## 4 Discussion and Results
A list of measures of fit for both training and validation processes is summarised in Table 5 as follows. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**(a) Training Process**} & \multicolumn{5}{c}{**(b) Validation Process**} \\ \hline
**Method** & **N** & **RSquare** & **RASE** & **Method** & **N** & **RSquare** & **RASE** \\ \hline K Nearest Neighbours & 5,263,447 & 1.0000 & 0.1386 & Neural Boosted & 1754307 & 0.9968 & 1.2711 \\ Bootstrap Forest & 5,263,447 & 1.0000 & 0.1468 & Bootstrap Forest & - & - & - \\ Boosted Tree & 5,263,447 & 0.9999 & 0.1603 & Boosted Tree & - & - & - \\ Neural Boosted & 3,509,140 & 0.9968 & 1.2688 & K Nearest Neighbours & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: A compilation of the outcomes obtained from comparing predictions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Penalty Function** & **Description** \\ \hline Squared & \(\sum\beta_{i}^{2}\) & This approach is recommended when a significant number of \(x\) factors are believed to be influential in enhancing the predictive capacity of the model. \\ \hline Absolute & \(\sum\lvert\beta_{i}\rvert\) & If one is faced with a substantial number of \(x\) variables and suspects that only a subset of them significantly contribute to the predictive capacity of the model, either of the following approaches can be employed. \\ \hline Weight Decay & \(\sum\frac{\beta_{i}^{2}}{1+\beta_{i}^{2}}\) & Does not employ a penalty. This option is suitable for situations where there is a substantial volume of data and expeditious completion of the fitting procedure is desired. Nevertheless, this alternative may result in models exhibiting inferior predictive accuracy compared to models that incorporate a penalty.  
\begin{tabular}{c c} \hline \hline
**Method** & **Penalty Function** & **Description** \\ \hline Squared & \(\sum\beta_{i}^{2}\) & This approach is recommended when a significant number of \(x\) factors are believed to be influential in enhancing the predictive capacity of the model. \\ \hline Absolute & \(\sum\lvert\beta_{i}\rvert\) & If one is faced with a substantial number of \(x\) variables and suspects that only a subset of them significantly contribute to the predictive capacity of the model, either of the following approaches can be employed. \\ \hline Weight Decay & \(\sum\frac{\beta_{i}^{2}}{1+\beta_{i}^{2}}\) & Does not employ a penalty. This option is suitable for situations where there is a substantial volume of data and expeditious completion of the fitting procedure is desired. Nevertheless, this alternative may result in models exhibiting inferior predictive accuracy compared to models that incorporate a penalty.  
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**(a) Training Process**} & \multicolumn{5}{c}{**(b) Validation Process**} \\ \hline
**Method** & **N** & **RSquare** & **RASE** & **Method** & **N** & **RSquare** & **RASE** \\ \hline K Nearest Neighbours & 5,263,447 & 1.0000 & 0.1386 & Neural Boosted & 1754307 & 0.9968 & 1.2711 \\ Bootstrap Forest & 5,263,447 & 1.0000 & 0.1468 & Bootstrap Forest & - & - & - \\ Boosted Tree & 5,263,447 & 0.9999 & 0.1603 & Boosted Tree & - & - & - \\ Neural Boosted & 3,509,140 & 0.9968 & 1.2688 & K Nearest Neighbours & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of several penalty mechanisms used for differentiation. Table 6 displays the results of the suggested NtahH(3)NBoost(20) measure of fit for both the training and validation phases. The R\({}^{2}\) values are remarkably high for both the training (0.9967847) and validation (0.9967703) datasets, suggesting that the NtanH(3)NBoost(20) model accounts for almost all of the variability in the target variable. The marginal decline in the validation R\({}^{2}\) indicates a remarkably high degree of model precision and ability to generalise. The RASE scores for both training (1.2688147) and validation (1.2710539) are comparably low, indicating that the model's predictions closely match the actual data points.