Which equation represents a complete second-order model for two quantitative independent variables?
A) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } ^ { 2 } + \beta _ { 2 } x _ { 2 } ^ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } x _ { 2 } + \beta _ { 4 } x _ { 1 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } ^ { 2 } x _ { 2 } ^ { 2 }$
B) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 }$
C) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 } + \beta _ { 4 } x _ { 1 } ^ { 2 } + \beta _ { 5 } x _ { 2 } ^ { 2 }$
D) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } x _ { 2 } + \beta _ { 2 } x _ { 1 } ^ { 2 } + \beta _ { 3 } x _ { 2 } ^ { 2 }$

Question

Which equation represents a complete second-order model for two quantitative independent variables? 
A) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } ^ { 2 } + \beta _ { 2 } x _ { 2 } ^ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } x _ { 2 } + \beta _ { 4 } x _ { 1 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } ^ { 2 } x _ { 2 } ^ { 2 }$
B) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 }$
C) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 } + \beta _ { 4 } x _ { 1 } ^ { 2 } + \beta _ { 5 } x _ { 2 } ^ { 2 }$
D) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } x _ { 2 } + \beta _ { 2 } x _ { 1 } ^ { 2 } + \beta _ { 3 } x _ { 2 } ^ { 2 }$

Quizplus · Accepted Answer

A complete second-order model for two quantitative independent variables includes not only the linear terms ($\beta_1 x_1$ and $\beta_2 x_2$), the squared terms ($\beta_4 x_1^2$ and $\beta_5 x_2^2$), but also the interaction term ($\beta_3 x_1 x_2$). Option C includes all these components, making it a complete second-order model.

Which Equation Represents a Complete Second-Order Model for Two Quantitative