Question

If the two lines of regression are $x+4y=3$ & $3x+y=15$, then the value of 'x' for given value of y=3 is

• A. -9
• B. 4
• C. 5
• D. None of these

Answer 1

The correct option is B 4

Given lines are $x+4y=3$ (i)
& $3x+y=15$ (ii)
We first check which of the line (i) & (ii) is line of regression y
on x and x on y. Let line $x+4y=3$ be the line of regression x on y, then
other be the line of regression y on x.
$\therefore$ From (i) i.e. line of regression x on y we have $x=-4y+3$
$\therefore$ $b_{xy}$=regression coefficient x on $y=-4$ and $3x+y=15$
$\therefore y=-3x+15$
$\therefore$ $b_{yx}$=regression coefficient y on x=-3
Now count $r^2=b_{yx}{b}_{xy}=(-4)(-3)=12$
$\Rightarrow$ $\left|r\right|=2\sqrt{3}$
which is not possible as $0\le r^2\le 1$. So our assumption is wrong
and line x+4y=3 is line of regression y on x & $3x+y=15$ is line of
regression x on y.
$\therefore 3x+y=15$
$\Rightarrow$ $x=\frac{15-y}{3}$
$\Rightarrow x=\frac{15-3}{3}=4$ (By putting $y=3$)