Is there any solution to fit plane onto sampling data?

For example I have the variables x, y (or higher dimensional data in general) and a probability distribution p(x,y). I want to approximate p(x,y) as a linear function, a plane in this case, at least somewhere in the domain. However I only have samples from the distribution. In case of big amount of data the easy way is to collect them into bins, and fit a plane onto the estimated density function. But I dont want to compress data, I would like to extract the maximum information and use the points itself. Are there any method to do this?

Answer 1

[Peter Borda]

I'm not sure if I understand the problem correctly, but if you have a high number of sample point on which you have to fit a plane of any dimensions, you can use this method:

http://stackoverflow.com/questions/10900141/fast-plane-fitting-to-many-points

[Mr M.]

NOT, not, and NOT! I don't want to fit to points which belongs to the plane. I do not have (x,y,z) triples, I only have (x,y) samples from the p(x,y) density.

[Nikola Stan]

having (x,y,p(x,y)) is equivalent to having (x,y,z) triplets