a. Compute the equation of the least-squares line. b. What is the value of r? c. Does the linear relationship between perceived stress and telomere length account for a large or small proportion of the variability in telomere length? Justify your answer.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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The paper "Accelerated Telomere Shortening in
Response to Life Stress" (Proceedings of the National
Academy of Sciences (2004): 17312-17315) described
a study that examined whether stress accelerates
aging at a cellular level. The accompanying data on a
measure of perceived stress (x) and telomere length (y)
were read from a scatterplot that appeared in the
paper. Telomere length is a measure of cell longevity.
5.38
Perceived
Telomere
Perceived
Telomere
Stress
Length
Stress
Length
5
1.25
20
1.22
1.32
20
1.30
1.5
20
1.32
7
1.35
21
1.24
10
1.3
21
1.26
11
1
21
1.30
12
1.18
22
1.18
13
1.1
22
1.22
14
1.08
22
1.24
14
1.3
23
1.18
15
0.92
24
1.12
15
1.22
24
1.50
15
1.24
25
0.94
17
1.12
26
0.84
17
1.32
27
1.02
17
1.4
27
1.12
18
1.12
28
1.22
18
1.46
29
1.30
19
0.84
33
0.94
a. Compute the equation of the least-squares line.
b. What is the value of r?
c. Does the linear relationship between perceived
stress and telomere length account for a large or
small proportion of the variability in telomere
length? Justify your answer.
Transcribed Image Text:The paper "Accelerated Telomere Shortening in Response to Life Stress" (Proceedings of the National Academy of Sciences (2004): 17312-17315) described a study that examined whether stress accelerates aging at a cellular level. The accompanying data on a measure of perceived stress (x) and telomere length (y) were read from a scatterplot that appeared in the paper. Telomere length is a measure of cell longevity. 5.38 Perceived Telomere Perceived Telomere Stress Length Stress Length 5 1.25 20 1.22 1.32 20 1.30 1.5 20 1.32 7 1.35 21 1.24 10 1.3 21 1.26 11 1 21 1.30 12 1.18 22 1.18 13 1.1 22 1.22 14 1.08 22 1.24 14 1.3 23 1.18 15 0.92 24 1.12 15 1.22 24 1.50 15 1.24 25 0.94 17 1.12 26 0.84 17 1.32 27 1.02 17 1.4 27 1.12 18 1.12 28 1.22 18 1.46 29 1.30 19 0.84 33 0.94 a. Compute the equation of the least-squares line. b. What is the value of r? c. Does the linear relationship between perceived stress and telomere length account for a large or small proportion of the variability in telomere length? Justify your answer.
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What is the standard deviation around the least-squares line? Why is the denominator n-2?

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