The Pearson product-moment correlation coefficient is a measure of the linear relationship between two variables $X$ and $Y$, giving a value between +1 and −1.
The Pearson product-moment correlation coefficient is given by the following equation:
$\rho{_X}{_Y} = \frac{\text{Cov}(X,Y)}{\sqrt{\text{Var}(X)} \times \sqrt{\text{Var}(Y)}}$
where,
$\rho{_X}{_Y}$ = Pearson’s correlation coefficient;
$\text{Cov}(X,Y)$ = covariance of random variables $X$ and $Y$;
$\text{Var}(X)$ = variance of random variable $X$;
$\text{Var}(Y)$ = variance of random variable $Y$;
While Pearson's $\rho$ is invariant under linear transformations, it is not invariant under arbitrary monotone transformations, which are commonly applied to skewed datasets, such as square root or log transform. As such, this measure is not robust to outliers, compared to other (scale-free) measures of associations such as Spearman's $\rho$ or Kendall's $\tau$.
