Matrix multiple regression and modern biometric methods for prediction of biological indicators: examples


  • Inna Nazaraha Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • Yaroslav Nazaraha National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine



matrix multiple regression, methods of biometrics, biological indicators, prediction, singular-value decomposition


In this article, examples of prediction of biological indicators are considered. In this case, the classical methods of biometrics and methods based on matrix multiple regression are used. In order to solve the problem of estimation by the method of least squares for multiple matrix regression, a mathematical apparatus for the singular value decomposition (SVD) and pseudo-inversion technique for Moore–Penrose was used within the development of the concept of tuple operators. The empirical data for calculations were data from an experiment conducted at the Educational and Scientific Center “Institute of Biology and Medicine” (Taras Shevchenko National University of Kyiv). The calculations were made in Microsoft Office Excel and Wolfram Mathematica. The algorithm based on matrix multiple regression has the prediction accuracy in terms of the APE (absolute percentage error) criterion (the error is from 0% to 10%) higher than the accuracy of modern methods of biometrics (some errors are greater than 30%). As shown in the examples, matrix multiple regression can be an effective prediction instrument in biology with an acceptable planning processes accuracy.

Author Biographies

Inna Nazaraha, Taras Shevchenko National University of Kyiv, Kyiv

Inna M. Nazaraha,

Candidate of Technical Sciences (Ph.D.), a junior researcher at the Department of System Analysis and Decision Making Theory of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine.

Yaroslav Nazaraha, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Yaroslav R. Nazaraha,

a student at the Faculty of Biomedical Engineering of National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.


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Decision making and control in economic, technical, ecological and social systems