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Abstract
A class of multifactor designs for estimating the slope of second-order response surfaces is presented. For multifactor designs, the variance of the estimated slope at a point is a function of the direction of measurement of the slope and the design. If we average the variance over all possible directions, the averaged variance is only a function of the point and the design. By choice of design, it is possible to make this variance constant for all points equidistant from the design origin. This property is called slope rotatability ouer all directions, and the necessary and sufficient conditions for a design to have this property are given and proved. The class of designs with this property is discussed.