a)  Please generate or sketch a scatterplot of these data. Please also briefly explain what conclusions you can draw from this scatterplot. (b)  Please compute the Pearson correlation coefficient (Pearson’s r) between commute time and well-being index score. (c)  What can you conclude based on the value of your correlation coefficient and the associated scatterplot? Does a linear relationship exist between commute time and well-being index score? Why or why not?

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The Gallup Organization regularly surveys adult Americans regarding their commute time to work. In addition, they administer a Well-Being Survey.

 

According to the Gallup Organization, “The Gallup-Healthways Well-Being Index Composite Score is comprised of six sub-indices: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment and Basic Access.” A complete description of this index can be found at http://www.well-beingindex.com/ (Links to an external site.)

 

The data in the following table are based on the results of the survey, which represent commute time to work (in minutes) and well-being index score:

 

Commute Time (in minutes)

Gallup-Healthways Well-Being Index Composite Score

    5

69.2

  15

68.3

  25

67.5

  35

67.1

  50

66.4

  72

66.1

105

63.9

Source: The Gallup Organization

 

Required:

 

(a)  Please generate or sketch a scatterplot of these data. Please also briefly explain what conclusions you can draw from this scatterplot.

(b)  Please compute the Pearson correlation coefficient (Pearson’s r) between commute time and well-being index score.

(c)  What can you conclude based on the value of your correlation coefficient and the associated scatterplot? Does a linear relationship exist between commute time and well-being index score? Why or why not?

 

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