Question

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 2645 2980 3410 3835 4095 Miles per Gallon, y 25.5 18.7 19.2 13.7 13 (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Write the equation for the least-squares regression line. y=oxed{}x+oxed{} (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) (b) Interpret the slope and intercept, if appropriate. Choose the best interpretation for the slope. A. The slope indicates the mean weight. B. The slope indicates the mean miles per gallon. C. The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight. D. The slope indicates the ratio between the mean weight and the mean miles per gallon. E. It is not appropriate to interpret the slope because it is not equal to zero. Choose the best interpretation for the y-intercept. A. The y-intercept indicates the miles per gallon of the lightest car in the population. B. The y-intercept indicates the miles per gallon for a new car. C. The y-intercept indicates the mean miles for a car that weighs 0 pounds. 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. (c) Predict the miles per gallon of car C and compute the residual. Is the miles per gallon of this car above average or below average for cars of this weight? The predicted value is oxed{} miles per gallon. (Round to two decimal places as needed.) The residual is oxed{} miles per gallon. (Round to two decimal places as needed.)

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
2645
2980
3410
3835
4095
Miles per Gallon, y
25.5
18.7
19.2
13.7
13
(a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.
Write the equation for the least-squares regression line.
y=oxed{}x+oxed{}
(Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.)
(b) Interpret the slope and intercept, if appropriate.
Choose the best interpretation for the slope.
A. The slope indicates the mean weight.
B. The slope indicates the mean miles per gallon.
C. The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight.
D. The slope indicates the ratio between the mean weight and the mean miles per gallon.
E. It is not appropriate to interpret the slope because it is not equal to zero.
Choose the best interpretation for the y-intercept.
A. The y-intercept indicates the miles per gallon of the lightest car in the population.
B. The y-intercept indicates the miles per gallon for a new car.
C. The y-intercept indicates the mean miles for a car that weighs 0 pounds.
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.
(c) Predict the miles per gallon of car C and compute the residual. Is the miles per gallon of this car above average or below average for cars of this weight?
The predicted value is oxed{} miles per gallon.
(Round to two decimal places as needed.)
The residual is oxed{} miles per gallon.
(Round to two decimal places as needed.)

Added by Jason S.

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