# [R] statistical significance, nonlinear regression

Bert Gunter gunter.berton at gene.com
Thu Dec 25 04:23:52 CET 2008

```Tests of statistical significance and/or confidence intervals for individual
parameters in nonlinear regression are often meaningless and misguided.
Nonlinear regression is **inherently** different than linear regression. It
may make no physical sense whatever to eliminate *any* of the parameters
describing, say, a series of interrelated chemical interactions. Determining
what sequence of "nested" models to consider (which is the only thing that
makes sense) is typically difficult and subject specific. Finally,
statistical inference for nonlinear models is almost never exact, and the
standard (e.g. likelihood based) approximations can be way off for small
samples and certain data configurations.

As for references -- are you kidding?! There are tons of books and papers
out there. As you did not provide your identity, we have no idea what line
of work you're in -- but you might start by looking for tutorials on the
subject pitched to your profession and level of statistical understanding.

-- Bert Gunter
Genentech Nonclinical Statistics

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Sent: Wednesday, December 24, 2008 3:21 PM
To: r-help at r-project.org
Subject: [R] statistical significance, nonlinear regression

I am using nonlinear regression to fit a couple of variables to a set of
measurements. I would like to do some significance tests for the estimated
parameters. I am able to check the confidence intervals using the Jacobian
coming out of nonlinear regression.

I do see in a paper which shows t-value (it says estimated by White
method??), f-value, f-test, and j-test, are these available in matlab, or I
could code them myself but I need details about these tests. I would be glad
if you could provide a reference...

Thanks
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