Question

Two regression lines are represented by $4x+10y=9$ and $6x+3y=4$. Find the line of regression of $y$ on $x$.

Answer 1

Assuming $4x+10y=9$ to be regression line of $y$ on $x$.
$10y=-4x+9$

$y=-\frac{4}{10}x+\frac{9}{10}$

$\Rightarrow b_{yx}=\frac{-2}{5}$

Then $6x+3y=4$
$6x=-3y+4$

$x=-\frac{3}{6}y+\frac{4}{6}$

$\Rightarrow b_{xy}=-\frac{1}{2}$

Now, $b_{yx}\times b_{xy}=-\frac{2}{5}\times -\frac{1}{2}=\frac{1}{5}<1$

Which is true. Hence our assumption is true, i.e., regression line of y on x is 4x + 10y = 9