A dean of a business school has fit a regression model to predict college GPA ba
ID: 3259419 • Letter: A
Question
A dean of a business school has fit a regression model to predict college GPA based on a student's SAT score (SAT_Score), the percentile at which the student graduated high school (HS_Percentile) (for instance, graduating 4th in a class of 500 implies that 496 other students are at or below that student, so the percentile is 496/500 times 100 = 99), and the total college hours the student has accumulated (Total_Hours). The regression results are shown below. How would we interpret the coefficient for ''HS_Percentile'' in the context of the problem? Read carefully. The estimated mean GPA for a student with 0 total hours accumulated and a SAT score of 0 is 0.013 percentile rank points. For each one-point increase in high school percentile rank, we estimate that the mean GPA of students increases by about 0.013 points, holding Total_Hours and SAT_Score fixed. For each one-point increase in high school percentile rank, we estimate that the mean GPA of students increases by about 23.9 points. For each one-point Increase in high school percentile rank, wo estimate that the moan GPA of students increases by one point, holding Tota_Hours and SAT_Score fixed. For each one-point increase in high school percentile rank, we estimate that the mean GPA of students increases by about 0.0001 points, holding Tota_Hours and SAT_Score fixed. For each one-point increase in high school percentile rank, we estimate that the mean GPA of students increases by about 0.013 points.Explanation / Answer
In multiple regression, Y = a + b1x1 + b2x2 +b3x3 , we know the interpretation of slope as :
Interpretation of b1, if x1 increases by one unit, y will increase by b1 units ,assuming x2 and x3 are fixed.
Interpretation of b2, if x2 increases by one unit, y will increase by b2 units ,assuming x1 and x3 are fixed.
Interpretation of b3, if x3 increases by one unit, y will increase by b3 units ,assuming x1 and x2 are fixed.
Hence here interpretation slope b2 = 0.013 is given by ,
For each one -point increase in high school percentile rank, we estimate that the mean GPA of students increases by about 0.013 points, holding Total_Hours and SAT_Score fixed.