## 3 Results and Discussion  
The structure-analysis relationship approach relies on the construction of mathematical models that enable computing and finding (if possible) the correlation between the structure of a compound and its bioactivity [6]. In the case of peptides, the structure is understood as their amino acid sequences, whereas bioactivity refers to the measure of a molecule activity [25]. Usually, it is the concentration of a compound that corresponds to its-half maximal effect (like, e.g., IC\({}_{50}\)). Moreover, such a measure is usually transformed into logarithms [26]. The calculations were made using SCIGRESS software, as the QSAR model development in SCIGRESS is GUI-driven (i.e., graphical user interface), that is, by a user-interactive process with the possibility of manual removal of hard-to-mechanistically-interpret descriptors. This is an advantage of this software over other tools, like, e.g., RDKit/Scikit-learn Python scripts [27; 28], where the feature (descriptor) selection process is mostly automated and based on statistical parameters, with no simple way of taking descriptor mechanistic interpretability. Analyses concerned 46 di- and 33 tripeptide DPP IV inhibitors. According to [PERSON] [29], the number of samples (i.e., cases, objects) in the datasets should not be too small or too big. The low number of samples results in false-positive or false-negative results, which may lead to uncertain conclusions in biological and medical sciences [30]. The upper limit of the samples is often defined by the computer and the method by which the QSAR model was constructed [29]. The analysis using SCIGRESS was based on multilinear regression (MLR), i.e., a traditional approach in QSAR [31]. According to [PERSON] et al. [32], in MLR, the sample size depends on effect size, whereas the number of independent variables and recommendations for the number of chemicals are associated with the different criteria adopted by each researcher. Based on information from the theoretical model selection, [PERSON] and [PERSON] [30] tried to recommend the minimum N (understood as the number of samples) to correctly match a model to a data shape in regression models. In the words by [PERSON] and [PERSON] [30], \"statistical limbo may be better avoided and reproducibility may be improved if research based on regressions and meta-regressions uses \(N\geq 25\)\" [30]. Apart from the number of molecules (samples), the number of descriptors (variables) in a model is important. To conclude, the number of peptides taken for QSAR analysis in the present study is in line with the \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**DPP IV Inhibitors**} \\ \cline{2-3}  & **Dipeptides** & **Tripeptides** \\ \hline R\({}^{2}\) & 0.782 & 0.829 \\ Degrees-of-freedom adjusted & & 0.755 & 0.798 \\ R\({}^{2}\) & 0.737 & 0.710 \\ Average error & 0.255 & 0.209 \\ RMSEC & 0.343 & 0.296 \\ RMSECV & 0.377 & 0.386 \\ F-statistics & 28.773 & 26.228 \\ \(p\)-value & 0.0000 & 0.0000 \\ \(\alpha\) & 0.05 & 0.05 \\ \hline \hline \end{tabular} R\({}^{2}\)—determination coefficient; CVR\({}^{2}\)—correlation coefficient of leave-one-out cross-validation; RMSEC—root mean square error of calibration; RMSECV—root mean square error of cross-validation.  
\end{table} 
Table 1: Statistical parameters of QSAR models obtained for di- and tripeptides with DPP IV-inhibitory activity (understood as logIC\({}_{50}\)). above statement. However, due to a relatively small dataset, there was no possibility of performing a typical train/test dataset split. Instead, leave-one-out validation was used to measure the performance of the models (see discussion below). Table 1 shows the statistical results of analyses obtained for the di- and tripeptide DPP IV-inhibitory models. For both models, similar statistics were obtained in terms of the R\({}^{2}\) values, which were R\({}^{2}\) = 0.782 and R\({}^{2}\) = 0.829 for di- and tripeptides, respectively.