Author Question: (Situation P) Below are the results of a survey of America's best graduate and professional schools. ... (Read 53 times)

pragya sharda · **on:** Feb 14, 2020

(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.

School

GMAT

Acc. Rate

Salary

1.

Harvard

644

15.0% $

63,000

2.

Stanford

665

10.2

60,000

3.

Penn

644

19.4

55,000

4.

Northwestern

640

22.6

54,000

5.

MIT

650

21.3

57,000

6.

Chicago

632

30.0

55,269

7.

Duke

630

18.2

53,300

8.

Dartmouth

649

13.4

52,000

9.

Virginia

630

23.0

55,269

10.

Michigan

620

32.4

53.300

11.

Columbia

635

37.1

52,000

12.

Cornell

648

14.9

50,700

13.

CMU

630

31.2

52,050

14.

UNC

625

15.4

50,800

15.

Cal-Berkeley

634

24.7

50,000

16.

UCLA

640

20.7

51,494

17.

Texas

612

28.1

43,985

18.

Indiana

600

29.0

44,119

19.

NYU

610

35.0

53,161

20.

Purdue

595

26.8

43,500

21.

USC

610

31.9

49,080

22.

Pittsburgh

605

33.0

43,500

23.

Georgetown

617

31.7

45,156

24.

Maryland

593

28.1

42,925

25.

Rochester

605

35.9

44,499

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.
-----------------------------------------------------------------------
β₀ = -92040

1 = 228 s = 3213 r² = .66 r = .81 df = 23 t = 6.67
-----------------------------------------------------------------------

For the situation above, give a practical interpretation of r = .81.
◦ We can predict SALARY correctly 81% of the time using GMAT in a straight-line model.
◦ We estimate SALARY to increase 81% for every 1-point increase in GMAT.
◦ 81% of the sample variation in SALARY can be explained by using GMAT in a straight-line model.
◦ There appears to be a positive correlation between SALARY and GMAT.

wergv · **Reply #1 on:** Feb 14, 2020

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