How much gas? Refer to Exercise $40$. During March, the average temperature was $46.4$°F and Joan used $490$ cubic feet of gas per day. Find and interpret the residual for this month.

It is given in the question $40$that, The equation of the least-squares line is $\hat{y}=1425-19.87x$

During March, the average temperature was $46.4$°F and Joan used $490$ cubic feet of gas per day

Suppose you were to consider the consumption of gas; in this instance, "Temperature $\left(x\right)$" will clarify "Gas Consumption$\left(Y\right)$".

Thus, the explanatory variable is the temperature $\left(X\right)$and the response variable is gas consumption $\left(Y\right)$. The regression line is as follows:

$\hat{y}=1425-19.87x$

Temperature-maintenance gas consumption predicted

localid="1649937972067" $$\begin{gathered} {46.4}^{0}F,=1425-19.87\left(46.4\right) \\ =503.032 \end{gathered}$$

For the temperature to remain at localid="1649937977533" $46.4\mathrm{F},503.032$cubic feet of gas are predicted to be consumed, but localid="1649937982069" $490$cubic feet of gas were observed to be consumed.

localid="1649937986971" $$\begin{gathered} \text{residual}=\text{observed}\mathrm{Y}-\text{predected}Y \\ =Y-Y \\ =490-503.032 \\ =-13.032 \end{gathered}$$