However, since VIF neither detects multiple near-singularities nor identifies the source of singularities (Rawlings et al., 2001), condition index (CI) was evaluated for all variables within the models. This index is the square root

of the ratio of the largest eigenvalue to the corresponding eigenvalue from the matrix. Similar to VIF, the CI indicates weak dependencies when 10 > CI > 30 to high dependencies when CI > 30. Additional data to test the models were not available, thus cross-validation analysis was performed using the predicted residual sum of the squares (PRESS) statistics (Allen, 1971), which is the sum of squares of the difference between each observation find more and its prediction when that observation was not used in the prediction equation. The root mean square error from the cross validation analysis (CV-RMSE) was then calculated as the square root of the ratio between the PRESS statistic and the number of observations. The CV-RMSE is an indicator of the predictive power of the model, thus a small CV-RMSE is desirable. The significance level used for all

the statistical tests was α = 0.05 (p-value < 0.05). This p-value was used to evaluate if the variables included in the model were statistically significant as well. The squared semipartial check details correlation coefficients (SSCC) were calculated using partial sum of squares to determine the contribution from each variable to the models, while controlling the effects of other independent variables within the model. These coefficients represent the proportion of the variance from the dependent variable associated uniquely with much the independent variable. Stand age ranged from 11- to 26-year-old. Forest canopy was closed in all plots, except

for the plots in NSD that had the spacing twice as large as that traditionally used in forest operations, and the plots from RW18 that were thinned. Table 2 summarizes the average growth metrics of plots, within the study sites, as treatment and control, and in the case of NSD, these were distinguished by the number of trees per hectare. In RW19 all plots were classified as fertilized, since the stand had been under traditional forest management. Studies in which there were different levels of fertilization were classified together as fertilized, regardless of the rate and frequency of nutrient additions. In RW18, thinning was recently applied to some of the control and fertilized plots, thus the plots at this site were also classified by the number of trees per hectare. Individual tree height ranged from 4.8 to 27.9 m and averaged 15.7 m among all the study areas, the highest standard deviation (>2 m) from the mean of tree height was observed in the SETRES and Henderson studies. Crown length ranged between 0.8 (a damaged tree) and 10.8 m, and averaged 6.9 m.