Apply Linear Regression on A Synthetic Data - Computer Science Assignment Help

Assignment Task

1) Using numpy sample 200 numbers from a uniform distribution and store it into variable x. Generate y data using x and injecting noise from the gaussian distribution (i.e. y = 12x-4 + noise). Using matplotlib plot the data samples, configuring axis so all samples are clearly visible. Split the data into training (80%) and testing (20%) sets using scikit-learn

Note:

- Ensure to set the random seed to reproduce same random number during different execution times.

- The randn() function in numpy can be used to sample from the gaussian distribution. While rand() function samples from the uniform distribution

1) Similar to part one, generate 200 data samples but this time adjust values of x to be in the range of -3 to 3. Plot the data and split into training and testing

2) Use Linear Regression on the generated data and plot the results. Discuss your findings.

3) Combine polynomial features of the generated data using scikit-learn’s Polynomial Features and fit combined features to a linear regression using the training dataset. Generate 100 samples between -3 to 3 with uniform interval that will be used to generate predictions from the fitted model (note: numpy.linespace can be used to generate evenly spaced numbers). Compare the model’s prediction with the ground truth by plotting the prediction as a line and the ground truth as data points on the same graph.

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