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

question 63

Multiple Choice

(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. $\begin{array}{lllll} & \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \\ \hline\text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \\ \text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \\ \text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \\ \text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \\ \text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \\ \text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \\ \text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \\ \text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \\ \text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \\ \text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \\ \text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \\ \text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \\ \text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \\ \text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \\ \text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \\ \text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \\ \text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \\ \text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \\ \text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \\ \text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \\ \text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \\ \text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \\ \text { 23. } & \text { Georgetown } & 617 & 31.7 & 45,156 \\ \text { 24. } & \text { Maryland } & 593 & 28.1 & 42,925 \\ \text { 25. } & \text { Rochester } & 605 & 35.9 & 44,499\end{array}$ 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, give a practical interpretation of $r = .81$

• A) 81% of the sample variation in SALARY can be explained by using GMAT in a straight-line model.
• B) We estimate SALARY to increase 81% for every 1-point increase in GMAT.
• C) We can predict SALARY correctly 81% of the time using GMAT in a straight-line model.
• D) There appears to be a positive correlation between SALARY and GMAT.

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