## 4 Comparison of ML Models
### Model Validation  
Ensuring the accuracy and effectiveness of machine learning models is essential for reliable and precise predictions. Model validation techniques play a crucial role in this process by providing valuable insights into a model's performance and its ability to generalize to new data. One such technique is K-fold cross-validation, which divides the dataset into K subsets and trains the model K times, each time using a different subset as the validation set and the remaining subsets as the training set [38]. This approach enables a thorough evaluation of the model's performance across diverse subsets of the data, minimizing the risk of overfitting and yielding a more dependable estimate of its predictive accuracy. In our study, we use K-fold cross-validation, a widely used method for model validation to evaluate our model's accuracy and effectiveness [39]. We chose the value of K as 5 since it is a commonly accepted standard in machine learning and statistical analysis, \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Metric** & **LR** & **RR** & **Lasso** & **EN** & **DT** & **RF** & **GB** & **Ada** & **KNN** & **MLP** \\ \hline MSE (Without) & 0.0019 & 0.0019 & 0.0066 & 0.4753 & 0.1036 & 0.0651 & 0.0568 & 0.5739 & 4.0126 & 0.2136 \\ MSE (With) & 0.0006 & 0.0006 & 0.0072 & 0.5323 & 0.1260 & 0.0707 & 0.0563 & 0.6821 & 4.0238 & 1.8178 \\ MSE (Difference) & \(-\)0.0013 & \(-\)0.0013 & +0.0006 & +0.0570 & +0.0224 & +0.0056 & \(-\)0.0004 & +0.1082 & +0.0112 & +1.6042 \\ \hline MAE (Without) & 0.0225 & 0.0225 & 0.0531 & 0.3815 & 0.0701 & 0.0684 & 0.0969 & 0.6353 & 1.1145 & 0.3009 \\ MAE (With) & 0.0096 & 0.0096 & 0.0542 & 0.3905 & 0.0761 & 0.0716 & 0.0944 & 0.7073 & 1.1159 & 1.2135 \\ MAE (Difference) & \(-\)0.0128 & \(-\)0.0128 & \(-\)0.0011 & +0.0090 & +0.0060 & +0.0032 & \(-\)0.0026 & +0.0720 & +0.0014 & +0.9125 \\ \hline MedAE (Without) & 0.0131 & 0.0131 & 0.0412 & 0.1858 & \(7.5\times 10^{-5}\) & 0.0002 & 0.0289 & 0.6443 & 0.5996 & 0.1766 \\ MedAE (With) & 0.0034 & 0.0034 & 0.0435 & 0.2808 & \(8.0\times 10^{-5}\) & 0.0002 & 0.0265 & 0.7293 & 0.6004 & 1.1662 \\ MedAE (Difference) & \(-\)0.0097 & \(-\)0.0097 & +0.0023 & +0.0950 & +5.3 \(\times 10^{-6}\) & +0.00002 & \(-\)0.0024 & +0.0850 & +0.0008 & +0.9900 \\ \hline EVS (Without) & 0.8318 & 0.8318 & 0.396 & 0.89 & 0.8893 & 0.8933 & 0.8941 & 0.8692 & 0.5895 & 0.8799 \\ EVS (With) & 0.9469 & 0.9477 & 0.423 & 0.92 & 0.8870 & 0.8927 & 0.8942 & 0.8666 & 0.5884 & 0.8639 \\ EVS (Difference) & +0.1151 & +0.1159 & +0.027 & +0.04 & \(-\)0.0023 & \(-\)0.0006 & +0.0001 & \(-\)0.0026 & \(-\)0.0011 & \(-\)0.0160 \\ \hline R\({}^{2}\) (Without) & 0.8318 & 0.8318 & 0.396 & 0.89 & 0.8893 & 0.8933 & 0.8941 & 0.8692 & 0.5853 & 0.8799 \\ R\({}^{2}\) (With) & 0.9469 & 0.9477 & 0.423 & 0.92 & 0.8870 & 0.8927 & 0.8942 & 0.8666 & 0.5841 & 0.8639 \\ R\({}^{2}\) (Difference) & +0.1152 & +0.1159 & +0.027 & +0.04 & \(-\)0.0023 & \(-\)0.0006 & +0.0001 & \(-\)0.0026 & \(-\)0.0012 & \(-\)0.0160 \\ \hline RMSE (Without) & 0.024541 & 0.024312 & 0.0814 & 0.067995 & 0.009250 & 0.006527 & 0.012070 & 0.056705 & 0.082561 & 0.385213 \\ RMSE (With) & 0.023415 & 0.023098 & 0.0827 & 0.067421 & 0.009456 & 0.006803 & 0.012034 & 0.058123 & 0.082065 & 0.382731 \\ RMSE (Difference) & \(-\)0.001126 & \(-\)0.001214 & +0.0013 & \(-\)0.000574 & +0.000206 & +0.000276 & \(-\)0.000036 & +0.001418 & \(-\)0.000496 & \(-\)0.002482 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of evaluation metrics for various machine learning models. offering a good balance between computational efficiency and validation accuracy [38; 39]. Additionally, through cross-validation, we obtained scores for all machine learning models by evaluating performance metrics. In Table 8, the average performance metrics of the machine learning models are presented. The implementation of K-fold cross-validation ensures that the results are robust and reliable, forming a solid foundation for the analysis.