This case study involves Alumni, which are an important source of revenue for co

Question

This case study involves Alumni, which are an important source of revenue for colleges and universities. If administrators could determine the factors that influence increases in the percentage of alumni who make a donation (alumni giving rate), they might be able to implement policies that could lead to increased revenue. 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 managerial report should contain such as:

1. Run the simple linear regression analysis to develop an estimated equation that could be used to predict the alumni-giving rate by choosing graduation rate, % of classes under 20 students, or student/faculty ratio as the independent variable. Indicate the one with the highest R 2 .

2. Use the multiple linear regression analysis to develop an estimated regression equation that could be used to predict the alumni-giving rate given the graduation rate, % of classes under 20 students, and the student-faculty ratio. Is it a better fit compared with your answer in (1)? Any multicollinearity exists? Please show the correlation coefficients to comment.

3. What conclusion and recommendation can you derive from F and t tests in (2)?

4. With the multiple linear regression equation in (2), what will be the alumni-giving rate with the graduation rate as 85%, 60% of classes with fewer than 20 students, and student-faculty ratio as 12?

5. Any possible modification you suggest for a better-fit multiple linear regression model? Adding or dropping independent variable(s)? Change to any nonlinear model? Explain your suggestion.

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

Explanation / Answer

A. The two regression models are

Alumni Giving Rate (%) = - 62.9 + 0.898 Graduation Rate (%) + 0.316 % of Classes Under 20; with R-Sq = 63.5%

Alumni Giving Rate (%) = - 19.1 + 0.756 Graduation Rate (%) - 1.25 Student/Faculty Ratio with R-Sq = 70.0%

So will choose second model

B. The multiple linear regression equation is

Alumni Giving Rate (%) = - 20.7 + 0.748 Graduation Rate (%) + 0.029 % of Classes Under 20 - 1.19 Student/Faculty Ratio

Model 2 results for Collinearity Statistics

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

95% Confidence Interval for B

Collinearity Statistics

B

Std. Error

Beta

Lower Bound

Upper Bound

Tolerance

VIF

1

(Constant)

-19.106

15.550

-1.229

.226

-50.426

12.213

Graduation Rate

.756

.160

.484

4.717

.000

.433

1.078

.634

1.577

Student/Faculty Ratio

-1.246

.284

-.450

-4.382

.000

-1.819

-.673

.634

1.577

a. Dependent Variable: Alumni Giving Rate

Model 3 results for Collinearity Statistics

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

95% Confidence Interval for B

Collinearity Statistics

B

Std. Error

Beta

Lower Bound

Upper Bound

Tolerance

VIF

1

(Constant)

-20.720

17.521

-1.183

.243

-56.032

14.592

Graduation Rate

.748

.166

.479

4.508

.000

.414

1.083

.604

1.656

Student/Faculty Ratio

-1.192

.387

-.430

-3.082

.004

-1.971

-.413

.350

2.856

Classes Under 20

.029

.139

.029

.208

.836

-.252

.310

.365

2.742

a. Dependent Variable: Alumni Giving Rate

Since the Tolerance in above tables is greater than 0.20 which is considered as multi-collinearly does exist in the data. Comparative to all three model multiple regression model has the least collinearty.

C. There is the significant impacts of independent variables on Alumni Giving Rate

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

5941.015

2

2970.508

52.411

.000a

Residual

2550.464

45

56.677

Total

8491.479

47

a. Predictors: (Constant), Student/Faculty Ratio, Graduation Rate

b. Dependent Variable: Alumni Giving Rate

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

5943.531

3

1981.177

34.213

.000a

Residual

2547.948

44

57.908

Total

8491.479

47

a. Predictors: (Constant), Student/Faculty Ratio, Graduation Rate, Student/Faculty Ratio

b. Dependent Variable: Alumni Giving Rate

D Alumni Giving Rate (%) = - 20.7 + 0.748 * 85 (%) + 0.029 * 60% - 1.19 *12 = 30.34

E No I think the model is best fit with the above variables. No need to drop or add the data

Model 2 results for Collinearity Statistics

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

95% Confidence Interval for B

Collinearity Statistics

B

Std. Error

Beta

Lower Bound

Upper Bound

Tolerance

VIF

1

(Constant)

-19.106

15.550

-1.229

.226

-50.426

12.213

Graduation Rate

.756

.160

.484

4.717

.000

.433

1.078

.634

1.577

Student/Faculty Ratio

-1.246

.284

-.450

-4.382

.000

-1.819

-.673

.634

1.577

a. Dependent Variable: Alumni Giving Rate

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.