Question

If the regression equations of the variables $ x $ and $ y $ be $ x=19.13-0.83\,y $ and $ y=11.64-0.50\,x $ , then the correlation coefficient between $x$ and $y$ is:

• A. $ 0.66 $
• B. $ -0.64 $
• C. $ 0.001 $
• D. $ -0.001 $

Answer 1

Answer: (B)

If both regression coefficients are positive or negative,
then the correlation coefficient is positive or negative.
Given regression equations are
$x=19.13-0.83 y$ and $y=11.64-0.50 x$
Their corresponding regression coefficients are
$b_{x y}=-0.83$ and by $b_{y x}=-0.50 $
$\therefore $ Correlation coefficient $=-\sqrt{b_{x y} \times b_{y x}}$
$=-\sqrt{0.83 \times 0.50}$
$=-0.64$
If regression coefficients are of opposite sign, then correlation coefficient cannot be determined.