Question

It is not uncommon to see that alumni often give back to their schools. The question is, what factors influence their gratitude and goodwill and play an important role in them deciding how much to contribute? A sample of some top universities has been analyzed to determine if there is a relationship between the Alumni Giving rate (percentage of alumni who give) and factors like Graduation rate (percentage), % of class Under 20, and Student / Faculty ratio. Run a regression model to determine the relationship.  Answer the following questions based on the Excel table.    

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%
1.  Do you think this model is good?  That is, do you see an evidence of relationship? Pick the right option.  
2. What proportion of the variation in Alumni giving is explained by the three variables?
3. Suggest 2 variables (reasons) not in the table that can also be affecting the alumni giving rate.   
3. The coefficient for student / faculty ratio is negative in Excel output.  Give a reason as to why this is the case.  
5.  Find the alumni giving rate for Carnegie-Mellon from the table.  Compare this to your results in Q4.  What is the residual (error)?  

Answer 1

Answer:

Hello,

Let us run the regression the Excel, and following is output of the regression analysis,

Regression Statistics
Multiple R	0.836624531
R Square	0.699940606
Adjusted R Square	0.679482011
Standard Error	7.609724781
Observations	48

	df	SS	MS	F	Significance F
Regression	3	5943.531072	1981.177	34.21255	1.43E-11
Residual	44	2547.948094	57.90791
Total	47	8491.479167

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-20.72013433	17.52136501	-1.18256	0.243333	-56.0321	14.59186	-56.0321	14.59186
Graduation Rate	0.748182799	0.165959959	4.508213	4.8E-05	0.413712	1.082653	0.413712	1.082653
% of Classes Under 20	0.029040648	0.139321322	0.208444	0.835844	-0.25174	0.309824	-0.25174	0.309824
Student / Faculty Ratio	-1.192010694	0.386723104	-3.08234	0.003538	-1.9714	-0.41262	-1.9714	-0.41262

1. Do you think this model is good? That is, do you see an evidence of relationship?

-------- yes, in the ANOVA tables p-value is significant, so the model is good

2. What proportion of the variation in Alumni giving is explained by the three variables?   Can you suggest 2 factors that might be affecting alumni giving in real life but are't in the table? ---------- R-square value is 0.6999 i.e. approximatlly 0.70 variation is explained by three variables. we can suggest extra variable like income of students family and number of collages in the states. 3. The coefficient for student / faculty ratio is negative in Excel output. Explain. -------- the ration is negative means that if the faculty ratio in increases then the Alumni decreses. 4. If a university Carnegie-Mellon, (my school) has a graduation rate of 75, has 67% of the class under 20, and has a student / faculty ratio of 10, what percentage of the alumni will give money to university endowment as predicted by this model?   y=-20.72+(0.74*75)+(0.029*67)-(1.192*10) y=24.8

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