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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": [
"2021-03-19 08:18:46 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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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 0x7fbfc3fca7b8>]"
]
},
"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": 14,
"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": 15,
"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": 16,
"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": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean absolute error: 0.03\n",
"Residual sum of squares (MSE): 0.00\n",
"R2-score: 0.98\n"
]
}
],
"source": [
"# write your code here\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"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# split data into train/test\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"# build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(y_hat , test_y) )\n",
"\n",
"```\n",
"\n",
"</details>\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": "3.6.12"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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