Question

Alumni donations are an important source of revenue for college and universities. If administrators could determine the factors that could lead to increases in thepercentage 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 moresatisfied 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 mightlead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. Table 15.13 shows data for48 national universities (America’s Best Colleges, Year 2000 Edition). The column labeled Graduation Rate is the percentage of students who initially enrolled at theuniversity and graduated. The column labeled % of Classes Under 20 shows the percentage of classes offered with fewer than 20 students. The column labeledStudent-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 ofalumni that made a donation to the university.

School State Graduation Rate % of Classes Under 20 Student/Faculty Ratio Alumni Giving Rate
Boston College MA 85 39 13 25
Brandeis University MA 79 68 8 33
Brown University RI 93 60 8 40
California Institute of Technology CA 85 65 3 46
Carnegie Mellon University PA 75 67 10 28
Case Western Reserve University OH 72 52 8 31
College of William and Mary VA 89 45 12 27
Columbia University NY 90 69 7 31
Cornell University NY 91 72 13 35
Dartmouth College NH 94 61 10 53
Duke University NC 92 68 8 45
Emory University GA 84 65 7 37
Georgetown University DC 91 54 10 29
Harvard University MA 97 73 8 46
John Hopkins University MD 89 64 9 27
Lehigh University PA 81 55 11 40
Massachusetts Inst. of Technology MA 92 65 6 44
New York University NY 72 63 13 13
Northwestern University IL 90 66 8 30
Pennsylvania State University PA 80 32 19 21
Princeton University NJ 95 68 5 67
Rice University TX 92 62 8 40
Stanford University CA 92 69 7 34
Tufts University MA 87 67 9 29
Tulane University LA 72 56 12 17
U. of California-Berleley CA 83 58 17 18
U. of California-Davis CA 74 32 19 7
U. of California-Irvine CA 74 42 20 9
U. of California-Los Angeles CA 78 41 18 13
U. of California-San Diego CA 80 48 19 8
U. of California-Santa Barbara CA 70 45 20 12
U. of Chicago IL 84 65 4 36
U. of Florida FL 67 31 23 19
U. of Illinois-Urbana Champaign IL 77 29 15 23
U. of Michigan-Ann Arbor MI 83 51 15 13
U. of North Carolina-Chapel Hill NC 82 40 16 26
U. of Notre Dame IN 94 53 13 49
U. of Pennsylvania PA 90 65 7 41
U. of Rochester NY 76 63 10 23
U. of Southern California CA 70 53 13 22
U. of Texas-Austin TX 66 39 21 13
U. of Virginia VA 92 44 13 28
U. of Washington WA 70 37 12 12
U. of Wisconsin-Madison WI 73 37 13 13
Vanderbuilt University TN 82 68 9 31
Wake Forest University NC 82 59 11 38
Washington University - St. Louis MO 86 73 7 33
Yale University CT 94 77 7 50


Use regression analysis to develop an estimated regression equation that could be used to predict the alumni giving rate given graduation rate of students, percentageof classes with fewer than 20 students, and given the student-faculty ratio. Which of the three estimated regression equations provides the best fit? For thisestimated regression equation, perform and analysis of the residuals and discuss your findings and conclusions. What conclusions and recommendations can you derivefrom your analysis?

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.83644743
R Square	0.69964431
Adjusted R Square	0.68629516
Standard Error	7.52841155
Observations	48
ANOVA
	df	SS	MS	F	Significance F
Regression	2	5941.015045	2970.51	52.41118171	-
Residual	45	2550.464122	56.677
Total	47	8491.479167
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-19.1063129	15.55005873	-1.2287	0.225572429	-50.4257389	12.2131131	-50.4257389	12.2131131
Graduation Rate	0.75573539	0.160225775	4.71669	2.34782E-05	0.433024117	1.07844667	0.43302412	1.07844667
Student/Faculty Ratio	-1.24595353	0.284302295	-4.3825	6.95424E-05	-1.81856775	-0.67333932	-1.81856775	-0.67333932
y = -19.1063 + .7557 Graduation Rate – 1.2460 Student/Faculty Ratio
Increase the percentage of students that enroll as well as graduate. Decrease the student &faculty ratio.