• Станислав Григорьевич Радченко Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine



regression analysis, correct and incorrect problems, the theory of experiment planning, statistical models, system of orthogonal contrasts.


The author expounds statistical modeling of complex systems with the use of regression analysis for typical conditions of solution of real applied problems, when the model structure is unknown for the researcher. A necessity of using the experiment design, extended conception of orthogonality, and a system of   orthogonal contrasts is shown. The results of modeling the digital balance are presented which have confirmed the expediency of the offered approach and the methods used for obtaining the models. The quality criteria of the obtained model are characterized as the best ones. The model obtained is adequate, highly informative, maximum stable, semantic, all the coefficients are orthogonal to each other. The model use allows increasing 13.3 times the accuracy of the measuring device by the criterion of the average absolute error to 0.012%, and 11.2 times by the criterion of root-mean-square approximation error to 4.80%. The results of the use of the above stated conception of regression analysis have confirmed its efficiency. The method of statistical modeling can be successfully applied in the development of high-tech facilities, high technology, intelligent measuring instruments, machine building, instrument engineering, agrobiology, etc.


Zhidkov, N.P. (1980), Predislovie. Chto takoe matematika [Preface. What is mathematics], Znanie, Moskow, Russia.

Kolesov, I.M. (2001), Osnovy tehnologii mashinostroenija [Machine building technology principles], Visshaja shkola, Moskow, Russia.

Suslov, A.G. and Dalsky, A.M. (2002), Nauchnye osnovy mashinostroenija [Scientifi grounds of machine building], Mashinostroenie, Moskow, Russia.

Hinkelmann, K. and Kempthorne, O. (2007), Design and Analysis of Experiments, Introduction to Experimental Design. 2nd, 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.O., Berkovich, Yu.A., Erohin, A.N., ets. (2016), “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.

Laboratorija jeksperimental’no-statisticheskih metodov issledovanij (LESMI) [Laboratory of experimental-statistical methods of research], available at:

Sajt kafedri «Tehnologija mashinostroenija» Mehaniko-mashinostroitel’nogo instituta Nacional’nogo tehnicheskogo universiteta Ukraini «Kievskij politehnicheskij institut» [Department of Machine Building Technology, Mechanics and Machine Building Institute of the National Technical University of Ukraine “Kyiv Polytechnic Institute”], available at:





Original study