CONSTRUCTION OF MATHEMATICAL MODELS USING THE METHODS OF CORRELATION AND REGRESSION ANALYSIS

Abstract

The article discusses the construction of a mathematical model using the methods of correlation and regression analysis in determining the functional relationship between the quantities. When conducting an experiment, it is often necessary to establish the interdependence between two or more quantities in order to obtain an empirical formula. In some cases, this is a simple task, because these connections are almost obvious or known in advance. As a rule, to establish the relationship between different indicators, factors and characteristics is not a trivial task. There is a need to use some hypothesis in the form of functional dependence. In other words, it is necessary to replace this functional dependence with a fairly simple mathematical expression. Such a mathematical expression can be a linear equation or a polynomial. In order to use such experimental data to determine such a mathematical or functional relationship between variables, the methods of correlation and regression analysis are used. Correlation analysis provides an answer to the statistical hypothesis of the absence or presence of a relationship between variables with some predetermined confidence probability. Determination of the functional dependence between different values on their experimental values is carried out using regression analysis. It is based on the well-known method of least squares. Proposing one or another regression equation, the researcher determines both the very existence of the relationship between variables and its mathematical form. Regression analysis considers the relationship between the dependent quantity and non-dependent variables. This relationship is represented using a mathematical model, that is, an equation that connects the dependent and independent variables. Processing of experimental data using correlation and regression analysis allows us to build a statistical mathematical model in the form of a regression equation. Thus, the methods of correlation and regression analysis are closely related.