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@dmalc
Created October 17, 2020 22:10
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Created on Skills Network Labs
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{
"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": {
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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": 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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('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": 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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('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": [
"2020-10-17 22:03:09 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": 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://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)\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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WwZeebCF74pKkrbd//6kAX7WyUpVryxjikqStt7y8vnJtiCEuSdp609PrK9eGGOKSpK23sABTU6eXTU1V5doyhrgkaeu1WrC4CDMzEFEtFxed1LbFnJ0uSWpGq2VoN8yeuCRJhTLEJUkqlCEuSVKhDHFJ0sb5aNWRcmKbJGljfLTqyNkTlyRtjI9WHTlDXJK0MT5adeQMcUnSxvho1ZEzxCVJG+OjVUeu0RCPiMsi4khEHI2Ia3tsb0XEofrz2Yi4qMn6SJK2kI9WHbnGZqdHxG7gHcALgePAbRFxc2Z+pWO3bwDPz8zvRcTlwCLwzKbqJEnaYj5adaSa7IlfAhzNzLsz80HgRmBf5w6Z+dnM/F69+nng3AbrI0laL+8D39GavE/8HOCejvXj9O9lvxb4eIP1kSSth/eB73hN9sSjR1n23DHil6lC/I1rbJ+PiKWIWDpx4sQWVlGStCbvA9/xmgzx48B5HevnAvd27xQRTwXeBezLzO/0OlFmLmbmXGbO7d27t5HKSpK6eB/4jtdkiN8GXBAR50fEGcCVwM2dO0TENPAh4JWZ+bUG6yJJWi/vA9/xGgvxzDwJXAPcCtwF/I/MPBwRV0fE1fVu/wF4LPDOiLg9Ipaaqo8kaZ28D3zHi8yel6l3rLm5uVxaMuslaVu029U18OXlqge+sOCkthGIiIOZOddd7hPbJGnS9buNrNWCb34THnqoWhrgO4qvIpWkSeZtZEWzJy5Jk8zbyIpmiEvSJPM2sqIZ4pI0ybyNrGiGuCSNu34T17yNrGiGuCSNs9WJa8eOQeapiWurQe7rRIvmfeKSNM5mZ6vg7jYzU90ypiJ4n7gkjbO1hsyduDbWvE9ckkrX717v6enePXEnro0Fe+KSVLp+93o7cW2sGeKSVIJ+M8z7DZk7cW2sOZwuSTvdoEejDhoyb7UM7TFlT1ySdoq1etuDHo3qkPnEsicuSTtBv972oBnmq71sXxk6ceyJS9J26Xddu19ve5hHo/rK0IlkiEvSdhj05LR+vW2Hy7UGQ1ySttJGr2v36207w1xr8Jq4JG2VzVzXXlg4/Vg4vbftDHP1YE9cktajqeva9ra1AfbEJWlYg+7X7tfbfv/7+/e0V89haGsd7IlL0rC8rq0dxhCXpG4bfSPYoFnk3gamLeZwuiR12swbwXzoirZZZOao67Auc3NzubS0NOpqSBpXs7O9g3pmZu0Z5A6Lq2ERcTAz57rLHU6XpE6+EUwFMcQlTZ5+t4kNcyuY17W1QxjikibLoMef+ohTFcQQlzRZBt0m5pC5CmKISypTvyHxftsG3SYGDpmrGIa4pJ1pUEivNSQ+aLh8mNd6SoUwxCU1p18Q99s+KIj7DYkPGi73mrfGSWYW9bn44otT0jrdcEPmzExmRLW84Yb1bd/IuW+4IXNqKrOK4eozNTXc9pmZ08tXPzMz1bERvbdH9N+2FT+vNALAUvbIxJGH8no/hri0hibCtN95Bx07KIj7bR8UxP2OHfTnSgUyxKXSjSJMBwX8ZoK43/ZBde5Xr0F1lgpkiEudmhg+Hmb7Ro/dqWG6mWM384+HzbazVBhDXDvTTgzEzRy7mR5iU9eIRzWs3eQwvjRhDHFtzijCdFSB2NTQdIlhupm22szvhqTTGOLdNvuXSxOhtlOPHVWY7sRA3MzQ9KiuEW/md2Ozw9qStsRIQhy4DDgCHAWu7bE9gLfX2w8Bzxh0zi0J8a0Y5msi1HbqsaMK01EFYlND06O8RrwZhrQ0ctse4sBu4OvAE4EzgDuAC7v2eTHw8TrMnwV8YdB5tyTEN/OX6aDt43jsqMJ0VIHY1NC014glbdAoQvyXgFs71t8EvKlrnz8FXtGxfgQ4u995tyTENxM8g7aP47GjCtNRBWKT13m9RixpA0YR4i8H3tWx/krguq59Pgo8p2P9k8Bcv/PaEx/BsaPsXY4qEA1TSTvIKEL8ih4h/idd+3ysR4hf3ONc88ASsDQ9Pb351vCa+PqOXT3e3qUkjYTD6d02GzyjmCU+ymMlSSOzVohHtW3rRcQe4GvAC4C/BW4DrsrMwx37vAS4hmqC2zOBt2fmJf3OOzc3l0tLS43UWZKknSgiDmbmXHf5nqb+wMw8GRHXALdSzVQ/kJmHI+Lqevv1wC1UAX4UWAFe01R9JEkaN42FOEBm3kIV1J1l13d8T+B1TdZBkqRxtWvUFZAkSRtjiEuSVChDXJKkQhnikiQVyhCXJKlQhrgkSYVq7GEvTYmIE8CxLTzlWcC3t/B84872Gp5tNTzbani21fDGqa1mMnNvd2FxIb7VImKp11Nw1JvtNTzbani21fBsq+FNQls5nC5JUqEMcUmSCmWIw+KoK1AY22t4ttXwbKvh2VbDG/u2mvhr4pIklcqeuCRJhRrLEI+IAxFxf0Tc2VF2UUR8LiK+HBF/ERGP6tj21Hrb4Xr7T9XlF9frRyPi7RERo/h5mrSetoqIVkTc3vF5KCKeVm+zrU5vq4dFxHvr8rsi4k0dx9hWp7fVGRHx7rr8joi4tOOYSWir8yLif9W/J4cj4g11+c9GxF9GxN/Uy8d0HPOmuk2ORMSLOsrHur3W21YR8dh6/x9ExHVd5xqPtsrMsfsAzwOeAdzZUXYb8Pz6+28Bb66/7wEOARfV648Fdtffvwj8EhDAx4HLR/2zjbKtuo77J8DdHeu21em/V1cBN9bfp4BvArO2Vc+2eh3w7vr744CDwK4JaquzgWfU3x8JfA24EHgrcG1dfi3wlvr7hcAdwMOB84GvT8rfWRtoqzOB5wBXA9d1nWss2mose+KZ+Wngu13FTwY+XX//S+Bl9fdfBQ5l5h31sd/JzB9HxNnAozLzc1n9F38f8NLGK7/N1tlWnV4BfADAturZVgmcGRF7gJ8GHgS+b1v1bKsLgU/Wx90P/B0wN0FtdV9mfqn+/vfAXcA5wD7gvfVu7+XUz76P6h+IP8rMbwBHgUsmob3W21aZ+UBmfgb4Yed5xqmtxjLE13An8Ov19yuA8+rvTwIyIm6NiC9FxO/V5ecAxzuOP16XTYK12qrTP6MOcWyrXm11E/AAcB+wDLwtM7+LbdWrre4A9kXEnog4H7i43jZxbRURs8DTgS8Aj8/M+6AKL6pRCqja4J6Ow1bbZaLaa8i2WsvYtNUkhfhvAa+LiINUwzAP1uV7qIZbWvXyNyLiBVRDLN0mZSr/Wm0FQEQ8E1jJzNXrnbbVT7bVJcCPgSdQDXn+24h4IrZVr7Y6QPWX6BLwx8BngZNMWFtFxCOADwL/OjO/32/XHmXZp3zsrKOt1jxFj7Ii22rPqCuwXTLzq1RD50TEk4CX1JuOA5/KzG/X226hupZ3A3BuxynOBe7dtgqPUJ+2WnUlp3rhULWhbXV6W10FfCIz/wG4PyL+DzAH/DW21WltlZkngd9e3S8iPgv8DfA9JqStIuJhVKHUzswP1cXfioizM/O+evj3/rr8OKePjq22y0T8f7jOtlrL2LTVxPTEI+Jx9XIX8O+A6+tNtwJPjYip+vrl84Gv1EMyfx8Rz6pnLb4K+MgIqr7t+rTVatkVwI2rZbZVz7ZaBn4lKmcCzwK+alv9ZFvV/++dWX9/IXAyMyfm/8H6Z/vvwF2Z+Ucdm24GXl1/fzWnfvabgSsj4uH15YcLgC9OQnttoK16Gqu2GvXMuiY+VL3E+4B/oPoX12uBN1DNZPwa8J+pH3RT7//PgcNU1+ze2lE+V5d9Hbiu85hx+WygrS4FPt/jPLZVR1sBjwD+vP69+grwu7bVmm01CxyhmqT0P6ne1jRJbfUcqqHcQ8Dt9efFVHfKfJJqVOKTwM92HLO/bpMjdMyqHvf22mBbfZNqkuUP6t/FC8eprXximyRJhZqY4XRJksaNIS5JUqEMcUmSCmWIS5JUKENckqRCGeLShKvvZf9MRFzeUfabEfGJUdZL0mDeYiaJiHgK1X3tTwd2U91/e1lmfn0D59qdmT/e2hpK6sUQlwRARLyV6qUtZ9bLGapXzu4B/iAzP1K/dOL99T4A12TmZ6N6B/jvUz3g5WmZeeH21l6aTIa4JADqR59+ierFJB8FDmfmDRHxaKp3Lz+d6mlZD2XmDyPiAuADmTlXh/jHgKdk9XpMSdtgYl6AIqm/zHwgIv6M6vGUvwn8WkT8Tr35p4BpqpdEXBcRT6N6S9uTOk7xRQNc2l6GuKROD9WfAF6WmUc6N0bEHwDfAi6imhj7w47ND2xTHSXVnJ0uqZdbgdfXb3giIp5el/8McF9mPgS8kmoSnKQRMcQl9fJm4GHAoYi4s14HeCfw6oj4PNVQur1vaYSc2CZJUqHsiUuSVChDXJKkQhnikiQVyhCXJKlQhrgkSYUyxCVJKpQhLklSoQxxSZIK9f8AYYTfqv5b1r0AAAAASUVORK5CYII=\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 0x7f62ce28bf98>]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"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": [
"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": 15,
"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": 16,
"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": 17,
"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",
"# 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"
]
},
{
"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",
"| 2020-08-27 | 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
}
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