Question 6: Prediction – 9 points For this question, use the testData. a. Using testData and with the previously built models (listed below), predict the Target variable. For each model, calculate the average of the predicted responses. i) Full linear regression model from question 1a (model1) (0.75 point) ii) Reduced model from question 2b (model2) (0.75 point) iii) Stepwise forward-backward model from question 3b (both_model) (0.75 point) iv) Elastic Net model from question 5d (enet.model) (0.75 point) Compare the results. (1 point) b. Using the first row of testData, calculate the 99% prediction interval using model2 (reduced model). (1 point) c. (Note: No code is required to answer Q6c) Discuss the trade-offs and considerations involved in selecting the best predictive model for diabetes disease progression from the following approaches: forward stepwise regression, best subset selection using Mallow’s Cp, ridge regression, and elastic net regression. In your discussion, address the following points: (4 points) Model Complexity vs. Interpretability: How does each method balance model complexity and interpretability? Which methods tend to produce more interpretable models, and which ones might lead to more complex models? Handling Multicollinearity: Explain how each method deals with multicollinearity among predictors. Which methods are more effective in reducing the impact of multicollinearity, and why? Bias-Variance Trade-Off: Compare the expected bias-variance trade-off for each method. Which methods are likely to provide the best balance between bias and variance, and what are the potential drawbacks of these methods? Practical Considerations: Discuss any practical considerations, such as computational efficiency, ease of implementation, and the availability of software tools, that might influence the choice of method in a real-world scenario.
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