Question

We expect a car’s highway gas mileage to be related to its city gas mileage (in mpg). Data for all 1209 vehicles in the government’s 2016 Fuel Economy Guide give the regression line

highway mpg=7.903+(0.993×city mpg)

for predicting highway mileage from city mileage.

(a) What is the slope of this line? (Enter your answer rounded to three decimal places.)

slope:

What does the numerical value of the slope tell you?

On average, highway mileage increases by 0.993 mpg for each additional mpg in city mileage.

On average, highway mileage increases by 7.903 mpg for each additional mpg in city mileage.

For every 7.903 mpg in city gas mileage, highway gas mileage increases about 0.993 mpg.

On average, highway mileage decreases by 0.993 mpg for each additional mpg in city mileage.

Highway gas mileage increases with city gas mileage by 7.903 mpg for each additional mpg in city mileage.

(b) What is the intercept? (Enter your answer rounded to three decimal places.)

intercept:

mpg

Why is the value of the intercept not statistically meaningful?

The value of the intercept represents the predicted highway mileage for slope 0.

The value of the intercept represents the predicted highway mileage for city gas mileage of 0 mpg, and such a prediction would be invalid, since 0 is outside the range of the data.

The value of the intercept is an average value calculated from a sample.

The value of the intercept represents the predicted highway mileage for city gas mileage of 0 mpg, and such a car does not exist.

(c) Find the predicted highway mileage, ?̂, for a car that gets 15 miles per gallon in the city. (Enter your answer rounded to three decimal places.)

?̂=   mpg

Find the predicted highway mileage, ?̂, for a car that gets 23 miles per gallon in the city. (Enter your answer rounded to three decimal places.)

?̂= mpg

Answer 1

(a)

The slope of the line is 0.993.

Correct option is:

On average, highway mileage increases by 0.993 mpg for each additional mpg in city mileage.

(b)

The intercept is 7.903.

Correct option is:

The value of the intercept represents the predicted highway mileage for city gas mileage of 0 mpg, and such a car does not exist.

(c)

The predicted value for city-mpg = 15 is

highway mpg=7.903+(0.993×15) = 22.798

The predicted value for city-mpg = 23 is

highway mpg=7.903+(0.993×23) = 30.742