Chapter 3.2, Problem 39E

To determine

To calculate and interpret the residual for the cubs.

Answer to Problem 39E

Residual is $17.002$ .

Explanation of Solution

It is given in the question the regression line that,

  $\widehat{y}=60.7+0.139x$

And it is given that the Chicago cubs had $103$ wins and spent $\$182$ million on payroll. Thus,

  $\begin{array}{l}x=182\\ y=103\end{array}$

Thus, the predicted number of wins is as:

  $\begin{array}{l}\widehat{y}=60.7+0.139x\\ =60.7+0.139(182)\\ =85.998\end{array}$

Therefore, the residual for the cubs will be calculated as:

  $\begin{array}{l}\text{Residual}=y-\widehat{y}\\ =103-85.998\\ =17.002\end{array}$

This then implies that we underestimated the number of wins for the Chicago cubs by $17.002$ wins, when making the predictions using the regression line.