Two of the least absolute value methods are considered, called so by analogy with the method of least squares. In this paper, the fi rst method, which is known as the least absolute deviations method, is called the absolute ordinate regression. It was proposed by Laplace; nowadays calculations, which are usually carried out by iteration, require computers. In this paper, we present another method of calculation. The second method is called the absolute normal regression and is presented here for the fi rst time. An algorithm for calculating the coeffi cients of regression and an assessment for their quality are developed. These methods are not necessarily associated with random variables only; they are of much wider use than just that. The results are important for addressing the most economic problems of current interest such as building a road system with the least total length and the like.