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Weights in NonlinearRegress / NonlinearFit. Versus data errors

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  • Subject: [mg85326] Weights in NonlinearRegress / NonlinearFit. Versus data errors
  • From: "Kristof Lebecki" <lebecki-hates-SPAM at ifpan.edu.pl>
  • Date: Wed, 6 Feb 2008 05:38:34 -0500 (EST)

Dear all,



Introduction: it happens that we, physicists have to fit a given function
y(x) to a set of experimentally derived points {x_i,y_i}, i=1..n. I use for
that NonlinearRegress.



It happenes, however, that the experimental points are known with different
accuracy. (We call usually such inaccuracy as an error.) Assume that we have
a vector of triples {x_i,y_i,dy_i}, i=1..n. Now, dy_i describes the
 "y-error" of every point we want to fit.



My first idea was to use Weights for that. Weights defined as:

       {w_i}= {1/dy_i} (the smaller the error the higher the weight).

But my experienced colleague pointed out that what actually is here
minimized is: chi^2= \sum_i w_i*(e_i)^2. He prefers that sum to be
dimensionless, thus he argues that the weights should be defined as:

       {w_i}= {1/(dy_i)^2}



And what is your opinion?




Regards, Kris



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