The well-known psychologist Dr. Elbod has established what he calls his Generalized Anxiety Scale (GAS). The GAS, which is a scale from 0 to 10, measures the "general anxiety" of an individual, with higher GAS scores corresponding to more anxiety. (Dr. Elbod's assessment of anxiety is based on a variety of measurements, both physiological and psychological.) We're interested in making predictions about individuals' sleep behavior based on their GAS scores. The bivariate data below give the GAS score (denoted by x) and the number of hours of sleep last night (denoted by y) for each of the fifteen adults in a study. The least-squares regression line for these data has equation ŷ=8.48 -0.29x. This line, along with a scatter plot of the sample data, is shown below. GAS score, x Sleep time, y (in hours) 3.8 8.5 3.5 7.8 4.9 6.1 10+ 1.5 8.6 6.0 8.1 9+ x x 4.0 6.6 8.0 6.8 9.0 5.2 Sleep time (in hours) x 7.0 6.7 6+ 3.0 7.1 s+ 9.0 6.0 8.2 5.6 0 10 1.0 7.2 GAS score 6.7 5.8 2.1 8.3 Send data to calculator Send data to Excel Based on the study's data and the regression line, answer the following. From the regression equation, what is the predicted sleep time (in hours) when the GAS score is 4.0? Round your answer to one or more decimal places. (b) What was the observed sleep time (in hours) when the GAS score was 4.0?
The well-known psychologist Dr. Elbod has established what he calls his Generalized Anxiety Scale (GAS). The GAS, which is a scale from 0 to 10, measures the "general anxiety" of an individual, with higher GAS scores corresponding to more anxiety. (Dr. Elbod's assessment of anxiety is based on a variety of measurements, both physiological and psychological.) We're interested in making predictions about individuals' sleep behavior based on their GAS scores. The bivariate data below give the GAS score (denoted by x) and the number of hours of sleep last night (denoted by y) for each of the fifteen adults in a study. The least-squares regression line for these data has equation ŷ=8.48 -0.29x. This line, along with a scatter plot of the sample data, is shown below. GAS score, x Sleep time, y (in hours) 3.8 8.5 3.5 7.8 4.9 6.1 10+ 1.5 8.6 6.0 8.1 9+ x x 4.0 6.6 8.0 6.8 9.0 5.2 Sleep time (in hours) x 7.0 6.7 6+ 3.0 7.1 s+ 9.0 6.0 8.2 5.6 0 10 1.0 7.2 GAS score 6.7 5.8 2.1 8.3 Send data to calculator Send data to Excel Based on the study's data and the regression line, answer the following. From the regression equation, what is the predicted sleep time (in hours) when the GAS score is 4.0? Round your answer to one or more decimal places. (b) What was the observed sleep time (in hours) when the GAS score was 4.0?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 81E
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Transcribed Image Text:The well-known psychologist Dr. Elbod has established what he calls his Generalized Anxiety Scale (GAS). The GAS, which is a scale from 0 to 10, measures the
"general anxiety" of an individual, with higher GAS scores corresponding to more anxiety. (Dr. Elbod's assessment of anxiety is based on a variety of
measurements, both physiological and psychological.)
We're interested in making predictions about individuals' sleep behavior based on their GAS scores. The bivariate data below give the GAS score (denoted by x)
and the number of hours of sleep last night (denoted by y) for each of the fifteen adults in a study. The least-squares regression line for these data has equation
ŷ=8.48 -0.29x. This line, along with a scatter plot of the sample data, is shown below.
GAS score, x
Sleep time, y
(in hours)
3.8
8.5
3.5
7.8
4.9
6.1
10+
1.5
8.6
6.0
8.1
9+
x
x
4.0
6.6
8.0
6.8
9.0
5.2
Sleep time
(in hours)
x
7.0
6.7
6+
3.0
7.1
s+
9.0
6.0
8.2
5.6
0
10
1.0
7.2
GAS score
6.7
5.8
2.1
8.3
Send data to calculator
Send data to Excel
Based on the study's data and the regression line, answer the following.
From the regression equation, what is the predicted sleep time (in hours) when the GAS score is 4.0? Round your
answer to one or more decimal places.
(b) What was the observed sleep time (in hours) when the GAS score was 4.0?
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