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Created on Cognitive Class Labs
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://ibm.box.com/shared/static/cw2c7r3o20w9zn8gkecaeyjhgw3xdgbj.png\" width = 400, align = \"center\"></a>\n",
"# <center>Non Linear Regression Analysis</center>"
]
},
{
"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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Importing required libraries"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"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 = 2*(x) + 3."
]
},
{
"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('Indepdendent 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",
"$$ y = \\log(a x^3 + b x^2 + c x + d)$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a look at a cubic function's graph."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"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('Indepdendent 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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some other types of non-linear functions are:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Quadratic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = X^2 $$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"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('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exponential"
]
},
{
"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": 8,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"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.exp(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Indepdendent 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}"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"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('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sigmoidal/Logistic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = a + \\frac{b}{1+ c^{(X-d)}}$$"
]
},
{
"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",
"\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('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"ref2\"></a>\n",
"# Non-Linear Regression example"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For an example, we're going to try and fit a non-linear model to the datapoints corrensponding 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. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2020-01-27 15:30:33 URL:https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/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": 12,
"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://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/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)"
]
},
{
"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 deaccelerates slightly in the 2010s."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"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:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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S2+kf3f1vzTdkZlcBVwEMGzasjXFEOp9bnlnOnup6fvW5CaSqLyEJSTydzmUBV/LRTuf2N1xlS3/VzZuhphG5BnESkA28bWZz3H31h97kPguYBTBlypSPNGUVSURvrinm8Xe3cs0JhzJ6oLqXlvDE09fQ34GBwCnAa0S6lyhv9R0RW4ChMdNDiHRP0Xyd59290t2LgdeBiXFsWyShVdc1csMT75Gfl8M1Jx4adhxJcvEUgkPd/Sag0t3/CpwBjI/jffOBkWaWb2YZwAXA7GbrPAUca2ZpZtaNyKmjFYh0cX96ZQ2bSqr42TnjyErXiGMSrgPpdK7UzMYB24ER+3uTuzeY2TXAC0AqcK+7LzOzq6PLZ7r7CjN7HlgCNAF3u/vSNuyHSMJYuX0Pd72+js9PHqJB6KVTiKcQzDKz3sCNRL7Rdwduimfj7v4c8FyzeTObTf8a+HVcaUUSXFOT84PH36Nndjo3nH5Y2HFEgNb7Ghrg7jvc/e7orNeBgzsmlkjX9OC8Tby7qZTffWEivXMywo4jArR+jWCxmb1kZl+KdkMtIh/DzvIafvX8SmYc0lc9i0qn0lohGAz8BjgWWG1mT5rZ+WamMfNE2uDmZ1ZQ29DELWePUzcS0qnssxC4e6O7vxC9oWwo8BfgbGC9mT3QUQFFuoLXVhfx9OJCvn78oRzcr3vYcUQ+JJ7mo7h7HZGuIVYAe4CxQYYS6Upq6hu56cmlHNwvh6uP12U26XxaLQRmNszMrjWzd4BniDQDPcvdj+iQdCJdwO3/KWBTSRW3nD2OzDTdMyCdT2utht4icp3gEeAqd9cANSIHqGBnBTNfW8u5RwzWPQPSabV2H8EPgNfdXX37iLSBu3PTk0vJTk/lhjN0z4B0Xq1dLH5NRUCk7Z5ctJW31+3i+6eNIa97ZthxRPYprovFInJgyqrqueWZFRwxrBcXTlXX6dK57bcQmFl+PPNE5AO3vrCS3VV13HL2OFI0zoB0cvEcETzWwrxH2zuISFfx7qbdPDhvE5fPyOfwQbopXzq/1loNjSEyGE2umZ0bs6gnMQPUiMgHGhqb+OETS+nfI5PvfHpU2HFE4tJaq6HRwJlAL+AzMfPLgS8HGUokUf3t7Y0s37aH2y86ku6Z8XTuKxK+ff6luvtTwFNmdrS7v92BmUQS0vayGn774io+Oaofp48fGHYckbjF85WlwMxuIDIYzfvrxzFmsUhSufnZ5dQ3OTefdbg6lZOEEk8heAp4A3gZaAw2jkhien11Ec8u2cZ3Th7F8L45YccROSDxFIJu7v79wJOIJKia+kZ+9NRSDs7L4SvHqVM5STzxNB99xsxODzyJSIK689W1bNhVxc3qVE4SVDyF4FtEikGNme0xs3Iz2xN0MJFEsK6ogjtfXctnJw7imEPVqZwkpv2eGnL3Hh0RRCTRuDs3PbWUzPQUbjxTncpJ4oqniwkzs0vM7Kbo9FAzmxZ8NJHObfbiQv5bsIvrTh1D/x66x1ISVzynhu4AjgYuik5XALcHlkgkAZRV1XPzM8uZOLQXF01Tp3KS2OJpNTTd3Y80s3cB3H23mWUEnEukU/v1iyspqazjviumkapO5STBxXNEUG9mqYADmFk/oCnQVCKd2DubdvPA3E18ccYIxg1Wp3KS+OIpBH8CngD6m9nPgDeBnweaSqSTqm9s4obH32NAjyy+++nRYccRaRfxtBp6wMwWAicBBpzt7isCTybSCd375npWbi9n5iWT1amcdBmtdUPdJ2ZyJ/BQ7DJ3LwkymEhns7mkij+8vIZPHTaAUw4fEHYckXbT2leahUSuCxgwDNgdfd0L2ARolDJJGu7Oj2cvwwx+qk7lpItpbfD6fHc/GHgB+Iy757l7XyJjFDzeUQFFOoNn39vGKyt38u1PjWJwr+yw44i0q3guFk919+f2Trj7v4Djgosk0rmUVdXzk9nLGTe4J1ccMyLsOCLtLp5CUGxmN5rZCDMbbmY/BHbFs3EzO9XMVplZgZld38p6U82s0czOize4SEf55fMrKams5ZfnTiAtNZ7/MiKJJZ6/6guBfkSakD4J9I/Oa1X03oPbgdOAscCFZjZ2H+v9isgpKJFOZd76Eh6at4krP5Gvewaky4qn+WgJkR5ID9Q0oMDd1wGY2cPAWcDyZut9A3gMmNqGnyESmNqGRn7w+BIG98rm2ydrIHrpuvZbCMxsFPA9PjpU5Yn7eetgYHPM9BZgerNtDwbOAU6klUJgZlcBVwEMG6Z+XaRj3PZKAWuLKrnviql0y9A9A9J1xfPX/QgwE7ibAxuqsqX2dd5s+g/A9929sbXmeO4+C5gFMGXKlObbEGl3K7bt4c5X13LuEYM5fnT/sOOIBCqeQtDg7ne2YdtbgKEx00OAwmbrTAEejhaBPOB0M2tw9yfb8PNE2kVjk3P9Y0vIzU7npjM/cllLpMuJpxA8bWZfI3KxuHbvzDjuLJ4PjDSzfGArcAEfdGW9dxvv35RmZvcBz6gISNj+8t/1LN5Sxp8uPILeOepoV7q+eArBF6PP18bMc6DVUbrdvcHMriHSGigVuNfdl5nZ1dHlM9uQVyRQG4or+c2LqzhpTH8+M+GgsOOIdIh4Wg21uSuJ6I1ozzWb12IBcPfL2/pzRNpDU5Nz3WNLSE9J4ZZzxqkbCUka8QxV2S16Q9ms6PRIMzsz+GgiHev+uRuZt76Em84cy0G56kZCkkc8N5T9BagDZkSntwC3BJZIJASbS6r45b9W8slR/fj8lCFhxxHpUPEUgkPc/VagHsDdq2m5aahIQmpqcr7/2BJSzPjFueN1SkiSTjyFoM7MsvlgqMpDiGk9JJLoHpi7kbfW7uIHp49Rz6KSlOJpNfRj4HlgqJk9ABwDXB5kKJGOsqG4kp8/FzkldNE03bUuySmeVkMvmdk7wFFETgl9y92LA08mErDGJud7jywmPdW49XMTdEpIkla8HagcB3yCyOmhdCI3l4kktHveXMeCjbv5/fkTGZibFXYckdDE03z0DuBq4D1gKfAVM7s96GAiQVq1vZzfvLiaUw4fwNmTBocdRyRU8RwRHAeMc/e9F4v/SqQoiCSkmvpGvvXwu/TMSuNn56iVkEg8rYZWERm8fq+hwJJg4ogE77cvrmLl9nJ+fd5E8rpnhh1HJHTxHBH0BVaY2bzo9FTgbTObDeDunw0qnEh7+29BMXe9sZ5LjxrOCWPUvbQIxFcIfhR4CpEOUFpVx3f/uZiD++Vww+mHhR1HpNOIp/noa2Y2HBjp7i9Hby5Lc/fy4OOJtA9357pHl7Crspa7LjuG7IzUsCOJdBrxtBr6MvAo8OforCFEBrEXSRj3z9nIi8t3cN0pYxg/RIPQi8SK52Lx14ncTbwHwN3XADq5KgljxbY93PzsCo4b1Y8rP9HmXtVFuqx4CkGtu9ftnTCzND469rBIp1RV18A3HnqX3Ox0fvuFiaSkqKmoSHPxFILXzOwGINvMTiYymP3TwcYS+fjcnRufXMraogp+/4VJaioqsg/xFILrgSIiN5F9hciIYzcGGUqkPfxj/mYef2cr3zxxJJ8YmRd2HJFOK55WQ01m9iTwpLsXdUAmkY9tWWEZP5q9jE8cmsc3TxoZdhyRTm2fRwQW8RMzKwZWAqvMrMjMdF+BdGp7aur52gPv0KdbBn+8YBKpui4g0qrWTg39D5HWQlPdva+79wGmA8eY2bc7JJ3IAWpqcr7zj0Vs3V3NbRcdQV9dFxDZr9YKwWXAhe6+fu8Md18HXBJdJtLp/PHfa3h5xU5uOnMsU0b0CTuOSEJorRCktzQATfQ6QXpwkUTa5qXlO/jjv9dw3uQhXHb08LDjiCSM1gpBXRuXiXS4gp0VfPsfi5gwJJdbzh6nrqVFDkBrrYYmmtmeFuYboOGcpNPYXVnHlX+dT2ZaCjMvmUxWuvoREjkQ+ywE7q7/TdLp1TU0cfX9C9lWWsNDV01nUK/ssCOJJJx4xywW6XTcnR89tZS560v4w/mTmDxcF4dF2iKeO4tFOqW73ljHw/M3c80Jh3L2ERp3WKStVAgkIT21aCs/f24lZ4w/iO+cPCrsOCIJTYVAEs5ba4v53iOLmZbfRz2KirQDFQJJKKu2l/OVvy9kRN8c7rp0iloIibSDQAuBmZ1qZqvMrMDMrm9h+cVmtiT6eMvMJgaZRxLbxl2VXHrPXLplpHLfl6aR2033NYq0h8AKgZmlArcDpwFjgQvNbGyz1dYDx7n7BOBmYFZQeSSxbS+r4ZJ75lLf2MT9V05nsJqJirSbII8IpgEF7r4uOsLZw8BZsSu4+1vuvjs6OYfIeMgiH1JSWccl98ylpKKO+66YxsgBPcKOJNKlBFkIBgObY6a3ROfty5XAv1paYGZXmdkCM1tQVKQhEZJJaVUdl94zl00lVdz9xalMHNor7EgiXU6QhaClphwtjnVsZicQKQTfb2m5u89y9ynuPqVfv37tGFE6s9KqyJHAmh0V/PnSyRx9SN+wI4l0SUHeWbwFGBozPQQobL6SmU0A7gZOc/ddAeaRBFJWVc8l98xl9fYK/nzZZE4Y3T/sSCJdVpBHBPOBkWaWb2YZwAXA7NgVzGwY8DhwqbuvDjCLJJBdFbVcfM+cSBG4VEVAJGiBHRG4e4OZXQO8AKQC97r7MjO7Orp8JvAjoC9wR7Tb4AZ3nxJUJun8tpfVcPHdc9haWs2syyZzvIqASODMvcXT9p3WlClTfMGCBWHHkABs3FXJxXfPpbSqnnsvn8q0fHUiJ9JezGzhvr5oq/dR6RTe21LGFffNp7GpiQe/PJ0JQ9Q6SKSjqIsJCd1/Vu3k/Flvk5mWwiNXH60iINLBdEQgoXp43iZ++ORSxgzswV8un0r/nhr8TqSjqRBIKBoam/jFv1Zyz5vr+