The ability to fit data to more than two independent variables is not available in Curve Fitting Toolbox.
To work around this issue, you can generate your own objective function and use functions from Optimization Toolbox to fit your data to more than two variables.
However, if the multivariate function is linear in the coefficients you can construct a linear system and solve it.
For example, let us assume a polynomial described by the following equation,
F = a0 + a1 .* X + a2 .* Y + a3 .* Z + a4 .* X .* Z
If "X", "Y", "Z" , are the three independent variable vectors and "F" the dependent variable vector with your data, you can express this system of equations as
F = D * u
where
- "D" is a matrix you can define in MATLAB as
>> D = [ones(length(X), 1), X, Y, Z, X .* Z ]
(Note that the number of rows is equal to the number of points in your data and the number of columns is the number of coefficients in your particular polynomial)
- "F" is the vector with the dependent variable data
In this situation, the polynomial coefficients are represented by a vector
u = [a0; a1; a2; a3; a4].
You can use the Left Matrix Division operator "\" to find this vector of coefficients as
>> u = D \ F
