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 - 0.004 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 was the model predicts for a car with that

Explanation:

A residual is calculated as the actual value minus the predicted value. A positive residual means the actual value is greater than the predicted value. In this context, the regression model predicts fuel economy (mpg) based on horsepower (HP). So, a positive residual for a car means its actual fuel economy (mpg) is higher than what the model predicts for a car with that horsepower (HP).
A residual of 3 means the actual fuel economy of the car is 3 mpg higher than the value predicted by the regression model \(mpg = 46.87-0.004HP\) for a car with that particular horsepower.

Answer:

In this context, to say that a certain car has a positive residual means that the actual fuel economy (mpg) was higher than the model predicts for a car with that horsepower (HP). A residual of 3 means the car's actual fuel economy is 3 mpg higher than the value predicted by the regression model for its horsepower.