Question

The two lines of regression are $x+2y-5=0$ and $x+3y-8=0$. The coefficient of correlation between $x$ and $y$ is

• A. $-0.72$
• B. $0.72$
• C. $-0.82$
• D. $0.82$

Answer 1

The correct option is C $-0.82$

Given two lines $x+2y-5=0,x+3y-8=0$.

Consider $x+2y-5=0$

$\Rightarrow x=-2y+5$

$\Rightarrow r_1=-2$

Consider $x+3y-8=0$

$\Rightarrow y=-\frac{1}{3}x+\frac{8}{3}$

$\Rightarrow r_2=-\frac{1}{3}$

We know that $r^2=r_1\times r_2$

$\Rightarrow r^2=-2\times -\frac{1}{3}$

$\Rightarrow r^2=\frac{2}{3}$

$\Rightarrow r=\pm \sqrt{\frac{2}{3}}$

We know that, If both regression coefficients are negative, $r$ would be negative.

$\Rightarrow r=-\sqrt{\frac{2}{3}}=-0.82$