Chapter 4.2, Problem 4.29E

(a)

To determine

To predict the number of laps that John will complete using the regression line.

Answer to Problem 4.29E

John will complete $4\frac{2}{3}$ laps.

Explanation of Solution

The regression line is:

  $y=10-\frac{2}{3}x$

Replace $x\text{ with }8$ in this:

  $\begin{array}{l}y=10-\frac{2}{3}x\\ =10-\frac{2}{3}(8)\\ =\frac{30}{3}-\frac{16}{3}\\ =\frac{14}{3}\\ =4\frac{2}{3}\end{array}$

John will complete $4\frac{2}{3}$ laps.

(b)

To determine

To predict the number of laps that Ezekiel will complete using the regression line why or why not.

Answer to Problem 4.29E

We cannot use the regression line to predict the amount of laps that Ezekiel will complete.

Explanation of Solution

The regression line is:

  $y=10-\frac{2}{3}x$

Replace $x\text{ with 16}$ in this:

  $\begin{array}{l}y=10-\frac{2}{3}x\\ =10-\frac{2}{3}(16)\\ =\frac{30}{3}-\frac{32}{3}\\ =-\frac{2}{3}\end{array}$

It is not possible to run a negative amount of laps, thus we cannot use the regression line to predict the amount of laps that Ezekiel will complete.