The correlation coefficient of $X$ and $Y$, denoted by $Cor(X,Y)$ or just $\rho_{x,y}$ is defined as $\rho_{x,y} = \frac{Cov(X,Y)}{\sigma_X \sigma_Y}$ This represents "scaled" [[covariance]], where correlation is always between $-1$ and $1$. In general terms, an absolute value between 0.4 and 0.6 is a moderate relationship, 0.6 and 0.8 is a strong relationship and above 0.8 is a very strong relationship. If $X$ and $Y$ are [[independent]], $\rho_{x,y} = 0$. For linear functions of $X$ where $Y = aX + b$, the correlation coefficient will be $1$ if $a > 0$ and $-1$ if $a < 0$. If $Corr(X,Y) = 0$ we say $X$ and $Y$ are uncorrelated (however they may or may not be independent). ## R Correlation is `cor()` in [[R]].