Question

Assertion :If lines of regression y on $x\&x$ on y are respectively $y=kx+4\&x=4y+5$ then $kϵ[0,\frac{1}{4}]$. Reason: $0\le r^2\le 1$.

• 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.

$\because$ Line of regression $y$ on $x$ is $y=kx+4$
$\therefore b_{yx}=k$ and line of regression $x$ on $y$ is $x=4x+5$
$\therefore b_{xy}=4$
Now $b_{yx}{b}_{xy}=4k=r^2$
Also, $0\le r^2\le 1\Rightarrow 0\le 4k\le 1$
$\Rightarrow 0\le k\le \frac{1}{4}\Rightarrow k\in [0,\frac{1}{4}]$
Hence Assertion (A) & Reason (R) both are individually correct and Reason (R) is the correct explanation of Assertion (A).