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The formulas for error propagation from the random error sources to the three-dimensional (3-D) coordinate errors of laser footprints of an airborne laser scanning (ALS) system were deduced. Based on large-scale sample data, multiple linear regression experiments were carried out to obtain the standardized regression coefficients of the random errors for the 3-D coordinate errors under different flight heights (from 500 to 6000 m above ground level). The standardized regression coefficients were used to quantitatively evaluate the impacts of the random errors and to sort the impacts on the order of importance. The variation of the impacts of the random errors with increasing flight height and tilt angle of the mirror was also analyzed. The experimental results provide an important guide for error budget of various sensors in the ALS system so as to effectively suppress or compensate significant errors and to improve the performance of the ALS system.