eSoftxx8ZF0z9Sfo0gY9D9POlxZVT3XPPQOb6wp5vIZI7jxjMNIS9VZSpGwqBBIh1q5fQ9fvf8dtuyu4pfnjueCacPCjiSS9FQIpMM8unALNz75Hj2y0nnwy0cxdYSah4p0BioEErjqukZ++vQyHp6/maMP7ssfL5xE/x66KCzSWagQSKCWbi3jmw+/y/riSr52/CF85+RRuh4g0smoEEggGpucu95Yx29fXEXfnEweuHI6Mw7NCzuWiLRAhUDaXcHOcq59dAnvbirl1MMH8otzx9M7JyPsWCKyDyoE0m7qG5u46411/OHlNXTLSOWPF0zisxMHEe1QUEQ6KRUCaRfzN5Rw4xNLWbWjnNPGDeR/zxpHvx6ZYccSkTioEMjHsrO8hlufX8WjC7cwuFc2sy6dzKcPHxh2LBE5ACoE0iY19Y3c/cY67nx1LXWNTXz1+EP4xomH0i1Df1IiiUb/a+WANDQ28fi7W/nDS6spLKvhlMMHcP1ph5GflxN2NBFpIxUCiUtTk/PMe9v4w0urWVdcyYQhufzu/EkcdbAGlBdJdCoE0qr6xiZmLyrkjlcLWFtUyegBPfjzpZP59NgBag0k0kWoEEiLKmobeGTBZu5+Yz1bS6sZM7AH/3fhEZw+/iBSU1QARLoSFQL5kA3Flfx9zkb+OX8z5bUNTBnem5vPPpwTRvfXEYBIF6VCINQ1NPHyih08OHcTbxYUk5ZinDnhIK44Jp+JQzVspEhXp0KQpNydpVv38Ng7W5i9uJCSyjoG98rmuyeP4gtThzJAQ0aKJA0VgiSzekc5zyzZxrNLCllbVElGWgonjx3AeUcO4ZOj+un8v0gSUiHo4pqanHc3l/LS8h28tHw7a4sqSTGYnt+XL30inzPHDyK3W3rYMUUkRCoEXVBxRS1vrinmtdVFvLGmiOKKOtJSjOkH9+GLM0Zw6riBGhhGRN6nQtAFlFTWMX9DCXPW7eLttbtYub0cgD45GXxyZB4njOnP8aP7k5utb/4i8lEqBAmmsclZvaOcxZtLWbS5lPkbSlhbVAlAZloKU0f04dpTBvGJQ/MYPziXFJ3zF5H9UCHoxGrqG1mzo4IV2/ewbGsZSwv3sLxwD9X1jQDkZqczeXhvPjd5CFOG92Hi0Fwy01JDTi0iiUaFoBMoq6pn/a5K1hdXsGZHBQU7I48Nuypp8sg6ORmpjB3Uk/OnDmXi0FwmDulFfl6ObvISkY9NhaAD1IMhgRAAAAnsSURBVNQ3UlhazdbSarburmbL7mo2lVS9/yiprHt/3bQUY3jfbowc0J3PTBzEmIE9GD2wByP65ug0j4gEQoWgjdydPTUNlFTWsauilqLyWoqjzzv21LKjvIYde2rZXlbN7qr6D703NcUY1CuLYX26ccrhA8jPy2FE3xzy83IY3jeHjLSUkPZKRJJRoIXAzE4F/gikAne7+y+bLbfo8tOBKuByd38nyEx7uTu1DU1U1jZQWdtIRW0DFbUNlNfUU14Ted5T00BZdT1lVfWUVtexu6qe0qrI8+7KOhr2nreJkWKQ1z2T/j0zGZSbxeThvTgoN5uBPbMY3Dubwb2yGZibRXqqPuxFpHMIrBCYWSpwO3AysAWYb2az3X15zGqnASOjj+nAndHndvfqqp3c/Mxyquoao48G6hs/+kHeXFZ6CrnZ6eRmp9OrWwb5eTkc2S2D3jkZ9M3JoE9OBn27Z5LXPYN+PTLp0y2DNH3Ii0gCCfKIYBpQ4O7rAMzsYeAsILYQnAX8zd0dmGNmvczsIHff1t5hemanM2ZgT7plpEYemWl0z0wjJyOVnMw0emSl0T0zne5ZafTMSqNndjo9stLUCkdEurwgC8FgYHPM9BY++m2/pXUGAx8qBGZ2FXAVwLBhw9oU5shhvTny4t5teq+ISFcW5DmMlpq4ND8XE886uPssd5/i7lP69evXLuFERCQiyEKwBRgaMz0EKGzDOiIiEqAgC8F8YKSZ5ZtZBnABMLvZOrOByyziKKAsiOsDIiKyb4FdI3D3BjO7BniBSPPRe919mZldHV0+E3iOSNPRAiLNR68IKo+IiLQs0PsI3P05Ih/2sfNmxrx24OtBZhARkdapwbuISJJTIRARSXIqBCIiSc4ip+kTh5kVARvDztEGeUBx2CFCkIz7nYz7DMm534m0z8PdvcUbsRKuECQqM1vg7lPCztHRknG/k3GfITn3u6vss04NiYgkORUCEZEkp0LQcWaFHSAkybjfybjPkJz73SX2WdcIRESSnI4IRESSnAqBiEiSUyEIgZl9z8zczPLCzhI0M/u1ma00syVm9oSZ9Qo7U5DM7FQzW2VmBWZ2fdh5gmZmQ83sP2a2wsyWmdm3ws7UUcws1czeNbNnws7ycakQdDAzG0pkHOdNYWfpIC8B49x9ArAa+EHIeQITM073acBY4EIzGxtuqsA1AN9198OAo4CvJ8E+7/UtYEXYIdqDCkHH+z1wHS2MxNYVufuL7t4QnZxDZPChrur9cbrdvQ7YO053l+Xu29z9nejrciIfjIPDTRU8MxsCnAHcHXaW9qBC0IHM7LPAVndfHHaWkHwJ+FfYIQK0rzG4k4KZjQCOAOaGm6RD/IHIF7qmsIO0h0DHI0hGZvYyMLCFRT8EbgA+3bGJgtfaPrv7U9F