. Competition for national forest timber in the Northern, Pacific Southwest, and Pacific Northwest regions. Timber Pacific States; Forests and forestry Pacific States. APPENDIX 5. THE USE OF DISCRIMINANT FUNCTIONS TO MONITOR SALES Discriminant functions were estimated for both competitive and noncom- petitive sales. The definition of competitive sales was given in the section, "Definitions and Available ; The objective was to estimate functions that combined various physical and cost characteristics observed on each sale and were effective in distinguishing between competitive a
. Competition for national forest timber in the Northern, Pacific Southwest, and Pacific Northwest regions. Timber Pacific States; Forests and forestry Pacific States. APPENDIX 5. THE USE OF DISCRIMINANT FUNCTIONS TO MONITOR SALES Discriminant functions were estimated for both competitive and noncom- petitive sales. The definition of competitive sales was given in the section, "Definitions and Available ; The objective was to estimate functions that combined various physical and cost characteristics observed on each sale and were effective in distinguishing between competitive and noncompetitive sales. The basic problem can be visualized as studying the extent to which different populations overlap one another or diverge from one another. For example, visualize two slightly overlapping populations shown as follows:. In this case, the leftmost population will represent noncompetitive sales, the rightmost competitive sales. Given that the sales have been classified a priori, a linear function (the discriminant function) is estimated for each population which measures the distance (Z) between the two population means (X). These equations are: n Z = 7 + Z Y X ; (9) 1 i=2 li li-1 n Z = Y + E Y X (10) 2 21 2i 2i-l; where Z is the distance between population means, Y jl is the intercept term for the jill population, and Y ji is the coefficient for population characteristic X^ of the jih population. The estimated discriminant functions are then used to classify all sales as either competitive or noncompetitive, regardless of the a priori classification, based on the chajracteristics of each sale. The classifi- cation procedure is relatively straightforward. For each sale, the Z values are computed using each discriminant function. In this case, if 7,1 is greater than Z2, then the sale is classified as having the characteristics of a noncompetitive sale. Reverse the sequence and the sale is classified as competitive in the sense that the characteristics of the
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