An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weights of various cars and their miles per gallon.

Car	A	B	C	D	E
Weight (pounds), x	2635

2925

3450

3800

4205

Miles per Gallon, y	27.2

27.3

18.7

16.7

15.4

Question content area bottom

Part 1

(a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.

Part 2

Write the equation for the least-squares regression line.

ModifyingAbove y with caret

equalsnegative 0.00868xplus50.61

(Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.)

Part 3

(b) Interpret the slope and intercept, if appropriate.

Part 4

Choose the best interpretation for the slope.

A.

The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight.

B.

The slope indicates the mean miles per gallon.

C.

The slope indicates the ratio between the mean weight and the mean miles per gallon.

D.

The slope indicates the mean weight.

E.

It is not appropriate to interpret the slope because it is not equal to zero.

Part 5

Choose the best interpretation for the y-intercept.

A.

The y-intercept indicates the mean miles for a car that weighs 0 pounds.

B.

The y-intercept indicates the miles per gallon for a new car.

C.

The y-intercept indicates the miles per gallon of the lightest car in the population.

D.

The y-intercept indicates the mean miles per gallon for a car that weighs 0 pounds.

E.

It is not appropriate to interpret the y-intercept because it does not make sense to talk about a car that weighs 0 pounds.

Part 6

(c) Predict the miles per gallon of car

Upper B

and compute the residual. Is the miles per gallon of this car above average or below average for cars of this weight?

Part 7

The predicted value is

50.22

miles per gallon.

(Round to

two

decimal

places

as needed.)

Part 8

The residual is

negative 22.932

miles per gallon.

(Round to

two

decimal

places

as needed.)

Part 9

Is the value above or below average?

It is

below

average.

It is

above

average.

Part 10

(d) Draw the least-squares regression line on the scatter diagram of the data and label the residual.

Part 11

Which of the following represents the data with the residual shown in red?

A.

250043001429MPGWeight

A scatter diagram has a horizontal axis labeled "MPG" from 2500 to 4300 in increments of 100 and a vertical axis labeled "Weight" from 14 to 29 in increments of 1. The following 5 points are plotted, listed here from left to right: (2640, 27.2); (2930, 27.4); (3450, 18.8); (3800, 16.8); (4210, 15.4). There is a line, falling from left to right, passing through points (2600, 28) and (4200, 14.2). The line passes within 3 vertical units of all plotted points. A red vertical line segment is drawn from the plotted point at (2830, 27.4) to the line at (2830, 26). All coordinates are approximate.

B.

142925004300WeightMPG

A scatter diagram has a horizontal axis labeled "Weight" from 14 to 29 in increments of 1 and a vertical axis labeled "MPG" from 2500 to 4300 in increments of 100. The following 5 points are plotted, listed here from left to right: (15.4, 4210); (16.8, 3800); (18.8, 3450); (27.2, 2640); (27.4, 2930). There is a line, falling from left to right, passing through points (14.2, 4200) and (28, 2600). The line passes within 3 vertical units of all plotted points. A red horizontal line segment is drawn from the plotted point at (27.4, 2930) to the line at (25.2, 2930). All coordinates are approximate.

C.

142925004300MPGWeight

A scatter diagram has a horizontal axis labeled "MPG" from 14 to 29 in increments of 1 and a vertical axis labeled "Weight" from 2500 to 4300 in increments of 100. The following 5 points are plotted, listed here from left to right: (15.4, 4210); (16.8, 3800); (18.8, 3450); (27.2, 2640); (27.4, 2930). There is a line, falling from left to right, passing through points (28, 2600) and (14.2, 4200). The line passes within 3 vertical units of all plotted points. A red horizontal line segment is drawn from the plotted point at (26.4, 2930) to the line at (25.2, 2930). All coordinates are approximate.

D.

250043001429WeightMPG