDFJeUc+GYSawvKeeJK4cyqFvrqCNJI6AjCpEMsa6kjIvHTGb15jIev3IoQwraRh1JGgkVCpEMsGrzDi4aM5m1W8t45PJChvZuF3UkaURUKETqueUbtnPB/01i645KnrxqKIf3VJGQ9FKhEKnH5qzeyuWPfUp5VQ3PXD2cg7urTULSL5JCYWb3AKcDFcAi4Ap33xxnu6VACVANVLl7YRpjikTq44XruebJaTRvksPzo46kb+eWUUeSRiqqq54mAoPc/RBgPnBzgm2Pd/dDVSSkMXll+koue+xTurRpykvfP0pFQiIV1VCoE2JmJwHfjSKHSH1TU+P8+e353PvOQob1bsfoSwtp3Ux3XEu06kMbxZXA87Wsc2CCmTnwsLuPTl8skfQqLa/iR89PZ8LstZx7eHd+ddYgmuRkRx1LJHWFwszeBjrHWXWru78SbnMrUAU8XcvbHO3uq8ysEzDRzOa6+/u17G8UMAqgoKBgn/OLpNPi4m18/+nPmL+2hNtOG8AVR/dSL7BSb6SsULj7iYnWm9llwGnACe7utbzHqvB5nZmNBYYCcQtFeLQxGqCwsDDu+4nUR699sYqbXpxBXk4Wj185lG/26Rh1JJH/ENVVTyOAG4Fj3X17Lds0B7LcvSScPhm4I40xRVKqrLKaO1+fzdOTl3N4z7bcd8EQurZpFnUska+Jqo3ir0ATgtNJAJPc/Voz6wqMcfeRwH7A2HB9DvCMu78VUV6ROjWjaDM/en46i4pLGXXM/vz0lL4aS0LqraiuejqwluWrgJHh9GJgcDpziaRaZXUND7y7iPveWUCHFk148iqdapL6rz5c9STSKHy+fBM3vzSTuWtKOPPQrtxxxiBa5+vSV6n/VChEUqykrJI/TJjP458spVPLJjx8yeGcMjDeBYEi9ZMKhUiK1NQ4/5hWxN3j57KhtIJLhvfkp6f01ZClknFUKERS4JNFG/jNuDnMXLmFwwra8MhlRzC4R5uoY4nsFRUKkTo0s2gLd4+fywcL1tOldVP+cv6hnDG4q26ek4ymQiFSB75YsZm/vruQibPX0iY/l1tH9ueSI3vSNFddcEjmU6EQ2UvuzieLNvDgvxbxwYL1tGqaw/Un9OGqb/amldohpAFRoRDZQ2WV1bw6fRWPfrSEuWtK6NAijxtH9OPi4QVqqJYGSYVCJEnz15bw7KfLeemzlWzZUUm/zi25+5xDOOPQrjrFJA2aCoVIAhu2lfPGzNWM/Xwlny/fTG62ccrAzlw4rIAj92+vRmppFFQoRHaxqbSCibPX8uas1XywYD1VNU6/zi25dWR/zj6sG+1bNIk6okhaqVCIAEvWl/LO3HW8M3ctkxZvpLrG6d62GVd9ozffGdKN/l1aRR1RJDIqFNIobdleySeLN/DhwmI+XLCepRuC3u77dGrBqGP2Z+SgLgzq1kqnlkRQoZBGwN1ZtaWMz5dvYsqSjXy6dBNz12zFHfLzshm+f3suP6oXJ/Tfjx7t8qOOK1LvqFBIg7OupIwvV25l1sotzFy5hekrNrOupByAZrnZHN6zLTeccBBHHdiewd3bkJejcSBEElGhkIzk7mwsrWBRcSkL121jwboS5q0JHhtKK/69Xa/2+Rx1QHuGFLTl0B5tGNC1lQYIEtlDKhRSb5VXVbNmSxkrN+1gxabtrNi4g+Ubt7NsQylL1peytazq39s2y83moP1acEL/TvTt3IqBXYOHboAT2XdRjZl9J3AmUAOsAy4PR7fbdbsRwF+AbIIhUu9Ka1BJie0VVWzYVsH6beWsD5+LS8pZu7WMtVuD59Vbyli/rfw/XpedZXRp3ZTeHZpzxqFd6dW+OQd2asEBHVvQrU0zsrLU8CySClEdUdzj7j8HMLMfArcB18ZuYGbZwP3ASUARMMXMXnX32ekOK1+pqXF2VFZTWl5FaUXwvK28im1lwXNJWSVby6rYuqOSLTGPTdsr2by9gk3bKyirrIn73m3zc9mvVVP2a9WUAV1a0bVNM7q0aUq3Ns0oaJdP59ZNddpIJAJRjZm9NWa2OeBxNhsKLAzHzsbMniM4CmlQhaKmxqlxp9odd6iuCaZrapzqGqcmZll1dfhcU0NVuL6q2qmqcaqqg2WV1TXhshoqdz5XORXVNVRW11BR9dVz+c7nqhrKK2sor6qm7N/PwfSOymp2VATzpRVVtX7J7yovJ4vWzXJp0yyX1s1y6damKYO6tqJt8zza5ufRvkUeHVrk0a55Ezq1bEL7Fnk0yVE3GCL1UWRtFGb2a+BSYAtwfJxNugErYuaLgGGpzHTafR+wo6I6qFoeVC93D5/BCb7Mg8dXy2titwmna8Iv+9htgkewzc4CEKW8nCyaZGeRl5NF09xsmuR8Nd00N4v2LfLIz8umaW42zXKzyc/LJj8vJ3hukkOLJtk0z8uhRdMcWjbJpXmTbFo1y6Vl0xx96Ys0ICkrFGb2NhBvYOBb3f0Vd78VuNXMbgauA36x61vEeW2t36xmNgoYBVBQULBXmft0aklFVQ1YsHMzC5//cx6DrJh1WWZYuCIrZn7ns2FkZwXzGGSbkWXhtlnBdHbWV8uy/2MZZGdlkZNlZGXZv5+zzcjJDuazs4zc7GCbnOwscrONnKzwOSwEudlGblYwnZcTbKubyUQkGSkrFO5+YpKbPgO8wdcLRRHQI2a+O/C1Bu+Y/Y0GRgMUFhbu1Z/qf/reoXvzMhGRBi2SlkEz6xMzewYwN85mU4