Right, but there's a glaring statistical error. Schools are very stratified by skill level. So you may have someone with a 1550 and a 2.5 HS GPA, sitting next to someone with a 1300 and a 3.8 HS GPA. One smart slacker, one hard worker who isn't quite so facile.

Of course SAT scores won't be predictive in that case. You'd want to look at SAT scores controlling for other admissions factors, which is basically SAT scores controlling for every variable admissions cares about, which of course means that no variable in particular has predictive power.

But if you want to see how strongly SAT scores correlate with academic performance, the way to do it would be to take some students who belong at, e.g., ASU, and somehow sneak them into Harvard.