FORMALIZATION OF THE PROBLEM OF CONSTRUCTION OF LINEAR MULTIPLICATIVE REGRESSIONS IN THE FORM OF A PARTIAL-BOOLEAN LINEAR PROGRAMMING PROBLEM

Авторы: 
Дата поступления: 
10.05.2017
Год: 
2017
Номер журнала (Том): 
УДК: 
519.237.5
DOI: 

10.26731/1813-9108.2017.3(55).101-105

Файл статьи: 
Страницы: 
101
105
Аннотация: 

When constructing regression models, one of the main problems is the selection of their structural specification. At present, there are already very large numbers of such specifications, and these numbers are constantly growing. The article focuses on the construction of linear multiplicative regressions belonging to the class of models that are linear in parameters, and in which various combinations of products of independent variables are used as regressors. Nowadays, the technology of organizing a "competition" of models is used to construct such models, which is to form a number of their alternative variants with predetermined properties and the subsequent choice of the most acceptable variant on the basis of a set of formal and substantive criteria. In this formulation, the problem is very time-consuming. Therefore, in order to reduce the time of its solution, the problem of constructing a linear multiplicative regression is formalized as a problem of partial-Boolean linear programming. With the help of linear constraints, one can control the nature of the occurrence of independent variables in the right-hand side of linear multiplicative regressions.

Список цитируемой литературы: 

1.      Aivazyan S.A., Mkhitaryan V.S. Prikladnaya statistika i osnovy ekonometriki [Applied statistics and the foundations of econometrics]. Moscow: Yuniti Publ., 1998, 1022 p.

2.      Draper N., Smith H. Applied regression analysis. New York: Wiley-Interscience, 1966, 407 p. (Russ. ed.: Dreiper N., Smit G. Prikladnoi regressionnyi analiz. Book 1. In 2 books. Moscow: Finansy i statistika, 1986, 366 p.).

3.      Draper N., Smith H. Applied regression analysis. New York: Wiley-Interscience, 1966, 407 p. (Russ. ed.: Dreiper N., Smit G. Prikladnoi regressionnyi analiz. Book 2. In 2 books. Moscow: Finansy i statistika, 1986, 351 p.).

4.      Seber G. Linear regression analysis. New York: John Wiley and Sons, 1977. (Russ. ed.: Seber Dzh. Lineinyi regressionnyi analiz. Moscow: Mir Publ., 1980, 456 p.).

5.      Dougherty Ch. Introduction to Econometrics. New York Oxford. Oxford University Press, 1992 (Russ. ed.: Dougerti K. Vvedenie v ekonometriku. Moscow: INFRA-M Publ., 2009, 465 p.).

6.      Kleiner G.B. Proizvodstvennye funktsii [Production functions]. Moscow: Finansy i statistika Publ., 1986, 239 p.

7.      Bazilevskii M.P., Noskov S.I. Algoritm postroeniya lineino-mul'tiplikativnoi regressii [Algorithm for constructing linear multiplicative regression]. Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie [Modern technologies. System analysis. Modeling]. Irkutsk, 2011, No.1(29), pp. 88–92.

8.      Bazilevskii M.P. Avtomatizatsiya protsessa postroeniya lineino-mul'tiplikativnykh regressionnykh modelei [Automation of the process of constructing linear multiplicative regression models]. Materialy vtoroi mezhvuzovskoi nauchno-prakticheskoi konferentsii «Transportnaya infrastruktura Sibirskogo regiona» [Proceedings of the second interuniversity scientific and practical conference "Transport infrastructure of the Siberian region"]. Irkutsk, 2011, pp. 325–328.

9.      Noskov S.I. Tekhnologiya modelirovaniya ob"ektov s nestabil'nym funktsionirovaniem i neopredelennost'yu v dannykh [The technology of modeling objects with unstable functioning and uncertainty in the data]. Irkutsk: Oblinformpechat' Publ., 1996, 320 p.

10.    Bazilevskii M.P., Noskov S.I. Tekhnologiya organizatsii konkursa regressionnykh modelei [Technology of the competition of regression models]. Informatsionnye tekhnologii i problemy matematicheskogo modelirovaniya slozhnykh system [Information technologies and problems of mathematical modeling of complex systems]. Irkutsk, 2009, Issue 7, pp. 77-84.

11.    Bazilevskii M.P., Noskov S.I. Metodicheskie i instrumental'nye sredstva postroeniya nekotorykh tipov regressionnykh modelei [Methodical and instrumental means for constructing some types of regression models]. Sistemy. Metody. Tekhnologii [Systems. Methods. Technologies]. Bratsk, 2012, No.1(13), pp. 80–87.

12.    Noskov S.I., Bazilevskii M.P. Programmnyi kompleks avtomatizatsii protsessa postroeniya regressionnykh modelei [Software complex for automation of the process of constructing regression models]. Mezhdunarodnyi zhurnal prikladnykh i fundamental'nykh issledovanii [International Journal of Applied and Fundamental Research]. Moscow, 2010, No.1, pp. 93–94.

13.    Kuznetsov A.V., Sakovich V.A., Kholod N.I. Vysshaya matematika: Matematicheskoe programmirovanie [Higher mathematics: Mathematical programming]. Minsk: Vysheishaya shkola Publ., 1994, 286 p.

14.    Korbut A.A., Finkel'shtein Yu.Yu. Diskretnoe programmirovanie [Discrete programming]. Moscow: Nauka Publ., 1969, 370 p.