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?
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
(b) Please compute the Pearson
(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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