# Thread: Correlation & linear regression

1. ## Correlation & linear regression

Y and Z are two random variables with Correlation of YZ of 0.5
IF X=2Z-1, then correlation of XZ is equal to;

Can anyone help? Thanks in advance

2. Correlation coefficient between X and Z = $\frac{Cov(X,Z)}{\sqrt{Var(X)}\sqrt{Var(Z)}}$ where
$Cov(X,Z) = Cov(2Z-1,Z) = 2Var(Z)$
and
$Var(X) = Var(2Z-1) = 4Var(Z)$

Now put these values in the first expression.

For further reasons behind this simplification, see Properties of Covariance and Properties of Variance

Note- By the way, your question is either incomplete or partially wrong since the answer has nothing to do with Correlation between Y and Z. Also, you need to know Var(Z).