Question

For two variables x and y. the two regression coefficients are $b_x=-\frac{3}{2}$ and $b_y=-\frac{1}{6}$.
The correlation coefficient between x and y is :

• A. $-\frac{1}{4}$
• B. $\frac{1}{4}$
• C. $-\frac{1}{2}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $-\frac{1}{2}$

We know that, for two variables $x$ and $y$

$r=\pm \sqrt{b_x{b}_y}$

Where $b_x$ and $b_y$ are the regression coefficients

and $r$ is the correlation coefficient between $x$ and $y$

Also, the sign of $r$ is same as the sign of regression coefficients

$\therefore r=-\sqrt{\frac{-3}{2}\times \frac{-1}{6}}$

$\therefore r=\frac{-1}{2}$