## 3 Results
### Partial Least Squares Regression and VIP Statistics  
PLSR was applied to gain further information in the selection of the most informative variables to describe the effects of the two soil management practices compared. The method was applied to the whole set of soil indicators and considering grain yield and grain protein content as single response variables (PLS1) and as multiple response variables (PLS2). When wheat grain yield was considered as single response variable, the first two factors accounted cumulatively for 47.20% of total variance in predictors and 48.17% in the response variable. VIP coefficient profiles (Figure 3a) showed that the highest values were recorded for Olsen P and P\({}_{\text{MAC}}\), followed by TOC, TEC, pH and Mg\({}^{2+}\) (for the chemical variables) and by clay, RFC and AC (for the physical variables). The use of grain protein content as response variable further modified the rank of indicators selected. The first two factors accounted cumulatively for 49.54% of total variance in predictors and 23.59% in response. The greatest PLS-VIP statistics values were recorded for N and Olsen P, followed by WEN and sand, thus indicating the contribution of macro-elements, with particular regard to N (total and labile form), in affecting grain protein concentration (Figure 3b). In addition, TOC, TEC, Ca\({}^{2+}\) and pH showed important contribution. The inspection of both VIP profiles (Figure 3a,b) underlined the role of physical soil indicators (P\({}_{\text{MAC}}\), AC and RFC), which were selected as important variables in both analyses. Finally, PLSR was carried out considering simultaneously, as response variables, the grain yield and protein content (PLS2). The first two factors extracted accounted cumulatively for 48.56% of total variation in predictors and 27.16% in the response variable. From the inspection of the VIP profile (Figure 3c), the role of available nutrients (Olsen P and, secondary, WEN) and hydrological variables (P\({}_{\text{MAC}}\), AC and RFC) in explaining plant response emerged again. These variables were followed by soil carbon contents (TOC and TEC), pH and exchangeable cations. The inclusion of a response variable in PLSR--yield, protein content or both--significantly modified the rank of soil indicators selected, giving greater emphasis to plant macro-nutrients (available P and N), particularly when the grain protein content was used as dependent variable. These results underline the importance of using combined approaches to explore the data and interpret the behavior of the system investigated. Finally, for a further exploratory purpose, PCA was carried out on the variables more frequently selected with the combined use of SDA, PCA and PLSR, namely TOC, TEC, Olsen P, WEN, RFC, P\({}_{\text{MAC}}\) and AC. Figure 4 shows that the seven variables were able to discriminate the treatments under investigation. Additionally, a clear improvement in the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Step** & **Number** & **Entered** & **Removed** & **Partial** & **F Value** & **Pr \textgreater{} F** & **Wilks\({}^{\prime}\)** & **Pr \textless{}** & **Average** & **Pr \textgreater{}** \\ \hline \multicolumn{2}{c}{**In**} & \multicolumn{2}{c}{**R-Square**} & \multicolumn{2}{c}{**Lambda**} & **Lambda** & **Squared** & **ASCC** \\  & & & & & & & **Can Corr** & \\ \hline
1 & 1 & TOC & 0.8297 & 97.46 & \textless{}0.0001 & 0.17026571 & \textless{}0.0001 & 0.82973429 & \textless{}0.0001 \\
2 & 2 & RFC & 0.5631 & 24.49 & \textless{}0.0001 & 0.07439379 & \textless{}0.0001 & 0.92560621 & \textless{}0.0001 \\
3 & 3 & WEOC & 0.3941 & 11.71 & 0.003 & 0.0450772 & \textless{}0.0001 & 0.9549228 & \textless{}0.0001 \\ \hline \end{tabular}
\end{table} 
Table 6: Summary selection of STEPDISC procedure carried out on the whole dataset of chemical, physical and biological indicators. percentage of variance explained by the first two components (89.34%) was observed in comparison to the analysis performed on the whole set of soil indicators.