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MathGroup Archive 2007

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Re: Curve-fitting/data analysis question...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73422] Re: Curve-fitting/data analysis question...
  • From: "Robert Dodier" <robert.dodier at gmail.com>
  • Date: Fri, 16 Feb 2007 00:56:33 -0500 (EST)
  • References: <200702110615.BAA11578@smc.vnet.net><er1c1m$7vm$1@smc.vnet.net>

sherifffruitfly wrote:

> On Feb 14, 2:16 am, "Robert Dodier" <robert.dod... at gmail.com> wrote:

> > I would be interested to hear whether the total chi-square is
> > sensitive to the placement of the cut-off point.
>
> I haven't noticed that - but that doesn't imply that it isn't there to
> be noticed.

It would probably be interesting & useful to plot the total goodness
of fit as a function of the placement of the cut-off point.

> I *have* however noticed the following. For decreasing x, it's
> difficult to distinguish an exponential from a constant function. So
> really the bulk of the goodness-of-fit work is being done for
> increasing x of the linear models - linear models fail dramatically
> when the data becomes "exponential-ish".
>
> Is it reasonable to apply the above thought to your suggestion of
> minimizing the total goodness of fit by way of somehow weighting the
> linear part more heavily than the exponential, and then minimizing?

You would want to weight the errors to the left and right of the
cut-off point differently only if there is some sense in which errors
on one side cost you more than on the other. You haven't mentioned
that so far, so I'll assume that's not the case.

HTH
Robert Dodier



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