# Multidimensional regresion

1. May 7, 2008

### mhill

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

could we find a plane $$0=Ax+By+Cz+D$$ 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 $$0=g(x,y,z)$$ is a minimum , as a certain generalization to the 'least square problem' but in arbitrary dimension

2. May 7, 2008