Ok so say I'm comparing two groups. I can do it this way ##Y_{i}=b_{1}*I(G1)+b_{2}*I(G2)+e_{i}## where I(G1) is 1 if in group 1 and 0 if not. I(G2) is 1 if in group 2 and 0 if not. In that case, my design matrix will not have a column of ones.(adsbygoogle = window.adsbygoogle || []).push({});

However, if I reparameterise to ##Y_{i}=b_{0}+b_{2}*I(G2)+e_{i}## since I know I(G2) and I(G1) has to sum to 1. I will get a design matrix with ones in the first column. I think there is a theorem that says that the residuals sum to 0 if this is the case.

Now, does this mean that the residuals sum to zero for the first parameterization as well? After all, the two models should be equivalent.

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# A Residuals summing to zero?

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