Question

A statistics student examined whether a relationship exists between city miles per gallon (mpg) and highway miles per gallon (mpg) for cars. The miles per gallon of a car describe the typical number of miles the car can drive on one gallon of gas. Using a random sample of 50 cars, 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:

Given the regression equation for predicted highway miles per gallon

`\text{Predicted highway mpg =} 1.14($city mpg) +5.8`

The slope of the function =1.14

Therefore, when the vehicle's city miles per gallon increases by 1 mile per gallon, the predicted highway miles per gallon increase by 1.14 miles per gallon.

The correct option is C.