What is the correlation between two variables? Traditional answers^{ }offer summary assessments such as Pearson’s r and regression^{ }coefficients. But new computing techniques make it possible^{ }to construct conceptually simple hypotheses that describe the^{ }full joint distribution of two variables, making it possible^{ }to “mine” the correlation for information that was previously^{ }unused. This article begins with evidence of systematic anomalies^{ }in the empirical joint distribution of height-weight data and^{ }follows with a hypothesis that explains these anomalies in terms^{ }of a theoretical joint distribution relative to a linear equation.^{ }The hypothesis has serious consequences because even in traditional^{ }examples, while it offers an improved fit to the data, its estimates^{ }of the linear center do not correspond to traditional least^{ }squares estimates of the linear relation for the same two variables.

**Key Words:** correlation • association • regression • least squares • categorical data