Traditional significant wave height (SWH) estima- tion from HF radar typically relies on spectral analysis of the received radar signals. This process was previously simplified by establishing a linear relationship between SWH and the standard deviation of received HF radar voltages under first- order scattering. Building on this approach, this paper presents a physics-informed regression model that incorporates second- order scattering effects through a quadratic formulation derived from a Neumann expansion. The proposed method is evaluated using HF radar data collected in July 2018 at Argentia, New- foundland, with collocated buoy measurements as ground truth. The model achieves a minimum root-mean-square error (RMSE) of approximately 19 cm.