## 4 Model Results
### Performance Analysis  
The accuracy and reliability of a model developed using data mining approaches are highly dependent on the number of data points used. [PERSON] and [PERSON] [26] proposed a minimum data-to-variable ratio of 3, with 5 being a safer value. This indicates that a large dataset is necessary to develop a reliable model using data mining approaches. In the present study, the high data-to-variable ratio of 96.4 provided a solid foundation for the developed M5P algorithm and enabled it to make accurate predictions. The correlation coefficient (R) is a widely used measure of the correlation between observed and predicted values. However, it may not always be reliable, especially when the data range is wide, and data points are distributed around their mean. In such cases, the R\({}^{2}\) parameter is a more suitable measure to evaluate the correlation between observed and predicted values. In the present study, the R\({}^{2}\) parameter was used as an unbiased estimate to measure the degree of correlation between the observed and predicted values. The use of R\({}^{2}\) provides a more accurate representation of the correlation between the observed and predicted values and helps to ensure the reliability of the model. In addition to R\({}^{2}\), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) are both used as statistical error metrics to measure the absolute difference between predicted and actual (measured) values in a dataset. These error metrics are commonly used in machine learning and data mining to evaluate the performance of predictive models. The lower the values of RMSE and MAE, the closer the predicted values are to the actual values, indicating a better model performance. The use of these parameters ensures that the model predictions are as accurate as possible. The performance of the developed M5P algorithm on both the training and testing datasets was evaluated in this study. The results are presented in Table 2, which provides statistical error parameters commonly used to evaluate ML algorithms, and Figure 5, which provides a graphical representation of the algorithm performance. Figure 5, which is a scatter plot, depicts the predicted values of the M5P algorithm versus the actual values for both the training and testing datasets. The optimal line in the scatter plot represents perfect agreement between the predicted and actual values. Therefore, the closer the points are to the optimal line, the better the algorithm performance. The little scattering observed around the optimal line indicates that the M5P algorithm predicted values that align well with the actual values for both datasets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistics** & **RMSE** & **R** & **R\({}^{2}\)** & **MAE** \\ \hline Training & 77.1034 & 0.9857 & 0.9716 & 47.9516 \\ Testing & 71.9993 & 0.9806 & 0.9616 & 48.3483 \\ Total & 76.1038 & 0.9849 & 0.9700 & 48.0491 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: M5P model performance in predicting the punching shear capacity of RC flat slab. Figure 5: Cross plots of the proposed M5P correlations for both the training and testing set. In the scatter plot for the training dataset, the points are tightly clustered around the optimal line, indicating that the algorithm predicted values that are close to the actual values. Similarly, in the scatter plot for the testing dataset, the points are also clustered around the optimal line, albeit with slightly more scatter than the training dataset. The scatter observed around the optimal line in both datasets is relatively small, indicating that the algorithm can accurately predict the values of interest. Table 2 provides statistical error parameters that further support the conclusion that the developed M5P algorithm performs well on both datasets. The MAE and RMSE values for the training and testing datasets are relatively low, indicating that the algorithm predicted values that are close to the actual values.