Optimizing education resource allocation using grey model forecasting of school age populations.

This study enhances the applicability and accuracy of the Grey Model (GM) (1,1) for forecasting school-aged populations. This is achieved by employing a buffering operator to optimize school-aged population data, thereby reducing interference from policy changes and environmental factors. Additionally, Locally Weighted Linear Regression is introduced to refine the calculation of the developmental grey number and endogenous control grey number, which significantly improves the model's ability to fit volatile and complex data trends. Building upon the foundational GM(1,1) and grey system theory, an integrated predictive framework is developed to capture changes in school-aged population dynamics. The enhanced GM (1,1) model's performance is evaluated by comparing its residuals with those of the traditional GM (1,1) model, enabling assessment of the model's trend-fitting accuracy. Based on the population forecasts, tailored strategies for educational resource allocation are formulated. The dataset spans from 2013 to 2020, a period marked by profound socioeconomic shifts in China that generated distinct population mobility patterns. The results demonstrate marked improvements in the enhanced GM (1,1) model's predictive accuracy, as evidenced by significantly smaller residuals compared to the traditional model. For example, in 2018-2020, the traditional GM (1,1) model produced residuals of - 14.462, - 4.405, and 5.467, respectively, whereas the enhanced model's residuals were substantially reduced to 0.399, 0.132, and 3.707. These findings indicate that the proposed model more precisely captures the evolving trends of the school-aged population. The study proposes data-driven and scientifically grounded strategies for optimizing the allocation of educational resources, thus providing valuable guidance for education policy formulation and implementation. By integrating grey system theory with local regression techniques, this study presents a novel methodological approach that advances school-aged population prediction and educational resource planning, with both theoretical value and practical relevance.