CASE PROBLEM ALUMNI GIVING Alumni donations are an important source of revenue for colleges and universities. If administrators could determine the factors that could lead to 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. The following table shows data for 48 national universities. The Graduation Rate column is the percentage of students who initially enrolled at the university and graduated. The % of Classes Under 20 column shows the percentages of classes with fewer than 20 students that are offered. The Student/Faculty Ratio column is the number of students enrolled divided by the total number of faculty. Finally, the Alumni Giving Rate column is the percentage of alumni who made a donation to the university Graduation Rate % of Classes Under 20 Student Faculty Ratio Alumni Giving Rate State MA MA RI CA 85 79 93 85 39 68 60 65 25 33 40 46 75 Boston College Brandeis University Brown University California Institute of Technology Carnegie Mellon University Case Western Reserve Univ. College of William and Mary Columbia University Comell University Dartmouth College Duke University Emory University 72 PA OH VA NY NY NH NC GA 89 90 91 94 92 84 67 52 45 69 72 61 68 65 10 8 12 7 13 10 8 7 28 31 27 31 35 53 45 37 (Continued) Graduation Rate % of Classes Under 20 Student Faculty Ratio Alumni Glving Rata State MA MD PA 91 97 89 81 92 54 73 64 55 65 10 B 9 11 6 29 46 27 40 44 72 NY IL PA Georgetown University Harvard University Johns Hopkins University Lehigh University Massachusetts Institute of Technology New York University Northwestern University Pennsylvania State Univ. Princeton University Rice University Stanford University Tufts University Tulane University University of California-Berkeley University of California-Davis University of California-Irvine University of California- Los Angeles University of California- San Diego University of California- 90 80 95 92 92 87 72 83 63 66 32 68 62 69 67 56 58 13 B 19 5 8 7 9 12 17 13 30 21 67 40 34 29 17 18 CA MA LA CA 7 CA CA 74 74 78 32 42 41 19 20 18 9 13 CA 80 48 19 8 CA 70 45 20 12 Managerial Report 1. Use methods of descriptive statistics to summarize the data. 2. Develop an estimated simple linear regression model that can be used to predict the alumni giving rate, given the graduation rate. Discuss your findings. 3. Develop an estimated multiple linear regression model that could be used to predict the alumni giving rate using the Graduation Rate, % of Classes Under 20, and Student/ Faculty Ratio as independent variables. Discuss your findings. 4. Based on the results in parts (2) and (3), do you believe another regression model may be more appropriate? Estimate this model, and discuss your results. 5. What conclusions and recommendations can you derive from your analysis? What universities are achieving a substantially higher alumni giving rate than would be expected, given their Graduation Rate, % of Classes Under 20, and Student/Faculty Ratio? What universities are achieving a substantially lower alumni giving rate than would be expected, given their Graduation Rate, % of Classes Under 20, and Student/ Faculty Ratio? What other independent variables could be included in the model