Elastic Net and Ridge (Machine Learning)

Lasso (α = 1) sets some coefficients to exactly zero. Ridge (α = 0) shrinks all coefficients but keeps every variable. Elastic net blends both. In this exercise, compare all three using plot_dataset.dta.

Using the training set and the global macro $inputs, run elasticnet linear with alpha(1) (this is lasso — confirm it matches Exercise 2). Save results as alph1.
Run elastic net with alpha(0.5). Save results as alph5.
Run ridge with alpha(0). Save results as alph0.
Compare results using lassocoef.

If a model does not converge, remember you can change the search space and/or the stopping rule.

How many variables with nonzero coefficients are in each model?
How does the number of selected variables change as α moves from 1 (lasso) to 0.5 (elastic net) to 0 (ridge)? Why?
Compare the out-of-sample MSE across the three models. Which performs best? Is the difference large?

For the final model comparison challenge, you will need the predictions from your best-performing elastic net model. Assume alpha(0.5) is the best. Use estimates restore alph5 and then use predict yhat_enet to generate predictions for the entire dataset.