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Mike

"In other words, if X causes Y, then X and Y must be correlated.
...
That statement is true if there is nothing else in the system but X and Y."

This only holds if by correlation you/they mean more generally any relationship or association. If you are using the narrower statistical meaning of linear relationship than it is trivially falsifiable with a variety of nonlinear relationships, even in the absence of other variables.

Kaiser

Mike: Good point. I generally think of "correlation" as admitting any functional relationship revealed in a scatter plot of X and Y, in parallel with thinking "regression" is more general than fitting a straight line. It's a good reminder that the typical correlation printed by a software measures linear correlation, just like the basic regression assumes a linear model.

Clur

I have been following your blog for a while now (and also Andrew's one) but I have never written a comment... until now. I am doing it to let you know that I am very happy you took the time to explain in simple words what Andrew talked about. I don't have an advanced education in math or stats but I enjoy learning more about those topics. But sometimes it's hard to follow Andrew's post and the comments there. So your post written in simple terms with simple and more in depth explanations is very welcome. Thanks again. 

Kaiser

Clur: thank you for leaving the kind note. It's gratifying to hear I'm having the desired effect on my readers.

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