# [SciPy-User] How to estimate error in polynomial coefficients from scipy.polyfit?

David Goldsmith d.l.goldsmith@gmail....
Sun Mar 28 22:26:17 CDT 2010

```On Sun, Mar 28, 2010 at 11:36 AM, <alan@ajackson.org> wrote:

> Crack permeability goes like the third power of the opening (that is,
> fluid flow through cracks - think gas or oil in a fractured rock).
>

Power law or polynomial: from a regression stand point, there's quite a big
difference.

And for many problems, the Taylor expansion might appropriately be taken out
> to
> third order. Sometimes the even orders cancel out so to get the first
> non-linear effects you have to go to third order. Can't think of a specific
> offhand, but I've seen it quite a few times.
>

A slightly less-idealized pendulum.

> >I'm no expert, but the power required to overcome aerodynamic drag varies
> with the cube of speed

Same comment as above.

In my experience, compared to multi-term polynomial models, power law models
are comparatively common (though I acknowledge that, as the power is one of
the fit parameters, there's no a priori guarantee that it'll be an integer;
indeed, since the integers have measure zero rel. the reals, the odds of
getting an integer are zero, *unless* there is some "physical" reason why it
should be an integer).

DG

> -- though the physics behind that is pretty well understood.
> >
> >I guess if you were doing a bulk estimate of all of the other factors
> (fluid density & viscosity, drag coeff, etc) this would be an applicable use
> case.
> >
> >Like I said, I'm hardly an expert...
> >-paul h.
> >
> ># -------------------------
> >From: scipy-user-bounces@scipy.org [mailto:scipy-user-bounces@scipy.org]
> On Behalf Of David Goldsmith
> >Sent: Thursday, March 25, 2010 8:41 PM
> >To: SciPy Users List
> >Subject: Re: [SciPy-User] How to estimate error in polynomial coefficients
> from scipy.polyfit?
> >
> >[snip]
> >
> >On this note, perhaps some of our experts might care to comment: what
> "physics" (in a generalized sense) gives rise to a polynomial dependency of
> degree higher than two?  The only generic thing I can think of is something
> where third or higher order derivatives proportional to the independent
> variable are important, and those are pretty uncommon.
> >
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>
> --
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