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Epictetus comments on Causality does not imply correlation - Less Wrong
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Correlation only looks for linear relationships. For example, suppose we have a random variable X that takes values -2, -1, 1, or 2 each with probability 1/4. Define the random variable Y=X^2. The correlation is 0. Despite a functional relationship (causality if I've ever seen it), the two variables are uncorrelated.