12.20 Rankings of research universities. Refer to the College Choice 2015 Rankings of National Research Universities, Exercise 11.29 (p. 633). Data on academic reputation score, average financial aid awarded, average net cost to attend, median salary during early career, percentage of alumni who feel their work makes a better place, and percentage of science, technology, engineering, and math (STEM) degrees awarded for the top 50 research universities are saved in the file. Information on the top 10 schools are reproduced in the table. Consider a first-order multiple regression model to predict academic reputation score (y) using financial aid awarded (x1), net cost (x2), early career salary (x3), work makes a better place percentage (x4), and percentage of STEM degrees (x5). TOPUNIV Early Better Pay Rank Academic Financial University Rep. Score Aid Cost Place STEM 1 Harvard 2 MIT 3 Stanford 4 Columbia 5 Yale 6 CalTech 7 Dartmouth 8 Penn 9 Duke 99 pts. $41,555 $14,455 $61,400 65% 34,641 38,522 37,934 39,771 31,445 38,148 35,539 33,191 34,469 28% 20,629 74,900 55 19,233 65,900 62 21,274 60,200 56 18,479 60,300 68 22,645 72,600 66 20,490 56,300 45 21,821 60,300 55 24,134 60,600 59 22,973 57,500 63 92 79 94 29 95 29 97 21 91 93 91 20 92 19 92 35 10 Johns 89 26 Hopkins a. Use statistical software to fit the model to the data. Give the least squares prediction equation. b. Find and give a practical interpretation of the standard deviation of the model, s. c. Find and give a practical interpretation of the coeffi- cient of determination, R2. d. Conduct a test of the overall adequacy of the model using α .05. e. Find a 90% confidence interval for the B coefficient associated with work makes a better place percentage (x4), Interpret the result.
12.20 Rankings of research universities. Refer to the College Choice 2015 Rankings of National Research Universities, Exercise 11.29 (p. 633). Data on academic reputation score, average financial aid awarded, average net cost to attend, median salary during early career, percentage of alumni who feel their work makes a better place, and percentage of science, technology, engineering, and math (STEM) degrees awarded for the top 50 research universities are saved in the file. Information on the top 10 schools are reproduced in the table. Consider a first-order multiple regression model to predict academic reputation score (y) using financial aid awarded (x1), net cost (x2), early career salary (x3), work makes a better place percentage (x4), and percentage of STEM degrees (x5). TOPUNIV Early Better Pay Rank Academic Financial University Rep. Score Aid Cost Place STEM 1 Harvard 2 MIT 3 Stanford 4 Columbia 5 Yale 6 CalTech 7 Dartmouth 8 Penn 9 Duke 99 pts. $41,555 $14,455 $61,400 65% 34,641 38,522 37,934 39,771 31,445 38,148 35,539 33,191 34,469 28% 20,629 74,900 55 19,233 65,900 62 21,274 60,200 56 18,479 60,300 68 22,645 72,600 66 20,490 56,300 45 21,821 60,300 55 24,134 60,600 59 22,973 57,500 63 92 79 94 29 95 29 97 21 91 93 91 20 92 19 92 35 10 Johns 89 26 Hopkins a. Use statistical software to fit the model to the data. Give the least squares prediction equation. b. Find and give a practical interpretation of the standard deviation of the model, s. c. Find and give a practical interpretation of the coeffi- cient of determination, R2. d. Conduct a test of the overall adequacy of the model using α .05. e. Find a 90% confidence interval for the B coefficient associated with work makes a better place percentage (x4), Interpret the result.
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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Question
Transcribed Image Text:12.20 Rankings of research universities. Refer to the College
Choice 2015 Rankings of National Research Universities,
Exercise 11.29 (p. 633). Data on academic reputation score,
average financial aid awarded, average net cost to attend,
median salary during early career, percentage of alumni
who feel their work makes a better place, and percentage
of science, technology, engineering, and math (STEM)
degrees awarded for the top 50 research universities are
saved in the file. Information on the top 10 schools are
reproduced in the table. Consider a first-order multiple
regression model to predict academic reputation score
(y) using financial aid awarded (x1), net cost (x2), early
career salary (x3), work makes a better place percentage
(x4), and percentage of STEM degrees (x5).
TOPUNIV
Early Better
Рay
Rank
Academic Financial
University Rep. Score
Aid
Cost
Place STEM
1 Harvard
2 MIT
3 Stanford
99 pts.
$41,555 $14,455 $61,400 65%
20,629 74,900 55
19,233 65,900 62
21,274 60,200 56
18,479 60,300 68
22,645 72,600 66
20,490 56,300 45
21,821 60,300 55
24,134 60,600 59
22,973 57,500 63
28%
92
34,641
38,522
37,934
39,771
31,445
38,148
35,539
33,191
34,469
79
94
29
4 Columbia
5 Yale
6 CalTech
7 Dartmouth
8 Penn
9 Duke
95
29
21
97
91
93
20
91
92
92
19
35
10 Johns
89
26
Hopkins
a. Use statistical software to fit the model to the data.
Give the least squares prediction equation.
b. Find and give a practical interpretation of the standard
deviation of the model, s.
c. Find and give a practical interpretation of the coeffi-
cient of determination, R2.
d. Conduct a test of the overall adequacy of the model
using a = .05.
e. Find a 90% confidence interval for the B coefficient
associated with work makes a better place percentage
(x4). Interpret the result.
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