Chapter 12.1, Problem 11E

(a)

To determine

To find out how many clusters of beetle larvae would you predict in a circular plot with $5$ tree stumps cut by beavers.

Answer to Problem 11E

We predict that there will be $58.184$ clusters of beetle larvae in a circular plot with $5$ tree stumps cut by beavers.

Explanation of Solution

Now, as we know that in the previous exercise the computer output of this data is given. And also as we know the general regression equation be as:

  $\widehat{y}=a+bx$

And the estimate a and b are given in the column of the computer output “Coef”:

  $\begin{array}{l}\widehat{y}=a+bx\\ \Rightarrow \widehat{y}=-1.286+11.894x\end{array}$

Thus, we will evaluate it for finding clusters of beetle larvae in a circular plot with $5$ tree stumps cut by beavers as:

  $\begin{array}{l}\widehat{y}=a+bx\\ \Rightarrow \widehat{y}=-1.286+11.894x\\ =-1.286+11.894(5)\\ =58.184\end{array}$

Thus, this means that we predict that there will be $58.184$ clusters of beetle larvae in a circular plot with $5$ tree stumps cut by beavers.

(b)

To determine

To explain about how far do you expect the prediction in part (a) to be from the actual number of clusters of beetle larvae.

Answer to Problem 11E

The prediction will be off by $6.41939$ on average.

Explanation of Solution

It is given in the part (a) that:

We predict that there will be $58.184$ clusters of beetle larvae in a circular plot with $5$ tree stumps cut by beavers.

Then as it is given in the computer output that,

  $s=6.41939$

Thus, the expected error made when making predictions is given by $\sigma$ which is estimated by s . thus, we expect that the prediction will be off by $6.41939$ on average.