Abstract
The paper considers the problem of regression analysis with indeterminate explanatory and explained variables. A quality criterion for estimating the regression coefficients is formulated and justified, taking into account possible significant differences in the accuracy of assigning different variables. The study considers a method of calculating the regression coefficients in accordance with the concept of least squares. The proposed approach provides a reasonable compromise between the conflicting requirements: the maximum compactness of the fuzzy value function of the explained variable and the minimal deviation of the solution from the modal one. The problem is solved by minimizing the complex criterion, the terms of which determine the level of satisfaction of these requirements. An additional advantage of the approach is that the original problem, fuzzy by the nature of the initial data, is reduced to solving two usual problems of mathematical programming. The problem of fuzzy comparator identification is considered when the values of the explained variable are not defined but can be ranked by the descending of any chosen indicator. To solve this problem, the study proposes a method for estimating regression coefficients based on solving a fuzzy system of linear algebraic equations
Highlights
Regression analysis is a powerful and effective statistical method of constructing mathematical models that describe the relationship between the indicator of the functioning of the analyzed system y and the conditioning, explanatory independent variables F1, F2,..., Fm
The sought connection is usually described by the Kolmogorov-Gabor polynomial, which in the simplest case has the form y j = x0 + Fj1x1 + Fj2x2 + ... + Fjm xm + ε j
Fji is the value of the i-th independent variable in the j-th experiment; i = 0,1, 2,...,m, and j = 1, 2,...,n
Summary
Regression analysis is a powerful and effective statistical method of constructing mathematical models that describe the relationship between the indicator of the functioning of the analyzed system y and the conditioning, explanatory independent variables (factors) F1, F2,..., Fm. In order to reveal this connection, a series of experiments ( ) is conducted in which each experiment Fj1, Fj2,..., Fjm determines its corresponding result, i.e., the value of the dependent variable y j , where j = 1, 2,....,n. The sought connection is usually described by the Kolmogorov-Gabor polynomial, which in the simplest case has the form y j = x0 + Fj1x1 + Fj2x2 + ... Fji is the value of the i-th independent variable in the j-th experiment; i = 0,1, 2,...,m, and j = 1, 2,...,n.
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