Question

The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a well-being test. Complete parts (a) through (d) below.

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Commute Time (in minutes)	Well-Being Score	Open in StatCrunch + Copy to Clipboard + Open in Excel +
44	69.569.5
1616	68.568.5
2525	67.867.8
3434	67.167.1
5151	66.966.9
6868	65.865.8
103103	63.163.1

(a) Which variable is likely the explanatory variable and which is the response variable?

A.

The explanatory variable is commute time and the response variable is the well-being score because well-being score affects the commute time score.

B.

The explanatory variable is the well-being score and the response variable is commute time because commute time affects the well-being score.

C.

The explanatory variable is the well-being score and the response variable is commute time because well-being score affects the commute time.

D.

The explanatory variable is commute time and the response variable is the well-being score because commute time affects the well-being score.

Your answer is correct.

(b) Draw a scatter diagram of the data. Which of the following represents the data?

A.

01106070Commute Time (min)Score

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A scatter diagram has a horizontal axis labeled “Commute Time (minutes)” from 0 to 110 in increments of 10 and a vertical axis labeled “Score” from 60 to 70 in increments of 1. The following 7 approximate points are plotted, listed here from left to right: (4, 63.2); (16, 69.6); (26, 65.8); (34, 68.6); (52, 67.0); (68, 67.8); (104, 67.2). The vertical spread of the points decreases from left to right.

B.

60700110Commute Time (min)Score

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A scatter diagram has a horizontal axis labeled “Commute Time (minutes)” from 60 to 70 in increments of 1 and a vertical axis labeled “Score” from 0 to 110 in increments of 10. The following 7 approximate points are plotted, listed here from left to right: (63.2, 104); (65.8, 68); (67.0, 52); (67.2, 34); (67.8, 26); (68.6, 16); (69.6, 4). The points follow the general pattern of a straight line that falls from left to right.

C.

01106070Commute Time (min)Score

Edit Coordinates(0,0)

A scatter diagram has a horizontal axis labeled “Commute Time (minutes)” from 0 to 110 in increments of 10 and a vertical axis labeled “Score” from 60 to 70 in increments of 1. The following 7 approximate points are plotted, listed here from left to right: (4, 63.2); (16, 65.8); (26, 67.0); (34, 67.2); (52, 67.8); (68, 68.6); (104, 69.6). The points follow the general pattern of a curve that rises from left to right at a decreasing rate.

D.

01106070Commute Time (min)Score

Edit Coordinates(0,0)

A scatter diagram has a horizontal axis labeled “Commute Time (minutes)” from 0 to 110 in increments of 10 and a vertical axis labeled “Score” from 60 to 70 in increments of 1. The following 7 approximate points are plotted, listed here from left to right: (4, 69.6); (16, 68.6); (26, 67.8); (34, 67.2); (52, 67.0); (68, 65.8); (104, 63.2). The points follow the general pattern of a straight line that falls from left to right.Your answer is correct.

(c) Determine the linear correlation coefficient between commute time and well-being score.

requals=nothing

(Round to three decimal places as needed.)

The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a well-being test. Complete parts (a) through (d) below.

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Click the icon to view the critical values for the correlation coefficient.

Commute Time (in minutes)	Well-Being Score
Commute Time (in minutes)	Well-Being Score
44	69.569.5
1616	68.568.5
2525	67.867.8
3434	67.167.1
5151	66.966.9
6868	65.865.8

Answer 1

a)

The explanatory variable is commute time and the response variable is the well-being score because commute time affects the well-being score.

Option - (D)

b)

01106070 Commute Time (min)Score

Edit Coordinates(0,0)

A scatter diagram has a horizontal axis labeled “Commute Time (minutes)” from 0 to 110 in increments of 10 and a vertical axis labeled “Score” from 60 to 70 in increments of 1. The following 7 approximate points are plotted, listed here from left to right: (4, 63.2); (16, 69.6); (26, 65.8); (34, 68.6); (52, 67.0); (68, 67.8); (104, 67.2). The vertical spread of the points decreases from left to right.

Option - (A)

c)

R square (R²) equals 0.9758. It means that the predictors (X_i) explain 97.6% of the variance of Y.
Adjusted R square equals 0.9710.
The coefficient of multiple correlation (R) equals 0.9878. It means that there is a very strong direct relationship between the predicted data (ŷ) and the observed data (y).