For the case of two independent variables $x _ { 1 }$ and $x _ { 2 }$ , which of the following statements are not true?
A) $Y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \varepsilon$
Is the first-order no-interaction model
B) $Y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } \left( x _ { 1 } + x \right) ^ { 2 } + \varepsilon$
Is the second-order no interaction model
C) $Y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 } + \varepsilon$
Is the model with first-order predictors and interaction
D) $Y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 } + \varepsilon$
Is the complete second-order or full quadratic model is
E) All of the above statements are true.

Question

Quizplus · Accepted Answer

Statement B is not true because it incorrectly describes the second-order no interaction model. The term $\beta _ { 3 } \left( x _ { 1 } + x \right) ^ { 2 }$ is not a standard form for a second-order model without interaction. A second-order no interaction model would typically include squared terms for each independent variable separately, such as $\beta _ { 3 } x _ { 1 }^2 + \beta _ { 4 } x _ { 2 }^2$, without interaction terms.

For the Case of Two Independent Variables x1x _ { 1 }x1​

For the Case of Two Independent Variables $x _ { 1 }$