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

[David Goldsmith]

On Mon, Mar 29, 2010 at 7:34 AM, Robert Kern <robert.kern at gmail.com> wrote:

> On Sun, Mar 28, 2010 at 22:26, David Goldsmith <d.l.goldsmith at gmail.com>
> wrote:
> > On Sun, Mar 28, 2010 at 11:36 AM, <alan at 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.
>
> "Third power" == "x**3". He's not talking about a power law.
>

Yes, I know that, but from a regression stand point, unless there's an
offset (constant) term (in which case a two parameter polynomial fit is what
you'll be doing) if your model is simply y = ax**3, aren't you better off
doing the regression as if you were doing a power law, albeit w/ a fixed
power (i.e., log transforming the data first, fixing the slope parameter at
three, and then regressing to find the constant term, i.e., log(a))?

In other words, I was soliciting examples of situations where a true
polynomial (as opposed to a monomial) model was appropriate - I maintain
that if your model is a monomial (integer power law model, w/ only one
term), then, as far as regression is concerned, it is more appropriate to
think of it as a power law model w/ a fixed parameter, not as a polynomial
model.  From this perspective, the number of "naturally occurring"
polynomial models is greatly reduced.

DG


>
> --
> Robert Kern
>
> "I have come to believe that the whole world is an enigma, a harmless
> enigma that is made terrible by our own mad attempt to interpret it as
> though it had an underlying truth."
>  -- Umberto Eco
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