Part2. Goal/Objective: Apply linear regression on a synthetic data of the form y = 0.75x + 2x2 + 1.1. A) 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 testingPART 1 QUESTION FOR REFERENCE IN ATTACHED PHOTOB)Use Linear Regression on the generated data and plot the results. Discuss your findings.C)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. Note:PolynomialFeatures Reference:Be sure to not include_bias when combining polynomial features Goal/Objective: Apply linear regression on a synthetic data of the form y = 12x - 4.1) Using numpy sample 200 numbers from a uniform distribution and store it into variablex. 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 areclearly visible. Split the data into training (80%) and testing (20%) sets using scikit-learnNote:Ensure to set the random seed to reproduce same random number during differentexecution times.import numpy as npimport numpy. random as rndnp. random.seed (10) import numpy as npfrom>>> X = np.arange (6).reshape (3, 2)>>> Xsklearn.preprocessingarray([[0, 1],[2, 3],[4, 5]])>>> poly>>>poly.fit transform (X)1.],6.19.],4.13.12.15., 16., 20., 25.]])[ 1or 4.,>>> poly = Polynomial Features interaction_only=True)>>>poly.fit transform (X)0.F=Polynomial Features (2)array([[ 1.,[ 1.,array([[ 1.,[ 1.p[ 1.,0.f4.,1.,1.s3.15.10.fimport Polynomial Features0.],0.f6.].20.]])

Answered: Part2. Goal/Objective: Apply linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Part2. Goal/Objective: Apply linear regression on a synthetic data of the form y = 0.75x + 2x² + 1.

1. A) 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

PART 1 QUESTION FOR REFERENCE IN ATTACHED PHOTO

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

C)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.

Note: