       Re: Nonlinear Regression Oddities and Questions

• To: mathgroup at smc.vnet.net
• Subject: [mg93139] Re: Nonlinear Regression Oddities and Questions
• From: dh <dh at metrohm.ch>
• Date: Tue, 28 Oct 2008 04:54:40 -0500 (EST)
• References: <gdugc6\$jr0\$1@smc.vnet.net>

```
Hi Andrew,

I can only guess what is going on.

First, did you check that both confidence levels are identical?

Further,it could be that Mathematica calculates the confidence intervalls using

error propagation technique. This methods relies on linearizaton, that

means, it is only correct for small errors.  On the other hand, Monte

Carlo does not have this limitation. Anyway if this is true, both method

should agree with small errors.

Daniel

Andrew Cameron Beveridge wrote:

> I am fitting a function with known errors to determine the Confidence

> Intervals of the fitted parameters.

>

> For each data point I have an associated error, that is, the Standard

> Deviation of the measurement.

>

> I can send the data to anyone interested.

>

> In Mathematica I use the function NonlinearRegress with Weights->Standard

> Deviation^(-2). I get an answer for the Confidence Interval.

>

> I then tested the data using a plotting program, pro Fit. In pro Fit the

> Confidence Interval is determined by a Monte Carlo bootstrapping method.

> Random data is generated within the error bars and a fit is made; this is

> done 500 times. The confidence interval gives a range of values from the

> Monte Carlo result.

>

> The two programs give much different answers.

>

> Do anyone has experience with the validity of the Mathematica results. I

> do not know which program is correct.

>

>

> Regards,

> Andrew

>

--

Daniel Huber

Metrohm Ltd.

Oberdorfstr. 68

CH-9100 Herisau

Tel. +41 71 353 8585, Fax +41 71 353 8907

E-Mail:<mailto:dh at metrohm.com>

Internet:<http://www.metrohm.com>

```

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