Re: [Phys-L] weighted linear regression using spreadsheets

[brian whatcott <betwys1@sbcglobal.net>]

On 4/3/2020 11:17 AM, John Denker via Phys-l wrote:
> On 4/2/20 1:33 PM, bernard cleyet wrote:
>
> > I think the fit (is a Marquardt) treats each datum equally unless one weights the data.
> Let's discuss the topic of averaging and/or curve fitting.
> Note that I consider averaging to be just a particularly simple
> form of curve fitting.
>
> Pedagogical suggestion:
>    A) When introducing the topic, don't even mention weights.
>     Let all fits be unweighted, by which we mean equally-weighted.
>
>    B) On the next turn of the pedagogical spiral, the motto
>     should be:
>     -- All averages are weighted averages.
>     -- All fits are weighted fits.
>
> In my world, equally-weighted data is the exception not the
> rule.
>
> > Whether the scale (ordinate) is linear of log, the fit is the same.
> Really?  I must be misunderstanding that sentence, because I
> don't see how it could be true.  Scaling the data has a huge
> effect on the weights.  Indeed this is an arcane but effective
> way of controlling the weights, if that's what you want, as
> discussed below.
>
> =================================== /snip/
Apropos straight line log fits vs curve fits to data,
I generated an exponential dataset: 1,2,4,8,16,32,64,128,256
I added a +50 error at each end of the series, like this:
51,2,4,8,16,32,64,128,306

Exponential data on a linear scale explains a lot
of the variance between fitted curve and data: R^2 = 95%
https://imgur.com/CypXrtF

Log of exponential data on a log scale explains some of the
variance between the fitted straight line and data: R^2 = 54%
https://imgur.com/08CJgeo

Not sure how convincing this is of the virtue of taking the
a least squares fit of the data, rather than its log,
but that is the hope.....

Brian W