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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: the mathematic relationship between two series of data
Date: Sun, 13 Jul 2008 11:26:02 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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"ZHANG Hong" <oceanzhhd@gmail.com> wrote in message 
<g5cm9h$r70$1@fred.mathworks.com>...
> Hi, John,
> 
> I had read your reply repeatly and I do appreciate your 
> help and suggestions.
> 
> Yes, As you say both data itself including its 
> orgin/background, noise, and what we expected it to be will 
> affect the final result of datafitting. It is not easy to 
> relate the curvefitting function to the real life meaning 
> of the dataset especially when you got unexpected result 
> which you at first thought it would be the same as many 
> experimental studies had proved to. In this condition, i 
> always look back to my data and see whether it is the 
> geographic condition, data collectiong process or other 
> factors that affect it, or if it is really an emergency 
> that many other system might have.
> 
> Cheers!
> 
> Hong

As a continuation of my last response,
normally, I'd suggest a spline fit as a
starting point. Is an interpolating spline
appropriate for you? It all depends on
what you will do with the curve and what
your goals are.

A least squares spline or a smoothing
spline are also options to be considered.
Since it sounds as if you do not have any
mechanistic or physical model for your
data, splines are often a good choice. But
even then there are issues to consider. Do
you have important information in your
knowledge of the process? Must it be
monotone? Do you know something about
the curvature of the relationship to be
modeled? Do you have a measure of the
noise variance on this data?

For example, my own utility, estimatenoise,
estimates the standard deviation to be
roughly 0.005. But is this consistent with
your own knowledge of the process?

sqrt(estimatenoise(A,B))
ans =
    0.0047606

John