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.

y = - 0.0635x + 69.050 ;

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

67.1

Step-by-step 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)

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.