## 2 Method Description
### The Second Phase of the Proposed Method
Some datasets, such as \"Airfoil\", \"Concrete\", \"Dee\", \"HO\", \"Laser\", \"NT\", \"PL\", \"Plastic\", and \"Quake\", show no change in error with variations in \(a\) as the error values remain constant. In contrast, other datasets exhibit significant variations. For example, on the \"Baseball\" dataset, the error decreases from 86.19 for \(a=0.001\) to 77.46 for \(a=0.005\) then increases again to 81.97 for \(a=0.01\). Similarly, on the \"MB\" dataset, the error drastically decreases from 5.49 for \(a=0.001\) to 0.56 for \(a=0.005\) and further to 0.48 for \(a=0.01\). On datasets like \"FA\" and \"FY\", the error increases as \(a\) changes from 0.001 to 0.005, then decreases again for \(a=0.01\). On the \"Treasury\" dataset, the error shows a slight decline as \(a\) increases. In conclusion, the parameter \(a\) has a significant impact on the model's performance on certain datasets, while on others, its effect is negligible. The lowest average error observed for \(a=0.005\) suggests that this value is generally optimal for the model, though further tuning may be required for specific datasets. Cases with high variability in errors highlight the need for deeper analysis and optimization of the \(a\) parameter based on the characteristics of each dataset. Figure 7: Statistical comparison of the obtained experimental results for the regression datasets. \begin{table}
\begin{tabular}{c c c c} \hline
**Dataset** & \(a\) = **0.001** & \(a\) = **0.005** & \(a\) = **0.01** \\ \hline Alcohol & 31.28\% & 30.88\% & 31.77\% \\ \hline Appendicitis & 15.27\% & 15.77\% & 15.57\% \\ \hline Australian & 21.00\% & 21.03\% & 20.77\% \\ \hline Balance & 12.95\% & 13.13\% & 13.29\% \\ \hline Cleveland & 50.82\% & 50.64\% & 51.11\% \\ \hline Circular & 4.19\% & 4.01\% & 4.08\% \\ \hline Dermatology & 36.13\% & 36.81\% & 36.67\% \\ \hline Hayes-Roth & 33.54\% & 33.44\% & 34.10\% \\ \hline Heart & 15.33\% & 15.15\% & 15.22\% \\ \hline HeartAttack & 18.52\% & 18.80\% & 18.88\% \\ \hline HouseVotes & 3.74\% & 3.60\% & 4.12\% \\ \hline Ionosphere & 7.39\% & 7.38\% & 7.29\% \\ \hline Liverdisorder & 27.92\% & 28.27\% & 28.49\% \\ \hline Lymphography & 20.64\% & 20.57\% & 30.33\% \\ \hline Mammographic & 17.21\% & 17.15\% & 17.14\% \\ \hline Parkinsons & 15.35\% & 14.35\% & 15.23\% \\ \hline Phoneme & 16.62\% & 16.74\% & 16.00\% \\ \hline Pima & 23.59\% & 24.09\% & 23.99\% \\ \hline Popfailures & 4.80\% & 4.82\% & 4.86\% \\ \hline Regions2 & 25.54\% & 25.62\% & 25.75\% \\ \hline Saheart & 29.64\% & 29.93\% & 29.22\% \\ \hline Segment & 40.83\% & 41.41\% & 41.96\% \\ \hline Sonar & 18.25\% & 17.80\% & 17.83\% \\ \hline Spiral & 22.52\% & 22.00\% & 22.27\% \\ \hline StatHeart & 19.52\% & 19.35\% & 19.58\% \\ \hline Student & 5.11\% & 5.03\% & 5.25\% \\ \hline Transfusion & 24.59\% & 24.70\% & 24.64\% \\ \hline Wdbc & 5.00\% & 5.05\% & 5.07\% \\ \hline Wine & 7.71\% & 7.88\% & 7.90\% \\ \hline Z\_F\_S & 3.16\% & 3.66\% & 2.79\% \\ \hline Z\_O\_N\_F\_S & 46.77\% & 46.83\% & 47.06\% \\ \hline ZO\_NF\_S & 3.63\% & 3.63\% & 3.63\% \\ \hline ZONF\_S & 1.79\% & 1.81\% & 1.74\% \\ \hline ZOO & 4.50\% & 6.87\% & 4.60\% \\ \hline
**Average** & **18.67\%** & **18.77\%** & **19.06\%** \\ \hline \end{tabular}
\end{table} 
Table 4: Experimental results for the classification datasets using a series of values for perturbation factor \(a\). Figure 8 compares different values of the parameter \(a\) for the classification datasets. The p-values for the comparisons \(a=0.001\) vs. \(a=0.005\) (\(p=0.36\)), \(a=0.001\) vs. \(a=0.01\) (\(p=0.071\)), and \(a=0.005\) vs. \(a=0.01\) (\(p=0.17\)) indicate that the differences between the parameter values are not statistically significant. This suggests that varying the parameter \(a\) within this range does not substantially affect the model's performance on these datasets. Figure 9 presents corresponding comparisons for the regression datasets, where a similar result is observed.