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

David Goldsmith d.l.goldsmith@gmail....
Mon Mar 29 12:55:52 CDT 2010

```On Mon, Mar 29, 2010 at 10:47 AM, <josef.pktd@gmail.com> wrote:

> On Mon, Mar 29, 2010 at 1:31 PM, David Goldsmith
> <d.l.goldsmith@gmail.com> wrote:
> > On Mon, Mar 29, 2010 at 7:34 AM, Robert Kern <robert.kern@gmail.com>
> wrote:
> >>
> >> On Sun, Mar 28, 2010 at 22:26, David Goldsmith <d.l.goldsmith@gmail.com
> >
> >> wrote:
> >> > 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.
> >>
> >> "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.
>
> That looks to me like splitting hairs.
>
> It depends on the statistical model for the regression error, e.g.
>
> y = ax**3 + u   where u is normal, additive noise,
> or
> y = ax**3 *z   where z is log-normal, multiplicative noise
> ln(y) = ln(a) + 3*ln(x) + u  with u = ln(z)
>
> I would do it

Do what?

DG

> if I want to estimate or test if 3 is the correct power,
> but not if 3 is known.
>
> Josef
>
> >
> > 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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> >
> >
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