A novel wavelet-based scheme to increase coefficient independence in hyperspectral images is introduced for lossless coding. The proposed regression wavelet analysis (RWA) uses multivariate regression to exploit the relationships among wavelettransformed components. It builds on our previous nonlinear schemes that estimate each coefficient from neighbor coefficients. Specifically, RWA performs a pyramidal estimation in the wavelet domain, thus reducing the statistical relations in the residuals and the energy of the representation compared to existing wavelet-based schemes. We propose three regression models to address the issues concerning estimation accuracy, component scalability, and computational complexity. Other suitable regression models could be devised for other goals. RWA is invertible, it allows a reversible integer implementation, and it does not expand the dynamic range. Experimental results over a wide range of sensors, such as AVIRIS, Hyperion, and Infrared Atmospheric Sounding Interferometer, suggest that RWA outperforms not only principal component analysis and wavelets but also the best and most recent coding standard in remote sensing, CCSDS-123.