Suppose X and Y are random variables such that Y aX b wher

Suppose X and Y are random variables such that Y = a*X + b, where a and b are constants; thus Y is a linear function of X. What is the correlation (X,Y)?

Solution

The correlation of two perfectly linearly related variables is either 1 or -1.

Thus,

if a > 0, rho = 1.

if a < 0, rho = -1

if a = 0, rho = 0 [ANSWERS]