Alumni donations are an important source of revenue for colleges and universities. If administrators could determine the factors that influence increases in the percentage of alumni who make a donation, they might be able to implement policies that could lead to increased revenues. Research shows that students who are more satisfied with their contact with teachers are more likely to graduate. As a result, one might suspect that smaller class sizes and lower student-faculty ratios might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. Table 14.14 shows data for 48 national universities ( America's Best Colleges, Year 2000ed.). The column labeled % of Classes Under 20 shows the percentage of classes offered with fewer than 20 students. The column labeled Student/Faculty Ratio is the number of students enrolled divided by the total number of faculty. Finally, the column labeled Alumni Giving Rate is the percentage of alumni that made a donation to the universityp.664
1. Develop numerical and graphical summaries of the data.
2. Use regression analysis to develop an estimated regression equation that could be used to predict the alumni giving rate given the percentage of classes with fewer than20 students.
3. Use regression analysis to develop an estimated regression equation that could be used to predict the alumni giving rate given the student-faculty ratio.
4. Which of the two estimated regression equations provides the best fit? For this estimated regression equation, perform an analysis of the residuals and discuss your findings and conclusions.
5. What conclusions and recommendations can you derive from your analysis?
|
College
|
% of Classes Under 20
|
Student/Faculty Ratio
|
Alumni Giving Ratio
|
|
Boston College
|
39
|
13
|
25
|
|
Brandeis University
|
68
|
8
|
33
|
|
Brown University
|
60
|
8
|
40
|
|
California Institute of Technology
|
65
|
3
|
46
|
|
Carnegie Mellon University
|
67
|
10
|
28
|
|
Case Western Reserve Univ.
|
52
|
8
|
31
|
|
College of William and Mary
|
45
|
12
|
27
|
|
Columbia University
|
69
|
7
|
31
|
|
Cornell University
|
72
|
13
|
35
|
|
Dartmouth College
|
61
|
10
|
53
|
|
Duke University
|
68
|
8
|
45
|
|
Emory University
|
65
|
7
|
37
|
|
Georgetown University
|
54
|
10
|
29
|
|
Harvard University
|
73
|
8
|
46
|
|
John Hopkins University
|
64
|
9
|
27
|
|
Lehigh University
|
55
|
11
|
40
|
|
Massachusetts Inst. of Technology
|
65
|
6
|
44
|
|
New York University
|
63
|
13
|
13
|
|
Northwestern University
|
66
|
8
|
30
|
|
Pennsylvania State Univ.
|
32
|
19
|
21
|
|
Princeton University
|
68
|
5
|
67
|
|
Rice University
|
62
|
8
|
40
|
|
Stanford University
|
69
|
7
|
34
|
|
Tufts University
|
67
|
9
|
29
|
|
Tulane University
|
56
|
12
|
17
|
|
U. of California-Berleley
|
58
|
17
|
18
|
|
U. of California-Davis
|
32
|
19
|
7
|
|
U. of California-Irvine
|
42
|
20
|
9
|
|
U. of California-Los Angeles
|
41
|
18
|
13
|
|
U. of California-San Diego
|
48
|
19
|
8
|
|
U. of California-Santa Barbara
|
45
|
20
|
12
|
|
U. of Chicago
|
65
|
4
|
36
|
|
U. of Florida
|
31
|
23
|
19
|
|
U. of Illinois-Urbana Champaign
|
29
|
15
|
23
|
|
U. of Michigan-Ann Arbor
|
51
|
15
|
13
|
|
U. of North Carolina-Chapel Hill
|
40
|
16
|
26
|
|
U. of Notre Dame
|
53
|
13
|
49
|
|
U. of Pennsylvania
|
65
|
7
|
41
|
|
U. of Rochester
|
63
|
10
|
23
|
|
U. of Southern California
|
53
|
13
|
22
|
|
U. of Texas-Austin
|
39
|
21
|
13
|
|
U. of Virginia
|
44
|
13
|
28
|
|
U. of Washington
|
37
|
12
|
12
|
|
U. of Wisconsin-Madison
|
37
|
13
|
13
|
|
Vanderbuilt University
|
68
|
9
|
31
|
|
Wake Forest University
|
59
|
11
|
38
|
|
Washington University-St. Louis
|
73
|
7
|
33
|
|
Yale University
|
77
|
7
|
50
|