Each year U.S. News & World Report conducts its
"Survey of America's Best Graduate and Professional Schools." The
top 25 business schools in 1991, 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 | 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 | 55,269 |
7 | Duke | 630 | 18.2 | 53,300 |
8 | Dartmouth | 649 | 13.4 | 52,000 |
9 | Virginia | 630 | 23 | 55,269 |
10 | Michigan | 620 | 32.4 | 53.3 |
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 | 44,119 |
19 | NYU | 610 | 35 | 53,161 |
20 | Puru | 595 | 26.8 | 43,500 |
21 | USC | 610 | 31.9 | 49,080 |
22 | Pittsburgh | 605 | 33 | 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.
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b0 = -92040 b1 = 228
R2 = .66
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For the situation above, give a practical interpretation of the
estimated slope.
We estimate GMAT to increase 228 points for every $1 increase in SALARY. |
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We estimate SALARY to increase $228 for every 1-point increase in GMAT. |
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The value has no practical interpretation since a GMAT of 228 is nonsensical and outside the range of the sample data. |
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We expect to predict SALARY to within 2(228) = $456 of its true value using GMAT in a straight-line model. |
slope= 228
y intercept =-92040
Therefore, regression equation is ,
Salary = 228*GMAT -92040
Option B) is correct.
We estimate SALARY to increase $228 for every 1-point increase in GMAT.
Each year U.S. News & World Report conducts its "Survey of America's Best Graduate and Professional...