The problem of determining the response of tree ring width growth to monthly climate is examined in this study. The objective is to document which of the available regression methods are best suited to deciphering the complex link between tree growth variation and climate. Tree-ring response function analysis is used to determine which instrumental climatic variables are best associated with tree-ring width variability. Ideally such a determination would be accomplished, or verified, through detailed physiological monitoring of trees in their natural environment. A statistical approach is required because such biological studies on mature trees are currently too time consuming to perform. The use of lagged climatic data to duplicate a biological, rather than a calendar, year has resulted in an increase in the degree of intercorrelation (multicollinearity) of the independent climate variables. The presence of multicollinearity can greatly affect the sign and magnitude of estimated regression coefficients. Using series of known response, the effectiveness of five different regression methods were objectively assessed in this study. The results from each of the 2000 regressions were compared to the known regression weights and a measure of relative efficiency computed. The results indicate that ridge regression analysis is, on average, four times more efficient (average relative efficiency of 4.57) than unbiased multiple linear regression at producing good coefficient estimates. The results from principal components regression are slight improvements over those from multiple linear regression with an average relative efficiency of 1.45.

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