Question

a study that examined the relationship between the fuel economy (mpg) and horsepower for 15 models of cars produced the regression model mpg = 46.87 - 0.084 hp. in this context, what does it mean to say that a certain car has a positive residual? what does it mean to say a certain car has a residual of 3?
in this context, to say that a certain car has a positive residual means that the gas mileage was greater than the model predicts for a car with that horsepower.
what does it mean to say a certain car has a residual of 3?
a. a residual of 3 means that car drives 3 more miles per gallon of gas than the model predicts.
b. a residual of 3 means that car drives 3 less miles per gallon of gas than the model predicts.
c. a residual of 3 means that car has 3% more horsepower but receives the same gas mileage as the less powerful model.
d. a residual of 3 means that car has 3% less horsepower but receives the same gas mileage as the more powerful model.

Explanation:

The residual is calculated as the observed value minus the predicted value. A positive residual means the observed value (gas mileage) is greater than the predicted value. For a residual of 3, it means the observed gas mileage (miles per gallon) is 3 units more than what the regression model predicts for that specific horsepower.

Answer:

A. A residual of 3 means that car drives 3 more miles per gallon of gas than the model predicts.