PCR vs PLS: When Fewer Features Beat More

How much should a baseball team pay its players? The 1986 Major League season gives us 263 hitters with 19 statistics each: at-bats, hits, home runs, years played, and more. Predicting salary from performance sounds like a textbook regression problem, but 19 correlated features make it anything but. Throw them all into a linear regression and the model fits the training data beautifully but falls apart on held-out players. The coefficient estimates are wildly unstable, and salary predictions swi