Question

The data below represent commute times​ (in minutes) and scores on a​ well-being survey. Complete parts​ (a) through​ (d) below. Commute Time​ (minutes), x 5 15 30 35 50 84 105 ​Well-Being Index​ Score, y 69.1 67.8 66.2 65.9 64.6 62.6 60.2 ​(a) Find the​ least-squares regression line treating the commute​ time, x, as the explanatory variable and the index​ score, y, as the response variable. y=negative 0.083−0.083x+69.04069.040 ​(Round to three decimal places as​ needed.) ​(b) Interpret the slope and​ y-intercept, if appropriate. Interpret the slope. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. For an index score of​ zero, the commute time is predicted to be nothing minutes. ​(Round to three decimal places as​ needed.) B. For every unit increase in index​ score, the commute time falls by nothing​, on average. ​(Round to three decimal places as​ needed.) C. For a commute time of zero​ minutes, the index score is predicted to be nothing. ​(Round to three decimal places as​ needed.) D. For every unit increase in commute​ time, the index score falls by nothing​, on average. ​(Round to three decimal places as​ needed.) E. It is not appropriate to interpret the slope.

Answer 1

Answer:

(a) $\hat y=69.04-0.083\cdot x$

(b) D. For every unit increase in commute​ time, the index score falls by 0.083​, on average.

Step-by-step explanation:

(a)

Form the least-squares regression line using Excel as follows:

Go to Data → Data Analysis → Regression

A dialog box will open.

Select the X and Y variable.

Press Ok.

The regression output is attached below.

The least-squares regression line is:

$\hat y=69.04-0.083\cdot x$

(b)

The slope of a regression line is the average rate of change in the dependent variable (y) with 1 unit change in the independent variable (x).

Here the slope value is -0.083. This value implies that with 1 minute change in the commute times the Well-Being Index​ Score falls by 0.083 units.

The intercept of a regression line is the average value of the dependent variable (y) when the independent variable (x) value is 0.

Here, the intercept value is 69.04. This value implies that for a person with commute time 0, their Well-Being Index​ Score is 69.04.

The correct option is:

D. For every unit increase in commute​ time, the index score falls by 0.083​, on average.