With the limitation of bivariate correlation, the Pearson correlation coefficients cannot demonstrate the real relationships when multicollinearity exists. Table 4Pearsons correlation coefficients (r) between certain selleck chem soil properties and dinoseb adsorption capacity coefficients.3.3. Path Analysis ResultsWith path analysis, we can decompose the correlations into direct and indirect effects. The effects are quantified with the path coefficients (Table 5). According to the path coefficients, the sequence of direct effects to Kf is OC > Clay > pH > CEC. Both zero-order correlation and path analysis show OC content has a significant positive effect on Kf, and the direct effect on Kf is much higher than the other three factors (path coefficient 1.056).

In the zero-order correlation matrix, pH is significantly correlated with Kf (correlation coefficient ?0.659). The path analysis shows that this correlation is mainly due to the correlation of pH with OC (path coefficient ?0.662). The direct effect of pH on Kf is low (path coefficient ?0.066). For CEC, with almost zero direct effect on Kf, it can be considered that the moderate correlation (correlation coefficient 0.436) with Kf is mainly due to the contribution of collinearity between OC content and CEC. Clay content has negative direct effect on Kf (path coefficient ?0.216), although the indirect effect due to correlation with OC is more obvious (path coefficient 0.746). Contrast to that, the correlation coefficient shows that Clay has a positive relationship with Kf. Dinoseb is a weak acid with a pH of 4.4�C4.

62 [20] and is mainly in anionic form at the pH of the studied soils [34]. Therefore, it is more reasonable that its affinity to soil was negatively correlated with the content of the negatively charged clays. Table 5Path analysis coefficients to Kf of soil factors.3.4. Stepwise Multiple-Linear Regression ResultsBased on the correlation matrix in Table 4 and path analysis coefficients in Table 5, it is obvious that it is not independent between pairs of the soil properties and that makes the interpretation of multiple linear regression equations between the dinoseb Kf values and soil properties unreliable. The problem of multicollinearity among soil properties in linear model has been generally recognized in many studies [35, 36].

In order to overcome multicollinearity, stepwise regression, one of several standard procedures [27] for variable selection, was applied for multiple AV-951 linear regression in this study. Due to the small number of correlated variables (OC, pH, CEC, Clay), the backward elimination was performed starting with all four soil properties as controlled variables and successively eliminates one at a time. And the criteria based on t-statistics is to remove the lowest F-to-remove statistic which is bigger than 0.05.