Quiz2: Understand the model fitting

Using Numpy, Matplotlib and SkLearn tools introduced in the video lectures to:

1. Generate 500 random X values from -3 to 3.

2. Generate 500 Y values using distribution "y=0.5*X⁵ - X³ - X² +2+a little bit randomness (both positive and negative) "

e.g.

m = 500 np.random.seed(seed=5) X = 6 * np.random.random(m).reshape(-1, 1) - 3 y = 0.5 * X**5 -X**3- X**2 + 2 + 5*np.random.randn(m, 1)

# y with both positive and negative randomness added

3. Use X and Y as the whole dataset and use 200 samples as testing + 300 samples as training.

Testing and training sets must be disjoint.

4. Try Linear Regression and Polynomial Regression (PolynomialFeatures + LinearRegression) in SKLearn from degree 2 to 25 to fit the training data samples.

5. Calculate the loss using mean squared error loss = average ( sum (prediction - y)² ) for all the training samples after the model was selected.

6. Calculate the loss using mean squared error loss = average ( sum (prediction - y)² ) for all the testing samples after the model was selected and used for testing data predictions.

7. Plot the figures showing your predictions using degree =2, 5, 8, 10, 20. Include these figures in your report.

e.g. An example figure showing the fitting of using polynomial model degree=5

8. Plot a figure tracking the change of training and testing loss using different models (degree = 2....25). Include this figure in your report.

e.g.

9. Which degree number(s) is/are the best and why?

Provide your answer to this question in your report.