<p>This is the difficult with analyzing correlates rather than trying to measure casual effects. The best way to do this would be to come up with some kind of instrument which predicts SAT scores but is not correlated with graduation rates. Then we can being to isolate the causal effect of SAT scores on graduation rates. Even then, we’d have to combine this with a fixed effects model to remove the different factors at each institution. </p>
<p>Measuring the effect of an institution on students is much more difficult, maybe impossible, in a causal way, based on this information.</p>