Abstract
The aim of the article is to investigate the relationship between the number of active small and medium-sized businesses in Kazakhstan and the number of internal costs for research and development projects based on the use of economic and mathematical forecasting methods. As a result of the application of statistical and mathematical methods, the analysis of changes in the number of active SMEs and the volume of R&D expenditures in the Republic of Kazakhstan for the period 1999-2019 was carried out on the basis of constructing a paired linear regression model. The quality of the model was assessed, the interval for the lower and upper boundaries of the forecast of changes in the indicators of the number of active SMEs from the volume of R&D expenditures was calculated. An economic interpretation of the calculated data obtained because of constructing a linear paired regression model is given. It was revealed that the number of active SMEs by 94.5% is explained by the volume of internal R&D expenditures. A point forecast for the number of active SMEs has been calculated when the volume of internal R&D expenditures changes for 2022. The calculation of indicators of the lower and upper boundaries of the predicted value of the number of active SMEs has been carried out. With an increase in the volume of internal expenditures on R&D in the GDP of the Republic of Kazakhstan to 92,178 million tenge, the number of active small and medium-sized enterprises will be in the range from 1,244,436 to 1,669,622 units.