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Linear Regression with Errors in X and Y

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Calculates slope and intercept for linear regression of data with errors in X and Y.

Updated

Calculates slope and intercept for linear regression of data with errors in X and Y. The errors can be specified as varying point to point, as can the correlation of the errors in X and Y.

The uncertainty in the slope and intercept are also estimated.

This follows the method in D. York, N. Evensen, M. Martinez, J. Delgado "Unified equations for the slope, intercept, and standard errors of the best straight line" Am. J. Phys. 72 (3) March 2004.

The package includes an example and a Monte Carlo simulation verifying the estimated uncertainties.

Chenlu Liu

Shea

Shea (view profile)

Hi, similarly to Felix, I think the code is great and I'm wondering if it is possible to force the linear regression to go through the origin, i.e. a=0? Thank you

Maayan Yehudai

Maayan Yehudai (view profile)

Hi Travis,
I was wondering if this code provides with an MSWD value for the isochron linear fit.

Thanks

Juan

Juan (view profile)

Hi Travis,
It looks like code is supposed to do exactly what I am after, unfortunately I am having problems with your York_fit.m code:

at 40 ==> tmp=Y/[X; ones(1,N)]; shouldn't it be tmp=[Y/X; ones(1,N)]; ?

but even if I change this I am still encountering more errors:

??? Error using ==> times
Matrix dimensions must agree.

Error in ==> york_fit at 58
Y_bar=sum(W.*Y)/sum(W);

Felix

Felix (view profile)

I really like the code but is it possible to force the linear regression to go through the origin, i.e. a=0?

Travis Wiens

Travis Wiens (view profile)

Rainer Boegle: This method is only for a single input.

Rainer Boegle

Rainer Boegle (view profile)

Can I use multiple regression and
can I omit the offset in the model?
E.g. Y is explained by two betas corresponding with two different x (of same type of measurement, i.e. same error), but no offset is fitted?

Y = X*beta + error
where X = [x1; x2]

Antoni J. Canós

Stephan Koehler

Paul Behrens

Paul Behrens (view profile)

MATLAB Release
MATLAB 7.4 (R2007a)