Leverage in Central Composite Designs: A Surprise


Van Nostrand, R. Craig   (1990, ASQC)   Eastman Kodak, Rochester, NY

Annual Quality Congress, San Francisco, CA    Vol. 44    No. 0
QICID: 9531    May 1990    pp. 689-693
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Article Abstract

Central composite designs are useful when one needs to estimate a model with quadratic terms. In a regression, some data points with particular settings of the predictors´┐Ż variables have larger effects on the regression than others; these are called high leverage points. While designed experiments suffer less from differences in leverage, the factorial, axial, and center points in central composite designs have different leverages. Contrary to one's intuition, the axial points do not necessarily have the highest leverage; sometimes the center points do. The practical result is that if one only looks at the raw residuals, one can incorrectly identify a low leverage point as an outlier, when the real outlier is a high leverage point, leading to misleading regression coefficients. A real example is given.



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