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

question 80

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. $$\begin{array} { l l l l r } & \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \\\text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \\\text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \\\text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \\\text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \\\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \\\text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \\\text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \\\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \\\text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \\\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \\\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \\\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \\\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \\\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \\\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \\\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \\\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \\\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \\\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \\\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \\\text { 21. } & \text { USC } & 31.9 & 49,080 \\\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,900 \\\text { 23. } & \text { Georgetown } & 617 & 31.7 & 499\end{array}$$ 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 $r ^ { 2 } = .66$ .

• A) We estimate SALARY to increase \(\$ .66\) for every 1-point increase in GMAT.
• B) We can predict SALARY correctly \(66 \%\) of the time using GMAT in a straight-line model.
• C) \(66 \%\) of the sample variation in SALARY can be explained by using GMAT in a straight-line model.
• D) We expect to predict SALARY to within \(2 ( \sqrt { .66 } )\) of its true value using GMAT in a straight-line model.

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Definitions:

Binocular Cue

A visual signal that requires the coordination of both eyes to perceive depth and distance.

Three Dimensions

Usually refers to the three physical dimensions in which objects exist and move: height, width, and depth.

Distance Judgments

Distance judgments refer to the ability and the process by which individuals assess or estimate the distance of objects from themselves or other reference points.

Horizontal-Vertical Illusion

A visual illusion where horizontal segments appear longer than vertical segments of the same length due to perceptual biases.