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

question 88

Multiple Choice

Consider the model
$$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 1 } ^ { 2 } + \beta _ { 3 } x _ { 2 } + \beta _ { 4 } x _ { 3 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \beta _ { 6 } x _ { 1 } x _ { 3 } + \beta _ { 7 } x _ { 1 } 2 _ { x _ { 2 } } + \beta _ { 8 } x _ { 1 } x _ { 3 } + \varepsilon$$
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
$$\hat { y } = 8.8 - 1.1 x _ { 1 } + 3.2 x _ { 1 } ^ { 2 } + 1.6 x _ { 2 } - 4.4 x _ { 3 } + .02 x _ { 1 } x _ { 2 } + 1.3 x _ { 1 } x _ { 3 } + .01 x _ { 1 } 2 ^ { 2 } - .06 x _ { 1 } x _ { 3 }$$
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) \(\hat { y } = 8.8 - 1.6 x _ { 2 } - 4.4 x _ { 3 }\)
• D) \(\hat { y } = 8.8 - .22 x _ { 1 } + 3.15 x _ { 1 } 2\)

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Definitions:

Dermis

The layer of skin located beneath the epidermis, containing nerve endings, sweat glands, and hair follicles, responsible for the elasticity and strength of the skin.

Inflammatory Phase

The initial stage of the wound healing process, in which inflammation occurs to clean out the wound and prevent infection.

Hemostasis

The physiological process which stops bleeding at the site of an injury while maintaining blood in a fluid state within the vascular system.

Granulation

The formation of new, fibrous tissue during the healing process of a wound, characterized by small, red, grain-like bumps.