Question

The data below represent commute timesâ (in minutes) and scores on aâ well-being survey. Complete partsâ (a) throughâ (d) below.

Commute Timeâ (minutes), x â 5 20 25 35 60 72 105
Well-Being Indexâ Score, y 69.1 67.8 67.1 66.6 65.0 65.0 62.3

Required:
Find theâ least-squares regression line treating the commuteâ time, x, as the explanatory variable and the indexâ score, y, as the response variable.

Answer 1

y = - 0.0635x + 69.050 ;

For every unit increase in commute time, well being falls by 0.0635 on average ;

67.1

Explanation:

Given :

Commute Time (minutes), x : 5 20 25 35 60 72 105

Well-Being Index Score, y : 69.1 67.8 67.1 66.6 65.0 65.0 62.3

The regression model obtained is :

y = - 0.0635x + 69.050

Where ;

y = Well being Index Score

x = Commute time

Slope = - 0.06352

Intercept = 69.0504

2.)

The slope value, - 0.0635 gives the rate of change in y per unit increase in x.

3.)

Well being Index for a person with commute time of 30 minutes

x = 30

y = - 0.06352(30) + 69.0504

y = 67.1448

y = 67.1 (1 decimal place)