Question

From the two regression equations
$y=4x-5$ and $3x=2y+5$ find $\overline{x}$ and $\overline{y}$.

Answer 1

$y=4x-53x=2y+5$

We know, $y=byx(x-\overline{x})+c$

$x=bxy(y-\overline{y})+c$

(Solving both lines we will get $\overline{x}$ & $\overline{y}$ as both lines intersect at $(\overline{x},\overline{y})$)

$\therefore 3\overline{x}=2(4\overline{x}-5)+5$

$3\overline{x}=8\overline{x}-10+5$

Or $5\overline{x}=5$

$\overline{x}=1$

$\overline{y}=4\times 1-5$

Or $\overline{y}=-1$

$\overline{x}=1,\overline{y}=-1$