An admissions counselor, examining the usefulness of x1 = total SAT score and x2 = high school class rank in predicting y = freshman grade point average (GPA) at her university, has collected the sample data shown here and listed in file XR16055. Rank in high school class is expressed as a cumulative percentile, i.e., 100.0% reflects the top of the class.

a. Determine the multiple regression equation and interpret the partial regression coefficients.
b. What is the estimated freshman GPA for a student who scored 1100 on the SAT exam and had a cumulative class rank of 80%?
c. Determine the 95% prediction interval for the GPA of the student described in part (b).
d. Determine the 95% confidence interval for the mean GPA of all students similar to the one described in part (b).
e. Determine the 95% confidence interval for the population partial regression coefficients, β1 and β2.
f. Interpret the significance tests in the computer printout.
g. Analyze the residuals. Does the analysis support the applicability of the multiple regression model to these data?

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High Freshman SAT, School Freshman SAT, School GPA T 2.66 1153 61.5 2.10 1086 84.5 3.33 114 92.0 3.85 1237 94.4 2.51 1205 89.5 3.22 1205 97.0 2.92 163 95.9 1.95 1121 64.1 Rank GPA Tl Rank 2.45 1136 45.5 2.50 966 60.2 2.29 1023 74.0 2.24 976 86.4 1.81 1066 73.0 2.99 1076 55.2 3.14 152 72.1 1.86 955 51.0 3