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
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.
Using the excel spreadsheet provided to you, do regression analysis to answer the following questions. Include a screenshot of the regression results you used to answer each question. You can type your answer and insert graphs right after each question. Please highlight it with different fonts or format so it can be easily identified by others.
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?
\begin{tabular}{|c|c|c|c|c|c|} \hline University & State & GraduationRate & %ofClassesUnder20 & Student-FacultyRatio & AlumniGivingRate \\ \hline Boston College & MA & 85 & 39 & 13 & 25 \\ \hline Brandeis University & MA & 79 & 68 & 8 & 33 \\ \hline Brown University & RI & 93 & 60 & 8 & 40 \\ \hline California Institute of Technology & CA & 85 & 65 & 3 & 46 \\ \hline Carnegie Mellon University & PA & 75 & 67 & 10 & 28 \\ \hline Case Western Reserve Univ. & OH & 72 & 52 & 8 & 31 \\ \hline College of William and Mary & VA & 89 & 45 & 12 & 27 \\ \hline Colvmbia University & NY & 90 & 69 & 7 & 31 \\ \hline Cornell University & NY & 91 & 72 & 13 & 35 \\ \hline Dartmouth College & NH & 94 & 61 & 10 & 53 \\ \hline Duke University & NC & 92 & 68 & 8 & 45 \\ \hline Emory University & GA & 84 & 65 & 7 & 37 \\ \hline Georgetown University & DC & 91 & 54 & 10 & 29 \\ \hline Harvard University & MA & 97 & 73 & 8 & 46 \\ \hline Johns Hopkins University & MD & 89 & 64 & 9 & 27 \\ \hline Lehigh University & PA & 81 & 55 & 11 & 40 \\ \hline Massachusetts Inst. of Technology & MA & 92 & 65 & 6 & 44 \\ \hline New York University & NY & 72 & 63 & 13 & 13 \\ \hline Northwestern University & II & 90 & 66 & 8 & 30 \\ \hline Pennsylvania State Univ. & PA & 80 & 32 & 19 & 21 \\ \hline Princeton University & NJ & 95 & 68 & 5 & 67 \\ \hline Rice University & TX & 92 & 62 & 8 & 40 \\ \hline Stanford University & CA & 92 & 69 & 7 & 34 \\ \hline Tufts University & MA & 87 & 67 & 9 & 29 \\ \hline Tulane University & LA & 72 & 56 & 12 & 17 \\ \hline U. of California-Berkeley & CA & 83 & 58 & 17 & 18 \\ \hline U. of California-Davis & CA & 74 & 32 & 19 & 7 \\ \hline U. of California-Irvine & CA & 74 & 42 & 20 & 9 \\ \hline U. of California-Los Angeles & CA & 78 & 41 & 18 & 13 \\ \hline U. of California-San Diego & CA & 80 & 48 & 19 & 8 \\ \hline U. of California-Santa Barbara & CA & 70 & 45 & 20 & 12 \\ \hline U. of Chicago & II & 84 & 65 & 4 & 36 \\ \hline U. of Florida & FL & 67 & 31 & 23 & 19 \\ \hline U. of Illinois-Urbana Champaign & II & 77 & 29 & 15 & 23 \\ \hline U. of Michigan-Ann Arbor & MI & 83 & 51 & 15 & 13 \\ \hline U. of North Carolina-Chapel Hill & NC & 82 & 40 & 16 & 26 \\ \hline U. of Notre Dame & N & 94 & 53 & 13 & 49 \\ \hline U. of Pennsylvania & PA & 90 & 65 & 7 & 41 \\ \hline U. of Rochester & NY & 76 & 63 & 10 & 23 \\ \hline U. of Southern California & CA & 70 & 53 & 13 & 22 \\ \hline U. of Texas-Austin & TX & 66 & 39 & 21 & 13 \\ \hline U. of Virginia & VA & 92 & 44 & 13 & 28 \\ \hline U. of Washington & WA & 70 & 37 & 12 & 12 \\ \hline U. of Wisconsin-Madison & WI & 73 & 37 & 13 & 13 \\ \hline Vanderbilt University & TN & 82 & 68 & 9 & 31 \\ \hline Wake Forest University & NC & 82 & 59 & 11 & 38 \\ \hline Washington University-St. Lovis & MO & 86 & 73 & 7 & 33 \\ \hline Yale University & CT & 94 & 77 & 7 & 50 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|} \hline University & State & GraduationRate & %ofClassesUnder20 & Student-FacultyRatio & AlumniGivingRate \\ \hline Boston College & MA & 85 & 39 & 13 & 25 \\ \hline Brandeis University & MA & 79 & 68 & 8 & 33 \\ \hline Brown University & RI & 93 & 60 & 8 & 40 \\ \hline California Institute of Technology & CA & 85 & 65 & 3 & 46 \\ \hline Carnegie Mellon University & PA & 75 & 67 & 10 & 28 \\ \hline Case Western Reserve Univ. & OH & 72 & 52 & 8 & 31 \\ \hline College of William and Mary & VA & 89 & 45 & 12 & 27 \\ \hline Colvmbia University & NY & 90 & 69 & 7 & 31 \\ \hline Cornell University & NY & 91 & 72 & 13 & 35 \\ \hline Dartmouth College & NH & 94 & 61 & 10 & 53 \\ \hline Duke University & NC & 92 & 68 & 8 & 45 \\ \hline Emory University & GA & 84 & 65 & 7 & 37 \\ \hline Georgetown University & DC & 91 & 54 & 10 & 29 \\ \hline Harvard University & MA & 97 & 73 & 8 & 46 \\ \hline Johns Hopkins University & MD & 89 & 64 & 9 & 27 \\ \hline Lehigh University & PA & 81 & 55 & 11 & 40 \\ \hline Massachusetts Inst. of Technology & MA & 92 & 65 & 6 & 44 \\ \hline New York University & NY & 72 & 63 & 13 & 13 \\ \hline Northwestern University & II & 90 & 66 & 8 & 30 \\ \hline Pennsylvania State Univ. & PA & 80 & 32 & 19 & 21 \\ \hline Princeton University & NJ & 95 & 68 & 5 & 67 \\ \hline Rice University & TX & 92 & 62 & 8 & 40 \\ \hline Stanford University & CA & 92 & 69 & 7 & 34 \\ \hline Tufts University & MA & 87 & 67 & 9 & 29 \\ \hline Tulane University & LA & 72 & 56 & 12 & 17 \\ \hline U. of California-Berkeley & CA & 83 & 58 & 17 & 18 \\ \hline U. of California-Davis & CA & 74 & 32 & 19 & 7 \\ \hline U. of California-Irvine & CA & 74 & 42 & 20 & 9 \\ \hline U. of California-Los Angeles & CA & 78 & 41 & 18 & 13 \\ \hline U. of California-San Diego & CA & 80 & 48 & 19 & 8 \\ \hline U. of California-Santa Barbara & CA & 70 & 45 & 20 & 12 \\ \hline U. of Chicago & II & 84 & 65 & 4 & 36 \\ \hline U. of Florida & FL & 67 & 31 & 23 & 19 \\ \hline U. of Illinois-Urbana Champaign & II & 77 & 29 & 15 & 23 \\ \hline U. of Michigan-Ann Arbor & MI & 83 & 51 & 15 & 13 \\ \hline U. of North Carolina-Chapel Hill & NC & 82 & 40 & 16 & 26 \\ \hline U. of Notre Dame & N & 94 & 53 & 13 & 49 \\ \hline U. of Pennsylvania & PA & 90 & 65 & 7 & 41 \\ \hline U. of Rochester & NY & 76 & 63 & 10 & 23 \\ \hline U. of Southern California & CA & 70 & 53 & 13 & 22 \\ \hline U. of Texas-Austin & TX & 66 & 39 & 21 & 13 \\ \hline U. of Virginia & VA & 92 & 44 & 13 & 28 \\ \hline U. of Washington & WA & 70 & 37 & 12 & 12 \\ \hline U. of Wisconsin-Madison & WI & 73 & 37 & 13 & 13 \\ \hline Vanderbilt University & TN & 82 & 68 & 9 & 31 \\ \hline Wake Forest University & NC & 82 & 59 & 11 & 38 \\ \hline Washington University-St. Lovis & MO & 86 & 73 & 7 & 33 \\ \hline Yale University & CT & 94 & 77 & 7 & 50 \\ \hline \end{tabular}
