<p>There are 3 fundamental flaws with your approach.</p>
<p>1) you write "Northwestern accepts 30% of their applicants. In other words, you have to be in the 70th percentile of their applicant pool to be accepted. Based on the SAT, 70th perentile is an 1130. Therefore, a qualified candidate for Northwestern will score an 1130 or above for the two categories (rank + SAT's)." </p>
<p>But Northwestern (or any other selective school) does not simply rank their applicants by test scores & GPA, accepting those at the top. Your model of how admissions works bears a weak relationship to reality. Scores and class ranking are the factors that are weighed by adcoms which is far different from the deterministic role your model assigns them. If you looked at the acceptance rate against SAT, for example, you'd find a rising percentage as the SAT score rises. But not all 1500's get in, nor do all 1100's get rejected.</p>
<p>2) The most fundamental flaw is you've used the wrong table!! Your top 30% percentile number comes from SAT percentiles nationally. Even if Northwestern accepts the top 30% of its applicants based solely on SAT and ranking, that would be based on the population of kids applying to the school. Your number, 1130, is not what it takes to be in the top 30% of Northwestern applicants. Northwestern does not randomly draw from all HS students (which is the only way your number would make sense), so the top 30% of applicants have a SAT score substantially higher than 1130. If you checked the common data set info for Northwestern, you'd find that the 25th percentile of enrolled students is an SAT score of 1310 which should have warned you of serious deficiencies in your approach. </p>
<p>3) The same criticism holds about your model that holds in psychology, econ, and so many other disciplines that try to follow the model of hard sciences (or statistics). Your model ignores what it cannot measure. Admission to a competitive college depends on SAT and class rank, yes, but it also depends heavily on essays, ECs, teacher recs, and sometimes interviews. You mention as an aside that predictions from your model are reliable "as long as his EC's are not particularly dismal" but this completely ignores several important factors in admissions, and downplays the importance of those aspects not easily measured.</p>
<p>My recommendation is to abandon the project.</p>