No abstract

The article is about a problem of mathematical modeling of the natural resource potential of the Perm Territory by 1st and 2nd order finite-difference models. Such models can obtain better forecasts of complex socio-economic processes in comparison with the traditionally used linear multiple regression models. A high quality model of the natural resource potential with forecast possibi¬lities is one of the necessary conditions for the effective management of the natural resources of the region in order to ensure its sustainable economic development. Purpose of work. Aim of this work is work construction of finite-difference models of a natural resource potential complex indicators and an assessment of their prognostic properties. Materials and methods. Our research is based on Perm region statistical data for the period from 2001 to 2018. A multiple linear regression model is used as a comparison base. The natural resource potential complex indicator is calculated as a weighted sum of particular criteria characterizing the natural resources of the region. First and second order finite difference models are obtained by adding autoregressive terms of the first and second orders, respectively, to the multiple linear regression model. An estimation of the unknown parameters of the equations is carried out by a modified least squares method, which preserves the signs of the coefficients with the factors the same as in the original linear model. At the same time, the selection of explanatory factors and the assessment of the quality of the models are carried out based on the accuracy of the predicted values of the studied indicator. The results of the study. Components and factors of the natural resource potential is obtained, and a procedure for constructing finite-difference models is performed for three different time intervals: 2001–2018, 2001–2008, and 2008–2018. These intervals are chooseen because changes in the methodology for generating statistical data nearly 2008. Discussion and conclusions. The number of calculated predicted values was 18, and only in 4 out of 18 cases (22,2%) their quality is worse than forecasts obtained by the linear multiple model. So proposed modification of the multiple linear regression model with the addition of autoregressive terms makes it possible to improve the forecasting quality of the complex indicator of the natural resource potential of the region and, therefore, to make more effective decisions when managing its level.

In the issue we consider socio-economic processes modeling based on first and second order finite differences models. Since commonly used modeling methods have drawbacks and thus are not universal it was necessary to develop alternative methods which are better in some aspects. Specifically multiple linear regression models have limited prediction abilities, and differential regression coefficient evaluation method is quite complex and have some economically uninterpreted excess tunings. In our research we replaced first and second order derivatives in differential regression models with their finite differences equivalents and thus gained a multiple linear regression model modification which includes first and second order auto regression items. Estimation of their parameters can be done using a modification of least-squares method in which we demand that factor coefficients signs for models with and without auto regression items are the same. Due to additional items in the modified linear regression models their approximation capacity is greater than of a common model. However for application purposes model forecasting capacity is more important, i.e. the forecasting efficiency criterion is the most significant for a decision making. In order to estimate forecasting potential of modified multiple linear regression models we performed coefficient estimation of unmodified and modified equations for 59 various socio-economic data sets. We used shortened time series, so we could calculate model values and compare them to actual data. It was determined that modified multiple linear regression models allowed to make better predictions in 49 (76.3 %) cases. We can now assume that addition of auto regression items into multiple linear regression model can increase short-term forecasting efficiency.

In modern high-paced city environment effective rest is an essential element of satisfactory recreation and human physical and psychological health. It is also an important sector of the national economy and a person development tool. People leisure time structure extensively determines nation development level and is often considered as one of the life quality indexes. In order to study leisure time quality and quantity of Berezniki town of Perm region population we conduct a survey among people of different age and occupation. The questionnaire contained questions about total amount of respondent’s free time and preferred ways of spending it, including physical and social activities, different types of media and hobby. We discovered that total week average leisure time value is about 24 hours with standard deviation of 20 hours. Our study disclosed that most of respondent distribute their spare time between different types of leisure activities: 59.0 % of respondents prefer physical activities, 55.3 % of them like to rest at home, 30.5 % of respondents during their free time participate is social events. Nearly 56 % of respondents claim that they don’t have enough money for their spare time activities, 32 % of them are not satisfied with town outdoor physical activities infrastructure, 28 % – with social activities infrastructure. Ascertained problems solving is an important matter for social stability and economic progress.

In the article we consider a complex indicator of region natural resource potential modeling and forecasting quality improvement using different machine learning models. Problem under consideration importance is determined by the fact that the models traditionally used for these purposes demonstrate either low quality, or high configuration and parameters evaluation difficulty. The aim of the study is determination of machine learning models that provide the optimal values of various modeling quality metrics. Materials and methods. For this study purposes we considered the multiple linear regression, decision tree, random forest, gradient boosting and multilayer perceptron mo¬dels. We used the determination coefficient R2, the root mean square error of modeling RMSE, the average absolute error of modeling MAE, and the relative error of prediction for 1 and 2 time intervals as quality metrics. This study is based on data of the complex indicator of the Perm Region natural resource potential and the system of its determining factors in the time interval from 2001 to 2018. We evaluate models and calculate quality metrics using Pandas and Scikit-learn Python libraries in Jupiter Notebook environment. Results. According to our research the classical multiple linear regression model demonstrates the worst results for all quality metrics under consideration. The decision tree model demonstrates determination coefficient maximum value and minimum root mean square error and mean absolute error. Minimum relative forecasting error for 2017 is provided by the gradient boosting model, for 2018 – by the multilayer perceptron model. Conclusion. Our study allows us to affirm that nonlinear machine learning models for the task of region natural resource potential modeling and forecasting demonstrate better approximating and predictive properties compared to multiple linear regression and thus can be used to improve the quality of natural resource management.