Regression Case

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AlumniGivinganswer.xlsx
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Sheet1

SUMMARY OUTPUT Observation Predicted Alumni Giving Rate Residuals
U. of Michigan–Ann Arbor 35 24.9304217272 -11.9304217272
Regression Statistics Johns Hopkins University 15 36.9405552787 -9.9405552787
Multiple R 0.8364474315 U. of California–San Diego 30 17.6794014195 -9.6794014195
R Square 0.6996443056 Columbia University 8 40.1881977359 -9.1881977359
Adjusted R Square 0.6862951636 Northwestern University 19 38.9422442039 -8.9422442039
Standard Error 7.528411551 Georgetown University 13 37.2060725332 -8.2060725332
Observations 48 Stanford University 23 41.6996685224 -7.6996685224
U. of Wisconsin–Madison 44 19.8649748585 -6.8649748585
ANOVA U. of Washington 43 18.8437222106 -6.8437222106
df SS MS F Significance F Tufts University 24 35.4290844921 -6.4290844921
Regression 2 5941.0150450392 2970.5075225196 52.4111817061 0 U. of Virginia 42 34.2239473306 -6.2239473306
Residual 45 2550.4641216275 56.6769804806 College of William and Mary 7 33.2026946827 -6.2026946827
Total 47 8491.4791666667 U. of California–Davis 27 13.1449890599 -6.1449890599
New York University 18 19.1092394652 -6.1092394652
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% U. of California–Berkeley 26 22.4385146632 -4.4385146632
Intercept -19.1063129345 15.5500587341 -1.2286971555 0.225572429 -50.4257389281 12.2131130591 -50.4257389281 12.2131130591 U. of California–Los Angeles 29 17.4138841649 -4.4138841649
Student-Faculty Ratio -1.245953532 0.2843022946 -4.3824955181 0.0000695424 -1.818567747 -0.6733393169 -1.818567747 -0.6733393169 Washington University–St. Louis 47 37.1652561628 -4.1652561628
Graduation Rate 0.7557353933 0.1602257747 4.7166905247 0.0000234782 0.4330241175 1.078446669 0.4330241175 1.078446669 Boston College 1 28.9337995777 -3.9337995777
U. of Chicago 32 39.3916459722 -3.3916459722
Tulane University 25 20.3551929972 -3.3551929972
U. of California–Irvine 28 11.8990355279 -2.8990355279
RESIDUAL OUTPUT U. of Rochester 39 25.8700416342 -2.8700416342
Brown University 3 41.2094503837 -1.2094503837
Observation Predicted Alumni Giving Rate Residuals Vanderbilt University 45 31.6504075258 -0.6504075258
1 28.9337995777 -3.9337995777 Rice University 22 40.4537149905 -0.4537149905
2 30.629154878 2.370845122 U. of Pennsylvania 38 40.1881977359 0.8118022641
3 41.2094503837 -1.2094503837 Massachusetts Inst. of Technology 17 42.9456220544 1.0543779456
4 41.3933348975 4.6066651025 Emory University 12 35.6537853763 1.3462146237
5 25.1143062409 2.8856937591 Cornell University 9 33.4682119373 1.5317880627
6 25.3390071251 5.6609928749 Harvard University 14 44.2323919568 1.7676080432
7 33.2026946827 -6.2026946827 Brandeis University 2 30.629154878 2.370845122
8 40.1881977359 -9.1881977359 U. of Illinois–Urbana Champaign 34 20.3960093676 2.6039906324
9 33.4682119373 1.5317880627 Carnegie Mellon University 5 25.1143062409 2.8856937591
10 39.473278713 13.526721287 U. of North Carolina–Chapel Hill 36 22.9287328019 3.0712671981
11 40.4537149905 4.5462850095 U. of California–Santa Barbara 31 8.8760939548 3.1239060452
12 35.6537853763 1.3462146237 Pennsylvania State Univ. 20 17.6794014195 3.3205985805
13 37.2060725332 -8.2060725332 U. of Southern California 40 17.5977686786 4.4022313214
14 44.2323919568 1.7676080432 Duke University 11 40.4537149905 4.5462850095
