Consider the Model Where $x _ { 1 }$ Is a Quantitative Variable And

question 116

Short Answer

Consider the model $$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 1 }^{ 2} + \beta _ { 3 } x _ { 2 } + \beta _ { 4 } x _ { 3 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \beta _ { 6 } x _ { 1 } x _ { 3 } + \beta _ { 7 } x _ { 1 }^{ 2} { x _ { 2 } } + \beta _ { 8 } x _ { 1 }^{ 2} { x _ { 3 } } + \varepsilon$$
where $x _ { 1 }$ is a quantitative variable and $x _ { 2 }$ and $x _ { 3 }$ are dummy variables describing a qualitative variable at three levels using the coding scheme
$$x _ { 2 } = \left\{ \begin{array} { l l } 1 & \text { if level } 2 \\0 & \text { otherwise }\end{array} \quad x _ { 3 } = \left\{ \begin{array} { l l } 1 & \text { if level } 3 \\0 & \text { otherwise }\end{array} \right. \right.$$
The resulting least squares prediction equation is
$$\hat { y } = 8.8 - 1.1 x _ { 1 } + 3.2 x _ { 1 } ^ { 2 } + 1.6 x _ { 2 } - 4.4 x _ { 3 } + .02 x _ { 1 } x _ { 2 } + 1.3 x _ { 1 } x _ { 3 } + .01 x _ { 1 } { } ^ { 2 } x _ { 2 } - .06 x _ { 1 }^{2} x _ { 3 }$$
What is the equation of the response curve for $E ( y )$ when $x _ { 2 } = 0$ and $x _ { 3 } = 0$ ?
A) $\hat { y } = 8.8 - 1.1 x _ { 1 } + 3.2 x _ { 1 } { } ^ { 2 }$
B) $\hat { y } = 8.8 - 1.3 x _ { 1 } + 3.2 x _ { 1 } { } ^ { 2 }$
C) $y = 8.8 - .22 x _ { 1 } + 3.15 x _ { 1 } { } ^ { 2 }$
D) $y = 8.8 - 1.6 x _ { 2 } - 4.4 x _ { 3 }$

• A) \(\hat { y } = 8.8 - 1.1 x _ { 1 } + 3.2 x _ { 1 } { } ^ { 2 }\)
• B) \(\hat { y } = 8.8 - 1.3 x _ { 1 } + 3.2 x _ { 1 } { } ^ { 2 }\)
• C) \(y = 8.8 - .22 x _ { 1 } + 3.15 x _ { 1 } { } ^ { 2 }\)
• D) \(y = 8.8 - 1.6 x _ { 2 } - 4.4 x _ { 3 }\)

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Definitions:

Pueblo Gender Roles

Traditional roles and responsibilities assigned to men and women within Pueblo societies, often centered around family, religious ceremonies, and agriculture.

Spiritual Conquest

Refers to the process of religious conversion and implementation of Christianity, especially by European missionaries in the Americas during colonial times.

Religious Conflict

Disputes or conflicts between groups or individuals based on religious beliefs and practices.

Colonization

The act of establishing control over a territory by a foreign power, often involving the subjugation and exploitation of the indigenous population.