Mathematical description of the conceptual model of managing the development of regional socio-economic systems of the Russian Federation

The article is devoted to the problem of substantiating the verbal model of the system by mathematical methods. As such a model, a conceptual model for managing the development of regional socio-economic systems, developed earlier by the author, was chosen. Regression analysis was used. Thanks to this analysis, the dependence of the centroid of the model on the input indicators and the influence of the centroid of the model on the resulting indicators are revealed. The centroid of the model is a set of quantifiers of the state of labor resources, expressed by a tonal gap in the information environment. Three indicators characterizing natural factors, two indicators reflecting production factors, three indicators describing the state of the region's infrastructure and three indicators of social orientation were selected as input indicators. The model includes seven resulting indicators: four of which characterize the number of serious crimes associated with a threat to human life and health, two indicators show the death rate of the population as a result of suicide and alcohol poisoning, and one indicator reflects the number of unemployed in the region. The research resulted in a mathematically confirmed conceptual model for managing the development of regional socio-economic systems. Modeling is carried out on the example of one of the constituent entities of the Russian Federation - the federal city of St. Petersburg.