(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:

Standard Error

A statistical measure that estimates the accuracy of a sample mean by describing the dispersion of sample means around the population mean.

Sample Mean Difference

The difference between the mean values of two samples drawn from the same or different populations.

Population Means

The average value of a particular characteristic in the entire population.

Sampling Distribution

A sampling distribution is the probability distribution of a given statistic based on a random sample.