Question

Exercise 16 describes a regression model that uses a car’s engine displacement to estimate its fuel econ- omy. In this context, what does it mean to say that a certain car has a positive residual?

Answer 1

From the information, observe that there is a relationship between the fuel economy and engine size.

The regression model is,

Mpg = 36.25 – 3.867 Engine size

The residual is the difference between the actual value and predicted value.

Residual = y - ŷ

Here, y is the actual value and ŷ is the predicted value.

The car gets positive residual, if the actual value is greater than the predicted value.

Therefore, in this context, a certain car has a positive residual means that the actual mileage of that particular car is greater than the predicted mileage.