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

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 $8.468$ .