I would like to be able to represent my measurement results thought a mathematical form.
Unfortunately it seems that the variables are depending and i do not know the relation between them.
What I do have are measurement data from the different four variables at different values.
Once i fix the value of 3 variables, i get a linear behavior
.
Once I change the value of the 3 fixed variables and set other values, the linear behavior changes it properties (I get different values for 'a' and 'b').
Is there a way to fit a polynomial for such a non-linear behaviour?
Let us suppose that the model is linear with respect to all variables $x,y,w,z$. So, you can write $$F=a_0+a_1x+a_2y+a_3w+a_4z+a_5 xy+a_6xw+a_7xz+a_8yw+a_9yz+a_{10}wz+a_{11}xyw+a_{12}xyz+a_{13}ywz$$ So, you face a multilinear regression problem which is simple if you use matrix formulation.
This is jsut the generalization of $$F=a(y)+b(y) x \qquad \text{with}\qquad a(y)=c+dy \qquad \text{and}\qquad b(y)=e+fy$$ Replacing, you get $$F=c+e x+d y+f x y$$