Weighting of non-linear fit

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Bryan 2015-11-10

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https://ww2.mathworks.cn/matlabcentral/answers/254104-weighting-of-non-linear-fit

Hi,

I have made a rational fit function of some data using the cftool GUI. It works quite well.

I have some data points (X,Y) with standard error Ye (Y +/- Ye).

At first I made the rational fit model simply using the X,Y data points. But then I decided that I wanted to include the Y uncertainty of the data points in to model somehow. So I used weighting (w) to represent this, whereby:

w(i) = 1 / (Ye(i)^2))

w is a 1 by length(y) matrix

It worked!

However, I am a bit puzzeled. When I plot the model with observation bounds, I get larger observation bounds when I plot the unweighted model than when I plot the weighted model.

I thought that since the weighted model included data point uncertainty, that the observation bounds should be larger?

Have I done something wrong or am I just not yet understanding something that perhaps at first seems unintuitive?

Thanks Bryan