Towards a better understanding of correlation

Correlation is often used to assess both independence and linearity in two dimensions, but is not well understood in higher dimensions. Here we take a closer look at these uses of correlation in two dimensions and how these assessments might be extended to higher dimensions. Our discussion will focus on the simple case of understanding the nature of correlation for association models for two‐ and three‐way contingency tables, but can also be considered in a more general setting.