5.1 Association and Correlation
Definition 5.1. Two variables are associated if knowing the value of one provides information about the other. They are correlated if that association is linear, so that the scatter diagram is described by a straight line.
Correlation is therefore the special case, and the distinction matters. Two variables can be perfectly associated — \(Y=X^{2}\) on \([-1,1]\), say — and have correlation zero, because the relationship, though exact, is not linear and not monotonic. A correlation of zero never establishes independence.
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