Chapter 12.3, Problem 11AYU

An Unhealthy Commute The following data represent commute times (in minutes) and a score on a well-being survey.

Commute Time (minutes), x	Gallup-Healthways Well-Being Index Composite Score, y
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

Use the results from Problem 17 in Section 4.2 to answer the following questions:

1. a. Treating commute time as the explanatory variable, x, determine the estimates of β₀ and β₁.
2. b. Compute the standard error of the estimate, s_e.
3. c. Determine $s_{b_1}$.
4. d. A normal probability plot of the residuals indicates it is reasonable to conclude the residuals are normally distributed. Test whether a linear relation exists between commute tune and well-being index composite score at the α = 0.05 level of significance.
5. e. Construct a 95% confidence interval about the slope of the true least-squares regression line.