A+ZtbbzPKA84FX05FPRES+ElUbxV1m1pfg8thlhFc8mVlXgstgR7p7lZldB4wnuDz2UXf/MqK8IiKNVlRXPZ1Ty/JVwMiY+XHAuHTlEhGRr9NF6SIikpAKhYiIJKRCISIiCalQiIhIQioUIiKSkLlH241EKphZMcFlt5mmA7A+6hBp1hg/MzTOz63PXL/1dPeO8VY0yEKRqcxsqrsXRp0jnRrjZ4bG+bn1mTOXTj2JiEhCKhQiIpKQCkX9MjrqABFojJ8ZGufn1mfOUGqjEBGRhHREISIiCalQ1ENm9hMzczPrEHWWdDCze8xsrpnNMLOxZtYm6kypYmYjzGyemS00s5uizpMOZtbDzN41szlm9qWZXR91pnQxs2wz+9zMXo86y75QoahnzKwHcBKwPOosaTQRGOTuhwDzgZsjzpMSZpYN3A+cCgwALjCzAdGmSosq4H/cvT8wHPhBI/ncANcDc6IOsa9UKOqfPwH/S4JhXxsad5/g7lXh7CSC0QwboqHAQndf7O4VwHPAmRFnSjl3X+3un4XTJQRfnN2iTZV6ZtYd+DYwJuos+0qFoh4xszOAle7+RdRZInQl8GbUIVKkG7AiZr6IRvCFGcvMegFDgMkRR0mHPxP80VcTcY59FtUId42Wmb0NdI6z6lbgFuDk9CZKj0Sf291fCbe5leA0xdPpzJZGFmdZozlyNLMWwIvADe6+Neo8qWRmpwHr3H2amR0XcZx9pkKRZu5+YrzlZnYw0Bv4wswgOP3ymZkNdfc1aYyYErV97p3M7DLgNOAEb7jXbBcBPWLmuwOrIsqSVmaWS1Aknnb3l6LOkwZHA2eY2UigKdDKzJ5y94sjzrVXdB9FPWVmS4FCd8+UDsX2mpmNAP4IHOvuxVHnSRUzyyForD8BWAlMAS5s6GPBW/CXz+PARne/IeI4aRceUfzE3U+LOMpeUxuF1Ad/BVoCE81supk9FHWgVAgb7K8DxhM06L7Q0ItE6GjgEuBb4b/v9PAvbckQOqIQEZGEdEQhIiIJqVCIiEhCKhQiIpKQCoWIiCSkQiEiIgmpUEi9ZWbb9nD746LspXNP8+7y2svNrGsty5/dZVkHMys2syZJvnehmd2bxP7/Wsu6vf5c0jCoUIjUD5cDXysUwEvASWaWH7Psu8Cr7l6+uzc1sxx3n+ruP6ybmNIYqVBIvRceKbxnZv8Ix614Orzbd+f4DnPN7EPg7JjXNDezR81sSjgewJnh8svN7BUzeyscF+IXMa+52Mw+DW8IezjsFhwz22ZmvzazL8xskpntFy7vbWafhPu4c5fMPw2XzzCzX4bLeoVjMvxfOC7DBDNrZmbfBQqBp8N9N9v5PmGfSO8Dp8e8/fnAs2Z2uplNDj/f2zG5bjez0WY2AXgi9kjLzIaa2cfhaz42s74x79sj3s9ld59LGgF310OPevkAtoXPxwFbCPpGygI+Ab5B0IfOCqAPQYd7LwCvh6/5DXBxON2GoOuM5gR/ua8G2gPNgFkEX9L9gdeA3PA1DwCXhtMOnB5O3w38LJx+NWabH8TkPZlgrGQL874OHAP0Iuj08NBwuxdiMr5H0GVLvJ/DucDYcLorQf9Q2UBbvrpp9r+AP4TTtwPTgGYxP7+dP5dWQE44fSLwYjgd9+eyy79D3M8V9e+JHql/qFNAyRSfunsRgJlNJ/jS3QYscfcF4fKngFHh9icTdMr2k3C+KVAQTk909w3ha14iKDpVwOHAlPBgpRmwLty+guBLEYIv4JPC6aOBc8LpJ4Hfxez7ZODzcL4FQTFbHuadHvNevZL47K8DD5hZK+A84B/uXh2Od/C8mXUB8oAlMa951d13xHmv1sDjZtaHoADmxqyL93OZGrO+ts/1fhKfQTKYCoVkitjz8dV89btbWx80Bpzj7vP+Y6HZsDiv8XD7x9093uh6le6+8zWx+65t/wb81t0f3mXfveJ8jmbshrvvMLO3gLMITjv9KFx1H/BHd3817Hju9piXldbydncC77r7WWGe9xJ8ll3n434uafjURiGZbC7Q28wOCOcviFk3Hvh/MW0ZQ2LWnWRm7cK2gO8AHwH/BL5rZp3C7duZWc/d7P8jgi9ugIt22feVFoy/gJl12/m+CZQQdIxYm2eBHwP7EYwCCMHRwcpw+rLdvP9Osa+5fJd18X4usfbmc0kDoEIhGcvdywhONb0RNmYvi1l9J8FplRlmNiuc3+lDglNF0wnO0U9199nAz4AJZjaDYBzvLruJcD3B+M9TCL6Ad+aaADwDfGJmM4F/kLgIAPwNeGjXxuwYEwjaJ56PObq5Hfi7mX0AJNsd/d3Ab83sI4J2jlhf+7nErtzLzyUNgHqPlUbFzC4naKS9LuosIplCRxQiIpKQjihERCQhHVGIiEhCKhQiIpKQCoWIiCSkQiEiIgmpUIiISEIqFCIiktD/ByDQnCv9loi5AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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",
"\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": [
"2020-11-21 23:50:11 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",
