Multidimensional regresion

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i have this problem, given a series of values [tex] (x_{i} , y_{j} , z_{k}) =U [/tex]

could we find a plane [tex] 0=Ax+By+Cz+D [/tex] so the distance from the set of points given in 'U' and the plane with normal vector N=(A,B,C) is a minimum,

or in more general case the distance from the set of points 'U' and the function [tex] 0=g(x,y,z) [/tex] is a minimum , as a certain generalization to the 'least square problem' but in arbitrary dimension
 

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