What is a direct correlation?

Question

I have two contrary definitions of for the direct correlation between two variables $X$ and $Y$

• Their correlation coefficient is close to $1$.
• There is a direct causal relationship between the variables (ie. there is no $Z$ such that $Z$ causes $X$ and $Z$ causes $Y$)

Which one is correct?

Answer 1

I'm not a statistician (though I taught statistics about 35 years ago). But I'd say that the first definition is correct. One of the important points about correlation is that it should not be confused with causality. Remember the old joke: Smoking and cancer are correlated; does this mean that smoking causes cancer, or that cancer causes smoking. Neither one -- correlation by itself does not imply causality in either direction.

Answer 2

A correlation in which large values of one variable are associated with large values of the other and small with small; the correlation coefficient is between 0 and +1. Hope this helps