Question

The relationship between the correlation coefficient $r$ and the regression coefficient $b_{xy}$, and $b_{yx}$is

• A. $r=\frac{1}{2}(b_{xy}+b_{yx})$
• B. $r=\sqrt{b_{xy}.b_{yx}}$
• C. $r={(b_{xy}{b}_{yx})}^2$
• D. $r=b_{xy}+b_{yx}$

Answer 1

The correct option is B

$r=\sqrt{b_{xy}.b_{yx}}$

Explanation for the correct option:

Find the relationship between the correlation coefficient.

Regression coefficients of $y$ on $x=b_{yx}=r_{(y/x)}$

Regression coefficients of $x$ on $y=b_{xy}=r_{(x/y)}$

$b_{yx}.b_{xy}=r_{(y/x)}{r}_{(x/y)}$

$r^2=b_{yx}.b_{xy}$

$r=\sqrt{b_{yx}.b_{xy}}$

Hence, option $B$ is the correct answer.