## 4 Exploratory Analysis
### Pearson and Kendall Correlations  
The Pearson correlation coefficient, frequently denoted by the symbol \(\tau\), measures the linear relationship between two continuous variables. It quantifies the degree to which the variables move linearly together. The Pearson correlation coefficient ranges from \(-1\) to \(+1\), where \(-1\) represents a perfect negative linear relationship, \(+1\) represents a perfect positive linear relationship, and \(0\) represents the absence of a linear relationship [46; 47]. In contrast, the Kendall correlation coefficient, denoted by \(\tau\) (tau), is a rank-based correlation measure. It evaluates the strength and direction of the relationship between variables based on their ranks or ordinal positions. Kendall correlation applies to continuous and discrete variables, making it useful for analyzing nonlinear and nonparametric relationships [46; 47; 48].  
Pearson and Kendall correlations serve the same purpose of evaluating the strength and direction of the relationship between variables, but they are not simple measures. They differ in their underlying assumptions and data processing, adding a layer of interpretability.  
Figure 3 displays the strength and direction of the linear relationship between variables for Pearson correlation plots. Positive correlations are indicated by ascending values and more vibrant red hues, negative correlations by descending values and more vibrant purple hues, and no correlation by middle-ground values and white hues. For a Kendall correlation plot, Figure 4 depicts the strength and direction of the monotonic relationship between variables. Similarly, positive and negative correlations are presented, emphasizing monotonicity rather than linearity.  
Figure 3a depicts a robust positive linear correlation between \(\Delta\) variables. On the other hand, except for \(\Delta\)HBD and \(\Delta\)logP, the C-logP parameter exhibits a negative or no linear correlation with the remaining parameters. In contrast, in Figure 3b, the variables in the upper portion of the graph have a positive linear relationship, whereas the variables in the left portion from C-CGC to C-AGC and in the right lower portion have negative linear relationships. Comparing the Pearson correlation results of the success and failure  
datasets reveals contradictory behaviors, indicating that the correlations referring to the comparison values vary based on the case-sensitive decision. Thus, comparison variables do not exhibit correlations for determining compatibility, whereas they exhibit a negative linear correlation for determining incompatibility.  
In contrast, Kendall correlations reveal positive monotonic correlations between most delta variables and C-CGC and C-HGC. In contrast, the remaining comparison variables and AlogP exhibit negative monotonic or nonmonotonic correlations for Figure 4a. Regarding Figure 4b, it is determined that the correlations in the upper right portion of the graph display positive monotonic correlations between the variables and a small proportion of negative monotonic correlations dispersed throughout the entire graph. This graph displays more positive monotonic correlations than Figure 4b, which displays fewer variables with no monotonic correlations.  
In conclusion, the Pearson and Kendall correlations for the analysis of the success dataset (Figures 3a and 4a) exhibit a similar distribution of correlations around the variables. In contrast, the correlations between the variables in the graphs for the failure dataset (Figures 3b and 4b) differ significantly, with Figure 3b exhibiting stronger positive correlations than Figure 4b.