Chapter 4.2, Problem 4.34E

To determine

To confirm the value of the residual shown in the TI- $84$ screen shot for the month with an average temperature of ${49.4}^0\text{F}$ .

Answer to Problem 4.34E

Thus the residual is $76.643344$ .

Explanation of Solution

In the calculator corner, we note in the left image of the calculator screen that the residual corresponding with $x=49.4$ is,

Residual $=76.643344$

By the table on the page $152$ , the $y$ -value corresponding to is:

  $y=520$

Regression equation found in the previous calculator corner:

  $\begin{array}{l}\widehat{y}=a+bx\\ a=1425.027417\\ b=-19.87187775\end{array}$

Let us first determine the predicted value at $x=49.4$ :

  $\begin{array}{l}\widehat{y}=a+bx\\ =1425.027417-19.87187775(49.4)\\ \approx 443.356656\end{array}$

The residual is the difference between the observed $y$ -value and the predicted $y$ -value:

Residual $\begin{array}{l}=y-\widehat{y}\\ =520-443.356656\\ =76.643344\end{array}$

We note that the residual is exactly the same as the residual obtained in the calculator corner.