Case Problem 1 Alumni Giving Alumni donations are an important source of revenue for colleges and universities. 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 satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. The following table 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. LO 1 - Construct an estimated simple linear regression model that estimates how a dependent variable is related to an independent variable., 2 - Construct an estimated multiple linear regression model that estimates how a dependent variable is related to multiple independent variables., 3 - Compute and interpret the estimated coefficient of determination for a linear regression model., 4 - Assess whether the conditions necessary for valid inference in a least squares linear regression model are satisfied and test hypotheses about the parameters., 5 - Test hypotheses about the parameters of a linear regression model and interpret the results of these hypotheses tests., 9 - Use an estimated linear regression model to predict the value of the dependent variable given values of the independent variables.
Case Problem 1 Alumni Giving Alumni donations are an important source of revenue for colleges and universities. 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 satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. The following table 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. LO 1 - Construct an estimated simple linear regression model that estimates how a dependent variable is related to an independent variable., 2 - Construct an estimated multiple linear regression model that estimates how a dependent variable is related to multiple independent variables., 3 - Compute and interpret the estimated coefficient of determination for a linear regression model., 4 - Assess whether the conditions necessary for valid inference in a least squares linear regression model are satisfied and test hypotheses about the parameters., 5 - Test hypotheses about the parameters of a linear regression model and interpret the results of these hypotheses tests., 9 - Use an estimated linear regression model to predict the value of the dependent variable given values of the independent variables.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Chapter Review
Case Problem 1 Alumni Giving
Alumni donations are an important source of revenue for colleges and universities. 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 satisfied
graduates, which in turn might lead to increases in the percentage of alumni who make a
donation. The following table 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. LO 1 - Construct an estimated
simple linear regression model that estimates how a dependent variable is related to an
independent variable., 2 - Construct an estimated multiple linear regression model that
estimates how a dependent variable is related to multiple independent variables., 3 -
Compute and interpret the estimated coefficient of determination for a linear regression
model., 4 - Assess whether the conditions necessary for valid inference in a least squares
linear regression model are satisfied and test hypotheses about the parameters., 5 - Test
hypotheses about the parameters of a linear regression model and interpret the results of
these hypotheses tests., 9 - Use an estimated linear regression model to predict the value
of the dependent variable given values of the independent variables.

Transcribed Image Text:University
A
1
2 Boston College
3 Brandeis University
4 Brown University
5 California Institute of Technology
6 Carnegie Mellon University
7 Case Western Reserve Univ.
8 College of William and Mary
9 Columbia University
10 Cornell University
11 Dartmouth College
12 Duke University
13 Emory University
14 Georgetown University
15 Harvard University
16 Johns Hopkins University
17 Lehigh University
18 Massachusetts Inst. of Technology
19 New York University
20 Northwestern University
21 Pennsylvania State Univ.
22 Princeton University
23 Rice University
24 Stanford University
25 Tufts University
26 Tulane University
27 U. of California-Berkeley
28 U. of California-Davis
29 U. of California-Irvine
30 U. of California-Los Angeles
31 U. of California-San Diego
32 U. of California-Santa Barbara
33 U. of Chicago
34 U. of Florida
35 U. of Illinois-Urbana Champaign
36 U. of Michigan-Ann Arbor
37 U. of North Carolina-Chapel Hill
38 U. of Notre Dame
39 U. of Pennsylvania
40 U. of Rochester
41 U. of Southern California
42 U. of Texas-Austin
43 U. of Virginia
44 U. of Washington
45 U. of Wisconsin-Madison
46 Vanderbilt University
47 Wake Forest University
48 Washington University-St. Louis
49 Yale University
50
51
52
53
54
55
B
State
ΜΑ
ΜΑ
RI
CA
PA
OH
VA
NY
NY
NH
NC
GA
DC
ΜΑ
MD
PA
ΜΑ
NY
IL
PA
NJ
TX
CA
ΜΑ
LA
CA
CA
CA
CA
CA
CA
IL
FL
IL
MI
NC
IN
PA
NY
CA
TX
VA
WA
WI
TN
NC
MO
CT
C
Graduation
Rate
85
79
93
85
75
72
89
88
90
91
94
92
84
91
97
89
81
92
72
90
80
95
92
92
87
72
83
74
74
78
80
70
84
67
77
83
82
94
90
76
70
66
92
70
73
82
82
86
94
D
% of Classes
Under 20
39
68
60
65
67
52
45
69
72
61
68
65
54
73
64
55
65
63
66
32
68
62
69
67
56
58
32
42
41
48
45
65
31
29
51
40
53
65
63
53
39
4
44
37
37
68
59
73
77
E
Student-
Faculty Ratio
13
8
8
3
10
8
12
7
13
10
8
7
10
8
9
11
6
13
8
19
5
8
7
9
2528898
12
17
19
20
18
19
20
4
23
15
15
16
13
7
10
13
21
13
12
13
9
11
7
7
F
Alumni
Giving Rate
25
33
400
46
28
31
27
31
35
53
45
37
29
46
27
40
44
13
30
21
67
40
34
29
17
18
7
9
13
8
12
36
19
23
13
26
49
41
23
22
13
28
12
13
31
38
33
50
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
AA
AB
AC
AD
AE
AF
AG
AH
Al
AJ
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VIEWStep 6: Test hypotheses about the parameters for the linear regression model.
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