A clear graphical set of illustrations is the bottom row in this famous set: https://en.wikipedia.org/wiki/Correlation#/media/File:Correlation_examples2.svg htt

A clear graphical set of illustrations is the bottom row in this famous set: https://en.wikipedia.org/wiki/Correlation#/media/File:Correlation_examples2.svg https://en.wikipedia.org/wiki/Correlation#/media/File:Correl... They have clear dependence; if you imagine fixing ("conditioning") x at a particular value and looking at the distribution of y at that value, it's different from the overall distribution of y (and vice versa). But the familiar linear correlation coefficient wouldn't indicate anything about this relationship.