The sample covariance is defined as $\hat{\sigma}_{xy}:=\frac1{n-1} \sum_{i=1}^n (x_i -\bar{x})(y_i-\bar{y})$. What is the intuition for using the correction term $n-1$ instead of $n-2$. Because we have estimated $\bar{x}$ and $\bar{y}$, my intuition is that we lose two degrees of freedom.

  • $\begingroup$ All answers and comments were moved to the duplicate thread during the merge. The owner of one answer subsequently deleted it. Although he provided no reason, beware that he might have felt some aspect of it was incorrect or misleading. Therefore I must (reluctantly) decline to undelete or otherwise re-post that answer. $\endgroup$ – whuber Oct 30 '16 at 17:37