Chapter 4.5, Problem 4E

To determine

The correlation coefficient that doesn’t belong to the other three.

Answer to Problem 4E

The correlation coefficient that doesn’t belong to the other three is $-0.09$ .

Explanation of Solution

Given information: Four correlation coefficients: $r=-0.98,0.96,-0.09$ and $0.97$ are given.

  $-0.98$ is close to $-1$ , which means that the points lie close to a line with negative slope, i.e. there is correlation between the data.

  $0.96$ and $0.97$ are close to $1$ , which means that the points lie close to a line with positive slope, i.e. there is correlation between the data.

But, $-0.09$ is close to $0$ , the points do not lie close to any line and are widely scattered, there is no correlation.

Thus, the correlation coefficient that doesn’t belong to the other three is $-0.09$ .