Regression Plane Question

[markraz]

Hi, I need to fit a bunch of xyz points to a plane ax+by+cz + e = 0

I'm wondering if it is possible to take 2 arbitrary dimensions of the datapoints (such as XZ and YZ) and find the regression lines through the points in each respective plane.

Then calculate the cross product of Vector XZ and Vector YZ regression lines and find the Normal, and determine the plane. Will this work?
Thanks