Question

If the lines of regression of y on x and that of x on y are $y = kx + 4$ and $x = 4y + 5$respectively, then

• A. $k \leq 0$
• B. $k \geq 0$
• C. $0 \leq k \leq \frac{1}{4}$
• D. $0 \leq k \leq 1$

Answer 1

Answer: (C)

$0 \leq k \leq \frac{1}{4}$

Answer 2

We know that $m_{1}m_{2} \leq 1 \Rightarrow k.4 \leq 1 \Rightarrow k \leq \frac{1}{4}$

Also, $m_{1}$ and $m_{2}$ must be of same sign

$\therefore k \geq 0$. Hence, $0 \leq k \leq \frac{1}{4}$.