Chapter 3.2, Problem 40E

To determine

To calculate and interpret the residual for this month.

Answer to Problem 40E

Residual is $-13.032$ .

Explanation of Solution

It is given the regression line that:

  $\widehat{y}=1425-19.87x$

And it is given that the average temperature was ${46.4}^0$ F and Joan used an average of $490$ cubic feet of gas per day. So, we have,

  $\begin{array}{l}x=46.4\\ y=490\end{array}$

Thus, the average gas used per day is as:

  $\begin{array}{l}\widehat{y}=1425-19.87x\\ =1425-19.87(46.4)\\ =503.032\end{array}$

And therefore the residual is calculated as:

  $\begin{array}{l}\text{Residual}=y-\widehat{y}\\ =490-503.032\\ =-13.032\end{array}$

This then implies that we overestimated the mean amount of natural gas that Joan will use by $13.032$ cubic feet per day in a month, when making the prediction using the regression line.