The Model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$

question 97

Multiple Choice

The model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ was fit to a set of data.
A partial printout for the analysis follows:
$\begin{array} { r r r r r r r r r } \hline & & & \text { Actual } & \text { Predict } & & \text { Lower 95\% CL } & \text { Upper 95\% CL } \\\text { OBS } & \text { X1 } & \text { X2 } & \text { Value } & \text { Value } & \text { Residual } & \text { Predict } & \text { Predict } \\1 & 7781 & 644 & 74.707 & 83.175 & - 8.468 & 47.224 & 119.126 \\\hline\end{array}$

Interpret the value of the residual when $x _ { 1 } = 7,781$ and $x _ { 2 } = 644$ .

• A) Since the residual is not 0 , the model is not useful for predicting \(y\).
• B) The predicted \(\hat { y }\) is \(8.468\) less than the observed value of \(y\).
• C) Since the residual is negative, there is evidence of a negative linear relationship between \(y\) and at least one of the two independent variables.
• D) The predicted \(\hat { y }\) exceeds the observed value of \(y\) by \(8.468\).

---

Definitions:

Aggressiveness

A quality of being ready or likely to confront or attack, often reflecting in behavior that can be forceful, hostile, or assertive.

Psychopathic

Relating to psychopathy, a personality disorder marked by ongoing antisocial actions, lacking empathy and remorse, along with prominent, uninhibited, and narcissistic characteristics.

Undercontrolled

A personality trait describing individuals who have difficulty regulating their impulses and emotions.

Overcontrolled

Describing an individual who exhibits a high level of self-restraint, often at the expense of spontaneity or emotional expression.