Comparative analysis of different approaches to estimating the parameters of regression models using the least absolute deviations method using the example of modeling house prices based on a large sample
Abstract
Comparative analysis of different approaches to estimating the parameters of regression models using the least absolute deviations method using the example of modeling house prices based on a large sample
Incoming article date: 21.04.2025The 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