Abstract

This study aims to model the Human Development Index (HDI) in Indonesia based on education quality indicators using multivariable kernel regression, and to identify the optimal bandwidth selection method through Cross-Validation (CV) and Generalized Cross-Validation (GCV). Employing a quantitative modeling design, the research utilizes secondary data comprising educational and HDI indicators from 34 Indonesian provinces in 2023. The analysis applies multivariable kernel regression with a triangle kernel function, with mean years of schooling and expected years of schooling as predictor variables. Bandwidth optimization is performed using CV and GCV, and model performance is assessed through the coefficient of determination (R²) and Mean Absolute Percentage Error (MAPE). The results indicate that the GCV method yields a slightly better model, with R² of 86.32% and MAPE of 1.94%, compared to the CV method, which as an R² of 85.92% and MAPE of 1.96%. While both models show excellent forecasting accuracy, GCV demonstrates superior stability and predictive performance. These findings confirm that multivariable kernel regression, particularly when optimized with GCV, is an effective approach for modeling complex data patterns such as HDI based on educational indicators in Indonesia.

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