THE CREATION OF A REGRESSION MODEL BASED ON APPROXIMATION AND DISPERSION ANALYSIS OF STATISTICAL DATA
Authors: YERSHOVA N.M. 
Published: December 2023

Problem statement. The most difficult issue when creating statistical models is the choice of a mathematical form of connection, that is, an analytical function that connects the elements of the system being studied. The form of the connection equation is established on the basis of theoretical, technological considerations or intuition. When it is difficult to imagine the dependence in advance, then a correlation field of points is built for two signs, the location of which on the plane determines the direction of action and the form of communication. For a deep and comprehensive study of statistical relationships, the concepts of correlation and regression are used. The task of correlation analysis is to establish the direction of action and the form of communication type. The task of regression analysis is to build a mathematical model of regression in the form of the resulting characteristic average value dependence on factor characteristics. The parameters of the regression model should be selected in such a way that the line constructed by the model passes between the points and is located as close as possible to all points of the correlation field, that is, it passes almost through its center. The purpose of the article is to create a regression model based on approximation, correlation and dispersion analysis of observational data. Results. Data approximation for multidimensional samples of active and passive experiments was performed, approximating functions and regression models in general were obtained based on them. On specific examples, the relationship between the factor features was established, the factor feature was selected. The most significant in terms of the connection closeness with the resulting feature, and a multivariate regression model suitable for forecasting was obtained. A multivariate dispersion analysis of the active experiment data was carried out on the research example of the influence on the homogeneity coefficient of concrete cement brand, type of aggregate, test period and “production period: of concrete. Analysis of dispersion shows that the most significant factors are the cement grade, the test period, the “making period” of the concrete and their minor interaction and the type of aggregate. The proposed technique significantly simplifies the process of creating a regression model. Conclusions. The performed calculations prove that: on the basis of the approximation and correlation of the passive experiment observations, it is possible to establish a relationship between the factor characteristics, to choose the factor characteristic that is the most significant in terms of the connection closeness with the resulting characteristic, to obtain a multivariate regression model suitable for forecasting, and this allows simplify the procedure for creating a regression model by successively moving from a simple model to a complex one; dispersion analysis of active experiment data makes it possible to assess the impact of individual factors and the impact of interaction between them. The approximation proves that the regression models of the active experiment data are linear. This is also confirmed by dispersion analysis, because the interaction of factors is insignificant.