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

josef.pktd@gmai... josef.pktd@gmai...
Mon Mar 29 12:59:58 CDT 2010

```On Mon, Mar 29, 2010 at 1:55 PM, David Goldsmith
<d.l.goldsmith@gmail.com> wrote:
> 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?

"it" = (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))?

Josef

>
> 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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```