519.862.6 Analytical dependences between the determination coefficients and the ratio of error variances of the test items in Deming regression model

Bazilevsky M. P. (Irkutsk State Transport University)


doi: 10.18698/2309-3684-2016-2-104116

The article deals with the problem of building regression models, in which all variables have stochastic nature. To solve it, we propose to use the determination coefficient. We obtain analytical dependencies of the determination coefficients from the ratio of error variances of the test items. We set the optimization problem, assuming the maximization of the determination coefficients sum for each Deming regression equation. We give a model example of the numerical processing of Deming regression with its parameters and sign errors which are known.

[1] Aivazyan S.A. Prikladnaia statistika. V. 2: Osnovy ekonometriki [Applied statistics. Vol. 2: Fundamentals of econometrics]. Moscow, YuNITI-DANA Publ., 2001, 432 p.
[2] Noskov S.I. Tekhnologiya obyektov s nestabilnym funktsionirovaniem i neopredelennostyu v dannykh [Technology of the objects with unstable operation and the data uncertainty]. Irkutsk, Oblinformpechat Publ., 1996, 321 p.
[3] Gefan G.D. Ekonometrika [Econometrics]. Irkutsk, IrGUPS Publ., 2005, 84 p.
[4] Dreiper N., Smit G. Prikladnoi regressionnyi analiz [Applied regression analysis]. Moscow, Finansy i statistika Publ., 1986, 366 p.
[5] Timofeev V.S., Shchekoldin V.Yu., Timofeeva A.Yu. Informatika i ee primeneniya — Informatics and Applications, 2013, vol. 7, no. 2, pp. 60–68.
[6] Deming W.E. Statistical adjustment of data. New York, Dover, 2011, 288 p.
[7] Besalu E., de Julian-Ortiz J., Pogliani L. Match-Communications in Mathematical and in Computer Chemistry, 2010, no. 63, pp. 573–583.
[8] Huang L., Rattner A., Liu H., Nathans J. Tutorial: how to draw the line in biomedical research. eLife, 2013. Available at: https://elifesciences.org/content/2/e00638
[9] Bernard G., Bernadette B. Chemometrics and Intelligent Laboratory Systems, 2014, vol. 134, pp. 123–139. DOI 10.1016/j.chemolab.2014.03.006
[10] Dhanoa M.S., Sanderson R., Lopez S., Dijkstra J., Kebreab E., France J. Modelling Nutrient Digestion and Utilisation in Farm Animals, 2011, part 1, pp. 31–39. DOI 10.3920/978-90-8686-712-7_3
[11] Shaoji Xu. The American Statistician, 2014, vol. 68, iss. 4, pp. 277–281. DOI 10.1080/00031305.2014.962763
[12] Haeckel R., Wosniok W., Klauke R. Laboratoriums Medizin, 2013, vol. 37, iss. 3, pp. 147–163. DOI 10.1515/labmed-2013-0003
[13] Kallner A. Accreditation and Quality Assurance, 2014, vol. 19, iss. 6, pp. 451–457. DOI 10.1007/s00769-014-1089-9
[14] Glaister P. The Mathematical Gazette, 2001, no. 85, pp. 104–107.
[15] Dougerti K. Vvedenie v ekonometriku [Introduction to econometrics]. Moscow, INFRA-M Publ., 2009, 465 p.

Bazilevsky M. Analytical dependences between the determination coefficients and the ratio of error variances of the test items in Deming regression model. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 104-116

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