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

question 46

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

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Definitions:

Heights

The measurement of someone or something from base to top or head to foot.

Statistically Significant

An indication that the likelihood of the observed data, under the assumption of the null hypothesis, is low enough to reject the null hypothesis.

Electronic Control

The use of electronic systems to regulate the operation of mechanical devices, commonly found in automotive, industrial, and consumer appliance contexts.

Sampling

The process of selecting a subset of individuals from a statistical population to estimate characteristics of the whole population.