1fkjkNMIDHZmtg8U1BndXZGbdgceA/3H3PWHnCZKZnQnsdPeFZnZ82HnagwpBO3P3T7U038zGA/nAYjODyCmSd8xsmrtv78CI7W5f+7yXmX0ROBM4ybv2jStJOQa3maUTKQIPuPvjYefpAMcAnzWz04EsoKeZ3e/ul4Scq810Q1lIzGwDMMXdE6XnwjYxs1OB3wHHuXtR2HmCZGZpRC6InwRsJTJu90XuvizUYAGyyLeavwIl7v4/YefpaNEjgu+5+5lhZ/k4dI1AgnYb0AN4ycwWmdnM/b0hUUUviu8dp3sF8M+uXASijgEuBU6M/vsuin5TlgSiIwIRkSSnIwIRkSSnQiAikuRUCEREkpwKgYhIklMhEBFJcioE0qHMrOIA1z++vXp3NLOfmNn32mlb95nZeW1876SWmliaWY6Z7TKz3GbznzSzLxzA9geZ2aP7WWefv1cz25AMPePKB1QIRDreJOAjhcDdK4EXgbP3zosWhU8AcRVDM0tz90J3b1ORkuSkQiChiH4jfdXMHo2OV/BA9C7VvX36rzSzN4FzY96TY2b3mtn8aD/wZ0XnX25mT5nZ89GxAH4c854fRue9DIyOmX9IdP2FZvaGmY2Jzr/PzP5kZm+Z2bq93/ot4jYzW25mzwL9Y7Y12cxei27rBTM7KDr/VTP7lZnNM7PVZnasmWUA/wucH7356vxmv5qHgAtips8Bnnf3KjObFs31bvR5dMz+P2JmTwMvmtkIM1saXTYiun/vRB8zYrbd0yJjRCw3s5lm9pHPAzO7JJp/kZn92SJdbUtX4+566NFhD6Ai+nw8UEakP54U4G0i33yziPTgOZJIJ27/BJ6JvufnwCXR172IdOeQA1wObAP6AtnAUmAKMBl4D+gG9AQKiHQHAPBvYGT09XTglejr+4BHopnGEulWGiIF6SUgFRgElALnAenAW0C/6HrnA/dGX78K/Db6+nTg5ejry4Hb9vH7yQB2An2j088DZ0Rf9wTSoq8/BTwWs70tQJ/o9AhgafR1NyAr+noksCDm918DHBzdp5eA86LLNgB5wGHA00B6dP4dwGVh/w3p0f4PdTonYZrn7lsAzGwRkQ+wCmC9u6+Jzr8fuCq6/qeJdPa19zx/FjAs+vold98Vfc/jRIoKwBPuXhWdPzv63B2YATwSPQgByIzJ9aS7NwHLzWxAdN4ngYfcvREoNLNXovNHA+OIdKEBkQ/VbTHb2tsJ28Lo/rXK3euiOc8zs8eInEZ6Mbo4F/irmY0k0qtpesxbX3L3khY2mQ7cZmaTgEZgVMyyee6+DsDMHiLyO4u9tnASkWI6P7pv2USKlHQxKgQSptqY14188Pe4r35PDPicu6/60Eyz6S28x6Prt7StFKDU3SfFkSu2a+mWtmXAMnc/ej/bit2//XkIuDG67afcvT46/2bgP+5+jkX6/n815j2V+9jWt4EdwEQi+10Ts6yl31ksA/7q7l12VDmJ0DUC6WxWAvlmdkh0+sKYZS8A34i5lnBEzLKTzayPmWUTudj6X+B14BwzyzazHsBnADzSX/56M/t8dDtmZhP3k+t14AKLjFN7EHBCdP4qoJ+ZHR3dVrqZHb6fbZUT6YhvX/5D5DTO14kUhb1yifRqCpHTQfHIBbZFj3AuJXLEstc0M8uPXhs4H3iz2Xv/TeTIpD9A9Pc7PM6fKwlEhUA6FXevIXIq6NnoxeKNMYtvJnKqY0n0YujNMcveBP4OLCJy7nyBR4ZQ/MfeecAbMetfDFxpZouBZex/SMkngDVErjncCbwWzVtH5FrBr6LbWkTktFNr/gOM3cfFYqIf2o8RuebxesyiW4FfmNl/+fAHemvuAL5oZnOInBaKPXJ4G/glkWsq66P7GJtjOZEjkxfNbAmR6wgHxflzJYGo91FJeGZ2OZGxHa4JO4tIItIRgYhIktMRgYhIktMRgYhIklMhEBFJcioEIiJJToVARCTJqRCIiCS5/w88S56JL7VaaAAAAABJRU5ErkJggg==\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('Indepdendent 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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building The Model ###\n",
"Now, let's build our regression model and initialize its parameters. "
]
},
{
"cell_type": "code",
"execution_count": 16,
