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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
40
California Institute of Technology
65
3
46
Carnegie Mellon University
67
10
28
Case Western Reserve Univ.
52
31
College of William and Mary
45
12
27
Columbia University
69
7
Cornell University
72
35
Dartmouth College
61
53
Duke University
Emory University
37
Georgetown University
54
29
Harvard University
73
John Hopkins University
64
9
Lehigh University
55
11
Massachusetts Inst. of Technology
6
44
New York University
63
Northwestern University
66
30
Pennsylvania State Univ.
32
19
21
Princeton University
5
Rice University
62
Stanford University
34
Tufts University
Tulane University
56
17
U. of California-Berleley
58
18
U. of California-Davis
U. of California-Irvine
42
20
U. of California-Los Angeles
41
U. of California-San Diego
48
U. of California-Santa Barbara
U. of Chicago
4
36
U. of Florida
23
U. of Illinois-Urbana Champaign
15
U. of Michigan-Ann Arbor
51
U. of North Carolina-Chapel Hill
16
26
U. of Notre Dame
49
U. of Pennsylvania
U. of Rochester
U. of Southern California
22
U. of Texas-Austin
U. of Virginia
U. of Washington
U. of Wisconsin-Madison
Vanderbuilt University
Wake Forest University
59
38
Washington University-St. Louis
Yale University
77
50
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