What is the best way of fitting polynomial regression to 3 dimensional data?

Hello, I have elevation measurements consist of X , Y coordinates and elevation value for each point.I want to fit polynomial regression, splines and so on ... I am trying fitnlm with modelfun but so far I did not succeed in doing so ..I am new on Matlab and machine learning so if there is any suggestions of how to do the fitting,it would be great.Thank you ..

[dpb]

Multidimensional polynomial models aren't nonlinear -- use the fit function for those. Standard 2D models are available as builtin forms.

Splines are done with spline tool or could use interp2d

[Muhammad alaied]

Thank you dpb ,but does fit function works with 3 variables . Two variables as coordinates and one variable as a responce .. I have been trying it but it seems that it requires the data to have only two varialbes .I am trying regress function now , will see..Thanks again

[dpb]

You only have two independent variables, not three.

From doc link to modelnames from fit page one finds:

"For polynomial surfaces, model names are 'polyij', where i is the degree in x and j is the degree in y. The maximum for both i and j is five. The degree of the polynomial is the maximum of i and j. The degree of x in each term will be less than or equal to i, and the degree of y in each term will be less than or equal to j. See the following table for some example model names and equations, of many potential examples.

Examples of Polynomial Model Names for SurfacesEquations

poly21Z = p00 + p10*x + p01*y + p20*x^2 + p11*x*y

...

So, following their lead,

f=fit([X(:),Y(:)],Z(:),'poly22');

would fit your data with all terms of a quadratic in X,Y estimated.

I'd forgotten it, but you also have the option to choose either an interpolating or smoothing cubic spline...altho I don't recall for certain if the spline models inside it are more than one variable as opposed to surfaces.

[Muhammad alaied]

Yes this works ..Thank you..I am tryıng to accept your answer but I do not see the button . It seems like you wrote the answer as a comment.