If GPA(gpa after fall semester in college) is the dependent variable and SAT (score on the SAT) is the independent variable and I have the following parameter estimates:
Intercept: .66306
SAT: .00193
Than would I assume that every additional point a student received on their SAT score would increase the gpa after the fall semester by .00193. So for every addition 100, gpa would increase by .193?
That's what it means, but one should remember that (1) these are estimated average GPAs, and (2) one would expect that there's a lot of variability in GPAs beyond what is "explained" by differences in SAT scores; just how much unexplained variability remains is something that would be found in any statistician's report on something like this, and you haven't included that information in your posting; and (3) there may well be more to glean from the data than all this, but we don't have the data before us.
