I'm currently using Least Squares Method in order to calculate Best Fit Plane for a given 3 column vectors [X, Y, Z].
I've noticed that consistently I get that the average of the residuals of Z relative to ${Z_{BFP}}$ is zero.
e.g. E($Z_{i}$-${Z_{BFP_i}}$)=0, even though that this method is solving for the plane that minimizes the sum of the squares of the residuals (the vertical (Z) distance) and not for the plane that minimize the sum of the residuals.
I'm trying to understand if this behavior is a byproduct of the Least Squares Method or it is related to the specific distribution of the data I'm testing.