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*From*: brian whatcott <betwys1@sbcglobal.net>*Date*: Fri, 3 Apr 2020 14:48:49 -0500

On 4/3/2020 11:17 AM, John Denker via Phys-l wrote:

On 4/2/20 1:33 PM, bernard cleyet wrote:Apropos straight line log fits vs curve fits to data,

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/

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

**References**:**[Phys-L] Fwd: Re: six more days in Okla***From:*brian whatcott <betwys1@sbcglobal.net>

**Re: [Phys-L] Fwd: Re: six more days in Okla***From:*bernard cleyet <bernard@cleyet.org>

**Re: [Phys-L] Fwd: Re: six more days in Okla***From:*brian whatcott <betwys1@sbcglobal.net>

**Re: [Phys-L] Fwd: Re: six more days in Okla***From:*bernard cleyet <bernard@cleyet.org>

**[Phys-L] weighted linear regression using spreadsheets***From:*John Denker <jsd@av8n.com>

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