2
$\begingroup$

If $u=cx+dy$ and $v=cx-dy$ and $R$ is the co-efficient of correlation between variables $x$ and $y$ and variables $u$ and $v$ have 0 correlation, then how can I prove that $$s_us_v=2cds_xs_y\sqrt{1-R^2}$$.I do not think I made any progress at all and I request a solution so that I can study it.

I have a test tomorrow at school so I really need it.

Can anyone please post a complete solution?Sorry for appearing lazy but I would appreciate some help here. Thanks.

3 Answers 3