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. Send the output to Cell H90. 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% 

Questions:

1.Do you think this model is good?That is, do you see an evidence of relationship? Pick the right option.(Strong/Strong Positive/Weak/None)

2. What proportion of the variation in Alumni giving is explained by the three variables?

4.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?I got 47.3331%

5.Find the alumni giving rate for Carnegie-Mellon from the table.Compare this to your results in Q4.What is the residual (error)? Based on above I got: 0.1933

Regression Output                  SUMMARY OUTPUT Regression Statistics Multiple R 0.836624531 R Square 0.699940606 Adjusted R Square 0.679482011 Standard Error 0.076097248 Observations 48 ANOVA  df SS MS F Significance F Regression 3 0.59435311 0.198117702 34.21254509 1.4323E-11 Residual 44 0.25479481 0.005790791 Total 47 0.84914792     Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.207201343 0.17521365 -1.18256393 0.243333057 -0.5603213 0.14591857 -0.5603213 0.145918566 Graduation Rate 0.007481828 0.0016596 4.508212716 4.799E-05 0.00413712 0.01082653 0.0041371 0.010826531 % of Classes Under 20 0.000290406 0.00139321 0.208443674 0.835844489 -0.0025174 0.00309824 -0.0025174 0.003098243 Student / Faculty Ratio -0.011920107 0.00386723 -3.08233638 0.003538403 -0.019714 -0.00412621 -0.019714 -0.00412621 RESIDUAL OUTPUT Observation Predicted Alumni Giving Rate Residuals 1 0.285118499 -0.0351185 2 0.308249853 0.02175015 3 0.410672194 -0.01067219 4 0.411870137 0.04812986 5 0.254191921 0.02580808 6 0.251230554 0.05876945 7 0.328708357 -0.05870836 8 0.402760475 -0.09276047 9 0.339592881 0.01040712 10 0.394604214 0.13539579 11 0.405513617 0.04448638 12 0.356707881 0.01329212 13 0.370125885 -0.08012588 14 0.44437479 0.01562521 15 0.369986401 -0.0999864 16 0.283677904 0.1163221 17 0.428482612 0.01151739 18 0.19482449 -0.06482449 19 0.389969148 -0.08996915 20 0.174155872 0.03584413 21 0.463719422 0.20628058 22 0.403771179 -0.00377118 23 0.417724131 -0.07772413 24 0.355893964 -0.06589396 25 0.204711752 -0.03471175 26 0.227992138 -0.04799214 27 0.129264904 -0.0592649 28 0.120248862 -0.03024886 29 0.173725981 -0.04372598 30 0.178802375 -0.09880238 31 0.091192769 0.02880723 32 0.392468202 -0.0324682 33 0.028921274 0.16107873 34 0.198519596 0.0314804 35 0.249799507 -0.11979951 36 0.2272031 0.0327969 37 0.356520641 0.13347936 38 0.401598849 0.00840115 39 0.260512123 -0.03051212 40 0.17695677 0.04304323 41 0.047602911 0.08239709 42 0.338943327 -0.05894333 43 0.184230373 -0.06423037 44 0.19475575 -0.06475575 45 0.318775231 -0.00877523 46 0.292321358 0.08767864 47 0.373994789 -0.04399479 48 0.435011039 0.06498896