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.

Question

contestada

Respuesta :

warylucknow warylucknow · Answer 1 · 2020-10-13T11:58:34+02:00

Answer:

(a) [tex]\hat y=69.04-0.083\cdot x[/tex]

(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:

[tex]\hat y=69.04-0.083\cdot x[/tex]

(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.