# Root System and Its Relations with Soil Physical and Chemical Attributes in Orange Culture
## 3 Results
### Decision Tree  
Due to the large number of attributes assessed during the experiment, different attribute selection methods were applied in order to select only those that contributed effectively to the quality of the model. The values for hit rate (accuracy), error, Kappa statistics and number of rules generated for each soil type and selection method employed are presented in Table 5.  
Among the attribute selection methods applied, the Wrapper approach stood out from the others for presenting a higher hit rate (accuracy), presenting a value of 79.44% and 80.00%, number of rules of 24 and 20 and Kappa statistics of 0.68 and 0.69 for the areas under Utisol and Oxisol, respectively. The Kappa statistics for the Wrapper method were considered very good in both soils according to the reference values proposed by [26]. A tree pruning technique was used to reduce the overfitting effect and to decrease the number of internal nodes and, to that end, pruning was made using the value of four minimum numbers of objects for both soils, obtaining a total of 13 rules for Utisol and 11 rules for Oxisol. Among the 26 predictive attributes available in the database, for the area under Utisol, the Wrapper method selected seven: pH, depth, tillage system, contents of manganese, phosphorus, magnesium, and potential acidity present in the soil. The decision tree generated from these subsets of attributes is shown in Figure 4.  
According to the decision tree, the most important attribute for root volume in Utisol, i.e., the one at the top of the tree, was pH, which induces high orange plant root volume when the value is equal to 4.2. Another important rule present in the decision tree is that for pH values greater than 4.2 and depths smaller than or equal to 0.2 m, phosphorus was a determining factor in plant root development, showing that at levels below or equal to 33 mg dm\({}^{-3}\), root volume was high and at levels above 45 mg dm\({}^{-3}\) it was low. In deeper layers, that is, greater than 0.2 m, the tillage system induced high root volume when the triple tillage implement was used in contrast with minimum tillage and subsoiler tillage that presented medium volume. At depths greater than 0.5 m, manganese, phosphorus, magnesium contents and potential acidity presented as limiting factors for plant root volume. Manganese at contents below or equal to 0.5 mg dm\({}^{-3}\) induced low root volume, and contents above 0.5 mg dm\({}^{-3}\), depths of up to 2.10 m, phosphorus at concentrations below 1.0 mg dm\({}^{-3}\) and magnesium below or equal to 4.0 mg dm\({}^{-3}\) induced high root volume. In comparison, when phosphorus content was below 1.0 mg dm\({}^{-3}\) and magnesium above 4.0 mg dm\({}^{-3}\), medium plant volume was induced. Chemical attribute data can be seen in Tables S5-S8 (Supplemental Materials). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Hit** & **Error** & **Kappa** & **Rules** \\ \hline \multicolumn{5}{c}{**Utisol**} \\ \hline No selection & 72.78\% & 27.22\% & 0.57 & 47 \\ Chi-Square (\(\chi^{2}\)) & 72.74\% & 25.55\% & 0.66 & 39 \\ CSF & 72.78\% & 27.22\% & 0.57 & 47 \\ Wrapper & 79.44\% & 20.56\% & 0.68 & 24 \\ \hline \multicolumn{5}{c}{**Oxisol**} \\ \hline No selection & 62.22\% & 37.78\% & 0.41 & 40 \\ Chi-Square (\(\chi^{2}\)) & 64.44\% & 35.56\% & 0.44 & 48 \\ CSF & 68.89\% & 31.11\% & 0.51 & 32 \\ Wrapper & 80.00\% & 20.00\% & 0.69 & 20 \\ \hline \multicolumn{5}{l}{CFS: selection of attributes based on correlation. Chi-Square (\(\chi^{2}\)): chi-square method. Wrapper: wrapper method.} \\ \end{tabular}
\end{table} 
Table 5: Hit values (accuracy), number of rules generated and Kappa statistics for each attribute selection test applied, aiming at the induction of the decision tree.