Optimization of multivariate linear regression model for ionospheric disturbed index

A wide range of space weather indices have been developed, and the accurate identification of strong standardized associations is essential for ionospheric disturbance modeling. Using twelve space weather indices from 1998 to 2018, this study systematically compares the variable selection capability and stability of four multivariate linear regression methods, namely ordinary least squares (OLS), Ridge regression, Lasso regression, and Elastic Net, in modeling the Ionospheric Disturbed Index (IDI). By jointly considering variance inflation factor diagnostics, the interpretability of regression coefficients, and the physical relevance of space weather parameters, redundant variables (SYM-H, Electric field, and Ap) are progressively eliminated. A final set of nine key indices is identified, including SSN, F10.7, Dst, Kp, AE, Flow pressure, Plasma speed, Bz GSM, and upper atmospheric wind field. The results demonstrate that the Kp index consistently emerges as the strongest standardized association with IDI across all regression methods, while wind, Dst, AE, F10.7, SSN, and other indicators associated with neutral dynamics, geomagnetic activity, and solar variability also exert significant influence. Furthermore, the modeled IDI exhibits synchronous variations with single-point positioning (SPP) errors during intense geomagnetic storms, providing insight into the coupling between ionospheric disturbances and navigation performance. This study establishes a systematic framework for variable selection and model optimization in ionospheric disturbance modeling.