15 36.9405552787 -9.9405552787 California Institute of Technology 4 41.3933348975 4.6066651025
16 28.4027650686 11.5972349314 Case Western Reserve Univ. 6 25.3390071251 5.6609928749
17 42.9456220544 1.0543779456 Yale University 48 43.211139309 6.788860691
18 19.1092394652 -6.1092394652 U. of Texas–Austin 41 4.6071988497 8.3928011503
19 38.9422442039 -8.9422442039 Wake Forest University 46 29.1585004618 8.8414995382
20 17.6794014195 3.3205985805 Lehigh University 16 28.4027650686 11.5972349314
21 46.4587817662 20.5412182338 U. of Notre Dame 37 35.7354181171 13.2645818829
22 40.4537149905 -0.4537149905 Dartmouth College 10 39.473278713 13.526721287
23 41.6996685224 -7.6996685224 U. of Florida 33 2.8710271791 16.1289728209
24 35.4290844921 -6.4290844921 Princeton University 21 46.4587817662 20.5412182338
25 20.3551929972 -3.3551929972
26 22.4385146632 -4.4385146632
27 13.1449890599 -6.1449890599
28 11.8990355279 -2.8990355279
29 17.4138841649 -4.4138841649
30 17.6794014195 -9.6794014195
31 8.8760939548 3.1239060452
32 39.3916459722 -3.3916459722
33 2.8710271791 16.1289728209
34 20.3960093676 2.6039906324
35 24.9304217272 -11.9304217272
36 22.9287328019 3.0712671981
37 35.7354181171 13.2645818829
38 40.1881977359 0.8118022641
39 25.8700416342 -2.8700416342
40 17.5977686786 4.4022313214
41 4.6071988497 8.3928011503
42 34.2239473306 -6.2239473306
43 18.8437222106 -6.8437222106
44 19.8649748585 -6.8649748585
45 31.6504075258 -0.6504075258
46 29.1585004618 8.8414995382
47 37.1652561628 -4.1652561628
48 43.211139309 6.788860691

Data

University State % of Classes Under 20 Student-Faculty Ratio Graduation Rate GR2 Alumni Giving Rate SUMMARY OUTPUT
Boston College MA 39 13 85 7225 25
Brandeis University MA 68 8 79 6241 33 Regression Statistics
Brown University RI 60 8 93 8649 40 Multiple R 0.7559435914
California Institute of Technology CA 65 3 85 7225 46 R Square 0.5714507133
Carnegie Mellon University PA 67 10 75 5625 28 Adjusted R Square 0.5621344245
Case Western Reserve Univ. OH 52 8 72 5184 31 Standard Error 8.894328114
College of William and Mary VA 45 12 89 7921 27 Observations 48
Columbia University NY 69 7 90 8100 31
Cornell University NY 72 13 91 8281 35 ANOVA
Dartmouth College NH 61 10 94 8836 53 df SS MS F Significance F
Duke University NC 68 8 92 8464 45 Regression 1 4852.4618270788 4852.4618270788 61.3388789378 0.0000000005
Emory University GA 65 7 84 7056 37 Residual 46 3639.0173395879 79.1090725997
Georgetown University DC 54 10 91 8281 29 Total 47 8491.4791666667
Harvard University MA 73 8 97 9409 46
Johns Hopkins University MD 64 9 89 7921 27 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Lehigh University PA 55 11 81 6561 40 Intercept -68.7611827777 12.5826557253 -5.4647591318 0.000001821 -94.0887551098 -43.4336104455 -94.0887551098 -43.4336104455
Massachusetts Inst. of Technology MA 65 6 92 8464 44 Graduation Rate 1.1805159993 0.1507314789 7.8319141299 0.0000000005 0.8771092689 1.4839227298 0.8771092689 1.4839227298
New York University NY 63 13 72 5184 13
Northwestern University IL 66 8 90 8100 30 SUMMARY OUTPUT
Pennsylvania State Univ. PA 32 19 80 6400 21
Princeton University NJ 68 5 95 9025 67 Regression Statistics
Rice University TX 62 8 92 8464 40 Multiple R 0.836624531
Stanford University CA 69 7 92 8464 34 R Square 0.6999406058
Tufts University MA 67 9 87 7569 29 Adjusted R Square 0.6794820108
Tulane University LA 56 12 72 5184 17 Standard Error 7.6097247806
