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This paper sheds light on the least-square (LS)-based adaptive prediction schemes for lossless compression of natural images. Our analysis shows that the superiority of the LS-based adaptation is due to its edge-directed property, which enables the predictor to adapt reasonably well from smooth regions to edge areas. Recognizing that LS-based adaptation improves the prediction mainly around the edge areas, we propose a novel approach to reduce its computational complexity with negligible performance sacrifice. The lossless image coder built upon the new prediction scheme has achieved noticeably better performance than the state-of-the-art coder CALIC with moderately increased computational complexity