From: "jwmerrill@..." <jwmerrill@...>
Date: 2007-12-17T15:10:22+09:00
Subject: Re: Curve fitting to data

On Dec 16, 7:07 pm, Phil Rhoades <p...@pricom.com.au> wrote:

> I think GNUPlot requires the knowledge of the type of fn you are trying
> to fit - I want the software to TELL me what sort of fn it is eg for the
> data:
>
> -10     0
> -9      19
> -8      36
> -7      51
> -6      64
> -5      75
> -4      84
> -3      91
> -2      96
> -1      99
> 0       100
> 1       99
> 2       96
> 3       91
> 4       84
> 5       75
> 6       64
> 7       51
> 8       36
> 9       19
> 10      0
>
> http://www.zunzun.comtells me that the formula for this data is:
>
>         y = a( atan(x) ) + b( x2 ) + c( sinh(x) ) + offset
>
> I would like to be able to do this myself with my own (preferably Ruby)
> code.
>
> Thanks,
>
> Phil.

Isn't the result zunzun spit out "wrong"?  The data is most simply
described as an inverted parabola:

y = a x^2 + c

This points exactly to the problem others have mentioned.  Given a
large enough space of functions, you can fit practically anything, but
what does it mean?  Generally speaking, no one has any business
fitting 21 data points with 4 parameters.

JM