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## Re: bivariate linear Regression with correlated errors

 From: Henry F. Mollet Subject: Re: bivariate linear Regression with correlated errors Date: Wed, 25 Feb 2004 09:21:51 -0800 User-agent: Microsoft-Entourage/10.1.1.2418

```I assume that wpolyfit.m does what is called a y-on-x regression with all
the error associated with y and none with x. If both y and x have errors,
then I usually use a geometrical mean (GM) regression, where the diagonal
distance rather than the vertical distance to the line is minimized. (The GM
regression is the geometrical mean between the y on x and the corresponding
x on y regressions.) I would check for a start:
Ricker, W. E. 1973.  Linear regression in fishery research.  Journal of the
Fisheries Research Board of Canada 30: 409-434.

However, the use of a GM regression than been criticized but I cannot find
the relevant references w.r.t. linear regression. The same problem also
appears in for non-linear regression and was discussed in:
Kimura, D. K. 2000. Using nonlinear functional relationship regression to
fit fishery models.  Can. J. Fish. Aquat. Sci 57, 160-170.

This will lead to Kendall and Stuart (1977) The Advanced Theory of
Statistics, MacMillan Publ. Co. Inc. Vol.2
Chapter 28 The general Theory of Regression and
Chapter 29 Functional and Structural Relationships
where I got stuck. At the time (of getting stuck), I did not know about
Octave. Who knows, next time I look at Kimura (2002), I might be able to
program what I need using Octave.
Good luck, Henry

on 2/25/04 5:55 AM, Andreas Gaab at address@hidden wrote:

> Due to lack in statistics, I could need some help...
>
> -my data set is bivariate with highly correlated errors.
> -I need to calculate a weighted linear regression with a standard error on the
> slope
> -wpolyfit.m takes only  dy ...
> and my knowlege is too small to use basic statistics.
>
> Is there a possibility to enhance wpolyfit.m or can it be done with gls or ols
> ?
>
> The reference in literature, I would like to apply is:
> York, 1969, Least squares fitting of a straight line with correlated errors,
> Earth and Planetary Science Letters 5
> alternatively,
> Williamson 1968, Least-squares fitting of a straight line, Can. J. Phys. 46
>
> Thanks a lot in advance!
>
>
>
>
> ***********************************************
>            Andreas S. Gaab
>                PhD-student
>     Max-Plank-Institut f"ur Chemie
>
> surfto:www.mpch-mainz.mpg.de
> phoneto:06131/305-394
> mobileto:0177/7386928
> writeto:karmeliterplatz4.55116.mainz
>
> ************************************************
>
>
>
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