POV-Ray : Newsgroups : povray.advanced-users : Least Squares fitting Server Time23 Jun 2024 10:20:23 EDT (-0400)
 Least Squares fitting (Message 11 to 14 of 14)
 From: Bald Eagle Subject: Re: Least Squares fitting Date: 11 Mar 2023 20:15:00 Message:
"Kenneth" <kdw### [at] gmailcom> wrote:

> 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.
>
> 'sum of squares' etc, it kind of gives me the impression that Gauss et al came
> up with the method in an empirical way(?) rather than from any theoretical
> standpoint. And that it simply proved useful.

https://math.stackexchange.com/questions/63238/why-do-we-use-a-least-squares-fit
 From: Kenneth Subject: Re: Least Squares fitting Date: 11 Mar 2023 20:45:00 Message:
"Bald Eagle" <cre### [at] netscapenet> wrote:
>
> https://math.stackexchange.com/questions/63238/why-do-we-use-a-least-squares-fit
>

Those stackexchange links are proving to be fascinating and really informative;
thanks! Yes, I see now that 'squaring' has many purposes (and Pythagorean
antecedents) regarding the 'sum of squares' method. Lots to absorb!
 From: yesbird Subject: Re: Least Squares fitting Date: 11 Mar 2023 23:36:35 Message:
On 11/03/2023 23:44, Bald Eagle wrote:
> "yesbird" <nomail@nomail> wrote:
> I'm not sure how you reach that conclusion, since the function takes all of the
> randomly generated points and calculates the center point and radius of a single
> best-fitting sphere.   It fits a sphere to the data, not the other way around.
Yes, exactly, but I mean something like this:
https://www2.latech.edu/~jkanno/packing.pdf

Please find fixed Matlab function in attachment.
Btw, there is a free version of ML, which supports original syntax:
https://octave.org
--
YB

Attachments:

 From: Bald Eagle Subject: Re: Least Squares fitting Date: 16 Mar 2023 18:00:00 Message:
"Kenneth" <kdw### [at] gmailcom> wrote:

> Those stackexchange links are proving to be fascinating and really informative;
> thanks! Yes, I see now that 'squaring' has many purposes (and Pythagorean
> antecedents) regarding the 'sum of squares' method. Lots to absorb!

Apparently, Grant has been closely monitoring our conversations, and made a
video to explain the basics:

But what is the Central Limit Theorem?

3Blue1Brown