## 3 Results
### Correlation between Baring Capacity and Input Parameters  
To statistically estimate the relationship between the pile-bearing capacity and input parameters, SPSS software has been utilized. The correlation matrix between them is displayed in Figure 2, which shows a descriptive summary of the data distribution. The findings show a positive correlation between the pile-bearing capacity and other inputs, except for _X2_, _X4_, and _X5_, which appear to have a negative correlation (see Figure 2). This highlights that the decrease in these parameters tends to proportionally decrease the pile-bearing capacity. Moreover, Pearson correlation coefficient (\(R\)) and its significance between the pile-bearing capacity and other inputs is presented in Table 5. The findings prove that the significance is less than 0.05, except for _X3_, _X4_, and _X5_, showing that most correlations are statistically significant. Hence, according to [PERSON]'s classification (1986) [43], the pile  
Figure 1: Flowchart describing the key steps for the methodology of research to estimate the pile-bearing capacity. bearing capacity is significantly correlated with the input parameters, excluding _X3_, _X4_, and _X5_, which are poorly correlated. The results point out that these factors can have a complex nonlinear relationship with the pile-bearing capacity. Besides, in order to precisely model this complex phenomenon, new sophisticated machine-learning approaches should be developed. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & **Range** & **Minimum** & **Maximum** & **Mean** & **SD** & **Variance** & **Skewness** & \multicolumn{2}{c}{**Kurtosis**} \\ \cline{2-10}  & **Statistic** & **Statistic** & **Statistic** & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Statistic**} & \multicolumn{1}{c}{**Stat.**} \\ \hline _X2_ & 148.00 & 0.00 & 148.00 & 32.3741 & 3.28447 & 32.84 & 1078.77 & 2.011 & 0.241 & 4.570 & 0.478 \\ \hline _X3_ & 36.62 & 0.00 & 36.62 & 25.5803 & 0.96535 & 9.653 & 93.191 & \(-\)1.310 & 0.241 & 0.855 & 0.478 \\ \hline _X4_ & 8.11 & 5.38 & 13.49 & 10.2029 & 0.18409 & 1.840 & 3.389 & \(-\)0.406 & 0.241 & 0.262 & 0.478 \\ \hline _X5_ & 6.86 & 10.14 & 17.00 & 13.6823 & 0.16987 & 1.698 & 2.885 & 0.073 & 0.241 & \(-\)0.076 & 0.478 \\ \hline _X6_ & 2277.00 & 14.00 & 2291.00 & 494.99 & 60.23 & 602.32 & 362,794.16 & 1.502 & 0.241 & 1.286 & 0.478 \\ \hline _X7_ & 1.52 & 0.07 & 1.59 & 0.4327 & 0.04656 & 0.46562 & 0.217 & 1.128 & 0.241 & \(-\)0.233 & 0.478 \\ \hline _X8_ & 83.80 & 14.20 & 98.00 & 27.1120 & 1.86024 & 18.60 & 346.048 & 2.761 & 0.241 & 6.962 & 0.478 \\ \hline \(Y\) & 51,560.00 & 540.00 & 52,100.00 & 5133.12 & 929.01 & 9290.14 & 86,306,843.19 & 4.043 & 0.241 & 16.258 & 0.478 \\ \hline \end{tabular}
\end{table} 
Table 4: Descriptive statistics of the collected samples (Std. Error = standard error, SD = standard deviation). Figure 2: The correlation matrix between the pile-bearing capacity and soil parameters (green points: concrete material; blue points: steel material).