Question

We expect a car's highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). Data for all 1137 vehicles in the government's Fuel Economy Guide give the regression line

highway mpg = 6.785 + (1.033 * city mpg)

for predicting highway mileage from city mileage.

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

Say in words what the numerical value of the slope tells us.

Highway gas mileage increases with city gas mileage by 6.785 mpg for each additional mpg in city mileage.On the average, highway mileage increases by 6.785 mpg for each additional mpg in city mileage.    On the average, highway mileage increases by 1.033 mpg for each additional mpg in city mileage.On the average, highway mileage decreases by 1.033 mpg for each additional mpg in city mileage.For every 6.785 mpg in city gas mileage, highway gas mileage increases about 1.033 mpg.

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

Explain why the value of the intercept is not statistically meaningful.

Because this is the highway mileage for zero city mpg.Because this is an average value, calculated from a sample.    Because this is the highway mileage for slope 0.

(c) Assume a strong linear correlation. Find the predicted highway mileage for a car that gets 13 miles per gallon in the city. (Round your answer to two decimal places.)
mpg

Find the predicted highway mileage for a car that gets 28 miles per gallon in the city. (Round your answer to two decimal places.)
mpg

(d) Make a graph of the regression line for city mileages between 10 and 50 mpg.

Answer 1

The regression line is highway mpg = 6.785 + (1.033 * city mpg)

a.

The slope of this line is 1.033.

On the average, highway mileage increases by 1.033 mpg for each additional mpg in city mileage.

b.

The intercept is 6.785.

Because this is the highway mileage for zero city mpg

c.

The predicted highway mileage for a car that gets 13 miles per gallon in the city is 20.214

Highway mpg = 6.785 + (1.033 * city mpg)

Highway mpg = 6.785 + (1.033 * 13) = 20.214

The predicted highway mileage for a car that gets 28 miles per gallon in the city is 35.709.

Highway mpg = 6.785 + (1.033 * city mpg)

Highway mpg = 6.785 + (1.033 * 28) = 35.709

d.

The regression line for city mileages between 10 and 50 mpg.