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Abstract In regression problems alternative criteria of “best fit” to least squares are least absolute deviations and least maximum deviations. In this paper it is noted that linear programming techniques may be employed to solve the latter two problems. In particular, if the linear regression relation contains p parameters, minimizing the sum of the absolute value of the “vertical” deviations from the regression line is shown to reduce to a p equation linear programming model with bounded variables; and fitting by the Chebyshev criterion is exhibited to lead to a standard-form p+1 equation linear programming model.
Harvey M. Wagner (1959) studied this question.