"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:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fa5c09f6b38>]"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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V5tEgjEvl+qMeukgEyN9TTNa0JRw/6WHWbSMZlNoq3CVJMMK4VK4/6qGLhNnq7Yf4wQtfUO6Bv9+uMI8qgZbErYelcv1RoIuEUc7WIib89QuSE+OZc8e59OnYItwlSU2Ecalcf4IKdDMbZ2brzCzfzB7y83pLM/uHma0ws1wzmxj6UkViy+f5+7h+2pe0bdaI1+84l25tm4a7JKmpMC6V648556rewSweWA9cCBQCS4EJzrm8Cvs8DLR0zj1oZu2AdUBH51xpoONmZma67OzsEDRBJPp8vHY3d8xcRreUprxy63DaN28c7pIkSphZjnMu099rwfTQhwP5zrlNvoCeDVxZaR8HNDfvNcnNgCKgrBY1i8Ss91buZPKMHM7q0JzZk0cqzCVkggn0LkBBheeFvm0VPQucDewAVgH3Oec8lQ9kZpPNLNvMsvfu3XuGJYtEr7k5hdz72jIGpbZi1m0jaN00KdwlSQwJJtD9rQRUeZzmYmA50BkYBDxrZqed3XHOTXXOZTrnMtu1a1fjYkWi2StfbOX+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/bOuT1VHTczM9NlZ2fXtn6RM3b0RBm3v5LDZ/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+HpEqJWm/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/tzbf7tDDVNigAAAnxSURBVNea4xI7gu2Jl5RAfDyUl59+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/1WcA36v76qtXw/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/ARnGfxvy3p3RAAAAAElFTkSuQmCC\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:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"# Lets normalize our data\n",
"xdata =x_data/max(x_data)\n",
"ydata =y_data/max(y_data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### How we find the best parameters for our fit line?\n",
"we can use __curve_fit__ which uses non-linear least squares to fit our sigmoid function, to data. 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."
]
},
{
"cell_type": "code",
"execution_count": 19,
"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 regresssion model."
]
},
{
"cell_type": "code",
"execution_count": 20,
"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",
"Can you calculate what is the accuracy of our model?"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean absolute error: 0.03\n",
"Residual sum of squares (MSE): 0.00\n",
"R2-score: 0.58\n"
]
}
],
"source": [
"# write your code here\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) )"
]
},
{
"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",
"-->"
]
},
{
"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](http://cocl.us/ML0101EN-SPSSModeler).\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](https://cocl.us/ML0101EN_DSX)\n",
"\n",
"### Thanks for completing this lesson!\n",
"\n",
"Notebook created by: <a href = \"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>\n",
"\n",
"<hr>\n",
"Copyright &copy; 2018 [Cognitive Class](https://cocl.us/DX0108EN_CC). This notebook and its source code are released under the terms of the [MIT License](https://bigdatauniversity.com/mit-license/).​"
]
}
],
"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": "3.6.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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