# Mean accuracy for sum of squares/variance

Formality says that when computing the sample variance or sum of squares one computes a sample mean with the sample data given.

If for some reason I had access to a better estimate of the mean (from a bigger sample) then can I use that mean instead of the mean from the given sample?

I want to compute the $R^2$ and t-statistic from a regression analysis, for which I need $\text{SSX}$ and $\text{SSY}$ as the sum of squares from data set Y and data set X. This SSX/Y are basically the variance(X)*(n-1)=SSX and variance(Y)*(n-1)=SSY. So if for my regression analysis I use a smaller sample than the one I actually have. After this I need to compute $R^2$ for example, in which I wish to sue a better estimate of the mean/variance using a bigger sample. This seems consistent with the conceptual theory with me, as a better estimate is always desired, and considering that both data sets (smaller and extended sample) are from the same population.

Is there a reason not to do this?

• Normally SSX is defined such that $\text{SSX} = \text{Var}(X)\times (n-1)$ not $\text{Var}(X)/ (n-1)$. Please check. – Glen_b Aug 4 '14 at 11:11
• You are right, my bad. – A Ram Aug 4 '14 at 11:23