COMPARATIVE STUDY OF FUNCTIONAL LINEAR REGRESSION AND AN INTERACTION MODEL FOR MODELING RAINFALL IN INDONESIA

Khusnia Nurul Khikmah (Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Surabaya, Indonesia)
A'yunin Sofro (Actuarial Sciences Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Surabaya, Indonesia)

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 20 No 3 (2026): BAREKENG: Journal of Mathematics and Its Application

Regression is a widely used statistical modeling method. Its applications have evolved, including functional data analysis, which offers flexibility by modeling data over specific time intervals with varying case-specific observations. Functional regression has several categories, one of which is functional prediction regression. This study uses functional prediction regression to model comprehensive climate data from the World Bank Climate Change Knowledge Portal, specifically Indonesia’s average annual temperature and rainfall from 1951 to 2016. An advantage of functional prediction regression is its ability to model based on the dataset. We compare two models: the first with a functional linear effect and the second with a linear interaction combination effect. The models are estimated using boosting and the Generalized Additive Model for Location, Scale, and Shape (GAMLSS). Results show that the functional linear model better fits Indonesia's rainfall data, yielding a smaller Akaike's Information Criterion by 170.351.