The article is devoted to the study of the problem of estimating unknown parameters of linear regression models using the least absolute deviations method. Two well-known approaches to identifying regression models are considered: the first is based on solving a linear programming problem; the second, known as the iterative least-squares method, allows one to obtain an approximate solution to the problem. To test this method, a special program was developed using the Gretl software package. A dataset of house prices and factors influencing them, consisting of 20640 observations, was used for computational experiments. The best results were obtained using the quantreg function built into Gretl, which implements the Frisch-Newton algorithm; the second result was obtained using an iterative method; and the third result was achieved by solving a linear program using the LPSolve software package.

Keywords: regression analysis, least absolute deviations method, linear programming, iterative least squares method, variational weighted quadratic approximation method

This article examines the previously studied linear in factors and non-linear in parameters modular regression model containing unary module operations. Through the use of binary, ternary, ..., l-ary module operations, a generalization of modular regression was proposed for the first time. A special case of generalization is considered - regression with a multiary operation modulus. The problem of accurately estimating such a model using least absolute deviations is reduced to a mixed integer 0-1 linear programming problem. Using data on farm productivity built into the Gretl econometric package, classical linear regression and modular regression with a multivariate operation were built. The quality of approximation of the proposed modular regression turned out to be higher than the quality of the linear model.

Keywords: regression analysis, modular regression, least absolute deviations, multiary operation modulus, mixed integer 0-1 linear programming problem