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Modelling and Data Analysis
2025. Vol. 15, no. 2, 139–151
doi:10.17759/mda.2025150208
ISSN: 2219-3758 / 2311-9454 (online)

Identification of linear regression parameters and a mathematical rule for generating values of a dummy variable included in the model

 
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Abstract

Context and relevance. The task of constructing regression models in a situation where explanatory variables are categorical is currently relevant. Categories can reflect, for example, gender (male and female), level of higher education (bachelor's degree, specialist degree, and master's degrees), or seasons (winter, spring, summer, and autumn). To introduce dichotomous categories into the model, dummy variables are used. These take the value 1 if a certain feature is present, and 0 if it is absent. The values ​​of these dummy variables are often determined by predefined rules. Objective. The aim of the work is to formulate a problem of simultaneous identification of parameters of multiple linear regression models and values of dummy variables included in them. Hypothesis. The hypothesis is that the formulated problem can be formalized in terms of the apparatus of mathematical programming. Methods and materials. The least absolute deviations method is used to estimate the unknown regression parameters. Results. The task of identifying these features is formalized as a mixed 0-1 integer linear programming problem. Its solution gives not only estimates of the linear regression and optimal values of the dummy variable, but also a rule by which these values are identified. The rule is based on the transformation of a linear combination of explanatory variables using the integer function floor. Based on known data on the operation of an evaporator at a large industrial enterprise, 4 types of linear regressions with a dummy variable were constructed. Conclusions. Since the process of constructing linear regressions using our method also identifies a rule for forming a dummy variable, it allows them to be used for solving forecasting problems. After identifying the rule, it is possible, if necessary, to re-estimate the obtained linear regressions, for example, using the ordinary least squares method, which has a more extensive set of model validation criteria.

General Information

Keywords: regression analysis, dummy variable, integer function floor, least absolute deviations method, mixed 0-1 integer linear programming problem

Journal rubric: Numerical Methods

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2025150208

Received 10.04.2025

Accepted

Published

For citation: Bazilevskiy, M.P. (2025). Identification of linear regression parameters and a mathematical rule for generating values of a dummy variable included in the model. Modelling and Data Analysis, 15(2), 139–151. (In Russ.). https://doi.org/10.17759/mda.2025150208

© Bazilevskiy M.P., 2025

License: CC BY-NC 4.0

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Information About the Authors

Mikhail P. Bazilevskiy, Candidate of Science (Engineering), Associate Professor, Department of Mathematics, Irkutsk State Transport University (ISTU), Irkutsk, Russian Federation, ORCID: https://orcid.org/0000-0002-3253-5697, e-mail: mik2178@yandex.ru

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