The software for co-ordinate measuring machine (CMM) is used for approximating geometric elements in plane (2d) and in space (3d) by approximation algorithms when number of measuring points obtained is larger than the minimum number of points necessary for element definition. Orthogonal regression methods are discussed in this paper. For 2d and 3d cases and they are compared with methods for defining straight line using linear regression. The advantage of orthogonal regression over linear regression is shown by comparing variance of measuring point displacement from both approximation line types.Algorithms for orthogonal regression make it possible to determine optimum position of a straight line for which value of variance of point distance from the line is the lowest possible. The tests have been performed on the Carl Zeiss CMM.