## 5 Results and Industrial Interpretation
### Regression  
As for regression experiments (Table 6), there is one method that significantly beats all others in all the variables to be predicted, which is Rotation Forest of REP-Trees. Again, the ensembles are in the lead. Linear regressors (i.e., Linear Regression and Linear SVM) are left in the tail positions, which suggests that these are not linear problems. As with classification problems, a single decision tree is still the best performing non-ensemble method. WEKA gives the name ZeroR to the naive regressor that always predicts the average. For that reason, it is at the end, since by definition RRS will always take a value of 100%. ZeroR is taken as the baseline. The average of the absolute error was calculated for the best method (i.e., Rotation Forest of REP-Tree) and for ZeroR (Table 7), to compute the physical magnitude of the error committed. The absolute error is defined as the absolute value of the difference between the actual value and the predicted value. The table shows average absolute errors ranging from 0.68 \({}^{\circ}\)C for \(T_{H}\), to 1.99 \({}^{\circ}\)C to \(T_{z}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\mathbf{\Delta}\) & \(\mathbf{V}\) & \(\mathbf{D}\) & **Method** & \(\mathbf{T_{H}}\) & \(\mathbf{T_{x}}\) & \(\mathbf{T_{y}}\) & \(\mathbf{T_{z}}\) \\ \hline
36 & 36 & 0 & Rotation Forest of REP-Tree & **55.072** & **61.526** & **60.957** & **64.021** \\
28 & 32 & 4 & Bagging of REP-Tree & 55.582 * & 62.668 * & 62.208 * & 65.121 * \\
20 & 28 & 8 & Iterated Bagging of REP-Tree & 56.124 * & 63.446 * & 62.892 * & 65.952 * \\
11 & 23 & 12 & REP-Tree & 58.935 * & 67.659 * & 67.012 * & 70.949 * \\
5 & 20 & 15 & k-NN & 64.560 * & 68.794 * & 67.817 * & 71.014 * \\ \(-7\) & 13 & 20 & Radial Basis Function SVM & 78.018 * & 85.287 * & 85.299 * & 88.811 * \\ \(-9\) & 12 & 21 & Multilayer Perceptron & 79.858 * & 87.524 * & 87.074 * & 90.586 * \\ \(-22\) & 6 & 28 & Linear Regression & 93.251 * & 95.243 * & 94.902 * & 95.927 * \\ \(-26\) & 4 & 30 & Linear SVM & 94.522 * & 95.681 * & 95.800 * & 97.122 * \\ \(-36\) & 0 & 36 & ZeroR (i.e., always predict the average) & 100.000 * & 100.000 * & 100.000 * \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Ranking of RMSE in the regression problems. V is the number of times the method has a better statistically significant RMSE when compared with the other 9 methods through the 4 predicted variables. D is the number of times the method has a worse statistically significant RMSE when compared with the other 9 methods through the 4 predicted variables. The ordering criteria \(\Delta\), is equal to V – D. The columns \(T_{H}\), \(T_{x}\), \(T_{y}\) and \(T_{z}\) have the average RMSE figures for the method using \(10\times 10\)CV. (*) represents this method has an average RMSE that is significantly worse than the one for the best ranked method. The best RRSEs for each predicted variable are highlighted in bold. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Rotation Forest of REP-Tree** & **ZeroR** \\ \hline \(T_{H}\) & 0.68 & 1.43 \\ \(T_{x}\) & 1.40 & 2.49 \\ \(T_{Y}\) & 1.47 & 2.63 \\ \(T_{Z}\) & 1.99 & 3.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average of the absolute error for the best method, and the error that would be committed if the average of \(T_{H}\), \(T_{x}\), \(T_{y}\), \(T_{z}\) were always predicted (i.e., if ZeroR is used). For a deeper understanding of temperature behavior, Figure 4 was plotted. Figure 4 shows the box-plot diagram for the four motor temperatures. In the box-plot diagrams the data are split into four quartiles depending on their value: the lower, second, third and upper quartiles, each of them with 25% of the data. The box-plot diagrams show: (1) the median of the variable with a green line; (2) the area with 50% of the middle data (data in the second and third quartiles) with a blue box; (3) two black lines or whiskers; and, (4) the data outside the whiskers with black circles.