Question

Assertion :If the coefficient of correlation between two variables x & y is 0.4 & the regression coefficient x on y is 0.2, then regression coefficient y on x be 0.8. Reason: $b_{yx}=r\frac{{\sigma }_y}{{\sigma }_x}\&b_{xy}=r\frac{{\sigma }_x}{{\sigma }_y}$

• A. Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.
• B. Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion.
• C. Assertion is true Reason is false.
• D. Assertion is false Reason is true.

Answer 1

The correct option is A Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.

$\because b_{yx}=r\frac{{\sigma }_x}{{\sigma }_y}and{b}_{xy}=r\frac{{\sigma }_y}{{\sigma }_x}$
$\because b_{yx}\cdot b_{xy}=r^2$
$\Rightarrow b_{yx}\left(0.2\right)={\left(0.4\right)}^2(\text{Given}{b}_{yx}=0.2,r=0.4)$
$\Rightarrow b_{yx}=0.8$