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 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 15.13 shows data for 48 national universities (America’s Best Colleges, Year 2000 Edition). The column labeled Graduation Rate is the percentage of students who initially enrolled at the university and graduated. 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 university.

University 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 Univ. 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 Johns 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 Univ. 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–Berkeley 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 Vanderbilt 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
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? Please show most of your work using Excel Data Analysis Toolpak.

Answer 1

1) summary :-

we use excel command to find summary as,

2) simple regression for dependent variable alumni giving rate and independent variable graduation rate

H0 : alumni giving rate independ on graduation rate.

H1: alumni giving rate depends on graduation rate.

Decision rule :-

i) if F calculated < Fcritical then accept null hypothesis H0 at level of significance 0.05

ii) if F calculated > Fcritical then reject  null hypothesis H0 at level of significance 0.05

Result :-

  F calculated (61.3388)> Fsignificant(5.23818E-10)

then reject null hypothesis H0 at level of significance 0.05

Interpritation :- alumni giving rate depends on graduation rate.

3) to 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.

H0 :  graduation rate % of class under 20 and student/ faculty ratio does not affect on Alumini giving rate

H1: graduation rate % of class under 20 and student /faculty ratio does not affect on Alumini giving rate

the table is ,

for the model, from decision rule

Result :

F calculated (34.21255)> Fsignificant(1.43233E-11)  

then reject null hypothesis H0 at level of significance 0.05

Conclusion :-

graduation rate % of class under 20 and student /faculty ratio does not affect on Alumini giving rate

4) 5) adjusted R² of first simple regression model = 0.5621344

adjusted R² of second multiple regression model = 0.679482

here, adjusted R² (0.679482) > adjusted R² ( 0.5621344)

Conclusion :- the second model is good