Q. The coefficient of correlation (r) and the two regression coefficients $b_{yx},\ b_{xy}$ are related as
A) $r = \frac{b_{xy}}{b_{yx}}$
B) $r = b_{xy} \times b_{yx}$
C) $r = b_{xy} + b_{yx}$
D) $r = (sign\ b_{yx})\sqrt{b_{xy}\ b_{yx}}$
Explanation
(d)
We know that,
$r = \pm \sqrt{b_{yx}.b_{xy}}$
Also we know that sign of $r,\ b_{xy},b_{yx}\ are\ all\ same.$
$\therefore r = (sign\ of\ b_{yx})\sqrt{b_{yx}.b_{xy}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.