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 x 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 1150, a high school percentile rank of 85, and total accumulated hours of 18? In the calculation and answer, use three decimal places.

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.53292259 0.284006487 0.283486772 0.557515239 4137 ANOVA df MS Regression Residual Total 3 509.5632077 169.8544 546.4662 4.0431E-299 41331284.632456 0.310823 41361794.195664 Intercept SAT Score HS Percentile Total Hours Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 0.042678049 0.070175203 -0.60816 0.5431120.18025921 0.094903113 0.0014913646.48677E-05 22.99086 3.6-1100.001364189 0.00161854 0.013087778 0.000548313 23.86919 4.5E-1180.01201279??? 0.001926045 0.000246629 7.809486 7.23E-15 0.001442519 0.00240957

Explanation / Answer

Y = -0.0427 + 1150*0.0015 + 85 * 0.01309 + 0.001926 * 18

Y = 2.830

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