POV-Ray : Newsgroups : povray.advanced-users : Least Squares fitting : Re: Least Squares fitting Server Time15 Jul 2024 20:36:20 EDT (-0400)
 Re: Least Squares fitting
 From: Kenneth Date: 11 Mar 2023 19:45:00 Message:
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"Bald Eagle" <cre### [at] netscapenet> wrote:
> "Kenneth" <kdw### [at] gmailcom> wrote:
> > That's a really nice result of fitting a set of data points to a function.
>
> It's the reverse.  I'm fitting the function describing a line, circle, and
> sphere to the measured data.  It's "as close to all of the data points as
> it can be _simultaneously_".  And so the overall error is minimized.

Got it. Sorry for my reversed and lazy way of describing things.

> > The general idea of finding the AVERAGE of a set of data points is
> > easy enough to understand...
>
> This is an acceptable method, and of course can be found in early
> treatments of computing the errors in data sets.
>
> > But why is 'squaring' then used? What does that actually
> > accomplish? I have not yet found a simple explanation.
>
> "it makes some of the math simpler" especially when doing multiple dimension
> analyses.
>
> (the variance is equal to the expected value of the square of the distribution
> minus the square of the mean of the distribution)
>

So the (naive) question that I've always pondered is, would CUBING the
appropriate values-- instead of squaring them-- produce an even tighter fit
between function and data points? (Assuming that I understand anything at all
about why even 'squaring' is the accepted method, ha.) Although, I imagine that
squaring is perhaps 'good enough', and that cubing would be an unnecessary and
more complex mathematical step.