Chapter 4.2, Problem 4.35E

To determine

To find out the statement in the question is true or false and also it will be true if $r^2=0.7$ and explain.

Answer to Problem 4.35E

The statement is false but it is true for $r^2$ .

Explanation of Solution

The statement in the question is false because r gives only information about the direction and the strength of the relationship.

For the square of the correlation $r^2$ , however, we know,

The square of the correlation $r^2$ is the fraction of the variation in the values of y that is explained by the least square regression of $y\text{ on }x$ .

Thus it is true for $r^2$ .