I was just reading the College Board report today that looked at whether high school GPA, SAT score, or both was the best predictor of first-year college GPA: Students with Discrepant High School GPA and SAT Scores.
The interesting thing about this particular study was that they separated the students into 3 groups: those for which the SAT and HS GPA said the same thing, those for which the SAT was much higher than expected from GPA (smart but lazy? rebellious?), and those for whom the SAT was much lower than expected (slow but teacher pleasers? bad test takers?).
The correlation with first-year GPA was not good for any of the predictions (highest R2 value was 0.232 for regression using both HS GPA and SAT scores with the group for which the two predictors were in close agreement). The worst predictions were for using the high-school GPA when it it was much higher than the SAT (rampant grade inflation?)—only R2 0.127.
What interested me was that for both the “discrepant” groups, the lower of the two measures was the better predictor of future performance. That raised an immediate question for me, which unfortunately the unimaginative researchers at College Board did not consider: how good a predictor would the minimum of the HS GPA and SAT score (both converted to Z-scores) be? My guess is that it would be a better predictor than either alone, and probably better than the standard linear regression of both. But I have no access to any data to confirm or refute that conjecture.
I suspect that success in college is best achieved by those who have both brains well tuned for test taking and a willingness to work within the system, so that a low SAT or HS GPA limits performance in college. The minimum function serves as an “AND” operator, in a way that linear regression can’t really mimic.