Question

The correlation coefficient between two variables $X$ and $Y$ is found to be $0.6$. All the observations on $X$ and $Y$ are transformed using the transformations $U=2-3X$ and $V=4Y+1$. The correlation coefficient between the transformed variables $U$ and $V$ will be:

• A. $-0.5$
• B. $+0.5$
• C. $-0.6$
• D. $+0.6$

Answer 1

Answer: (C)

$-0.6$

$Corr(X,Y)=0.6$

$\therefore Corr(U,V)=\frac{Corr(2-3X,4Y+1)}{\sqrt{Var\left(U\right)Var\left(V\right)}}=\frac{Corr(-3X,4y)}{\sqrt{-3^2}\sqrt{4^2}}=\frac{-12Corr(X,Y)}{12}=-0.6$