Recursive least-squares (RLS) based prediction methods are very popular in lossless compression of hyperspectral imaging. Adaptive selection of number of bands used in the prediction in RLS based methods increases compression performance significantly. However, this process brings additional computational load. In this work, a sample reduction based fast adaptive method to determine the number of bands required for prediction is proposed. Performance of the proposed method is compared to the-state-of-the-art methods in terms of bitrates and computation times and obtained results are discussed.