Chapter 12, Problem 29PT4

To determine

To explain the effect on the value of r².

Answer to Problem 29PT4

(e) It would have no effect on the value of r² because it lies on the least-squares regression line.

Explanation of Solution

Given:

  

The options are:

(a) It would decrease the value of r2 because the added point is an outlier.

(b) It would increase the value of r² because any point added to the data would increase the percent of variation in bear weight that can be explained by the least-squares regression line.

(c) It would increase the value of r² because the added point lies on the least-squares regression line and is far from the point $(\overline{x},\overline{y})$ .

(d) It would have no effect on the value of r² because the added point lies far from the point $(\overline{x},\overline{y})$ .

(e) It would have no effect on the value of r² because it lies on the least-squares regression line.

The bear was recently captured will given a data point that will be in the upper right corner of the scatterplot. Therefore, the added point will not be an outlier, because it lies in the continuation of the linear pattern. Hence, it would have no effect on the value of r² because it lies on the least-squares regression line.