Polynomial fitting with dependent variables

How can I obtain a polynomial fitting in Matlab having coefficients depending on another variable ? e.g I have variables X1 and Y and I want to find the line (polynomial of degree 1) that fits Y=f(X1)=p0+p1*X1. That would result in the two polynomial coefficients p0,p1 with the function polyfit. Now, I would like to obtain a fitting for which the coefficients p0,p1 depend (linearly) on another variable X2 so p0=f1(X2)=a*X2+b, p1=f2(X2)=c*X2+d.

That would finally result in Y=f1(X2)+f2(X2)*X1.

How to do that ?

Thanks in advance.

Answer 1

[Torsten]

In this case, your model is of the form

Y=c*X1*X2+d*X1+a*X2+b

and you have to estimate the coefficients a,b,c and d.

Since this model is also linear in the coefficients, you can use the same method as for the model

Y=p0+p1*X1

Best wishes

Torsten.