Question 1 (8 marks)

Part (a) - 3 marks:

• Mention bias-variance trade-off (1 mark)
• Discuss how regularization reduces variance at cost of slight bias (1 mark)
• Mention multicollinearity handling or overfitting prevention (1 mark)

Part (b) - 3 marks:

• Split data into k folds (1 mark)
• Create grid of λ values and compute k-fold CV error for each λ (1 mark)
• Select λ with minimum CV error (1 mark)

Part (c) - 2 marks:

• Variable selection interpretation - only 4 predictors are truly important (1 mark)
• Model is more interpretable/parsimonious (1 mark)

Question 2 (8 marks)

Part (a) - 3 marks:

• Correct GAM form: Y = β₀ + f₁(X₁) + f₂(X₂) + f₃(X₃) + ε (1 mark)
• Explanation of smooth functions fⱼ (1 mark)
• Discussion of usefulness for economic modeling (flexibility, interpretability) (1 mark)

Part (b) - 3 marks:

• Advantage 1: Flexibility to capture non-linear relationships (1 mark)
• Advantage 2: Interpretability through individual smooth functions (0.5 mark)
• Disadvantage: Additive assumption may be restrictive (1.5 marks)

Part (c) - 2 marks:

• Modified model: Y = β₀ + β₁X₁ + f₂(X₂) + f₃(X₃) + ε (1 mark)
• Explanation that X₁ enters linearly (1 mark)

Question 3 (9 marks)

Part (a) - 3 marks:

• Random forests: parallel independent trees (1 mark)
• RF combines via averaging/voting (0.5 mark)
• Boosting: sequential trees fitted to residuals (1 mark)
• Boosting uses weighted combination (0.5 mark)

Part (b) - 3 marks:

• RF parameters: B (number of trees), mtry (number of predictors at each split) with explanation (1.5 marks)
• Boosting parameters: B, λ (learning rate), d (tree depth) with explanation (1.5 marks)

Part (c) - 3 marks:

• Accuracy vs computational cost trade-off (1 mark)
• Production/real-time requirements and scalability (1 mark)
• Interpretability and business acceptance considerations (1 mark)