Question

The relationship between the correlation coefficient r and the regression coefficients $b_{xy}$ 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

Answer: (B)

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

Answer 2

Regression coefficients of y on x =$r = \sqrt{\left( \frac{- 3}{4} \right)\left( \frac{- 1}{4} \right)} = \frac{- \sqrt{3}}{4}$

Regression coefficients of x on y =$b_{xy} = r.\frac{\sigma_{x}}{\sigma_{y}}$

Then, $b_{yx}.b_{xy} = r.\frac{\sigma_{y}}{\sigma_{x}} \times r.\frac{\sigma_{x}}{\sigma_{y}}$

$r^{2} = b_{yx}.b_{xy}$ ⇒ $r = \sqrt{b_{yx}.b_{xy}}$.