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I've been looking through a bunch of error-in-variables models, but I can't find one that matches what I'm looking for (if it exists).

I am trying to do a simple (univariate) linear regression where I know the exact measurement error for each independent variable. Deming/orthogonal regression is too imprecise and I can't use instrumental variables because I don't have any exogeneous variables. Are there any models out there where I can plug in some "weights" for the measurement error of the independent variable?

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