How to do 2D surface fitting regression ?

I have data x, y are 2 independant variables , x is vector data 1x200, y is vector data 1x5, z is dependant variable which is matrix data dim 5x200. I am trying to fit polynomail surface to the given data in the form Z = p00 + p10*x + p01*y + p20*x.^2 + p11*x*y + p30*x.^3 + p21*x.^2*y since the variables dimension don't match , I got error when using the least error method to estimate the coffiecients P P=[1 x y x.^2 x*y x.^3 x.^2*y]\Z how to solve that? and represent it in matrix forms?

[Ahmet Cecen]

There is something wrong with the way you are setting up the problem. You cannot have independent variables with different dimensions for a regression problem. If x has 200 observations, y also needs to have 200 observations (not necessarily unique).

[Image Analyst]

He'd need to use meshgrid

[allX, allY] = meshgrid(x, y);

and then make sure the Z are associated with the correct coordinate. Or better yet, just start with a 5x200 image of Z. Then he can use polyfitn() like in my answer below.

Answer 1

[Image Analyst]

See polyfitn http://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn

I've attached a demo where I use it to do background correction.