Effective conception of regresion analysis


  • S. Radchenko Igor Sikorsky Kyiv Polytechnic Institute, Kyiv




regression analysis, mathematical modeling, model structure, system of orthogonal normalized contrasts, statistical efficiency of the model, model stability


The paper deals with the efficient conception of regression analysis, when modeling complex systems and processes. The work objective is the use of the method of formalized obtaining of the structure of multifactor regression model and stable estimation of its coefficient for construction of highly precise statistical models of the process of friction of a rubbing pair of a piston-cylinder in the internal combustion engine. It is supposed that the model structure is unknown for the author. Approximation of initial data is performed with the use of polynomial mathematical models. The idea of complete factor experiment is used as a theoretical ground of correct statistical modeling. The use of the complete factor experiment being impossible, it is recommended to use the multifactor regular plans on the basis of ЛПτ of uniformly distributed sequences. An extended conception of orthogonality of the obtained model has been proposed: the experiment design, model structure and structure elements of the model orthogonal to each other. The orthogonal structure of the multifactor statistical model allows obtaining statistically independent estimates of coefficients of the modeled function. Such a structure may be defined unambiguously with statistically significant coefficients. Normalization of orthogonal effects allows obtaining a maximally stable model structure, and, consequently, its coefficients. The solved problem will be well-posed The considered method of formalized obtaining of the structure of multifactor statistical model and stable estimation of its coefficients is used for constructing statistical models of tribotechnical characteristics of friction parameters of a pair cylinder-piston of the internal combustion engine. Three models have been obtained, which are characterized by good quality parameters: adequacy, informativeness, statistical efficiency, stability. The factors in the model structure are presented by orthogonal normalized contrasts. The models application allows analyzing the mechanisms of the going on phenomena and determining optimal operation conditions of the pair of piston-cylinder internal combustion engine. The results of using the extended conception of orthogonality, when constructing the models of friction parameters of the pair piston-cylinder, have confirmed the promising character of application of the considered approach, its efficiency and expediency in the design of regression statistical model of complex systems and processes.


Novickiy, P.V., Zograf, I.A. (1991), Ocenka pogreshnostej rezultatov izmerenij [Assessment of uncertainties of measurement results], Jenergoatomizdat, Leningrad, Russia.

Ajvazjan, S.A., Enyukov, I.S. and Meshalkin, L.D. (1985), Prikladnaja statistika. Issledovnija zavisimostej [Applied statistics. Explore dependencies], Finansi i statistika, Moskow, Russia.

Ajvazjan, S.A. and Mhitarjan, V.S. (2001), Prikladnaja statistika. Osnovi jekonometriki. Teorija verojatnostej i prikladnaja statistika [Applied statistics. The basics of econometrics. Vol.2, no 1, 2 nd. Probability theory and applied statistics], YNITI-DANA, Moskow, Russia.

Tihomirov, N.P. and Dorohina, E.Yu. (2007), Jekonometrika [Econometrics], Publishing “Jekzamen”, Moskow, Russia.

Drejper, N.R. and Смит, H. (2007), Prikladnoj regressionnij analiz [Applied regression analysis], izdatelskij dom “Wiljams”, Moskow, Russia.

Kobzar, A.I. (2006), Prikladnaja matematicheskaja statistika. Dlja inzhenerov i nauchnih rabotnikov [Applied mathematical statistics. For engineers and scientists], FIZMATLIT, Moskow, Russia.

Hinkelmann, K. and Kempthorne, O. (2007), Design and Analysis of Experiments, Introduction to Experimental Design. 2 nd edn., Wiley-Interscience, Vol. 1, (Wiley Series in Probability and Statistics).

Маlоv, S.V. (2013), Regressionnij analiz. Teoreticheskie osnovi i prakticheskie rekomendacii [Regression analysis. Theoretical bases and practical recommendations], Publishing St. Petersburg State University, St. Petersburg, Russia.

Radchenko, S.G. (2015), Formalizovannie i jevristicheskie reshenija v regressionnom analize [Formalized and heuristic solutions in regression analysis], Kornijchuk, Kyiv, Ukraina.

Konovalova I., Berkovich Yu.A., Erokhin A., and dr. (2016), Modelling of salad plants growth and physiological status in vitamin space greenhouse during lighting regime optimization, 41th COSPAR Scientific Assembly, Istanbul, Turkey.

Konovalova, I.O., Berkovich, Yu.A., Erohin, A.N., and dr. (2016), Optimizacija svetodiodnoj sistemi osveshchenija vitaninnoj kosmicheskoj oranzherei [Optimization of the LED lighting system vitamins space greenhouse] Аviakosmicheskaja i jekologicheskaja medicina. Vol. 50, no. 3, pp. 17–22.

Radchenko, S.G. (2011), Metodologija regressionnogo analiza [Methodology of regression analysis], Kornijchuk, Kyiv, Ukraina.

Brodsky, V.Z. (1976), Vvedenie v faktornoe planirovanie jeksperimenta [Introduction to the factor design of the experiment], Nauka, Moskow, Russia.

Radchenko, S.G. (2015), Analiz metodov modelirovanija slozhnih sistem [Analysis of methods of the model of complex systems], Matematichni mashini i sistemi, no 4. pp. 123–127.

Laboratorija jeksperimental’no-statisticheskih metodov issledovanij (LESMI) [Laboratory of experimental-statistical methods of research], available at: http://www.n-t.org/sp/lesmi

Sajt kafedri “Tehnologija mashinostroenija” Mehaniko-mashinostroitel’nogo instituta Nacional’nogo tehnicheskogo universiteta Ukraini “Kievskij politehnicheskij institute” [Department of Machine Building Technology, Mechanics and Machine Building Institute of the National Technical University of Ukraine “Kyiv Polytechnic Institute”], available at: http://tm-mmi.kpi.ua/index.php/ru/1/publications





Original study