Casualty Actuarial Society MAS-1 Practice Exam

Variable selection occurs when the method yields some predictors with zero coefficients, effectively removing them from the model. Lasso regression does this because it adds an L1 penalty on the coefficients. The L1 penalty drives some coefficients exactly to zero as the regularization strength increases, leaving only a subset of predictors in use. Ridge regression uses an L2 penalty and tends to shrink coefficients toward zero but rarely to zero, so it doesn’t perform variable selection in the strict sense. PCA and Partial Least Squares are projection techniques: PCA forms components that are combinations of all variables, not selectively keeping original ones, and PLS finds latent variables that maximize covariance with the response—again, not selective about maintaining original predictors. So, the method that performs variable selection is Lasso regression.