## 3 Results  
The results of the five procedures, one MLS and four ANN, are shown in Tables 4-9. Table 4 collects the MLS results for the eleven properties. In this table, in parenthesis the errors of the regression coefficients are given in vector form (\(\pm\)signs have been omitted, 2 nd line of each cell, 2 nd column). The training set for the elutropic value (El) includes pentane and tetrahydrofuran. Tables 5-8 collect the different ANN-MLP results for the set of variables (descriptors, either MMCI or MCI) of Table 4. In these tables, the first column gives the \(\delta^{v}\) type (see Appendix A), and the number of networks to train, \(\mathrm{Ntr}=10^{3}\) or \(10^{5}\) (when both numbers gave rise to similar results \(\mathrm{Ntr}=10^{3}\) was preferred), while the number of networks to retain is always 200. The activation functions together with the neuronal architecture are in the second column of Tables 5-8. In this column, 3 rd line, the number of epochs for which the ANN-MLP calculation runs are shown for each property. In the third column is the set of variables together with their statistics. In this column, second line, are shown the sensitivities. These values come from the sensitivity analysis that quantifies the importance of the input variables of the models. The r\({}^{2}\) and s, statistics were obtained with the EXCEL spreadsheet plotting the observed property, P, vs. the calculated one, P\({}_{\mathrm{dc}}\), once for the training and test compounds, N(aTR + bTE), and the second time for the training + test + evaluated compounds, N(+cEV), where a, b, and c are the number of points (i.e., compounds). We remind the reader that the MLS procedure has no test compounds, only training compounds, N(TR). No ANN weights are shown, due to their exceeding number, and because every time an ANN-MLP runs, different weights and sensitivity values are obtained. For comparison purposes it was decided to maintain throughout the ANN calculations (see Tables 5-8) the same number of outliers excluded throughout the MLS procedure, where the exclusion was done for residuals greater than 3s. Clearly, the ANN outliers differ from the MLS ones. In Table 5, the ANN results obtained with a single hidden neuron are given. Tables 6 and 7 display the multiple neuron cases: Table 6 with an externally imposed number of hidden neurons that was cycled from 2 to 12, and Table 7 with the number of hidden neurons chosen by the program (between 3 and 11). For UV, MS, and El the program sets this number between 3 and 10. For those cases where different sets of hidden nodes achieve similar modeling, the set with the minimal number of nodes was preferred. The subset of descriptors used to model the properties showed r intercorrelation lower than 0.93. We remind the reader that in a previous study [15] it was established that indices can be considered strongly correlated if r > 0.98. \begin{table}
\begin{tabular}{c c} \hline \hline \(\delta^{v}\)-Type & Regression Equations \\ \hline \(\delta^{v}_{\mathrm{po}}(1)\) & \(\mathrm{T_{b}}=237.5+139.1\,^{0}\chi+24.69\,\mathrm{D}^{v}+527.7\,^{0}\psi_{ \mathrm{I}}-25.91\,^{1}\psi_{\mathrm{I}}-1500\,^{0}\psi_{\mathrm{E}}+41.53\, \mathrm{T}_{\mathrm{\Sigma/M}}\) \\ \((24,31,3.5,69,21,222,10)\) \\ \(\mathrm{N(TR)}=45,\,r^{2}=0.821,\,s=22;\,\mathrm{N(+162\,\mathrm{U})}=61,\,r^{2 }=0.792,\,s=25\) \\ Excluded strong outliers: Formamide \& \(\mathrm{SO_{2}}\in\{\mathrm{EV}\}\) \\ \hline \(\delta^{v}_{\mathrm{po}}(50)\) & \(\varepsilon=2.804-12.05\,\chi^{v}_{\mathrm{t}}-5.99\cdot 10^{-5}\,\chi^{v}_{ \mathrm{d}}+132.7\,^{1}\chi^{v}_{\mathrm{s}}+0.021\,^{1}\psi_{\mathrm{Id}}-421.2 \,^{1}\psi_{\mathrm{E}}+38.12\,\mathrm{T}_{\mathrm{\Sigma/M}}\) \\ \((0.9,4.4,10^{-5},28,0.005,124,2.9)\) \\ \(\mathrm{N(TR)}=43,\,r^{2}=0.858,\,s=4.2;\,\mathrm{N(+16\,\mathrm{U})}=59,\,r^{2 }=0.896,\,s=5.5\) \\ Excluded strong outliers: ethylencarbonate \& quinoline \(\epsilon\) (TR), and MeOH \& \(\mathrm{MeOH}\,\&\mathrm{\,[EV]}\). \\ \hline \hline \end{tabular}
\end{table}