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	25	40	60	84	105
​Well-Being Index​ Score, y		69.2	68.1	67.2	66.5	65.3	64.7	62.8

​(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 = [ ] x + [ ]

​(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 a commute time of zero​ minutes, the index score is predicted to be [ ]

B. For every unit increase in index​ score, the commute time falls by [ ] on average

C. For an index score of​ zero, the commute time is predicted to be [ ] minutes

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

E. It is not appropriate to interpret the slope

Interpret the​ y-intercept. 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 [ ] minutes

B. For every unit increase in commute​ time, the index score falls by [ ] on average

C.For every unit increase in index​ score, the commute time falls by [ ] on average

D. For a commute time of zero​ minutes, the index score is predicted to be [ ]

E. It is not appropriate to interpret the​ y-intercept.

​(c) Predict the​ well-being index of a person whose commute time is 30 minutes

The predicted index score is [ ]

​(d) Suppose Barbara has a 20-minute commute and scores 67.1 on the survey. Is Barbara more​ "well-off" than the typical individual who has a 20-minute commute? Select the correct choice below and fill in the answer box to complete your choice.

​A) No, Barbara is less​ well-off because the typical individual who has 20-minute commute scores [ ]

B) Yes, Barbara is more​ well-off because the typical individual who has a 20-minute commute scores [ ]

Answer 1

(I'm solving all 4 parts, please upvote)

a.

y = -0.058*x + 69.018

b.

y intercept, x intercept is not appropraite as 0 commute time or happiness score mamke no sense

also x is independent so we interpret based on increase in commute time

For every unit increase in commute​ time, the index score falls by [ 0.058 ] on average

c.

y = -0.058*x + 69.018

= -0.058*30 + 69.018

= 67.278

d.

for typical individual :

y = -0.058*x + 69.018

= -0.058*20 + 69.018

= 67.858

score of barbara = 67.1

score of barbara < typical individual

answer : option A : No, Barbara is less​ well-off because the typical individual who has 20-minute commute scores [ 67.858]

(PLEASE UPVOTE, for the hardwork in this lengthy solution)