Bivariate Center and Range Regression Model using PCR and PLSR for interval-valued data

This research explores regression modeling for interval-valued data by combining the Bivariate Center and Range Model (BCRM) with Ordinary Least Squares (OLS), Principal Component Regression (PCR), and Partial Least Squares Regression (PLSR), respectively. Using the center–range representation for interval-valued variables expands the predictor space, leading to multicollinearity that may undermine model stability and interpretability. To address this, PCR and PLSR are integrated into the BCRM framework to reduce dimensionality through latent components while maintaining the inherent structure of interval-valued variables. The proposed methods are tested on three real-world datasets: Taiwanese temperature records, exchange rates, and air quality data. Results indicate that the Bivariate Center and Range Model with OLS provides a highly accurate baseline, with average RMSE values of 0.8111, 0.7678, and 22.7234 for the respective datasets. Compared to BCRM using OLS, the Bivariate Center and Range Model using the PLSR model achieves a better balance between prediction accuracy and model complexity, reducing the number of explanatory variables by about 25–30% while keeping prediction errors close to those of the BCRM–OLS baseline. These results suggest that the proposed approach offers an effective and reliable framework for regression analysis involving high-dimensional interval-valued data.