## 3 Results and Discussion
R\({}^{2}\) is a statistical parameter that shows which percent of endogenous variable is explained by exogenous variable(s) [33]. Endogenous and exogenous variables refer to the bioactivity of peptides and descriptors expressing their properties, respectively [14]. On the other hand, the parameter called adjusted R\({}^{2}\) (see Table 1) includes degrees of freedom, and its value is usually smaller than that of R\({}^{2}\)[16] (0.755 and 0.798, respectively (see Table 1)). The validity of the model was calculated by default using the leave-one-out (LOO) cross-validation procedure. The LOO procedure is the one of the simplest statistical procedures for model validation and relies on excluding each sample once and constructing the model without this sample to predict the value of a dependent variable (bioactivity) [34]. Moreover, the LOO procedure enables nearly unbiased estimation of the true generalization performance [35]. The statistical parameters of LOO cross-validation are represented by CVR\({}^{2}\) (correlation coefficient of leave-one-out cross-validation, also called Q\({}_{2}\)), RMSEC (root mean square error of calibration), and RMSECV (root mean square error of cross-validation). For di- and tripeptides, the CVR\({}^{2}\) values were 0.817 and 0.722, respectively (see Table 1), whereas the respective RMSECV values were 0.377 and 0.387. Usually, CVR\({}^{2}\)\(>\) 0.5 is found sufficient to prove model accuracy [36]. [PERSON] and [PERSON] [34] reported that relations of the above-mentioned statistics when using the LOO procedure should be as follows: R\({}^{2}\)\(>\) Q\({}^{2}\) and RMSEC \(<\) RMSECV. The statistics present in Table 1 meet these requirements. Moreover, according to [PERSON] and [PERSON] [34], the sufficient requirements for regression models include the following conditions: CVR\({}^{2}\)\(>\) 0.5 and R\({}^{2}\)\(>\) 0.6. The difference between R\({}^{2}\) and CVR\({}^{2}\) exceeding 0.2-0.3 indicates the model overfitting. Based on these findings, the models presented in this study could be considered statistically acceptable (see Table 1). The statistical significance of the estimated QSAR models was analyzed based on F-statistics (\(\alpha\) = 0.05), the values of which reached 28.773 and 26.228 for di- and tripeptides, respectively. The \(p\)-value was lower than \(\alpha\). To summarize, the results of computations made for CVR\({}^{2}\), F-statistics, and \(p\)-values indicate some significant relationships between descriptors and bioactivity (logIC\({}_{50}\)) of both DPP IV-inhibitory QSAR models and enable developing equations (see Figure 2a,b) for predicting the relationship between the structure and DPP IV-inhibitory activity of dipeptides/tripeptides. The names of the descriptors found in these equations are provided in the exact words as are given in the program used. The impact of individual descriptors on the DPP IV activity of di- and tripeptides is shown in Table 2. The respective plots referring to the correlations between the observed and the predicted activity of di- and tripeptide DPP IV inhibitors are shown in Figures 3 and 4, respectively. The predicted and observed values of logIC\({}_{50}\) for di- and tripeptides (tripeptides) are provided in Tables 3 and 4, respectively. Figure 2: Equations describing structure–activity relationships of dipeptide (**a**) and tripeptide (**b**) DPP IV inhibitors. Figure 4: Plot of the observed and predicted logIC\({}_{50}\) (ERM model) values for tripeptide DPP IV-inhibitory activity. The numbers in the plot refer to the peptide sequence provided in Table 4. CI—confidence interval. Figure 3: Plot of the observed and predicted logIC\({}_{50}\) (ERM model) values for dipeptide DPP IV-inhibitory activity. The numbers in the plot refer to the peptide sequence provided in Table 3. CI—confidence interval. Statistical parameters present in Table 2 can be explained as the weights showing the contribution of each descriptor as a factor influencing the activity of DPP IV inhibitors.