Consider the Model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$

question 3

Multiple Choice

Consider the model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ 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 $\hat { y } = 36.7 + 1.3 x _ { 1 } + 5.4 x _ { 2 } + 3.2 x _ { 3 }$ . What is the least squares regression equation associated with level 2?

• A) \(\hat { y } = 39.9 + 1.3 x _ { 1 }\)
• B) \(\hat { y } = 38.0 + 5.4 x _ { 2 }\)
• C) \(\hat { y } = 39.9 + 5.4 x _ { 2 }\)
• D) \(\hat { y } = 42.1 + 1.3 x _ { 1 }\)

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Definitions:

Satisficers

Individuals who make decisions that suffice to meet their needs rather than optimizing the best possible outcome.

Solutions

Solutions are answers or ways to effectively deal with a problem or challenge.

Cognitive Bias

A structured manner of diverging from the norm or logical reasoning in making judgments, allowing for conclusions about others and situations to be made in a way that lacks logical coherence.

Paid

Receiving monetary compensation for services rendered or work performed.