Praktikum_Machine_Learning/Regression/Muhammad Hafidz-Reg-NoneLinearRegression.ipynb
2025-11-19 09:32:34 +07:00

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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": 8,
"metadata": {},
"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": 9,
"metadata": {},
"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 = 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": 10,
"metadata": {},
"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": 11,
"metadata": {},
"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": 12,
"metadata": {},
"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": 13,
"metadata": {},
"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": 14,
"metadata": {},
"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": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2025-10-20 07:43:03 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": 15,
"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": 16,
"metadata": {},
"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": 17,
"metadata": {},
"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": 18,
"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": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x728d81060290>]"
]
},
"execution_count": 19,
"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": 20,
"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. 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": 21,
"metadata": {},
"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": 22,
"metadata": {},
"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": 23,
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean Absolute Error (MAE): 0.04\n",
"Mean Squared Error (MSE): 0.00\n",
"Root Mean Squared Error (RMSE): 0.05\n",
"R2-score: 0.96\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.metrics import r2_score, mean_squared_error, mean_absolute_error\n",
"from scipy.optimize import curve_fit\n",
"\n",
"# Misal fungsi sigmoid\n",
"def sigmoid(x, beta1, beta2):\n",
" return 1 / (1 + np.exp(-beta1*(x-beta2)))\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 metrics\n",
"mae = mean_absolute_error(test_y, y_hat)\n",
"mse = mean_squared_error(test_y, y_hat)\n",
"rmse = np.sqrt(mse)\n",
"r2 = r2_score(test_y, y_hat)\n",
"\n",
"print(\"Mean Absolute Error (MAE): %.2f\" % mae)\n",
"print(\"Mean Squared Error (MSE): %.2f\" % mse)\n",
"print(\"Root Mean Squared Error (RMSE): %.2f\" % rmse)\n",
"print(\"R2-score: %.2f\" % r2)\n",
"\n",
"# Optional: plot actual vs predicted\n",
"plt.scatter(test_x, test_y, label='Actual', color='blue')\n",
"plt.scatter(test_x, y_hat, label='Predicted', color='red')\n",
"plt.xlabel('X')\n",
"plt.ylabel('Y')\n",
"plt.title('Sigmoid Regression: Actual vs Predicted')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"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"
]
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"<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"
]
},
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"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"
]
}
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