Question

For the bivariate data, $r=0.3,\text{cov}(X,Y)=18,{\sigma }_x=3$. Find ${\sigma }_y$

Answer 1

Given, $r=0.3,\text{cov}(X,Y)18,{\sigma }_x=3$

Therefore, $r=\frac{\text{cov}(x,y)}{{\sigma }_x{\sigma }_y}$

$\Rightarrow 0.3=\frac{18}{3{\sigma }_y}$

$\Rightarrow {\sigma }_y=\frac{18}{0.9}$

$\Rightarrow {\sigma }_y=20$

Thus, value of ${\sigma }_y=20$.