Научный журнал Моделирование, оптимизация и информационные технологииThe scientific journal Modeling, Optimization and Information Technology
cетевое издание
issn 2310-6018

INVESTIGATION OF A TWO-FACTOR FULLY CONNECTED LINEAR REGRESSION MODEL

Bazilevskiy M.P.  

UDC 519.862.6
DOI: 10.26102/2310-6018/2019.25.2.008

  • Abstract
  • List of references
  • About authors

This paper is devoted to the study of a fully connected linear regression model, which is a synthesis of the pairing linear regression model and the Deming regression model. If multiple regression is based on the principle “independent variables influence dependent”, then the principle of fully connected regression is “all variables influence each other”. A fully connected regression is fairly simply estimated, devoid of multicollinearity effect, has a much more diverse interpretation than multiple regression, and is suitable for prediction. However, when building a fully connected regression, the ratio of error variances of independent variables remains unknown. In this paper, we find the ratio of error variances of independent variables that provides the best approximation qualities of the secondary fully connected regression model. The research results are presented in the form of a theorem. It follows from the theorem that the value of the coefficient of determination of the secondary model of a fully connected regression will be greatest either when it takes the form of a two-factor linear regression or the best one in the coefficient of determination of a single-factor linear regression. Thus, the selection of informative regressors in the regression model is carried out. It is established that the basis of such a selection is the complete consistency of the signs of the coefficients with independent variable signs of the corresponding correlation coefficients.

1. Kendall M., St’yuart A. Statisticheskie vyvody i svyazi. Glavnaya redakciya fiziko-matematicheskoj literatury izd-va «Nauka», 1973, 899 p. (in Russian)

2. Demidenko Е.Z. Linejnaya i nelinejnaya regressiya. Moscow: Finansy i statistika, 1981. 304 p. (in Russian)

3. Deming W.E. Statistical adjustment of data / W.E. Deming. – New York, Dover Publications, 2011. – 288 p.

4. Bazilevskij M.P. Analiticheskie zavisimosti mezhdu koefficientami determinacii i sootnosheniem dispersij oshibok issleduemyh priznakov v modeli regressii Deminga. Matematicheskoe modelirovanie i chislennye metody. 2016, no. 2, vol. 10, pp. 104–116. (in Russian)

5. Bazilevskij M.P. Analiticheskie zavisimosti dlya nekotoryh kriteriev adekvatnosti modeli regressii Deminga. Vestnik IrGTU. Irkutsk, 2016, vol. 20, no. 10, pp. 81–89. (in Russian)

6. Bazilevskij M.P. Metodika mnogokriterial'nogo vybora lyambda-parametra v modeli parnoj linejnoj regressii so stohasticheskimi peremennymi. Vestnik IrGTU. Irkutsk, 2017, vol. 21, no. 3, pp. 59–72. (in Russian)

7. Bazilevskij M.P. Sintez modeli parnoj linejnoj regressii i prostejshej EIVmodeli. Modelirovanie, optimizaciya i informacionnye tekhnologii. Voronezh, 2019, vol. 7, no. 1. URL: https://moit.vivt.ru/wpcontent/uploads/2019/01/Bazilevskiy_1_19_1.pdf. (in Russian)

8. Bazilevskij M.P. Dvuhfaktornaya model' polnosvyaznoj regressii s kvadratom svyazuyushchej peremennoj. Molodezh' i sovremennye informacionnye tekhnologii: sbornik trudov XVI Mezhdunarodnoj nauchno-prakticheskoj konferencii studentov, aspirantov i molodyh uchenyh. Tomsk, 2018, pp. 26– 27. (in Russian)

9. Bazilevskij M.P. Ocenivanie parametrov prostejshej modeli polnosvyaznoj linejnoj regressii. Dostizheniya i prilozheniya sovremennoj informatiki, matematiki i fiziki: materialy VII Vserossijskoj nauchno-prakticheskoj konferencii. Neftekamsk, 2018, pp. 179–184. (in Russian)

10. Gefan G.D. Ekonometrika. Irkutsk, 2005, 84 p. (in Russian)

Bazilevskiy Mikhail Pavlovich
Candidate of Technical Sciences
Email: mik2178@yandex.ru

Irkutsk State Transport University

Irkutsk, Russian Federation

Keywords: fully connected regression, multiple regression, deming regression, eivmodel, coefficient of determination, multicollinearity, subset selection in regression

For citation: Bazilevskiy M.P. INVESTIGATION OF A TWO-FACTOR FULLY CONNECTED LINEAR REGRESSION MODEL. Modeling, Optimization and Information Technology. 2019;7(2). Available from: https://moit.vivt.ru/wp-content/uploads/2019/05/Bazilevskiy_2_19_1.pdf DOI: 10.26102/2310-6018/2019.25.2.008 (In Russ).

167

Full text in PDF