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 State Rate % of Classes Under 20 Student/ Alumni Faculty Ratio Giving Rate Boston College MA Brandeis University MA Brown University RI California Institute of CA 5225 85 39 13 79 68 93 60 85 65 Technology Carnegie Mellon University PA 75 Case Western Reserve Univ. OH 72 College of William and Mary 89 Columbia University NY 90 Comell University NY 91 Dartmouth College NH 94 Duke University NC 92 Emory University GA 84 1246265 67 69 72 68 234 3883 08273018T 25 33 40 46 28 31 27 31 35 53 45 37 (Continued) % of Graduation Student/ Alumni Classes Faculty Giving State Rate Under 20 Ratio Rate Georgetown University DC 91 Harvard University MA 97 Johns Hopkins University MD 89 Lehigh University PA 81 Massachusetts Institute MA 92 13155 54 73 64 11 65 08816 B 9 24444 29 46 27 40 of Technology New York University NY 72 Northwestern University IL Pennsylvania State Univ. PA Princeton University NJ Rice University TX Stanford University CA Tufts University MA Tulane University LA University of CA 2282228 63 90 66 80 32 95 68 92 62 92 69 87 67 72 56 83 58 17 38658927 13 13 30 19 21 67 40 34 29 12 17 18 California-Berkeley University of California-Davis University of California-Irvine CA University of California- CA 333 CA 778 74 74 274 32 19 42 41 1280 13 763 9 Los Angeles University of California- San Diego Unimity of California CA 80 80 48 19 8 CA 70 ΛΕ 20 12 San Diego University of California- Santa Barbara CA 70 70 55 45 20 20 12 12 University of Chicago IL University of Florida FL 45 84 67 University of Illinois- IL 77 Urbana Champaign University of Michigan- MI Ann Arbor University of North NC Carolina-Chapel Hill University of Notre Dame IN University of Pennsylvania PA University of Rochester NY University of Southern Califomia CA University of Texas-Austin TX University of Virginia VA University of Washington University of WI Wisconsin-Madison Vanderbilt University Wake Forest University Washington University- St. Louis Yale University 토일 김삼중 스승들도 주문을 하 83 33 51 425 65 36 31 23 19 29 15 23 15 13 32 82 40 40 16 16 26 26 94 2200 53 90 65 76 63 70 53 3703 13 49 10 13 WA 1203 66 92 70 73 3433 39 21 44 13 37 12 37 13 2323 13 TN NC MO 8888 82 68 82 86 883 59 11 73 916 31 38 33 EN 222 223 41 23 22 13 28 12 CT 14 94 77 7 50 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?