Question

What are some of the possible reason for large correlations between a pair of variables, X and Y?

Answer 1

The correlation of a pair of random variables is a dimensionless number, ranging between +1 and -1. It is +1 only for a perfect upward-sloping relationship (where by “perfect” we mean that the observations all lie on a single line), and is -1 for a perfect downward-sloping relationship. The more widely-scattered the (X,Y) pairs are about a line, the closer the correlation is to 0. (Notice that the covariance of X with itself is Var(X), and therefore the correlation of X with itself is 1.)