"\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 decelerate slightly in the 2010s.\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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": [
"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",
"\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 0x7fe3894bf048>]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEDCAYAAAAlRP8qAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAp8UlEQVR4nO3deXxU1f3/8dcnG4Qdwg5ZWEWQPSyCFVqrIm7tV23FuIGKe+3397VqtYtd7KPa5etepEgVQangRhWlWltRQSRBtoQtrAk7hCUQICRzfn/M8DWGmWRCJpkl7+fjkUdm7tzcfA4k75w599xzzTmHiIhEv7hwFyAiIqGhQBcRiREKdBGRGKFAFxGJEQp0EZEYoUAXEYkRYQ10M5tuZnvMbHUQ+55vZsvMrMzMrq6wPd3McsxsuZnlmtkddVu1iEhksnDOQzez84EjwAzn3DnV7JsBtADuB+Y55+b6tifhbccJM2sGrAZGOed21GnxIiIRJqw9dOfcQqCo4jYz62FmH/h63Z+aWR/fvluccysBT6VjlDrnTvieNkLDSCLSQEVi+E0F7nXODcXbG3++ui8ws1QzWwkUAI+rdy4iDVFCuAuoyDdkMgqYY2anNjeq7uuccwXAADPrDLxtZnOdc7vrrlIRkcgTUYGO9x3DQefcoDP5YufcDjPLBb4FzA1lYSIikS6ihlycc4eBzWZ2DYB5Dazqa8ysq5kl+x63BkYD6+q8WBGRCBPuaYuvAYuBs8ys0MxuAbKAW8xsBZALXOnbd5iZFQLXAC/4euIAZwNLfPt/AvzRObeqvtsiIhJuYZ22KCIioRNRQy4iInLmwnZStG3bti4jIyNc315EJCrl5OTsc8618/da2AI9IyOD7OzscH17EZGoZGZbA72mIRcRkRihQBcRiRHVBnqwKyL6phWWV1wJUURE6k8wPfSXgHFV7WBm8cDjwIIQ1CQiImeg2kD3tyKiH/cCbwB7QlGUiIjUXK3H0M2sC/B9YEoQ+042s2wzy967d29tv7WIiFQQipOiTwIPOufKq9vROTfVOZfpnMts187vNEoRETlDoZiHngnM9i132xYYb2Zlzrm3Q3BsEZGYsXHvET7K203/Li0Z1bNtyI9f60B3znU79djMXgLeVZiLiEC5x7Fs2wE+ytvNh3m72bTvKAB3ju0RnkD3rYg4FmjrW+3wl0AigHOu2nFzEZGGpLTMw+cb9/H+qp18mLebAyUnSYw3RnZP4ebRGVxwdge6tEquk+9dbaA75yYEezDn3M21qkZEJAqVlnn4LH8v763cxYd5uzh8vIzmjRL4ztntuahvR87v3ZbmjRPrvI5Iu2ORiEhU8HgcSzYX8c7y7cxftdMb4o0TuLBvBy7t34nzerWlUUJ8vdakQBcRqYF1u4p566vtzFu+nR2HjtM0KZ6L+3XksoGdGN2z/kO8IgW6iEg1DpaU8vZX23k9u5C8nYeJjzPG9G7Hg5f04cK+HWiSFBlRGhlViIhEGI/H8cWm/cxeWsAHubsoLfNwTpcWPHp5Xy4b2Jm2zRqFu8TTKNBFRCrYf+QEf88u4LUvt1FQdIwWjROYMCyVHwxLpV/nluEur0oKdBFp8JxzLC84yCuLt/Luyp2UlnsY2b0N9190Fhf360jjxPCNi9eEAl1EGqwTZeXMW76DGYu3smr7IZomxXPt8FRuGJlOrw7Nw11ejSnQRaTBOXC0lFlLtvLSoq3sO3KCXu2b8Zsr+/H9IV1p1ih6YzF6KxcRqaEt+47y4mebmZNTwPGTHsb0bsdt3+rO6J4p+NajimoKdBGJeau3H+LZj/NZkLeLxLg4rhzUmVu/1Z2zOkbfsEpVFOgiErNyth7g2Y838O91e2neOIG7xvbgplEZtG/eONyl1QkFuojEFOccizft59mP81m0cT+tmyTyk4vP4oZz02lRD+uphJMCXURixtItRfxhwTq+3FxEu+aN+NmlZ3PdiLSIuZKzrjWMVopITFtZeJA//XM9n6zfS7vmjXj08r5cOzwtauaPh4oCXUSi1vrdxfzpn+tYkLubVk0S+eklfbjx3AySkxpWkJ+iQBeRqLP78HH+/M/1zMkpoElSAj/+bi9uOa9bvaw5HskU6CISNY6eKGPqwk1MXbiJMo+HiaO7cfe3e9KmaVK4S4sICnQRiXjlHsec7AL+9OF69haf4NIBnXjg4rNIT2ka7tIiigJdRCLakk37+eW8XNbuKmZoemumXD+Uoemtw11WRArmJtHTgcuAPc65c/y8ngU86Ht6BLjTObcipFWKSIOz69Bxfjd/DfNW7KBLq2Seu24I4/t3jIlL9OtKMD30l4BngRkBXt8MjHHOHTCzS4CpwIjQlCciDc2JsnJe/Gwzz36cT5nH8aMLenHnmB4NduZKTVQb6M65hWaWUcXriyo8/QLoGoK6RKQB+nTDXn7xTi6b9x3lor4d+PllfUlt0yTcZUWNUI+h3wK8H+JjikiM