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 68, and total accumulated hours of 78? In the calculation and answer, use three decimal places.

Explanation / Answer

The regression equation is:

y = -0.042678047 + 0.001491364 x1 + 0.013087778 x2 + 0.001926045 x3

For x1 = 1120, x2 = 68, x3 = 78,

y = -0.042678047 + 0.001491364 (1120) + 0.013087778 (68) + 0.001926045 (78)

y = 2.668

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