Suppose you want to determine if the student/faculty ratio impacts the alumni gi
ID: 3232834 • Letter: S
Question
Suppose you want to determine if the student/faculty ratio impacts the alumni giving rate. Use the data in “Problem 1, see below” to run a regression with a 93% confidence interval and answer the following five questions.
How much of the variation in alumni giving rate is explained by student/faculty ratio?
QUESTION 2
What is the coefficient for the independent variable?
QUESTION 3
Is it statistically significant?
QUESTION 4
What is the upper bound on student/faculty ratio for a 93% confidence interval?
QUESTION 5
What does the model predict for X college which has a student/faculty ratio of 16?
School
% of Classes Under 20
Student/Faculty Ratio
Alumni Giving Rate
Boston College
39
13
25
Brandeis University
68
8
33
Brown University
60
8
40
California Institute of Technology
65
3
46
Carnegie Mellon University
67
10
28
Case Western Reserve Univ.
52
8
31
College of William and Mary
45
12
27
Columbia University
69
7
31
Cornell University
72
13
35
Dartmouth College
61
10
53
Duke University
68
8
45
Emory University
65
7
37
Georgetown University
54
10
29
Harvard University
73
8
46
John Hopkins University
64
9
27
Lehigh University
55
11
40
Massachusetts Inst. of Technology
65
6
44
New York University
63
13
13
Northwestern University
66
8
30
Pennsylvania State Univ.
32
19
21
Princeton University
68
5
67
Rice University
62
8
40
Stanford University
69
7
34
Tufts University
67
9
29
Tulane University
56
12
17
U. of California-Berleley
58
17
18
U. of California-Davis
32
19
7
U. of California-Irvine
42
20
9
U. of California-Los Angeles
41
18
13
U. of California-San Diego
48
19
8
U. of California-Santa Barbara
45
20
12
U. of Chicago
65
4
36
U. of Florida
31
23
19
U. of Illinois-Urbana Champaign
29
15
23
U. of Michigan-Ann Arbor
51
15
13
U. of North Carolina-Chapel Hill
40
16
26
U. of Notre Dame
53
13
49
U. of Pennsylvania
65
7
41
U. of Rochester
63
10
23
U. of Southern California
53
13
22
U. of Texas-Austin
39
21
13
U. of Virginia
44
13
28
U. of Washington
37
12
12
U. of Wisconsin-Madison
37
13
13
Vanderbuilt University
68
9
31
Wake Forest University
59
11
38
Washington University-St. Louis
73
7
33
Yale University
77
7
50
School
% of Classes Under 20
Student/Faculty Ratio
Alumni Giving Rate
Boston College
39
13
25
Brandeis University
68
8
33
Brown University
60
8
40
California Institute of Technology
65
3
46
Carnegie Mellon University
67
10
28
Case Western Reserve Univ.
52
8
31
College of William and Mary
45
12
27
Columbia University
69
7
31
Cornell University
72
13
35
Dartmouth College
61
10
53
Duke University
68
8
45
Emory University
65
7
37
Georgetown University
54
10
29
Harvard University
73
8
46
John Hopkins University
64
9
27
Lehigh University
55
11
40
Massachusetts Inst. of Technology
65
6
44
New York University
63
13
13
Northwestern University
66
8
30
Pennsylvania State Univ.
32
19
21
Princeton University
68
5
67
Rice University
62
8
40
Stanford University
69
7
34
Tufts University
67
9
29
Tulane University
56
12
17
U. of California-Berleley
58
17
18
U. of California-Davis
32
19
7
U. of California-Irvine
42
20
9
U. of California-Los Angeles
41
18
13
U. of California-San Diego
48
19
8
U. of California-Santa Barbara
45
20
12
U. of Chicago
65
4
36
U. of Florida
31
23
19
U. of Illinois-Urbana Champaign
29
15
23
U. of Michigan-Ann Arbor
51
15
13
U. of North Carolina-Chapel Hill
40
16
26
U. of Notre Dame
53
13
49
U. of Pennsylvania
65
7
41
U. of Rochester
63
10
23
U. of Southern California
53
13
22
U. of Texas-Austin
39
21
13
U. of Virginia
44
13
28
U. of Washington
37
12
12
U. of Wisconsin-Madison
37
13
13
Vanderbuilt University
68
9
31
Wake Forest University
59
11
38
Washington University-St. Louis
73
7
33
Yale University
77
7
50
Explanation / Answer
Answer:
Suppose you want to determine if the student/faculty ratio impacts the alumni giving rate. Use the data in “Problem 1, see below” to run a regression with a 93% confidence interval and answer the following five questions.
How much of the variation in alumni giving rate is explained by student/faculty ratio?
55.1% of the variation in alumni giving rate is explained by student/faculty ratio.
QUESTION 2
What is the coefficient for the independent variable?
-2.0572
QUESTION 3
Is it statistically significant?
Calculated t= -7.516,P=0.0000 . It is significant.
QUESTION 4
What is the upper bound on student/faculty ratio for a 93% confidence interval?
Upper bound= -1.5494
QUESTION 5
What does the model predict for X college which has a student/faculty ratio of 16?
Regression line Alumni Giving Rate =53.0138-2.0572*student/faculty ratio
When x=20,
Predicted Alumni Giving Rate =53.0138-2.0572*16
=20.099
Regression Analysis
r²
0.551
n
48
r
-0.742
k
1
Std. Error
9.103
Dep. Var.
Alumni Giving Rate
ANOVA table
Source
SS
df
MS
F
p-value
Regression
4,680.1127
1
4,680.1127
56.49
1.54E-09
Residual
3,811.3665
46
82.8558
Total
8,491.4792
47
Regression output
confidence interval
variables
coefficients
std. error
t (df=46)
p-value
93% lower
93% upper
Intercept
53.0138
3.4215
15.495
7.06E-20
46.6668
59.3609
Student/Faculty Ratio
-2.0572
0.2737
-7.516
1.54E-09
-2.5649
-1.5494
Predicted values for: Alumni Giving Rate
93% Confidence Interval
93% Prediction Interval
Student/Faculty Ratio
Predicted
lower
upper
lower
upper
Leverage
16
20.099
16.773
23.426
2.889
37.310
0.039
Regression Analysis
r²
0.551
n
48
r
-0.742
k
1
Std. Error
9.103
Dep. Var.
Alumni Giving Rate
ANOVA table
Source
SS
df
MS
F
p-value
Regression
4,680.1127
1
4,680.1127
56.49
1.54E-09
Residual
3,811.3665
46
82.8558
Total
8,491.4792
47
Regression output
confidence interval
variables
coefficients
std. error
t (df=46)
p-value
93% lower
93% upper
Intercept
53.0138
3.4215
15.495
7.06E-20
46.6668
59.3609
Student/Faculty Ratio
-2.0572
0.2737
-7.516
1.54E-09
-2.5649
-1.5494
Predicted values for: Alumni Giving Rate
93% Confidence Interval
93% Prediction Interval
Student/Faculty Ratio
Predicted
lower
upper
lower
upper
Leverage
16
20.099
16.773
23.426
2.889
37.310
0.039
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