23fkBL99N4+3l++gW9umvDxpOGN6twt3WVEnZIFuZt/GG+jnVbHPZGAyQFpaWqi+tYhEKeccr2cX8Lv5aykpLeNHF/TirrE9GtwVnqESkkA3swHANOAS59z+QPs556biHWMnMzPTheJ7i0h0yt9zhIffWsWXm4sYntGG3/3XOfRsH1vL2da3Wge6maUBbwI3OOfW174kEYllZeUepn66iSc/3EByUjyPX9Wfa4amEhen2Su1Fcy0xdeAsUBbMysEfgkkAjjnpgC/AFKA533Ticqcc5l1VbCIRK/1u4u5f84KVhYe4tL+nXj0in60a94o3GXFjGBmuUyo5vVbgVtDVpGIxJyycg8vLNzEUx9toHnjBJ67bgiXDugU7rJijq4UFZE6tW6Xt1e+avshLh3QiV9f0Y+UZuqV1wUFuojUCY/HMf3zzTyxYB3NGyXwfNYQxvdXr7wuKdBFJOR2HjrG/XNW8Hn+fr57dgd+f1V/2qpXXucU6CISUu+u3MHDb66izOP4/X/154fDUrX+Sj1RoItISBQfP8kv3snlra+2Myi1FU/+cBAZbbW8bX1SoItIra0sPMg9r37F9oPH+PF3e3HPt3uSEB8X7rIaHAW6iJwx5xwvfraZxz9YS7tmjfj75JFkZrQJd1kNlgJdRM5I0dFSfjJnBf9au4cL+3bgD1cPoFUT3QounBToIlJjSzbt577Zyyk6Wsqjl/flplEZOvEZARToIhI05xwvLNzEHxasI61NE968aRTndGkZ7rLER4EuIkE5fPwk97++gn/m7ebS/p14/OoBNGukCIkk+t8QkWqt2XmYO2fmUHjgGD+/rC+TRmuIJRIp0EWkSnNzCvnZ26tomZzIbM1iiWgKdBHxq7TMw6/fzWXmF9s4t3sKz1w3WJfvRzgFuoicZm/xCe6alcPSLQe4fUx3fnLRWbpQKArof0hEvmFFwUEuf+YzVm0/xDMTBvPTS85WmIfKrFmQkQFxcd7Ps2aF9PDqoYvI/3kjp5CfvrWK9s0b8eado+nbuUW4S4ods2bB5MlQUuJ9vnWr9zlAVlZIvoX+7IoIZeUefvWPXP5nzgoy01sz757zFOah9sgjX4f5KSUl3u0hoh66SAN36NhJ7nl1GZ9u2Mek0d14eHwfDbHUhW3barb9DCjQRRqwLfuOMunlpRQUlfDEVQP4wbDUcJcUu9LSvMMs/raHSLV/hs1supntMbPVAV43M3vazPLNbKWZDQlZdSJSZxZt3MeVz33OgaOlzLxlhMK8rj32GDRp8s1tTZp4t4dIMO+rXgLGVfH6JUAv38dk4C+1L0tE6tKrS7Zx44tf0r55I965+zxGdE8Jd0mxLysLpk6F9HQw836eOjVkJ0QhiCEX59xCM8uoYpcrgRnOOQd8YWatzKyTc25nqIoUkdAo9zgee28N0z/fzJje7XjmusG0aJwY7rIajqyskAZ4ZaEYQ+8CFFR4Xujbdlqgm9lkvL140kI4biQi1SspLeO+2cv5MG83N4/K4GeXan55rAlFoPtbocf529E5NxWYCpCZmel3HxEJvT3Fx7n15WxWbz/Eo5f35ebR3cJdktSBUAR6IVDxbEpXYEcIjisiIbB+dzET/7aUoqOlvHBDJhf27RDukqSOhOL91jzgRt9sl5HAIY2fi0SGz/P3cdVfFlFa7uH1289VmMe4anvoZvYaMBZoa2aFwC+BRADn3BRgPjAeyAdKgIl1VayIBO+NnEIefGMl3ds1ZfrNw+jaukn1XyRRLZhZLhOqed0Bd4esIhGpFeccz/9nI39YsI7RPVP4y/VDNZOlvs2a5b2kf9s274VDjz1Wp7NbTtGVoiIxpNzjeHReLq98sZXvDerME1cPJClBM1nqVT0swhWI/qdFYsTxk+XcOTOHV77Yyu1juvPnHwxSmIdDPSzCFYh66CIx4MDRUm6dkc2ybQf45eV9mahpieFTD4twBaJAF4ly2w8e48YXl1Bw4BjPXTeE8f07hbukhq0eFuEKRO/HRKLYht3FXPX8IvYUn+CVScMV5pGgHhbhCkSBLhKlcrYe4Oopi/E4x+u3n6sFtiJFPSzCFYiGXESi0L/X7eHOmTl0bNGYV24ZQWobzTGPKHW8CFcgCnSRKPPWV4X8ZM5K+nRqzksTh9O2WaNwlyQRQoEuEkVe/Gwzv3k3j1E9UnjhhqE01wVDUoECXSQKOOf484freebjfC45pyNPXjuIRgnx4S5LIowCXSTCeTyOR/+Ry4zFW7l2WCqPfb8/8XH+Vq2Whk6BLhLBTpZ7uH/OCt5ZvoPbz+/OQ5f0wUxhLv4p0EUi1PGT5dw1axkfr93DA+PO4q6xPcNdkkQ4BbpIBCo+fpJbXs5m6ZYiHvv+OWSNSA93SRIFdGGRSIQpOlrKdX9dwrKtB3jq2sEK80g3axZkZEBcnPfzrFlhK0U9dJEIsvvwca6ftoRtRSX89cZMvt2nfbhLkqqEcalcf9RDF4kQBUUlXDNlMTsOHuPlScMV5tEgjEvl+qMeukgEyN9TTNa0JRw/6WHWbSMZlNoq3CVJMMK4VK4/6qGLhNnq7Yf4wQtfUO6Bv9+uMI8qgZbErYelcv1RoIuEUc7WIib89QuSE+OZc8e59OnYItwlSU2Ecalcf4IKdDMbZ2brzCzfzB7y83pLM/uHma0ws1wzmxj6UkViy+f5+7h+2pe0bdaI1+84l25tm4a7JKmpMC6V648556rewSweWA9