SCHEV has those, and some other, interesting data. Plotting the graduation v. Pell percentages leads to a graph with a remarkable correlation.
We can argue about the reasons for that 75% R-squared but the correlation is solid: For the 2008 entering class, Virginia colleges with larger Pell grant percentages had lower six-year graduation rates.
Note the pattern: THE University, W&M, JMU, Tech, and VSU all are outperforming; CNU, Radford, VCU, ODU, and UVa-Wise, otherwise.
The intercept suggests that, absent whatever effect the Pell population has, the graduation rate would be 85.6%.
Looking just at the research universities gives an even more astounding correlation, R-squared = 98%. VCU underperforms in this group. The 113% intercept suggests outperformance at the low-Pell end of the graph (or underperformance at the high-Pell end).
Hmmm. What about the SAT scores. SCHEV gives us the median scores (among others):
Looks like the SAT scores, especially math, are better predictors.
JMU outperforms on both graphs.
Rather than trying to graph all the possibilities, let’s just look at the correlation matrix (expressed as R, not R-squared):
Note the math/verbal R = 0.974 (R-squared = 95%), which speaks to the correlation of the math v. verbal SAT scores of Virginia students. As we saw above, the math SAT shows the best correlation with the graduation rate, with verbal next.
And here is that matrix for the six research universities.
Recalling that correlation does not tell us about causation, these data nonetheless say that the percentage of lower income students, as measured by Pell grant numbers, is a good predictor of graduation rate but that intelligence, as measured by the median SAT scores, is even better. Except at the research universities, where Pell, by a small margin, is King of the (statistical) Mountain.
If you would like to argue about whether those small R-squared differences mean anything and, otherwise, about the cosmic significance of all those large correlations, I’ll be glad to buy every second beer.