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Correlation and causality are not necessarily related.

My age is pretty well correlated with the number of TV sets in the world. But neither of them is caused by the other. In this particular example, they both happen to be correlated to time, but there need not be such a factor.

Conversely, let y = x2. Compile a set of pairs of x values, x = -m and x = +m and the corresponding y values, m2. Now, y is totally defined by x, but the correlation of y with x (not x2) for the above set of values will be zero. In this example x causes y but the relationship is not linear - the model is wrongly specified.

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Q: How is saying that two variables are correlated different from saying saying that one caused the other?
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