Instruction 13.41
An automotive engineer would like to be able to predict automobile fuel economy. She believes that the two most important characteristics that affect economy are engine power and the number of cylinders (4 or 6) of a car. She believes that the appropriate model is
$\begin{array}{l}Y = 40 - 0.05 X _ { 1 } + 20 X _ { 2 } - 0.1 X _ { 1 } X _ { 2 }\\\\\text { where } \begin{aligned}X _ { 1 } & = \text { engine power } \\X _ { 2 } & = 1 \text { if } 4 \text { cylinders, } 0 \text { if } 6 \text { cylinders } \\Y & = \text { economy expressed as kilometres. }\end{aligned}\end{array}$
-Referring to Instruction 13.41,the fitted model for predicting economy for 6-cylinder cars is______.

Question

Instruction 13.41
An automotive engineer would like to be able to predict automobile fuel economy. She believes that the two most important characteristics that affect economy are engine power and the number of cylinders (4 or 6) of a car. She believes that the appropriate model is

\begin{array}{l}Y = 40 - 0.05 X _ { 1 } + 20 X _ { 2 } - 0.1 X _ { 1 } X _ { 2 }\\\\\text { where } \begin{aligned}X _ { 1 } & = \text { engine power } \\X _ { 2 } & = 1 \text { if } 4 \text { cylinders, } 0 \text { if } 6 \text { cylinders } \\Y & = \text { economy expressed as kilometres. }\end{aligned}\end{array}

-Referring to Instruction 13.41,the fitted model for predicting economy for 6-cylinder cars is______.

Quizplus · Accepted Answer

For a 6-cylinder car, X₂ = 0, so the model simplifies to: Y = 40F1F1F1S1F1F1F10 - 0.05X₁ Substituting X₂ = 0 in the last term of the original model, we get: 20X₂F1F1F1S1F1F1F10 = 0 Therefore, the only term left in the simplified model for a 6-cylinder car is - 0.05X₁, which corresponds to choice C.

Instruction 13 -Referring to Instruction 13