Question

a partially destroyed laboratory data, only the equations giving the two lines of regression of x on y and y on x are available and are respectively, 7x-16y + 9 = 0, 5y - 4x-3 = 0. Calculate

the coefficient of correlation, x and y.

Answer 1

The given two equation are $7x-16y+9=0$ ......(1) and $5y-4x-3=0$ ........(2)

Suppose $7x-16y+9=0$ is regression equation of $y$ on $x$

$\implies 7x-16y+9=0$

$\implies 16y=7x+9$

$\implies y=\frac{7}{16}x+\frac{9}{16}$

$\implies y=0.4375 x+0.5625$

$\therefore byx=0.4375$

Again suppose $5y-4x-3=0$ is regression equation of $x$ on $y$

$\implies 5y-4x-3=0$

$\implies 4x=5y-3$

$\implies x=\frac{5}{4}y-\frac{3}{4}$

$\implies x=1.25y-0.75$

$\therefore byx=1.25$

So the coefficient of correlation $x$ and $y$ is ,

$r=+\sqrt{byx.bxy}$ [As $byx>0$ and $bxy>0]$

$\therefore r=\sqrt{\frac{7}{16}.\frac{5}{4}}=\sqrt{0.546875}=0.7395$