Sum of residuals ~ ε [Design Issues]

posted by ElMaestro  – Denmark, 2019-12-24 15:10 (662 d 20:39 ago) – Posting: # 21027
Views: 4,092

Hi both,

» I disagree. In the model ε = 0. However in the fit, the sum of residuals is only asymptotically 0. We shouldn’t speak of bias when we obtain something sufficiently close to the numeric resolution of the machine.

Perhaps I am getting it wrong; the sentence above sounds a little off and I have a feeling you may not be discussing the same thing?

The sum of residuals for a fitted normal linear model will be zero. Not asymptotically. If you sum them in R or any other software you will get zero, be it either like zero-zero or effectively zero, depending on the implementation.
This is because the underlying assumption is that epsilon be distributed with mean zero. If we end up with a non-zero sum, I'd say we have screwed up somewhere.

Try sum(resid(M))

Pass or fail!
ElMaestro

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