       Re: nonlinearfit for data with errors in both coordinates

• To: mathgroup at smc.vnet.net
• Subject: [mg112193] Re: nonlinearfit for data with errors in both coordinates
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Sat, 4 Sep 2010 04:00:23 -0400 (EDT)

```On 9/3/10 at 6:07 AM, ruth.lazkoz at ehu.es (Ruth Lazcoz Saez) wrote:

>It is not clear to me if mathematica can fit to a curve data with
>explicit errors in both variables=C3=82=C5=BD(x,y). If this is the case, can
>someone drop me a correct syntax line if my data are

>x={2.0,4.0,7.0} and xerrors={0.1,0.15,0.12} y={8.0,16.0,15.00} and
>yerrors={0.3,0.35,0.42}

All of the built in Mathematica functions for doing curve fits
are designed to deal with uncertainty in the y-coordinate only.
But it is possible to create fitting functions that deal with
uncertainty in both coordinates. Here, I assume when you say
error you really mean statistical uncertainty. If you actually
know the coordinates are in error by a fixed amount, the obvious
thing to do is adjust your data so the error term is zero then
do the curve fitting.

I note, you only have three data points. That is too few data
points to make any really useful estimate of confidence limites
for the parameters of whatever model you are fitting to your
data. And it is the confidence limits that are changed by
including uncertainty estimates into the fitting algorithm not
the best estimate of the model parameters.

I also note a plot of your data indicates the model to be fitted
must be non-linear given the values you have indicated for
uncertainty. Doing non-linear fitting is significantly more
challenging than doing linear fitting. Unless you have a very
simple model that can be transformed into a linear model, you
almost certainly don't have enough data to get robust estimates
of the model parameters.

The message here is, you are almost certainly proceeding down a
path that requires some fairly sophisticated
mathematical/statistical background that is very unlikely to
produce a better or more reliable answer than what you would get
by simply ignoring the uncertainty data.

```

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