MATLAB: Error in linear regression with predefined error in y

errorfitlinear regression

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.

Best Answer

Take a look at the lscov function and see if it does what you need.

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MATLAB: Polyfit – Forcing a non-zero intercept

I doubt that's possible with polyfit. If you are only using a first order regression model and you have access to one of the nonlinear curve fitting routines ( nlinfit in the Statistics Toolbox or lsqcurvefit in the Optimization Toolbox), the easiest way to do this is simply to use them with an objective function similar to:

Intercept = 5;
RegModel = @(B,X) B(1).*X + Intercept;

then:

beta0 = rand;
[Beta,R,J,CovB,MSE] = nlinfit(X, Y, RegModel, beta0);

You can use whatever sort of regression model you want, of course. In this one I used a simple single-parameter model.

You can specify whatever you want in a model function, and can fit as many parameters as you want (that are mathematically appropriate).

MATLAB: Help with basic fitting

Try

 [p,S] = polyfit(x,y,1)

The two elements of p are the coefficients m and q you are looking for.

Best Answer

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MATLAB: Polyfit – Forcing a non-zero intercept

MATLAB: Help with basic fitting

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