Praktikum-Machine-Learning/Fanysia Helena-ML0101EN-Reg-NoneLinearRegression.ipynb

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p style=\"text-align:center\">\n",
" <a href=\"https://skills.network\" target=\"_blank\">\n",
" <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
" </a>\n",
"</p>\n",
"\n",
"\n",
"# Non Linear Regression Analysis\n",
"\n",
"\n",
"Estimated time needed: **20** minutes\n",
" \n",
"\n",
"## Objectives\n",
"\n",
"After completing this lab you will be able to:\n",
"\n",
"* Differentiate between linear and non-linear regression\n",
"* Use non-linear regression model in Python\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the data shows a curvy trend, then linear regression will not produce very accurate results when compared to a non-linear regression since linear regression presumes that the data is linear. \n",
"Let's learn about non linear regressions and apply an example in python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"importing_libraries\">Importing required libraries</h2>\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Although linear regression can do a great job at modeling some datasets, it cannot be used for all datasets. First recall how linear regression, models a dataset. It models the linear relationship between a dependent variable y and the independent variables x. It has a simple equation, of degree 1, for example y = $2x$ + 3.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"y = 2*(x) + 3\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"#plt.figure(figsize=(8,6))\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Non-linear regression is a method to model the non-linear relationship between the independent variables $x$ and the dependent variable $y$. Essentially any relationship that is not linear can be termed as non-linear, and is usually represented by the polynomial of $k$ degrees (maximum power of $x$). For example:\n",
"\n",
"$$ \\ y = a x^3 + b x^2 + c x + d \\ $$\n",
"\n",
"Non-linear functions can have elements like exponentials, logarithms, fractions, and so on. For example: $$ y = \\log(x)$$\n",
" \n",
"We can have a function that's even more complicated such as :\n",
"$$ y = \\log(a x^3 + b x^2 + c x + d)$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a look at a cubic function's graph.\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"y = 1*(x**3) + 1*(x**2) + 1*x + 3\n",
"y_noise = 20 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, this function has $x^3$ and $x^2$ as independent variables. Also, the graphic of this function is not a straight line over the 2D plane. So this is a non-linear function.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some other types of non-linear functions are:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Quadratic\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = X^2 $$\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"\n",
"y = np.power(x,2)\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exponential\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An exponential function with base c is defined by $$ Y = a + b c^X$$ where b ≠0, c > 0 , c ≠1, and x is any real number. The base, c, is constant and the exponent, x, is a variable. \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"\n",
"Y= np.exp(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Logarithmic\n",
"\n",
"The response $y$ is a results of applying the logarithmic map from the input $x$ to the output $y$. It is one of the simplest form of __log()__: i.e. $$ y = \\log(x)$$\n",
"\n",
"Please consider that instead of $x$, we can use $X$, which can be a polynomial representation of the $x$ values. In general form it would be written as \n",
"\\begin{equation}\n",
"y = \\log(X)\n",
"\\end{equation}\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
" This is separate from the ipykernel package so we can avoid doing imports until\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"Y = np.log(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sigmoidal/Logistic\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = a + \\frac{b}{1+ c^{(X-d)}}$$\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"\n",
"Y = 1-4/(1+np.power(3, X-2))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"ref2\"></a>\n",
"# Non-Linear Regression example\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For an example, we're going to try and fit a non-linear model to the datapoints corresponding to China's GDP from 1960 to 2014. We download a dataset with two columns, the first, a year between 1960 and 2014, the second, China's corresponding annual gross domestic income in US dollars for that year. \n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2025-10-17 10:46:38 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",
"This is what the datapoints look like. It kind of looks like an either logistic or exponential function. The growth starts off slow, then from 2005 on forward, the growth is very significant. And finally, it decelerates slightly in the 2010s.\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 800x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,5))\n",
"x_data, y_data = (df[\"Year\"].values, df[\"Value\"].values)\n",
"plt.plot(x_data, y_data, 'ro')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Choosing a model ###\n",
"\n",
"From an initial look at the plot, we determine that the logistic function could be a good approximation,\n",
"since it has the property of starting with a slow growth, increasing growth in the middle, and then decreasing again at the end; as illustrated below:\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"Y = 1.0 / (1.0 + np.exp(-X))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"The formula for the logistic function is the following:\n",
"\n",
"$$ \\hat{Y} = \\frac1{1+e^{-\\beta_1(X-\\beta_2)}}$$\n",
"\n",
"$\\beta_1$: Controls the curve's steepness,\n",
"\n",
"$\\beta_2$: Slides the curve on the x-axis.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building The Model ###\n",
"Now, let's build our regression model and initialize its parameters. \n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def sigmoid(x, Beta_1, Beta_2):\n",
" y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))\n",
" return y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets look at a sample sigmoid line that might fit with the data:\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x73abb004ed10>]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"beta_1 = 0.10\n",
"beta_2 = 1990.0\n",
"\n",
"#logistic function\n",
"Y_pred = sigmoid(x_data, beta_1 , beta_2)\n",
"\n",
"#plot initial prediction against datapoints\n",
"plt.plot(x_data, Y_pred*15000000000000.)\n",
"plt.plot(x_data, y_data, 'ro')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our task here is to find the best parameters for our model. Lets first normalize our x and y:\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"# Lets normalize our data\n",
"xdata =x_data/max(x_data)\n",
"ydata =y_data/max(y_data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### How we find the best parameters for our fit line?\n",
"we can use __curve_fit__ which uses non-linear least squares to fit our sigmoid function, to data. Optimize values for the parameters so that the sum of the squared residuals of sigmoid(xdata, *popt) - ydata is minimized.\n",
"\n",
"popt are our optimized parameters.\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" beta_1 = 690.451712, beta_2 = 0.997207\n"
]
}
],
"source": [
"from scipy.optimize import curve_fit\n",
"popt, pcov = curve_fit(sigmoid, xdata, ydata)\n",
"#print the final parameters\n",
"print(\" beta_1 = %f, beta_2 = %f\" % (popt[0], popt[1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we plot our resulting regression model.\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 800x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(1960, 2015, 55)\n",
"x = x/max(x)\n",
"plt.figure(figsize=(8,5))\n",
"y = sigmoid(x, *popt)\n",
"plt.plot(xdata, ydata, 'ro', label='data')\n",
"plt.plot(x,y, linewidth=3.0, label='fit')\n",
"plt.legend(loc='best')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Practice\n",
"Can you calculate what is the accuracy of our model?\n"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean absolute error: 0.04\n",
"Residual sum of squares (MSE): 0.00\n",
"R2-score: 0.97\n"
]
}
],
"source": [
"# split data into train or test\n",
"\n",
"msk= np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"#build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(test_y, y_hat))\n"
]
},
{
"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(test_y,y_hat) )\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"tags": []
},
"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?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">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?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">Watson Studio</a>\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Thank you for completing this lab!\n",
"\n",
"\n",
"## Author\n",
"\n",
"Saeed Aghabozorgi\n",
"\n",
"\n",
"### Other Contributors\n",
"\n",
"<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
"\n",
"\n",
"## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n",
"\n",
"<!--## Change Log\n",
"\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",
"\n",
"\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python",
"language": "python",
"name": "conda-env-python-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.12"
},
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