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

question 73

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:


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

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