A university placement director is interested in the effect that grade point average (GPA) and the number of university activities listed on the résumé might have on the starting salaries of this year's graduating class. He has collected these data for a sample of 10 graduates:
| Graduate |
y = Starting Salary (Thousands) |
x1 = Grade Point Average |
x2 = Number of Activities |
| 1 |
$40 |
3.2 |
2 |
| 2 |
46 |
3.6 |
5 |
| 3 |
38 |
2.8 |
3 |
| 4 |
39 |
2.4 |
4 |
| 5 |
37 |
2.5 |
2 |
| 6 |
38 |
2.1 |
3 |
| 7 |
42 |
2.7 |
3 |
| 8 |
37 |
2.6 |
2 |
| 9 |
44 |
3 |
4 |
| 10 |
41 |
2.9 |
3 |
a. Determine the multiple regression equation and interpret the partial regression coefficients.
b. Dave has a 3.6 grade point average and 3 university activities listed on his résumé. What would be his estimated starting salary?
c. Determine the 95% prediction interval for the starting salary of the student described in part (b).
d. Determine the 95% confidence interval for the mean starting salary for all students like 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?