MODIFICATION OF THE DECOMPOSITION METHOD OF CONSTRUCTING MULTIVARIATE POLYNOMIAL REGRESSION WHICH IS LINEAR WITH RESPECT TO UNKNOWN COEFFICIENTS
DOI:
https://doi.org/10.20998/2079-0023.2024.02.01Keywords:
regression analysis, multivariate polynomial regression, redundant representation, decomposition method, individual algorithm, least squares methodAbstract
The authors created a universal method of constructing multivariate polynomial regression given by a redundant representation. The method is synthetic, it organically combines a decomposition method and the modified group method of data handling. First, the decomposition method is implemented, it consists in the decomposition of the multivariate problem into a sequence of subproblems of constructing univariate polynomial regressions and the corresponding systems of linear equations, the variables of which are estimates for the nonlinear terms of the multivariate polynomial regression. Partial cases that guarantee the finding of estimates with a predetermined value of their variances were considered. The formal algorithm for constructing coefficient estimates for nonlinear terms of the multivariate polynomial regression stops working on the first coefficient whose estimation with a predetermined accuracy is not achieved under the specified limitations on the number of tests. The estimation of all coefficients that were not found by the decomposition method is done by a heuristic method, which is an efficient modification of the group method of data handling. The increase in the efficiency of the synthetic method is achieved primarily by finding such new theoretically substantiated algorithmic procedures (aggregated operators) of the decomposition method, which significantly, in comparison with its previous version, increases the number of coefficients for nonlinear terms of a multivariate polynomial regression that can be found in advance given accuracy. The authors showed that this effect is achieved due to new theoretical provisions used in the visual analysis of the structure of the multivariate polynomial regression given by the redundant representation by a professional user. The given illustrative example facilitates the use of the presented results when solving practical problems.
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