An automotive engineer would like to be able to predict automobile mileages. She

Question

An automotive engineer would like to be able to predict automobile mileages. She believes that the two most important characteristics that affect mileage are horsepower and the number of cylinders (4 or 6) of a car. She believes that the appropriate model is

Y = 40 - 0.05X1 + 20X2 - 0.1X1X2
where X1 = horsepower
  X2 = 1 if 4 cylinders, 0 if 6 cylinders
  Y = mileage.


The fitted model for predicting mileages for 4-cylinder cars is ________.

A. 40 - 0.05X1

B. 60 - 0.10X1

C. 60 - 0.15X1

D. 40 - 0.10X1

The fitted model for predicting mileages for 6-cylinder cars is ________.

A. 40 - 0.10X1

B. 60 - 0.15X1

C. 40 - 0.05X1

D. 60 - 0.10X1

A. 40 - 0.05X1

B. 60 - 0.10X1

C. 60 - 0.15X1

D. 40 - 0.10X1

Explanation / Answer

The fitted model for predicting mileages for 4-cylinder cars is:

As X2 = 1 for 4 cylinders

Y = 40 - 0.05X1 + 20*1 - 0.1X1*1

or, Y = 50 - 0.15*X1

Answer: C. 60 - 0.15X1

The fitted model for predicting mileages for 6-cylinder cars is:

As X2 = 0 for 6 cylinders

Y = 40 - 0.05X1 + 20*0 - 0.1X1*0

or, Y = 40 - 0.05*X1

Answer: C. 40 - 0.05X1

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