SYNTHESIS OF LINEAR REGRESSION MODEL AND EIVMODEL

This paper is devoted to a synthesis of pair-wise linear regression model and simplest EiV-model (Errors-In-Variables model), better known as the Deming regression. The EIV model is a regression in which all variables contain random errors. Such models have a number of significant drawbacks, which makes it difficult to work with them. The synthesis proposed in the paper, called the two-factor model of a fully connected linear regression, is not only devoid of these shortcomings, but also has certain advantages. The main stages of the construction and analysis of two-factor models of fully connected linear regression are considered. The proposed fully connected linear regression model has much in common with the classical multiple regression model; however, these two types are based on completely different approaches. If multiple regression is based on the principle “independent variables affect the dependent one”, then the principle of fully connected regression is “all variables influence each other”. It is established that the approximation abilities of fully connected models do not exceed the capabilities of multiple regressions, but the former have a much more diverse interpretation. The developed synthesis can be used in the construction of multiple models as a tool for solving problems of reducing the dimensionality of data, eliminating multicollinearity and selecting informative regressors.

1. Ajvazyan S.A., Enyukov I.S., Meshalkin L.D. Prikladnaya statistika: issledovanie zavisimostej. Moscow, Finansy i statistika, 1985. 487 p. (in Russian)

2. Noskov S.I. Tehnologija modelirovanija ob’ektov s nestabil'nym funkcionirovaniem i neopredelennost'ju v dannyh. Irkutsk: RIC GP «Oblinformpechat'» Publ., 1996, 321 р. (in Russian)

3. Pirogov G.G., Fedorovskij Y.P. Problemy strukturnogo ocenivaniya v ehkonometrii. Moscow: Statistics Publ., 1979, 327 p. (in Russian)

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

5. Bazilevskiy M.P. Analytical dependences between the determination coefficients and the ratio of error variances of the test items in Deming regression model. Matematicheskoe modelirovanie i chislennye metody [Mathematical modeling and numerical methods]. 2016, no. 2, vol. 10, pp. 104-116. (in Russian)

6. Demidenko E.Z. Linejnaja i nelinejnaja regressii [Linear and nonlinear regressions]. Moscow: Finance and Statistics Publ., 1981, 304 р. (in Russian)

7. Kudrina M.A., Mishenev V.S. Algorithm of wave skeletonization of raster images. IV Mezhdunarodnaya konferenciya i molodezhnaya shkola «Informacionnye tekhnologii i nanotekhnologii» : sbornik trudov ITNT-2018 [IV International Conference and Youth School "Information Technologies and Nanotechnologies": a collection of works of ITNT-2018]. 2018, pp. 784- 792. (in Russian)

8. Kallner A., Chernichuk O.V., Horovskaya L.A. Comparison of the results of blood glucose measurements with the help of an interactive clinical laboratory evaluation and the method of Clark's error gratings. Kliniko-laboratornyj konsilium [Clinical laboratory consultation]. 2009, no. 4, pp. 14-15. (in Russian)

9. Smirnov M.B., Vanyukova N.A. Dependencies between the main structural and group parameters of the composition of the oils of the Volga-Ural oil and gas bearing basin according to NMR 1Н and 13С. Neftekhimiya [Petrochemistry]. 2017, vol. 57, no. 3, pp. 269-277. (in Russian)

10. Clinical Chemistry. Available at: http://clinchem.aaccjnls.org/.