Fitting hyperplanes by minimizing orthogonal deviations

Hyperplanes withm + 1 parameters are fitted by minimizing the sum of weighted orthogonal deviations to a set ofN points. There is no inverse regression incompatibility. For unweighted orthogonall ₁-fits essentially the same number of points are on either side of an optimal hyperplane. The criterion function is neither convex, nor concave, nor even differentiable. The main result is that each orthogonall _p -fit interpolates at leastm + 1 points, for 0 <p 1. This enables the combinatorial strategy of systematically trying all possible hyperplanes which interpolatem + 1 data points.