A more general observation that I’m sure has been stated many times but clicked for me while reading this: Once you condition on the output of a prediction process, correlations are residuals. Positive/negative/zero coefficients then map not to good/bad/irrelevant but to underrated/overrated/valued accurately.
(“Which college a student attends” is the output of a prediction process insofar as diff students attend the most selective college that accepts them and colleges differ only in their admission cutoffs on a common scoring function, I think).
A more general observation that I’m sure has been stated many times but clicked for me while reading this: Once you condition on the output of a prediction process, correlations are residuals. Positive/negative/zero coefficients then map not to good/bad/irrelevant but to underrated/overrated/valued accurately.
(“Which college a student attends” is the output of a prediction process insofar as diff students attend the most selective college that accepts them and colleges differ only in their admission cutoffs on a common scoring function, I think).
Very well stated. I would be interested in a link to something that describes that principle, the outcome of the prediction process.