# Combining summary statistics

Currently I add Var1+Var2=VarSUM12 and then perform a linear regression on VarSUM12~x to obtain test statistics for x and get insight into weak associations that are present across Var1 and Var2 with x.

I would like to combine summary statistics (coefficient and standard error) from the individual regressions (Var1~x and Var2~x) to obtain the coefficient/se of VarSUM12~x. I guess the coefficient is easy, but is it possible to combine the standard errors?

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$\text{Var}(Y_1+Y_2) = \text{Var}(Y_1)+\text{Var}(Y_2)+2\text{Cov}(Y_1,Y_2)$
I'm not sure I understand correctly the OP's question. But if $Y_1$ and $Y_2$ are jointly Gaussian, you should be able to push this a tad further: $cov(Y_1,Y_2)=(\mbox{Var}(Y_1+Y_2)-\mbox{Var}(Y_1-Y_2))/4$ –  user603 Apr 14 at 15:18