Selecting a suitable equation to represent a set of multifactor data that was collected for other purposes in a plant, pilot-plant, or laboratory can be troublesome. If there arekindependent variables, there are 2kpossible linear equations to be examined; one equation using none of the variables,kusing one variable,k(k– 1)/2 using two variables, etc. Often there are several equally good candidates. Selection depends on whether one needs a simple interpolation formula or estimates of the effects of individual independent variables. Fractional factorial designs for sampling the 2kpossibilities and a new statistic proposed by C. Mallows simplify the search for the best candidate. With the new statistic, regression equations can be compared graphically with respect to both bias and random error.