fit, NLLS and Levenberg–Marquardt

[<pl...@pi...>]

Hi,

'help fit' reports that the fit command uses Levenberg–Marquardt algo to 
do the fit.

I think this raises an important question that very often over-looked by 
many users of least-squares techniques even at maths PhD level.

Such techniques often only optimised the y error rather than the 
perpendicular error from the line. This is implicitly assuming y 
uncertainty >> x uncertainty.  While this condition is often satisfied 
in a controlled experiment there are many situations where this is not 
applicable and gets totally overlooked.

A common case is scatter plots which are frequently used to seek a 
relations between two quantities , each with significant errors / 
uncertainties.

In this situation the fitted line is "wrong". In fact it's the 
application that is wrong , hence the wrong result. This may or may not 
be apparent to the eye.

I have seen this happen so many times (including once in a PhD thesis 
report!) that I think it needs a serious health warning in the doc.

"Warning: using least-squares inappropriately can seriously damage your 
reputation". ;)

Firstly , could you confirm the basis on which this algo is applied in 
gnuplot? Does it only optimise vertical y residuals?


Thanks, Peter.