It is desired to build a regression model to predict $\mathrm { y } =$ the sales price of a single family home, based on the $x _ { 1 } =$ size of the house and $x _ { 2 } =$ the neighborhood the home is located in. The goal is to compare the prices of homes that are located in two different neighborhoods. A complete 2nd-order model is proposed. Which regression model proposes the complete 2nd-order model?
A) $\mathrm { E } ( \mathrm { y } ) = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } _ { 1 } + \beta _ { 2 } \mathrm { x } _ { 1 } ^ { 2 } + \beta _ { 3 } \mathrm { x } _ { 2 } + \beta _ { 4 } \mathrm { x } ^ { 2 }$
B) $\mathrm { E } ( \mathrm { y } ) = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } _ { 1 } + \beta _ { 2 } \mathrm { x } _ { 1 } ^ { 2 } + \beta _ { 3 } \mathrm { x } _ { 2 } + \beta _ { 4 } \mathrm { x } _ { 1 } \mathrm { x } _ { 2 } + \beta _ { 3 } \mathrm { x } _ { 1 } ^ { 2 } \mathrm { x } _ { 2 }$
C) $\mathrm { E } ( \mathrm { y } ) = \beta _ { 0 } + \beta _ { 1 \mathrm { x } _ { 1 } } + \beta _ { 2 } \mathrm { x } _ { 2 }$
D) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$

Question

Quizplus · Accepted Answer

A complete 2nd-order model includes all possible terms up to the second order: main effects, interaction terms, and squared terms for each predictor. Option B is the only choice that includes all these elements: main effects ($\beta_1 x_1$ and $\beta_3 x_2$), squared terms ($\beta_2 x_1^2$), and interaction terms ($\beta_4 x_1 x_2$ and an additional term for the interaction of $x_1^2$ and $x_2$, although this last term is not typically part of a standard complete 2nd-order model, it suggests a more complex interaction that might have been intended in the question).

It Is Desired to Build a Regression Model to Predict y=\mathrm { y } =y=

It Is Desired to Build a Regression Model to Predict $\mathrm { y } =$