## 3 Results
### Validation of the Developed Model  
The results of the internal validation experiments demonstrated both fitness and stability of the model. The most important techniques for internal validation are LOO, LMO, and _Y-scrambling_. The values achieved in these experiments showed a \(\text{Q}^{2}_{\text{LOO}}\) value of 0.680, an \(\text{RMSE}_{\text{cv}}\) value of 0.409, and \(\text{MAE}_{\text{cv}}\) = 0.316. Figure 6A shows the values predicted by LOO vs. the experimental \(\text{LogK}_{\text{d}}\) values. The model performance for internal validation  
Figure 5: Analysis of the applicability domain: (**A**) Williams plot—leverage values vs. standardized residuals; (**B**) Insubria graph—leverage values vs. predicted data.  
using LMO was Q\({}^{2}\)\({}_{\rm LMO}\) = 0.648; Figure 6B shows the correlation between descriptors and DAT binding affinity (Q\({}^{2}\)\({}_{\rm LMO}\) vs. K\({}_{\rm XY}\) values).  
The results of the _Y-scrambling_ procedure are shown in Figure 7: the values of R\({}^{2}\) and Q\({}^{2}\) of every iteration (_yellow_ and _red circles_, respectively) and their averages were R\({}^{2}\)\({}_{\rm Y-scr}\) = 0.098 and Q\({}^{2}\)\({}_{\rm Y-scr}\) = \(-\)0.174, as well as the respective values of these parameters for the model (_light_ and _dark blue_, for R\({}^{2}\) and Q\({}^{2}\), respectively).  
Figure 6: Internal validation of the model: (**A**) Scatter plot of experimental LogK\({}_{\rm d}\) vs. that predicted by LOO experiment; (**B**) plot of Q\({}^{2}\) values of LMO validations compared to the Q\({}^{2}\) value of the original model.  
The predictability of the model was tested using the set of external predictions of 12 compounds. Its parameters were R\({}^{2}_{\text{ext}}\) = 0.709, RMSE\({}_{\text{ext}}\) = 0.339, MAE\({}_{\text{ext}}\) = 0.302, PRESS\({}_{\text{ext}}\) = 1.381, Q\({}^{2}\)-F1 = 0.298, Q\({}^{2}\)-F2 = 0.250, Q\({}^{2}\)-F3 = 0.780, CCC\({}_{\text{ext}}\) = 0.772, r\({}^{2}\)m\({}_{\text{-}}\)aver = 0.424, and r\({}^{2}\)m\({}_{\text{-}}\)delta = 0.331, where R\({}^{2}_{\text{ext}}\) is the external determination coefficient; RMSE\({}_{\text{ext}}\) is the root-mean-square error in the external prediction; MAE\({}_{\text{ext}}\) is the mean absolute error in the external prediction; PRESS\({}_{\text{ext}}\) is the predictive residual sum of squares (external validation); Q\({}^{2}\)-F1, Q\({}^{2}\)-F2, and Q\({}^{2}\)-F3 are the explained variances in the external prediction; CCC\({}_{\text{ext}}\) is the concordance correlation coefficient; and r\({}^{2}\)m-aver and r\({}^{2}\)m-delta are the Roy criteria, average and delta, respectively [76]. The predictions of compounds in the external set are shown in Figures 4-6 (_blue circles_) and Table 3.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Compound** & **Exp. 1** ** & **Endpoint** & **Predicted** & **Residual** & **Leverage Value b ** \\ \hline
3 & 3.544 & 3.707 & 0.163 & 0.045 \\
11 & 3.556 & 3.116 & \(-\)0.440 & 0.043 \\
14 & 2.531 & 2.421 & \(-\)0.110 & 0.118 \\
19 & 3.634 & 4.032 & 0.398 & 0.070 \\
24 & 3.504 & 3.974 & 0.470 & 0.066 \\
33 & 3.815 & 3.650 & \(-\)0.165 & 0.059 \\
36 & 3.973 & 4.511 & 0.538 & 0.139 \\
39 & 3.637 & 3.164 & \(-\)0.473 & 0.087 \\
41 & 3.322 & 3.001 & \(-\)0.321 & 0.106 \\
50 & 3.462 & 3.538 & 0.076 & 0.115 \\
54 & 3.342 & 3.517 & 0.175 & 0.047 \\
56 & 4.210 & 4.511 & 0.301 & 0.139 \\ \hline \end{tabular}
\end{table}
Table 3: Experimental and predicted values (expressed as LogK\({}_{\text{d}}\)) of DAT affinity for the compounds in the prediction set.  
Figure 7: Scatter plot of the _Y-scrambled_ model compared to the original model.