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

Abstract

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.