The article presents fundamental approaches to the study of periods of development of socio-economic indicators and their mutual influence. The forms of influence of indicators on each other are investigated. The dynamic analysis of the standard of living of the population and the factors of social and economic spheres is completed with the tools of econometric modeling and canonical analysis. Birth rate, mortality, employment, unemployment, investments in fixed capital, GRP per capita, the account of resource production, the standard of living of the population and fixed assets according to the data of the Samara Region for the period 20062019, registered in the annual collections of state statistics bodies, are considered as indicators. The predicted values of the standard of living by various methods are calculated, confidence intervals for the studied indicators are constructed. By means of adaptive forecasting using the Brown model, forecast values are calculated and confidence intervals are constructed. Using the tools of canonical analysis, integral indicators are calculated and grouping by time factor is carried out. The spatial grouping of the time factor depending on the standard of living of the population and canonical integral factors is presented. According to the results of the analysis of autoregressive models, it was found that in terms of employment, unemployment, fertility, mortality, investment in fixed assets, GRP per capita, resource production and fixed assets, the impact of the indicator of the previous year is statistically significant, and in terms of the standard of living of the population statistically insignificant. In the second-order autoregression, it was found that all statistical indicators have an impact on the studied indicator, except for indicators of employment and the standard of living of the population. Thus, the forms of models of multiple linear regression, paired linear regression and autoregressive models allow us to assess the numerical impact of all indicators on the studied indicators, as well as their impact on the Standard of living of the population. Visualization of multidimensional data contributes to an in-depth analysis of indicators when grouping, for example, by the time factor.

Modern market conditions, burdened by the process of active restructuring of the economy under new circumstances related to geopolitical instability and the sanctions burden, change the concepts, principles and requirements for the quality of innovation management, as one of the main elements of the sustainable functioning of the enterprise and increasing its competitiveness, as innovation today is becoming the main aspect of maintaining competitive positions. The well-established models of organizational process management in Russian practice are characterized by conservatism and low efficiency. The innovative activity of most modern domestic enterprises, in comparison with the standards of developed countries, is characterized by low innovation activity, a large percentage of the use of traditional technologies and organizational and managerial methods, separation of production capabilities and ideas from dynamically changing market conditions. In fact, an increase in the efficiency of industrial enterprises in the field of innovation and an increase in its competitiveness, taking into account modern intensively changing and unstable conditions, should be achieved through a qualitative increase in the level of economic science and educational technologies, taking into account modern, including world standards of innovation management. In addition, it is necessary to concentrate on our own RD, possibly based on high-tech developments of friendly countries, and increasing the level of innovation activity within the country by industry. The successful implementation of innovation activities at industrial enterprises ultimately depends on management and management's approach to management and innovation activities. It is important to understand the importance and necessity of updating production standards, adapting management methods to market conditions, and the superiority of the final product over competitors inside and outside the country. Thus, the modeling of the innovation process at industrial enterprises today has a promising strategic role.

The transport system of Russia is an important component of the industrial infrastructure, and its development is one of the priorities of state activities. In the context of integrated regional development, transport is a tool for implementing the economic interests of subjects. Currently, the transport system of the Russian Federation is actively developing. This largely determines the development of economic indicators, such as imports and exports, as well as an increase in the volume of sales of goods of their own production. In this regard, it is important and relevant to study the current state of the transport system and the factors of its development. The paper explores the forms of dependent indicators of the road transport industry of the Volga Federal District. Due to the limited sample size, it is proposed to study this area using the formation of integral indicators using discriminant and canonical analysis methods. The use of canonical variables as integral indicators expands the possibilities of applying canonical correlation in other analyses, including in econometric modeling. The integral factor calculated by the discriminant analysis algorithm reduces the dimension and allows us to estimate the degree of crowding and the form of dependence between the integral variables in conditions of a small sample size.

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