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...ng trouble writing down an example that proves the benefit of this. I am beginning to suspect that because R's lm uses a QR decomposition under the hood, the instability that we used to see when we inverted (X'X) is no longer so serious as it used to be. When the columns in X are x1 x2 x3 x3squared then the QR decomposition is doing about the same thing as we would do if we replaced x3 and x3squared by the poly(x3, 2) results. Or not. I'm not arguing that, I'm thinking out loud, hoping you'll correct me. pj -- Paul E. Johnson Professor, Political Science Assoc. Director...