Regression Analysis Alumni donations are an important source of revenue for colleges and universities in the USA. 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 alumni who make a donation. The following table (1) shows data for 48 national universities. The graduation rate column is the percentage of students who initially enrolled at the university and graduated. The % of classes under 20 column shows the percentages of classes with fewer than 20 students that are offered. The student/faculty ratio column is the number of students enrolled divided by the total number of faculty. Finally, the alumni giving rate column is the percentage of alumni who 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 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–LosAngeles CA 78 41 18 13 U. of California–SanDiego 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–UrbanaChampaign IL 77 29 15 23 U. of Michigan–AnnArbor MI 83 51 15 13 U. of NorthCarolina–Chapel Hill NC 82 40 16 26 U. of NotreDame 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 a) Use methods of descriptive statistics to summarise the variables “alumni giving rate” and“graduation rate” b) Conduct the correlation analysis among all the variables, and discuss your findings c) Develop an estimated simple regression model that can be used to predict the alumni giving rate, given the graduation rate. Discuss your findings. d) Develop an estimated multiple regression model that could be used to predict the Alumni giving rate using Graduation Rate, % of Classes Under 20, and Student/Faculty Ratio as independent variables. Discuss your findings. What is the value of R-squared? Properly interpret its meaning. e) Based on the results in part (c) and (d), do you believe another model may be more appropriate? Estimate this model, and discuss your results. . f) What conclusion 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 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?

Regression Analysis Alumni donations are an important source of revenue for colleges and universities in the USA. 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 alumni who make a donation. The following table (1) shows data for 48 national universities. The graduation rate column is the percentage of students who initially enrolled at the university and graduated. The % of classes under 20 column shows the percentages of classes with fewer than 20 students that are offered. The student/faculty ratio column is the number of students enrolled divided by the total number of faculty. Finally, the alumni giving rate column is the percentage of alumni who 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 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–LosAngeles CA 78 41 18 13 U. of California–SanDiego 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–UrbanaChampaign IL 77 29 15 23 U. of Michigan–AnnArbor MI 83 51 15 13 U. of NorthCarolina–Chapel Hill NC 82 40 16 26 U. of NotreDame 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 a) Use methods of descriptive statistics to summarise the variables “alumni giving rate” and“graduation rate” b) Conduct the correlation analysis among all the variables, and discuss your findings c) Develop an estimated simple regression model that can be used to predict the alumni giving rate, given the graduation rate. Discuss your findings. d) Develop an estimated multiple regression model that could be used to predict the Alumni giving rate using Graduation Rate, % of Classes Under 20, and Student/Faculty Ratio as independent variables. Discuss your findings. What is the value of R-squared? Properly interpret its meaning. e) Based on the results in part (c) and (d), do you believe another model may be more appropriate? Estimate this model, and discuss your results. . f) What conclusion 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 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?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 12PPS

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Regression Analysis

Alumni donations are an important source of revenue for colleges and universities in the USA. 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 alumni who make a donation. The following table (1) shows data for 48 national universities. The graduation rate column is the percentage of students who initially enrolled at the university and graduated. The % of classes under 20 column shows the percentages of classes with fewer than 20 students that are offered. The student/faculty ratio column is the number of students enrolled divided by the total number of faculty. Finally, the alumni giving rate column is the percentage of alumni who 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
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–LosAngeles	CA	78	41	18	13
U. of California–SanDiego	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–UrbanaChampaign	IL	77	29	15	23
U. of Michigan–AnnArbor	MI	83	51	15	13
U. of NorthCarolina–Chapel Hill	NC	82	40	16	26
U. of NotreDame	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

a) Use methods of descriptive statistics to summarise the variables “alumni giving rate” and“graduation rate”
b) Conduct the correlation analysis among all the variables, and discuss your findings
c) Develop an estimated simple regression model that can be used to predict the alumni giving rate, given the graduation rate. Discuss your findings.

d) Develop an estimated multiple regression model that could be used to predict the Alumni giving rate using Graduation Rate, % of Classes Under 20, and Student/Faculty Ratio as independent variables. Discuss your findings. What is the value of R-squared? Properly interpret its meaning.
e) Based on the results in part (c) and (d), do you believe another model may be more appropriate? Estimate this model, and discuss your results. .
f) What conclusion 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 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?

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