cCBQCS4EJzrm8Cvs8DLR0zj1oZu2AdUBH51xpoONmZma67OzsEDRBJPp8vHY3d8xcRreUprxy63DaN28c7pIkSphZjnMu099rwfTQhwP5zrlNvoCeDVxZaR8HNDfvNcnNgCKgrBY1i8Ss91buZPKMHM7q0JzZk0cqzCVkggn0LkBBheeFvm0VPQucDewAVgH3Oec8lQ9kZpPNLNvMsvfu3XuGJYtEr7k5hdz72jIGpbZi1m0jaN00KdwlSQwJJtD9rQRUeZzmYmA50BkYBDxrZqed3XHOTXXOZTrnMtu1a1fDUkWi2ytfbOX+OSsY1aMtM24ZTgutZS4hFkygFwKpFZ53xdsTr2gi8Kbzygc2A31CU6JI9Pvrwk38/O3VXNCnPdNuyqRJki4BkdALJtCXAr3MrJuZJQHXAvMq7bMNuADAzDoAZwGbQlmoSDRyzvHURxt4bP4aLh3QiSk3DKVxom5MIXWj2m6Cc67MzO4BFgDxwHTnXK6Z3eF7fQrwG+AlM1uFd4jmQefcvjqsWyTiOef4/QdreeGTTVw1pCtPXD1AN6aQOhXUPHTn3HznXG/nXA/n3GO+bVN8YY5zbodz7iLnXH/n3DnOuZl1WbRIpPN4HI/Oy+WFTzZx/cg0/qAwj34RtKpiIBrIEwmxco/j4TdX8ffsAm77VjceHn+27jIU7SJsVcVAdOm/SAidLPfw339fzt+zC/jRd3oqzGNFhK2qGIh66CIhcqKsnHtf/Yp/5u3mwXF9uHNsj3CXJKESYasqBqIeukgIHCstZ/KMHP6Zt5tHL++rMI81EbaqYiAKdJFaOnKijIkvfcnCDXt5/Kr+3Dy6W7hLklCLsFUVA1Ggi9TCoWMnufHFJSzdcoAnfziIHw6LrB6bhEiEraoYiMbQRc5Q0dFSbpy+hHW7innuusGMO6dTuEuSupSVFXEBXpkCXeQM7Dl8nCzfzZyn3qCbOUtkUKCL1FDhgRKypi1hb/EJ/jZxGKN6tA13SSKAAl2kRjbvO0rWX7+g+EQZM28dwZC01uEuSeT/KNBFgrRuVzFZ05bgcY7XbhvJOV1ahrskkW9QoIsEYVXhIW6cvoTE+Dheu20kvTo0D3dJIqdRoItU48vNRUx6aSktkxN59bYRpKfoZs4SmRToIlX4z7o93DEzh86tkpl5ywg6t0oOd0kiASnQRQJ4f9VOfjT7K3q1b86MW4bTtlmjcJckUiUFuogfc3MKeWDuCgaltuJvE4fTMln3/5TIp0AXqeTlRVv45bxcRvdMYeoNmTRtpF8TiQ76SRXxcc7x7Mf5/OnD9VzYtwPPTBis+39KVFGgi+AN88feW8O0zzbz/cFdeOLqASTGa+06iS76iZUGr6zcwwNzVzLts83cPCqDP10zUGHekEXBvUMDCeqn1szGmdk6M8s3s4cC7DPWzJabWa6ZfRLaMkXqxomycu559Svm5BRy3wW9+OXlfYnTzZwbrlP3Dt26FZz7+t6hURLq5pyregezeGA9cCFQCCwFJjjn8irs0wpYBIxzzm0zs/bOuT1VHTczM9NlZ2fXsnyRM3f0RBm3v5LDZ/n7+MVlfZl0nm5M0eBlZHhDvLL0dNiypb6r8cvMcpxzmf5eC2YMfTiQ75zb5DvYbOBKIK/CPtcBbzrntgFUF+Yi4XbgaCkTX1rKqu2H+OM1A7l6aNdwlySRIEruHRpIMEMuXYCCCs8Lfdsq6g20NrP/mFmOmd3o70BmNtnMss0se+/evWdWsUgtbT94jKunLCJv52H+kjVEYS5fi5J7hwYSTKD7G1CsPE6TAAwFLgUuBn5uZr1P+yLnpjrnMp1zme3atatxsSK1tWF3MVf/ZRF7ik/wyqThXNSvY7hLkkgSJfcODSSYQC8EUis87wrs8LPPB865o865fcBCYGBoShQJjZytB7jmhcWUeRyv334uI7qnhLskiTRRcu/QQIIJ9KVALzPrZmZJwLXAvEr7vAN8y8wSzKwJMAJYE9pSRc7cv9ftIWvaF7RKTuTNO0dxdqcW4S5JIlVWlvcEqMfj/RwlYQ5BnBR1zpWZ2T3AAiAemO6cyzWzO3yvT3HOrTGzD4CVgAeY5pxbXZeFiwTrzWWFPDB3JWd1bM5LE4fTrrkW2ZLYVO20xbqiaYtS15xz/OWTjTzxwTpG9UjhhRuG0ryxFtmS6FbbaYsiUafc4/jVP3KZsXgrVwzszB+vGUhSgq7+lNimQJeYc/xkOffN/ooFubu5/fzuPDiuj67+lAZBgS4x5WBJKbe+nE3OtgO6+lMaHAW6xIyCohJu/tuXFBQd45kJg7lsQOdwlyRSrxToEhOWFxzk1peXUlrmYcYtwxmpOebSAOkskUS9D1bv4tqpi0lOiufNu0YpzCV4UbxUrj/qoUvUcs4x/fMt/Pa9PAZ2bcW0mzJ1I2cJ3qmlcktKvM9PLZULUXUxUUXqoUtUKvc4Hp2Xy2/ezWNcv47MnjxSYS4188gjX4f5KSUl3u1RSj10iTrFx09y3+zlfLx2D5PP785DmpYoZyLKl8r1R4EuUaWgqIRbX84mf+8Rfvu9c7h+ZHq4S5JolZbm/2YWUbJUrj8acpGosXRLEd977nN2HjrGjEnDFeZSO1G+VK4/CnSJCnNzCsn66xJaJCfy9t2jGd2zbbhLkmgX5Uvl+qNAl4jm8Th+//5a7p+zgmHdWvP2XaPp3q5ZuMuSaBNoemIUL5Xrj8bQJWIdPn6SH/tOfmaNSOPRK/qRGK8+iNRQDE5PDES/HRKR8vcc4XvPfs7C9Xv59ZX9+O33zlGYy5mJwemJgaiHLhHno7zd/Pjvy2mUEMesW0foVnFSOzE4PTEQBbpEDI/H8ey/8/nzh+vp36UlL9wwlM6tksNdlkS7GJyeGIjew0pEKD5+kjtn5fDnD9fzX4O7MOeOcxXmEhoxOD0xEPXQJezW7jrMnTOXsa2ohJ9f1pdJozMw05WfEiKnTnw+8oh3mCUtzRvmMXZCFBToEmZvLivk4bdW0aJxIq/dNpLh3dqEuySJRVlZMRnglQU15GJm48xsnZnlm9lDVew3zMzKzezq0JUosehEWTmPvLWK//f6CgZ2bcW7PzpPYS5SS9X20M0sHngOuBAoBJaa2TznXJ6f/R4HFtRFoRI7Cg+UcPesZawoPMQdY3pw/0W9SdCURJFaC2bIZTiQ75zbBGBms4ErgbxK+90LvAEMC2mFElM+WL2LB+auwDl44YahXNyvY7hLEokZwQR6F6CgwvNCYETFHcysC/B94DtUEehmNhmYDJAWg1OGJLDjJ8v53fw1zFi8lQFdW/LMhMGkpzQNd1kiMSWYQPc33cBVev4k8KBzrryq2QnOuanAVIDMzMzKx5AYtXHvEe559SvW7DzMred144FxfUhK0BCLSKgFE+iFQGqF512BHZX2yQRm+8K8LTDezMqcc2+HokiJXm/kFPLzd1bTKCGO6Tdn8p0+HcJdkkjMCibQlwK9zKwbsB24Friu4g7OuW6nHpvZS8C7CvOG7VDJSX72zmr+sWIHI7q14alrB9OxZeNwlyUS06p93+ucKwPuwTt7ZQ3wunMu18zuMLM76rpAiT6L8vcx7qmFvL9qJ/9zYW9evW2kwlzqR6BlchuIoC4scs7NB+ZX2jYlwL43174siUYnysr544J1/PXTzXRv25Q37xrFgK6twl2WNBQNaJncQMy58JybzMzMdNnZ2WH53hJ6a3cd5sezl7N2VzHXj0zj4fFn0yRJFyJLPcrI8L8IV3q69+YVMcLMcpxzmf5e02+c1EpZuYcXFm7iqY820CI5QSc+JXwa0DK5gSjQ5Yyt3XWYn8xZyarth7h0QCd+fUU/Upo1CndZ0lA1oGVyA1GgS42dLPcw5T8befrjDbRonMjzWUMY379TuMuShu6xx745hg4xu0xuIAp0qZHcHYd4YO5Kcncc5vKBnfnVFf1o0zQp3GWJNKhlcgNRoEtQSkrLePKjDbz42WZaN0lkyvVDGHeOeuUSYRrIMrmBKNClWv9eu4efvb2a7QePMWF4Kg+O60OrJuqVi0QaBboEtOfwcX71bh7vrdxJz/bNeP32c7VmuUgEU6DLacrKPcxYvJX//Wg9J8o8/M+Fvbl9TA8tqCUS4fQbKt+weON+Ln36M379bh6DUlvxwX3f4t4LeinMJfI08Mv8/VEPXQDYcfAYj81fw3srd9K1dTIv3DCUi/p20M2aJTLpMn+/dOl/A3estJxpn27i+f9sxOMcd43tye1jutM4MT7cpYkE1kAu8/dHl/7Laco9jre+2s4fF6xj1+HjjOvXkUcuPZvUNk3CXZpI9XSZv18K9Abosw37+N38NeTtPMzAri15esJgzV6R6KLL/P1SoDcga3Ye5vEP1vKfdXvp0iqZpycM5rL+nYiL0zi5RBld5u+XAr0B2LT3CP/70Qb+sWIHzRsn8PD4Ptx4bobGySV66TJ/vxToMazwQAlP/2sDbyzbTlJ8HHeN7cHk87vrKk+JLrNm+Q/uBn6Zvz8K9Bi04+Axpnyykde+3IaZcdO5Gdw5tgftmmtpW4kymp5YI5q2GEO27S/hL5/kMzenEOfgmsxU7v1OTzq3Sg53aSJnpgFPTwxE0xZjXP6eYp7/90beWbGD+Djj2mFp3D6mO11bawqiRDlNT6yRoALdzMYBTwHxwDTn3O8rvZ4FPOh7egS40zm3IpSFyulyth5g2qeb+CB3F40T4pk0OoPbvtWd9i0ah7s0kdDQ9MQaqTbQzSweeA64ECgElprZPOdcXoXdNgNjnHMHzOwSYCowoi4KbujKPY4P83YxdeEmlm07SMvkRO4e25NJ53XTjSYkuvk7+anpiTUSTA99OJDvnNsEYGazgSuB/wt059yiCvt/AXQNZZECR0+UMTenkOmfb2br/hJS2yTzqyv6cfXQrjRtpJEziXKBTn5Oner90PTEoASTBF2AggrPC6m6930L8L6/F8xsMjAZIE1vmYKSv+cIryzewhvLtnPkRBmD01rx0Lg+XNSvI/G6IEhixSOPfLMXDt7njzziPfmpAA9KMIHuLzX8To0xs2/jDfTz/L3unJuKdziGzMzM8EyviQJl5R4+WrOHV77Ywuf5+0mKj+PSAZ244dx0hqS1Dnd5IqGnk58hEUygFwKpFZ53BXZU3snMBgDTgEucc/tDU17DUlBUwuvZBczNKWTnoeN0btmYn1x8Fj8clkrbZppDLjGk8nh5mzaw309s6J18jQQT6EuBXmbWDdgOXAtcV3EHM0sD3gRucM6tD3mVMez4yXIW5O7i9ewCPs/fjxmc36sdj17Rjwv6tCchXjeWkBjjb7w8MRGSkqC09Ov9dPKzxqoNdOdcmZndAyzAO21xunMu18zu8L0+BfgFkAI877shQlmgie8CzjmWbTvIO8u3887yHRw6dpIurZL5fxf25uqhXXUhkMQ2f+PlJ09CSgo0a6aTn7UQ1PQI59