N-dimension curve fit how to

Can someone please walk me through how to do a polynomial curve fit to n-dimensional data? For example: I have a 3D matrix t = [i x j x k] of results for all combinations of 3 different variables x = [i x 1], y = [j x 1], and z = [k x 1], and we know it follows a polynomial fit (e.g. x = 4th order, y = 2nd order, and z = 2nd order). How do I set up the problem, define the fit equation, and find the fit parameters?

Answer 1

[Steven Lord]

See the Multiple Regression section on this documentation page. While that example only uses the first power of each of the variables x1 and x2 in the creation of the X coefficient matrix, you could use terms like x1.^2 and/or x1.*x2.^3 to create additional columns.

[Adam]

It seems like the solution shown in that doc is only for a single coefficient linear equation. How do you extend that to multi-order polynomial fit?

Answer 2

[Matt J]

Perhaps polyfitn will help,

https://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn