Not really. Zero correlation does not necessarily imply independence. From the example on this resource[1]: Let X be a normally distributed random variable wit

Not really. Zero correlation does not necessarily imply independence. From the example on this resource[1]: Let X be a normally distributed random variable with zero mean, and say Y = X^2. Clearly they are not independent. Covariance, which is needed for (pearson) correlation coefficient, can be calculated to be 0: Cov(X, Y) = E(XY) - E(X)E(Y) = E(X^3) - 0 (Since E(X) = mean(X) = 0) = 0 (Since X is centered at 0) [1] http://mathforum.org/library/drmath/view/64808.html http://mathforum.org/library/drmath/view/64808.html