x8YH6lbVMqPL4VuDW0pcWeTXuP8PbyHbyzfDtb95fQKCGOi/p15IeZqYzqkaJVDyX2+JuKGGhcvKgI9u2r3/pijOa71bHCAyW8v2oX767cwYrCQ5jB6B5tufc7vbi4XweaN04Md4kioVE5vMePh5dfPn0qosbL64wCvQ4UFJUwf9VO5q/ayYrCQwCc06UFj4w/m8sHdqZjS13JKTHG37j4lClQea2okhJITvaOj+tioZBToIeAc468nYf5KG8PH67ZxerthwHo36UlD47rw/j+HUlPaRrmKkVCxN8wir9x8UAL/xUVwSuv6GKhOqDVFs/QibJylmwq4qM1u/kobzc7Dh3HDAantuLifh0Z37+T7s8psadyTxxO721XpwGvlBgKWm0xRLbuP8on6/fyybq9LNq4n2Mny2mcGMe3erXjx9/tzbf7tNea4xI7gu2Jl5RAfDyUl59+DLNv9tQ1tFKnFOhVOFhSyhebili0cR8L1+9ly37vD3JamyZck9mVMb3bMbpnW93KTaJfsCc0A/XEy8v9j4vfdBPMn6+hlXqiQK/gyIkylm4pYvHG/SzauI/cHYdxDpIT4zm3RwoTR3djTO92ZLTVeLhEKX+9bgj+hGagnnh6+tc9eIV32DToMfS9xSfI3lLE0i0HWLqliLydhyn3OJLi4xic1opRPdoyqmcKA7u2IilBV2xKFAkmuMHbi05O9j+NMBB/PfGpUxXe9URj6HgXvFq7q5ivCg6yfNtBvtp2gE37jgLQKCGOQamtuGtsD4Z3a0NmehuSkzSMIlEq0FK0ycn+x79rekJTPfGIFZOB7vE4thaVsGr7IVZvP8TybQdZuf0gx096AEhpmsTgtFb8YFgqwzLa0L9LS/XAJXpV7o0fOVL74IbAJzSzshTgESrqA/1kuYeNe4+wZudhcrcfZtX2Q+TtOEzxiTIAkuLj6NelBROGpzEotRVD0lrTtXUyvjVnRKKbv954TaWkwLFjOqEZA6Iu0LfsO8qHebtZs/Mwa3YVk7+nmJPl3l5EUkIcZ3dqwZWDO9O/S0vO6dKS3h2ak6gVCyUWBDuNMJBAwf3UU97HGkaJelEX6Gt3FfPY/DV0aNGIPh1bMKZ3O87u1JyzO7WgW9umCm+JTYHGxYMN82CCWwEe9aJulsux0nKOnSzXDZElNgSajeKvJ+5vOCXQNEItRRuzqprlEnWBLhLxgg1pOL2XnZjoPRlZ+UYPVfXENY2wQakq0DU+IbFt1izIyIC4OO/nWbOq3l7bY5waGtm61TtDZOtWmDgRJk365rbJk+G++/zf6KFimMPXF/T4k57uDe/0dO8fglPPFeYNk3MuLB9Dhw51Imdk5kzn0tOdM/N+njnT//Y773SuSRPnvDHq/WjSJPD2mTNrf4yUlG9uC+VHoJqlQQGyXYBcVaA3dMGGo7+wq2rfUBwj0LZgA9bMfzDGx/vfnpJS+2PU1cep9vv7t5MGRYEeaqH4xYqEIK1JOCYmOpeUFNy+oThGoH0D9YDrO2BD8eHvD0igdiu8xafWgQ6MA9YB+cBDfl434Gnf6yuBIdUd84wCvb57iP621+TteiiGAuoySEMRjoH2DcUx6uojFN+vJr38qkK6Jj+jIs7VLtCBeGAj0B1IAlYAfSvtMx543xfsI4El1R23xoFek95kXYZjoLfg/n6RQzUUUFdBGksfgdpd+d/6TMa/a3IMhbTUsdoG+rnAggrPfwr8tNI+LwATKjxfB3Sq6rg1DvT09LoLtroMx2gM2EjuodfkD+ep7TV591bbY4jUsdoG+tXAtArPbwCerbTPu8B5FZ7/C8is6rg1DvRAvdpY+qjvIK1JOEbKGPqZDJvVhEJaIlxtA/0aP4H+TKV93vMT6EP9HGsykA1kp6Wl1awVkdRD9/cWvKbj0cG+ja/LIA3FrJNA+4biGApXkdPExpBLpIyhB3oLfib1RUKQikhUqW2gJwCbgG4VTor2q7TPpZVOin5Z3XGjdpZLVUFYl0MBIiKu6kAPai0XMxsPPOmb8TLdOfeYmd0B4JybYt7FxZ/FO72xBJjonKtyoRat5SIiUnO1vgWdc24+ML/StikVHjvg7toUKSIitaPFuUREYoQCXUQkRijQRURihAJdRCRGhO2ORWa2FziDW5QD0BbYF8JyIlGstzHW2wex30a1LzzSnXPt/L0QtkCvDTPLDjRtJ1bEehtjvX0Q+21U+yKPhlxERGKEAl1EJEZEa6BPDXcB9SDW2xjr7YPYb6PaF2GicgxdREROF609dBERqUSBLiISIyIm0M1supntMbPVFbYNNLPFZrbKzP5hZi0qvDbA91qu7/XGvu1Dfc/zzexp30qQYVeT9plZlpktr/DhMbNBvtcisn1Q4zYmmtnLvu1rzOynFb4mIttYw/YlmdnffNtXmNnYCl8Tqe1LNbN/+/4/cs3sPt/2Nmb2oZlt8H1uXeFrfuprxzozu7jC9ohrY03bZ2Ypvv2PmNmzlY4Vce0Dql8Pvb4+gPOBIcDqCtuWAmN8jycBv3Ffr9G+Ehjoe54CxPsef4n3phyGd432S8Ldtpq2r9LX9Qc2VXgeke07g//D64DZvsdNgC1ARiS3sYbtuxv4m+9xeyAHiIvw9nUChvgeNwfWA32BJ4CHfNsfAh73Pe6L9/4IjfDeL2FjJP8enkH7mgLnAXdw+m03I659zrnI6aE75xYCRZU2nwUs9D3+ELjK9/giYKVzboXva