Error in linear regression with predefined error in y

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Arjen
Arjen 2012-5-23
I'm fitting y=ax+b with polyfit. x has no errors, but every component y_i has an error equal to error_i = C_i*y_i. (So this is correlated right?) How do I determine the error in the slope a?
I've been thinking about not using polyfit and minimazing S = sum(w_i * ( y_i - fit_i)^2) myself. With w_i = 1/error_i^2. But I have no idea how this minimizing can be done.

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Tom Lane
Tom Lane 2012-5-24
Take a look at the lscov function and see if it does what you need.
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Tom Lane
Tom Lane 2012-5-29
You wanted an intercept. The equation a*1+b*x defines the intercept as "a." If every row of X has a 1 and an x value, you'll be fitting this equation with an intercept as the first element of the coefficient vector and the slope as the second element. The slope will then be computed for a general line, rather than one constrained to have an intercept equal to zero.

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Wayne King
Wayne King 2012-5-23
polyfit returns a least-squares fit, but not with weights as you suggest. Do you have the Statistics Toolbox? If so consider, robustfit.m or LinearModel.fit, which has options for robust fitting.
Also, perhaps a simple first-order linear model is not adequate for your data?
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Arjen
Arjen 2012-5-23
I've browsed a lot to find a simple linear fitting method. But I didnt find anything similar to a linear regression with errors on y... which actually suprises my a lot because this is a fairly easy problem... At least i thought so.
The robustfit is giving me what i need, but the method is rather frustrating... It asks for a function instead of a vector. I'm taking the stats.se as an error for the slope, but it 1e20 times bigger than the slope itself. And the fit is pretty good. Something is going wrong here...

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