U. of California–Berkeley CA 58 17 83 6889 18 Observations 48
U. of California–Davis CA 32 19 74 5476 7
U. of California–Irvine CA 42 20 74 5476 9 ANOVA
U. of California–Los Angeles CA 41 18 78 6084 13 df SS MS F Significance F
U. of California–San Diego CA 48 19 80 6400 8 Regression 3 5943.5310722702 1981.1770240901 34.2125450874 0
U. of California–Santa Barbara CA 45 20 70 4900 12 Residual 44 2547.9480943964 57.9079112363
U. of Chicago IL 65 4 84 7056 36 Total 47 8491.4791666667
U. of Florida FL 31 23 67 4489 19
U. of Illinois–Urbana Champaign IL 29 15 77 5929 23 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
U. of Michigan–Ann Arbor MI 51 15 83 6889 13 Intercept -20.7201343259 17.5213650128 -1.1825639333 0.2433330572 -56.0321252326 14.5918565808 -56.0321252326 14.5918565808
U. of North Carolina–Chapel Hill NC 40 16 82 6724 26 Graduation Rate 0.7481827994 0.1659599594 4.5082127163 0.00004799 0.4137124785 1.0826531202 0.4137124785 1.0826531202
U. of Notre Dame IN 53 13 94 8836 49 % of Classes Under 20 0.0290406482 0.1393213222 0.2084436736 0.8358444891 -0.251743027 0.3098243235 -0.251743027 0.3098243235
U. of Pennsylvania PA 65 7 90 8100 41 Student-Faculty Ratio -1.1920106942 0.3867231042 -3.0823363825 0.0035384034 -1.9713998988 -0.4126214896 -1.9713998988 -0.4126214896
U. of Rochester NY 63 10 76 5776 23
U. of Southern California CA 53 13 70 4900 22
U. of Texas–Austin TX 39 21 66 4356 13
U. of Virginia VA 44 13 92 8464 28 RESIDUAL OUTPUT
U. of Washington WA 37 12 70 4900 12 negative--low giving
U. of Wisconsin–Madison WI 37 13 73 5329 13 Observation Predicted Alumni Giving Rate Residuals Observation Predicted Alumni Giving Rate Residuals
Vanderbilt University TN 68 9 82 6724 31 Boston College 1 28.5118498755 -3.5118498755 U. of Michigan–Ann Arbor 35 24.9799506671 -11.9799506671
Wake Forest University NC 59 11 82 6724 38 Brandeis University 2 30.8249853487 2.1750146513 Johns Hopkins University 15 36.9986400552 -9.9986400552
Washington University–St. Louis MO 73 7 86 7396 33 Brown University 3 41.0672193539 -1.0672193539 U. of California–San Diego 30 17.8802375476 -9.8802375476
Yale University CT 77 7 94 8836 50 California Institute of Technology 4 41.1870136711 4.8129863289 Columbia University 8 40.276047484 -9.276047484
Carnegie Mellon University 5 25.4191921147 2.5808078853 Northwestern University 19 38.9969148452 -8.9969148452
Case Western Reserve Univ. 6 25.1230553817 5.8769446183 Georgetown University 13 37.0125884775 -8.0125884775
College of William and Mary 7 32.8708356565 -5.8708356565 Stanford University 23 41.7724130828 -7.7724130828
Columbia University 8 40.276047484 -9.276047484 Tufts University 24 35.5893964012 -6.5893964012
Cornell University 9 33.9592880629 1.0407119371 New York University 18 19.4824490412 -6.4824490412
Dartmouth College 10 39.4604214131 13.5395785869 U. of Wisconsin–Madison 44 19.4755749868 -6.4755749868
Duke University 11 40.5513617403 4.4486382597 U. of Washington 43 18.4230372829 -6.4230372829
Emory University 12 35.670788095 1.329211905 U. of California–Davis 27 12.9264903799 -5.9264903799
Georgetown University 13 37.0125884775 -8.0125884775 U. of Virginia 42 33.8943327121 -5.8943327121
Harvard University 14 44.4374789782 1.5625210218 College of William and Mary 7 32.8708356565 -5.8708356565
Johns Hopkins University 15 36.9986400552 -9.9986400552 U. of California–Berkeley 26 22.7992138163 -4.7992138163
