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Ridge Regression for Extracting Soybean Yield Factors¹

In breeding crops to enhance yield, factors hypothesized to influence yield are often highly inter correlated. This condition is called multicollinearity when the intercorrelated variables are related to yield in a multiple regression equation. Ridge regression is a useful tool for untangling intercorrelated factors in multiple regression. The technique was applied to a set of soybean [Glycine max (L.) Merr.] data, involving a range of planting dates and cultlvars varying widely in maturity, to identify phenological variables associated with yield. Variables with highly unstable, estimated regressmn coefficients that were identified by the ridge technique were also shown to be highly correlated in the principal components with the smallest eigenvalues. The time from last flower to maturity was shown to be strongly associated with yield in this context.

Key Words: Intercorrelated variables • Multicollinearity • Multiple regression • Standardized partial regression coefficients • Bias coefficient • Ridge trace • Variance inflation factor • Principal components analysis • Glycine max (L.) Merrill

² Professors and associate professor of agronomy, Univ. of Califronia, Davis.

Received for publication March 9, 1979.