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 40 50 84 105 ​Well-Being Index​ Score, y 68.9 67.6 65.8 64.9 64.0 61.5 58.8 ​(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. ModifyingAbove y with caret equalsnothingxplusleft parenthesis nothing right parenthesis ​(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 every unit increase in commute​ time, the index score

falls

by

nothing

​,

on average.

​(Round to three decimal places as​ needed.)

B.

For an index score of​ zero, the commute time is predicted to be

nothing

minutes.

​(Round to three decimal places as​ needed.)

C.

For every unit increase in index​ score, the commute time

falls

by

nothing

​,

on average.

​(Round to three decimal places as​ needed.)

D.

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

nothing

.

​(Round to three decimal places as​ needed.)

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

nothing

minutes.

​(Round to three decimal places as​ needed.)

B.

For every unit increase in commute​ time, the index score

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 index​ score, the commute time

falls

by

nothing

​,

on average.

​(Round to three decimal places as​ needed.)

E.

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

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

25

minutes.

The predicted index score is

nothing

.

​(Round to one decimal place as​ needed.)

​(d) Suppose Barbara has a

20

​-minute

commute and scores

66.2

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.

​(Round to one decimal place as​ needed.)

A.

​Yes, Barbara is more​ well-off because the typical individual who has a

20

​-minute

commute scores

nothing

.

B.

​No, Barbara is less​ well-off because the typical individual who has a

20

​-minute

commute scores

nothing

.

Answer 1

​(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

The least square regression equation is

Y=68.9921-0.0955X

​(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

For every unit increase in commute​ time, the index score falls by 0.095 on avearge.(option a is correct)

(c) Interpret the​ y-intercept. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

sol;

(c) Predict the​ well-being index of a person whose commute time is 25

sol:Y=68.9921-0.0955X

    Y=68.9921-0.0955(25)

    Y=68.9921-2.3875

Y=66.60

The predicted index score is 66.6