Suppose we collect the following information from a large number of junior and s
ID: 1168687 • Letter: S
Question
Suppose we collect the following information from a large number of junior and senior level college students:
Y = GPA in college (on a 4.0 scale)
X1 = Percentile in high school graduating class (for example, X1= 10 means the student was in
top 10% of class, X1= 90 means the student was in top 90% or bottom 10%, and so on)
X2 = SAT score (combined Math and Verbal scores out of 1600)
When we estimate the regression we come up with the following equation:
yˆ 1.4 .014x1 .0015x2
(4 points) Give specific interpretations for the coefficients in the model, and discuss whether or not they make sense.
(2 points) Based on this equation, what college GPA would you predict for Toby, a 6th year senior who loves to play hacky sack in the quad (by himself), was at the 20th percentile of his high school class, and scored 1100 on his SAT exam?
(4 points) Suppose two students finished high school with the same grades (so they were at the same percentile in their class). If the first student scored 180 points higher on her SAT, what is the predicted difference in college GPA for these two students? How much difference would there need to be in SAT score for you to predict a difference in GPA of 0.5? Do these predictions seem reasonable to you?
Explanation / Answer
a) GPA in college of a student will be positively affected by X1 and X2 . Thus the coefficient sign of these variables will be positive. If we control for X2 then if X1 increase by 1 then Y will increase by 0.014 Similarly controlling for X1, if X2 increases by 1 then Y will increase by 0.0015.
b) Y = 1.4 + 0.014(20) + 0.0015(1100) = 3.33
C) Predicted difference will be = 0.0015(180) = 0.27
The difference in sat score for predicted difference to be 0.5;
0.5 = 0.0015(sat score difference)
SAT score difference = 333.33
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