This paper investigates the relation between error distribution and predictive order of minimum mean abusolute error predictors (MMAE predictors) designed for lossless coding of grayscale images. Design of MMAE predictors reduces to the linear programming problem. Let k be the number of coefficients in a predictor (predictor order), we imagine that predictor order k may have a distribution shaping effect. Main purpose of this paper is to ensure that k has such an effect.