The sample correlation coefficient $R$ plays an important role in many statistical analyses. We study the moments of $R$ under the bivariate Gaussian model assumption, provide a novel approximation for its finite sample mean and connect it with known results for the variance. We exploit these approximations to present non-asymptotic concentration inequalities for $R$. Finally, we illustrate our results in a simulation experiment that further validates the approximations presented in this work.

Comment: 10 pages, preprint