Question 1
A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables:
x1 = high school GPA
x2 = SAT score
The admissions officer believes the relationship between college GPA and high school GPA is linear and the relationship between SAT score and college GPA is linear. She also believes that the relationship between college GPA and high school GPA depends on the student's SAT score. Write the regression model she should fit.
Question 2
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below:
Least Squares Linear Regression of Salary
Predictor
Variables Coefficient Std Error T P
Constant
-687.851
165.406
4.16
0.0001
Tuition
-11.3197
2.19724
-5.15
0.0000
GMAT
-0.96727
0.25535
-3.79
0.0003
TxG
0.01850
0.00331
5.58
0.0000
R-Squared
0.7816
Resid. Mean Square (MSE)
301.251
Adjusted R-Squared
0.7723
Standard Deviation
17.3566
Source DF SS MS F P
Regression
3
76523.8
25510.9
84.68
0.0000
Residual
71
21388.8
301.3
Total
74
97921.7
Cases Included 75 Missing Cases 0
The global-f test statistic is shown on the printout to be the value F = 84.68. Interpret this value.
◦ There is insufficient evidence, at α = 0.05, to indicate that at least one of the variables proposed in the interaction model is useful at predicting the average starting salary of graduates of MBA programs.
◦ There is insufficient evidence, at α = 0.05, to indicate that the interaction between average tuition and average GMAT score is a useful predictor of the average starting salary of graduates of MBA programs.
◦ There is sufficient evidence, at α = 0.05, to indicate that at least one of the variables proposed in the interaction model is useful at predicting the average starting salary of graduates of MBA programs.
◦ There is sufficient evidence, at α = 0.05, to indicate that the interaction between average tuition and average GMAT score is a useful predictor of the average starting salary of graduates of MBA programs.
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