Linear correlation

Simple linear correlations

The Pearson correlation coefficient indicates the strength of a linear relationship between two variables, but its value generally does not completely characterize their relationship. In particular, if the conditional mean of ${\displaystyle Y}$ given ${\displaystyle X}$, denoted ${\displaystyle \operatorname {E} (Y\mid X)}$, is not linear in ${\displaystyle X}$, the correlation coefficient will not fully determine the form of ${\displaystyle \operatorname {E} (Y\mid X)}$.