(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. \[\begin{array} { l l l l r }
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
\text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \
\text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \
\text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \
\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \
\text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \
\text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \
\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \
\text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \
\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \
\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \
\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
\text { 23. } & \text { Georgetown } & 617 & 31.7 & 456 \
\text { 24. } & \text { Maryland } & 593 & 28.1 & 499
\end{array}\]
The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using the 25 data points in the table are shown below. $$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, which of the following is not an assumption required for the simple linear regression analysis to be valid?
A) The errors of predicting SALARY have a mean of 0.
B) SALARY is independent of GMAT.
C) The errors of predicting SALARY have a variance that is constant for any given value of GMAT.
D) The errors of predicting SALARY are normally distributed.

Question

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. \[\begin{array} { l l l l r } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
\text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \
\text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \
\text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \
\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \
\text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \
\text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \
\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \
\text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \
\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \
\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \
\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
\text { 23. } & \text { Georgetown } & 617 & 31.7 & 456 \
\text { 24. } & \text { Maryland } & 593 & 28.1 & 499
\end{array}\] 
The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using the 25 data points in the table are shown below. $$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, which of the following is not an assumption required for the simple linear regression analysis to be valid?
A) The errors of predicting SALARY have a mean of 0.
B) SALARY is independent of GMAT.
C) The errors of predicting SALARY have a variance that is constant for any given value of GMAT.
D) The errors of predicting SALARY are normally distributed.

Quizplus · Accepted Answer

The assumption that SALARY is independent of GMAT is not required for simple linear regression. In fact, the purpose of regression is to model the relationship between the dependent variable (SALARY) and the independent variable (GMAT).

(Situation P) Below Are the Results of a Survey of America's