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 the index can be found at www.well-beingindex.com/. 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 Gallup-Healthways Well-Being
(in minutes) ...... Index Composite Score
5 ............ 69.2
15 ........... 68.3
25 ........... 67.5
35 ......... 67.1
50 ......... 66.4
72 ......... 66.1
105 ......... 63.9
(a) Which variable do you believe is likely the explanatory variable and which is the response variable?
(b) Draw a scatter diagram of the data.
(c) Determine the linear correlation coefficient between commute time and well-being index score.
(d) Does a linear relation exist between the commute time and well-being index score?