# Linear Model with 4 parameters

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Robert Demyanovich el 28 de Feb. de 2022
Comentada: Torsten el 28 de Feb. de 2022
I need to come up with an estimate for the starting values of the coefficients of a rational model. The rational model is:
One source says that I could do this by performing a linear fit on the model:
I'm using Matlab to fit the rational model, but it performs poorly if I don't use good starting points for the coefficients.
How can I use Matlab to perform this linear regression on 4 data points in order to get starting values for A0, A1, B1 and B2?
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Alex Sha el 28 de Feb. de 2022
Show the data and the code your have written
Torsten el 28 de Feb. de 2022
If you only have 4 data points, then the best fit parameters to the linear model will in most cases already be the best-fit parameters to the rational model. This is because you usually get a unique solution for 4 equations in 4 unknowns.

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### Respuestas (1)

Matt J el 28 de Feb. de 2022
Editada: Matt J el 28 de Feb. de 2022
Asssuming x and y are column vectors,
Q= [x.^0, x, -x.*y, -x.^2.*y,-y];
[~,~,V]=svd(Q,0);
coeffs=num2cell( V(:1:4)/V(end) );
[A0,A1,B1,B2]=deal(coeffs{:});
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