/c758rNrBPQwjm32Hn/1WcA36vz4oNQw/ZVNAF4DSCS2wc1bqMDmppZApAMlAKHI7mNNWxfX7y3YsQ5twc4CGRGePt2OueW+R4XA2uALsCVwMu+3V7m63qvxPtH+YRzbjOQDwyP1DbWtH3OuaPOuc+A4xWPE6ntgwgacglgNXCF7/E1QKrvcW/AmdkCM1tmZg/4tncBCit8faFvW6QK1L6Kfogv0Im+9kHgNs4FjgI7gW3AH51zRURfGwO1bwVwpZklmFk3YKjvtahon5llAIOBJUAH59xO8IYi3ncc4K27oMKXnWpLxLcxyPYFErHti/RAnwTcbWY5eN8ilfq2J+B9K5Tl+/x9M7sA79ufyiJ5Xmag9gFgZiOAEufcqTHbaGsfBG7jcKAc6Iz37fr/mFl3oq+Ngdo3He8vejbeu30tAsqIgvaZWTPgDeDHzrnDVe3qZ5urYntEqEH7Ah7Cz7aIaF9QdywKF+fcWrzDK5hZb7z3LgXvL8onzrl9vtfm4x3bnAl0rXCIrsCOeiu4hqpo3ynX8nXvHLztjpr2QZVtvA74wDl3EthjZp8DmcCnRFEbA7XPOVcG/Pep/cxsEbABOEAEt8/MEvGG3Szn3Ju+zbvNrJNzbqdvuGGPb3sh33xXeaotEftzWsP2BRKx7YvoHrqZtfd9jgN+Bpy67d0CYICZNfGNwY4B8nxvl4rNbKTvrPONwDthKD0oVbTv1LZrgNmntkVb+6DKNm4DvmNeTfHeXHxttLUxUPt8P5tNfY8vBMqccxH9M+qr50VgjXPuzxVemgfc5Ht8E1/XOw+41swa+YaVeuG9QXxEtvEM2udXpLYPiKhZLq/hHU89ifcv4C3AfXjPRK8Hfo/vylbf/tcDuXjHMJ+osD3Tt20j3htXW323JUTtGwt84ec4Edm+mrYRaAbM8f0f5gE/ifQ21rB9GcA6vCfePsK75Gmkt+88vEMHK4Hlvo/xeGeR/QvvO4x/AW0qfM0jvnaso8JMj0hs4xm2bwveE+FHfP/nfSO1fc45XfovIhIrInrIRUREgqdAFxGJEQp0EZEYoUAXEYkRCnQRkRihQBcRiREKdBGRGPH/ARnGfxuWiNipAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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",
"\n",
"we can use **curve_fit** which uses non-linear least squares to fit our sigmoid function, to data. Optimal 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 = 690.447527, 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 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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",
"\n",
"Can you calculate what is the accuracy of our model?\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# write your code here\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click **here** for the solution.\n",
"\n",
"<!-- Your answer is below:\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\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(y_hat , test_y) )\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Want to learn more?</h2>\n",
"\n",
"IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: <a href=\"https://www.ibm.com/analytics/spss-statistics-software\">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\">Watson Studio</a>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Thank you for completing this lab!\n",
"\n",
"## Author\n",
"\n",
"Saeed Aghabozorgi\n",
"\n",
"### Other Contributors\n",
"\n",
"<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
"\n",
"## Change Log\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",
"## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\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": "3.6.11"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment