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- Title
Mathematical modeling of nonlinear regression function at the central compositional design of experiment with any number of factors.
- Authors
Zinchenko, Tetiana; Syvolobova, Yana
- Abstract
Introduction. We are going to consider the task of building a multi nonlinear regression functions to any number of factors when using a central composite design of experiments. Materials and methods. The methods of mathematical statistics use for find the total (by factors) algorithm for calculating the coefficients of the regression multivariate functions of the second order with the use method of minimum squares and methods of linear algebra for finding the solution of sparse systems of linear algebraic equations with. Results and discussion. In most cases, for processing the results of experiments useing orthogonal scheme of the central compositional design of experiment. For m-factors the number of experiments of full factorial experiment is 2m. This number of experiments is insufficient to use nonlinear models of multivariate regression of the full form. It is therefore proposed to use the rotatable scheme of central compositional design. The number of experiments without repetitions is (2m 2m). More points allows to find a greater number of coefficients of a nonlinear regression function. Construction of nonlinear models of multivariate regression for an arbitrary number of factors requires special mathematical tools. For processing the results of experiments we use nonlinear model of multivariate regression. Coefficients of regression functions by the method of minimum squares is the problem of finding solutions of a system of algebraic equations. To solve the system of equations, it is necessary to calculate the appropriate number of determinants. Recurrence and direct formulas for computing sparse determinants of a special type of of n-th order were obtained for solving this problem. The main result is the general formulas coefficients of regression function of the second order that take into account the number of factors and the number of experiments. Conclusions. The results of mathematical modeling of nonlinear multivariate regression functions are recommended for use in determining the recipe of raw materials, for example, when optimizing the recipe of confectionery products. Formulas for calculating coefficients of multivariate regression functions of the second order can be used for any number of m-factors when applying rotatable central composite design of experiment with the appropriate number research.
- Subjects
COMPOSITE structures; NONLINEAR regression; LINEAR algebra
- Publication
Ukrainian Journal of Food Science, 2016, Vol 4, Issue 1, p131
- ISSN
2310-1008
- Publication type
Article