I read from a textbook that Gauss-Newton regression is also called 'artificial regression'. Please give me an example, how does it work? And what's the relation with Newton's method? Thank you.

  • $\begingroup$ there is a Gauss-Newton numerical optimisation method and there is such a thing as non-linear regression. There is no Gauss-Newton regression, at least I never heard about it. Could you please provide the context for your citation, it is not clear for example what is artificial? $\endgroup$ – mpiktas Mar 10 '11 at 16:55
  • $\begingroup$ @mpiktas I had the same reaction, but Googling turns up lots of hits. A context would nevertheless be quite helpful. $\endgroup$ – whuber Mar 10 '11 at 20:59
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    $\begingroup$ @whuber, from what I found, the Gauss-Newton regression is non-linear regression approximation. Instead of model $y=f(x,\beta)+\varepsilon$ model with Taylor expansion of $f$ is fitted: $y=f(x,\beta_0)+\frac{\partial f}{\partial \beta}(x,\beta_0)(\beta-\beta_0)+u$. Here is the link where this regression is described. Unfortunately (if you do not know French) it is French translation of this book. $\endgroup$ – mpiktas Mar 10 '11 at 21:15
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    $\begingroup$ the link I gave in previous comment answers your question quite nicely, look at the top of page 178 (the number not the actual PDF page). If no-one answers the question, I will attempt to translate. $\endgroup$ – mpiktas Mar 10 '11 at 21:35
  • $\begingroup$ @mpiktas Equation 6.06 and the discussion surrounding it are pretty revealing. (It's interesting that the book is not as freely available in English as it is in French!) $\endgroup$ – whuber Mar 10 '11 at 21:47

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