A dean of a business school has fit a regression model to predict college GPA ba

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. What would be the estimated mean GPA for a student with an SAT score of 1120, a high school percentile rank of 26, and total accumulated hours of 10? In the calculation and answer, use three decimal places.

Explanation / Answer

Here, fitted regression model is given by ,

GPA=-0.042678047+0.001491364*SAT_Score+0.013087778*HS_Percentile+0.001926045*Total_Hours

Here, we have to estimate mean of GPA for a student SAT_Score=1120,HS_Percentile=26,Total_Hours =10

Therefor ,

GPA=-0.042678047+0.001491364*1120+0.013087778*26+0.001926045*10

=1.987

Thus , estimated mean of GPA GPA for a student SAT_Score=1120,HS_Percentile=26,Total_Hours =10 is 1.987 .

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