Lehigh University 16 28.367790438 11.632209562 Washington University–St. Louis 47 37.3994788795 -4.3994788795
Massachusetts Inst. of Technology 17 42.8482611841 1.1517388159 U. of California–Los Angeles 29 17.3725981055 -4.3725981055
New York University 18 19.4824490412 -6.4824490412 Boston College 1 28.5118498755 -3.5118498755
Northwestern University 19 38.9969148452 -8.9969148452 Tulane University 25 20.4711751978 -3.4711751978
Pennsylvania State Univ. 20 17.4155871761 3.5844128239 U. of Chicago 32 39.2468201776 -3.2468201776
Princeton University 21 46.371942221 20.628057779 U. of Rochester 39 26.0512123212 -3.0512123212
Rice University 22 40.377117851 -0.377117851 U. of California–Irvine 28 12.024886168 -3.024886168
Stanford University 23 41.7724130828 -7.7724130828 Brown University 3 41.0672193539 -1.0672193539
Tufts University 24 35.5893964012 -6.5893964012 Vanderbilt University 45 31.8775230526 -0.8775230526
Tulane University 25 20.4711751978 -3.4711751978 Rice University 22 40.377117851 -0.377117851
U. of California–Berkeley 26 22.7992138163 -4.7992138163 U. of Pennsylvania 38 40.1598848912 0.8401151088
U. of California–Davis 27 12.9264903799 -5.9264903799 Cornell University 9 33.9592880629 1.0407119371
U. of California–Irvine 28 12.024886168 -3.024886168 Massachusetts Inst. of Technology 17 42.8482611841 1.1517388159
U. of California–Los Angeles 29 17.3725981055 -4.3725981055 Emory University 12 35.670788095 1.329211905
U. of California–San Diego 30 17.8802375476 -9.8802375476 Harvard University 14 44.4374789782 1.5625210218
U. of California–Santa Barbara 31 9.1192769152 2.8807230848 Brandeis University 2 30.8249853487 2.1750146513
U. of Chicago 32 39.2468201776 -3.2468201776 Carnegie Mellon University 5 25.4191921147 2.5808078853
U. of Florida 33 2.8921273595 16.1078726405 U. of California–Santa Barbara 31 9.1192769152 2.8807230848
U. of Illinois–Urbana Champaign 34 19.8519596101 3.1480403899 U. of Illinois–Urbana Champaign 34 19.8519596101 3.1480403899
U. of Michigan–Ann Arbor 35 24.9799506671 -11.9799506671 U. of North Carolina–Chapel Hill 36 22.7203100431 3.2796899569
U. of North Carolina–Chapel Hill 36 22.7203100431 3.2796899569 Pennsylvania State Univ. 20 17.4155871761 3.5844128239
U. of Notre Dame 37 35.6520641448 13.3479358552 U. of Southern California 40 17.6956769603 4.3043230397
U. of Pennsylvania 38 40.1598848912 0.8401151088 Duke University 11 40.5513617403 4.4486382597
U. of Rochester 39 26.0512123212 -3.0512123212 California Institute of Technology 4 41.1870136711 4.8129863289
U. of Southern California 40 17.6956769603 4.3043230397 Case Western Reserve Univ. 6 25.1230553817 5.8769446183
U. of Texas–Austin 41 4.7602911343 8.2397088657 Yale University 48 43.5011038672 6.4988961328
U. of Virginia 42 33.8943327121 -5.8943327121 U. of Texas–Austin 41 4.7602911343 8.2397088657
U. of Washington 43 18.4230372829 -6.4230372829 Wake Forest University 46 29.2321358302 8.7678641698
U. of Wisconsin–Madison 44 19.4755749868 -6.4755749868 Lehigh University 16 28.367790438 11.632209562
Vanderbilt University 45 31.8775230526 -0.8775230526 U. of Notre Dame 37 35.6520641448 13.3479358552
Wake Forest University 46 29.2321358302 8.7678641698 Dartmouth College 10 39.4604214131 13.5395785869
Washington University–St. Louis 47 37.3994788795 -4.3994788795 U. of Florida 33 2.8921273595 16.1078726405
Yale University 48 43.5011038672 6.4988961328 Princeton University 21 46.371942221 20.628057779