• There is at present a debate among educators and policymakers about the use of aptitude and achievement tests as part of college admissions. Some say aptitude tests should be used because they are minimally influenced by formal education. Others say that achievement tests should be used because they show what people actually know or can do. There are many complicated arguments that have some merit on both sides. Let's set all that to one side for a moment and think about the utility of such measures for a moment. Suppose what we want to do is to make good admissions decisions in the sense that we want to maximize our prediction of achievement in college from what we know from the end of high school in the area of mathematics.

  Let’s admit people to use Scholastic Aptitude Test SATQ (quantitative or math aptitude), and scores on a math College Level Examination Program CLEP test (math achievement) and we look at grades in the standard first-year math sequence (differential and integral calculus).

  a) What is the prediction model of math grades from the two tests

  b) If SATQ is taken out from CLEP and GPA then there is no correlation between GPA and CLEP remaining. Prove this.

  c) Once we know CLEP scores, there is no need to know SATQ or SATQ will add nothing to the prediction of GPA once we know CLEP. This means that the only part of SATQ which is helping in predicting GPA is because of variation in CLEP. If CLEP variation in SATQ is held constant, then SATQ is powerless to predict GPA. Prove this. The dataset is as follows:

   

• 
  
  • 
    

SATQ CLEP 500 30 550 32 450 28 400 25 600 32 650 38 700 39 550 38 650 38 700 39 550 38 650 35 550 31 GPA 2.8 3.0 2.9 2.8 3.3 3.3 3.5 3.7 3.3 3.5 3.7 3.4 2.9