Enhancing linear regression forecasting with an improved conjugate gradient method: Application to economic data

Sijun Tao; Nur Hamizah Abdul Ghani; Mohd Rivaie.

This study proposes an improved conjugate gradient (CG) method: the Tao-Rivaie-Hamizah (TRH) method and applies it to regression analysis of China's per capita disposable income over the past fifteen years. Unlike previous CG variants, TRH combines the numerator of the Hybrid Polak–Ribière–Polyak (HPRP) method with the denominator of the Hamoda–Rivaie–Mamat (HRM) method, thereby achieving faster convergence and enhanced robustness. Numerical experiments demonstrate that the TRH method generally outperforms several representative CG methods in terms of convergence speed and robustness. In economic applications, the TRH method yields smaller total relative errors and superior forecast values compared to Least Squares and Trend Line methods. These results validate the innovation and efficacy of the TRH method, providing a stable and effective solution for linear regression forecasting while further enriching and advancing the CG method.

KEYWORDS: Conjugate gradient method, Least Squares method, TRH method, Trend Line method, linear regression forecasting



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