Abstract:

This study explores the efficiency of polytrigonometric Regression models as viable alternatives to third-order polynomial regression models in curve fitting and predictive modeling. While polynomial regression is widely utilized for capturing nonlinear trends with characteristic turning points, polytrigonometric models integrate polynomial and trigonometric components, offering enhanced flexibility for diverse datasets, particularly when the underlying data structure is uncertain or may contain oscillatory characteristics. Simulated datasets of n = 10, 20, 50, 100, 200, and 500 were generated using third-order polynomial equations and fitted with both models. Model performance was evaluated using R², MSE, and p-values across the varying sample sizes. The Polytrigonometric models presented a reasonable proxy for the third order polynomial models for the various sample sizes, improving as sample sizes increases. The model's R² advanced from 0.723 at n=10 to perfect fit (R² = 1.000) at n ≥ 100, achieving high statistical significance (p < 0.0001) at larger sample sizes and strong performance (R² ≥ 0.978) at moderate sample sizes (n ≥ 50). A real-world agricultural dataset on tomato plant growth rates versus NPK fertilizer concentration of sample size n=300 was analyzed to validate the models under practical conditions. Findings reveal that the polytrigonometric model also demonstrated remarkable adaptability and progressive improvement with increasing sample size. The real-world dataset validated the model's practical utility, with R² = 0.649 (p < 0.001) explaining about 65% (64.9%) of the variance; a moderate-to-strong level representing substantial predictive capability for agricultural applications. While the polynomial model achieved superior performance on polynomial-structured data (R² = 0.885 for the real data). As theoretically expected, the polytrigonometric model's ability to attain strong performance using a fundamentally different mathematical framework demonstrates its versatility. Overall, this study confirms that the polytrigonometric model serves as a viable and practical alternative to polynomial regression, offering researchers a flexible tool that maintains strong predictive performance across diverse applications.