Question

A student studying statistics examined whether a relationship exists between the city miles per gallon (mpg) and highway miles per gallon (mpg) for cars and trucks. The miles per gallon of a vehicle describe the typical number of miles the vehicle can drive on one gallon of gas. Using a random sample of 50 cars and trucks, the student obtained the least- squares regression equation:

predicted highway mpg= 1.14- (city mpg)+5.8

Which statement below accurately describes the meaning of the number 1.14 in the regression equation?

a. If a vehicle's city mpg increases by 1 mile per gallon, its predicted highway mpg will decrease by 1.14 miles per gallon.
b. If a vehicle's city mpg increases by 1.14 mile per gallon, its predicted highway mpg will increase by 5.8 miles per gallon.
c. If a vehicle's city mpg increases by 1 mile per gallon, its predicted highway miles per gallon will increase by 1.14 miles per gallon.
d. If a vehicle's city mpg increases by 1.14 mile per gallon, its predicted highway mpg will increase by 1 mile per gallon.

Answer 1

c. If a vehicle's city mpg increases by 1 mile per gallon, its predicted highway miles per gallon will increase by 1.14 miles per gallon.

Explanation:

The equation that predicts highway mpg based on city mpg is:

`H=1.14C+5.8`

There is a positive relationship between city and highway mpg, which means that an increase in city mph results in an increase in highway mph. As for the magnitude of this increase, it is related to the slope of the equation which happens to be 1.14. This means that if a vehicle's city mpg increases by 1 mile per gallon, its predicted highway miles per gallon will increase by 1.14 miles per gallon.

The answer is alternative C.