An admissions counselor, examining the usefulness of x1 5 total SAT score and x2 5 high school class rank in predicting y 5 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.
High High
Freshman SAT, School Freshman SAT, School
|
GPA
|
Total
|
Rank
|
GPA
|
Total
|
Rank
|
|
2.66
|
1153
|
61.5
|
2.45
|
1136
|
45.5
|
|
2.10
|
1086
|
84.5
|
2.50
|
966
|
60.2
|
|
3.33
|
1141
|
92.0
|
2.29
|
1023
|
74.0
|
|
3.85
|
1237
|
94.4
|
2.24
|
976
|
86.4
|
|
2.51
|
1205
|
89.5
|
1.81
|
1066
|
73.0
|
|
3.22
|
1205
|
97.0
|
2.99
|
1076
|
55.2
|
|
2.92
|
1163
|
95.9
|
3.14
|
1152
|
72.1
|
|
1.95
|
1121
|
64.1
|
1.86
|
955
|
51.0
|
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 cumu- lative 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, /31 and/32.
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?