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Re: [Phys-L] LSF Slope Versus Average of Single Point Slopes



Bill Nettles wrote:

Is the LSF method developed based on the distribution of errors being a
Gaussian distribution?

If so, wouldn't a better test of DP's question involve generating a
non-Gaussian distribution of errors? (Of course, if LSF is a completely
general, distribution-free operation, never mind).


As far as I can recollect (and determine from my present references), the
LSF method for fitting a straight line does not depend on a Gaussian
distribution for the data. The equations for determining the slope and
y-intercept are independent of the data's error distribution. However, the
usual equations given do depend 1) on the x data being exact and all errors
being in the y data and 2)the y data errors having a constant variance which
does not depend on x. These two restrictions can be relaxed at the expense
of extra computational difficulty.

Also, textbook tests of goodness of fit for the computed slope and
y-intercept may depend on the data's error distribution being Gaussian. I
probably should have used one of these goodness of fit tests for the slope
rather than simply, first, looking only at the average slope value and then,
secondly, looking only at the std. dev. of the average slope value.

Don

Dr. Donald Polvani
Adjunct Faculty, Physics
Anne Arundel Community College
Arnold, MD 21012


-----Original Message-----
From: phys-l-bounces@mail.phys-l.org [mailto:phys-l-bounces@mail.phys-l.org]
On Behalf Of Bill Nettles
Sent: Monday, May 07, 2012 4:04 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] LSF Slope Versus Average of Single Point Slopes

Is the LSF method developed based on the distribution of errors being a
Gaussian distribution?

If so, wouldn't a better test of DP's question involve generating a
non-Gaussian distribution of errors? (Of course, if LSF is a completely
general, distribution-free operation, never mind).