Most studies find that the correlation between SAT scores and first-year college grades is not overwhelming, and that only 10 percent to 20 percent of the variation in first-year GPA is explained by SAT scores.John Allen Paulos, Who's Counting?
This association appears weaker than it is, however, for an interesting, but seldom noted statistical reason: Colleges usually accept students from a fairly narrow swath of the SAT spectrum.
The SAT scores of students at elite schools, say, are considerably higher, on average, than those of students at community colleges, yet both sets of students probably have similar college grade distributions at their respective institutions.
If both sets of students were admitted to elite schools or both sets attended community colleges, there would be a considerably stronger correlation between SATs and college grades at these schools.
Those schools that attract students with a wide range of SAT scores generally have higher correlations between the scores and first-year grades.
This is a general phenomenon; the degree of correlation between two variables depends on the range of the variables considered.