Analysis of a multifactorial model of a region with a strong agro-industrial cluster

. The article considers the structure of the gross regional product in a region with a strong agro-industrial cluster. The authors have built a multifactorial model of sustainable development on agriculture in the region. The possibility of using this model is justified on the basis of a comparative analysis of the predicted values of the effective feature by two methods.


Introduction
The development on agriculture in the regions is generally an important tool for maintaining the national security of the country, developing socio-economic potential and preserving the sustainable development of the region.
Currently, the study of the factors of sustainable development on agricultural regions [1] is more based on qualitative methods with the involvement of experts than on quantitative methods using multifactor modeling.
The relevance of the study is that the most important direction in determining the factors of sustainable development of regions with a strong agro-industrial cluster should be the construction of multifactor models in which the gross value added on agriculture is the effective factor.

Materials and methods
The theoretical basis of the research was made up of scientific works of domestic and foreign scientists and specialists in the field of research of factors of sustainable development of regions with a strong agro-industrial cluster, official statistical materials of the territorial body of the State statistics service for the Kursk region for 2005-2019.
The methodological basis of the research are general scientific methods of analysis and synthesis, methods of generalization and comparison, methods of logical analysis of theoretical and practical material, statistical methods of constructing multifactor models based on correlation and regression analysis and forecasting methods using a Microsoft Excel spreadsheet processor.

Results
The gross regional product is always the main indicator characterizing the level of development of the region, defined as the sum of the gross values added types of the economic activities of the region. Depending on the cluster structure of the region, a significant contribution to the gross regional product will be made by the branch of belonging to a strong cluster. Regarding the region with a strong agro-industrial cluster, we note that its difference from other regions is that agriculture has a significant impact on the sustainable development of the region as a whole and makes the greatest contribution to the formation of the gross regional product (Figure 1). Our study of the structure of the Gross Regional Product of the Kursk region ( Figure 1) showed that agriculture, manufacturing, mining and trade make the greatest contribution. It should be noted that during the study period (2016 -2019), there was a decrease in the share of gross value added on agriculture in the total volume of gross regional product by 1%, against the background of an increase in the gross value added on agriculture in the Kursk region by 18323.7 million rubles ( Figure 2). The decrease in the share on agriculture in the structure of the gross regional product, against the background of the growth of the gross value added on agriculture in 2016-2019, indicates the problems of the development on agriculture in the Kursk region.
It should be noted that if all factors are equal to zero, then the gross value added will have a negative value (-3611.86 million rubles).
The regression function was evaluated using the coefficient of determination (R2= 0.9835) and showed that 98.35% of the variation in gross value added is due to the influence of factors included in the multiple regression equation. The overall adequacy of the equation was obtained using Fisher's variance F-test, the significance of which was 0.004, that is, the coefficient of determination is significant at 1% level. This indicates that there is a direct relationship between the gross value added in agriculture and the selected dependent factors.
This multifactorial model of the gross value added on agriculture in the Kursk region (1) shows that an increase in investments in fixed assets on agriculture by 1 million rubles will lead to an increase in the gross value added on agriculture by 0.10 million rubles. The growth of monetary incomes of the population as a whole in the Kursk region by 1 million rubles will lead to a decrease in the gross value added on agriculture by 0.01 million rubles. An increase in wholesale trade turnover by 1 million rubles will lead to an increase in the gross value added on agriculture in the Kursk region by 0.30 million rubles.
To substantiate the application of this multifactor model, we conducted a comparative analysis of the calculated forecast value of the gross value added on agriculture in the Kursk region using the linear trend model and the multifactor model we built (Table 2). We think it's worth noting that the deviation of the forecast values for all three methods is insignificant, which is explained by mathematical rounding during calculations and is less than 1.3%.

Discussion
E3S Web of Conferences 389, 03020 (2023) https://doi.org/10.1051/e3sconf/202338903020 UESF-2023 Our results have shown that the gross value added on agriculture, as an effective factor in the sustainable development of the agro-industrial cluster of the Kursk region, is influenced by such factors as: investments in fixed assets of agriculture, cash income for the entire region, wholesale trade turnover in the whole region.
Regarding the values of the results obtained, it is worth emphasizing that the positive impact of investments in fixed assets of agriculture and wholesale trade turnover on the sustainable development of the agro-industrial cluster is logical. Since an increase in investments in fixed assets implies an expansion of production capacities in crop production and animal husbandry, and an increase in wholesale trade leads to the need the increasing the volume on agricultural production.
Doubt may cause negative influence of an increase in the monetary income of the population throughout the region. The logic says that an increase in the income of the population always leads to an improving the quality of life in the region and thereby contributes to the dynamic development of the region as a whole. Thus, we have carried out the construction of a multifactorial model to identify factors affecting the sustainable development of the agro-industrial cluster of the Kursk region. We believe that the negative influence can be explained by the following reasons: 1. Increase in household incomes due to high rates of wage growth, not accompanied by an adequate increase in labor productivity. Some experts characterize this phenomenon very negatively, insisting that the domestic economy is thereby "eating through" itself.
2. Despite the increase in their purchasing power, citizens are force due to the increase in inflation to limit their range of goods and services to the same list, but at higher prices. Therefore, it is not necessary to increase the volume of production of goods and services, including in agriculture.
3. According to the theory of J. Keynes, with the growth of the population's income, consumption increases, but not to the extent that income increases. It is possible to observe changes in the structure of the use of income of the population, namely, the share of consumption is decreasing, and the share of savings is growing. This phenomenon leads to an economic crisis of overproduction, including in agriculture [5].
Analysis of research literature on the issues of multifactorial modeling of economic growth in the region ( [5][6][7][8][9]) showed that two-factor models, based on labor and capital, are most often found both in practice and in theory. Comparing these two-factor models with the model we have built, we can note that labor and capital are also reflected in our model within the framework of household income and investments in fixed assets of agriculture.

Conclusion
In this article we examined the structure of the gross regional product of the Kursk region.