JM,


On Mon, 2007-12-17 at 15:10 +0900, jwmerrill / gmail.com wrote:
> 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.


Sorry, my cut and paste had a typo - I left out the "^", the formula
should have been:

         y = a( atan(x) ) + b( x^2 ) + c( sinh(x) ) + offset

which is closer to the parabola (and the zunzun display on the screen
seemed perfect) but yes, you are correct.

Thanks,

Phil.
-- 
Philip Rhoades

Pricom Pty Limited  (ACN 003 252 275  ABN 91 003 252 275)
GPO Box 3411
Sydney NSW      2001
Australia
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E-mail:  phil / pricom.com.au