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

question 81

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 $\hat { \beta } _ { 1 } = 228$ .

• A) We estimate SALARY to increase \(\$ 228\) for every 1-point increase in GMAT.
• B) We expect to predict SALARY to within \(2 ( 228 ) = \$ 456\) of its true value using GMAT in a straight-line model.
• C) The value has no practical interpretation since a GMAT of 228 is nonsensical and outside the range of the sample data.
• D) We estimate GMAT to increase 228 points for every \(\$ 1\) increase in SALARY.

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