## 2 Materials and Methods
### Pre-Processing Step
The \(p\)-values for all variables were below 0.05, suggesting a significant deviation from normal distribution. Notably, the low Shapiro-Wilk statistic values clearly illustrate the extent of this deviation. This deviation from normality may require additional procedures, such as normalization or transformation during the data analysis and modeling stages. Such statistical tests are crucial for understanding the characteristics of the data and ensuring more accurate results in the modeling phase. The results of the Shapiro-Wilk test, presented in Table 3, indicate that none of the variables are normally distributed. The \(p\)-values for all variables are below 0.05, suggesting a significant deviation from normal distribution. These findings confirm that the dataset has a non-normally distributed structure and support the need for applying techniques such as normalization or transformation during the data preprocessing phase. Sensitivity analysis (SA) is a highly popular feature selection method to highlight important features in a dataset [74]. It is performed to understand the overall effect of input variables on the model's output and to assess which variables have the potential to influence this output [74]. The formulas in Equations (2) and (3) were used to calculate the contribution of each variable to the predicted output [75; 76; 77]. \[N_{i}=\ f_{max}(x_{i})-f_{min}(x_{i}) \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature** & **Statistic** & \(p\)**-Value** & **Normal Distribution** \\ \hline MC & 0.9596 & \textless{}0.0001 & False \\ VM & 0.8876 & \textless{}0.0001 & False \\ FC & 0.9546 & \textless{}0.0001 & False \\ Ash & 0.7069 & \textless{}0.0001 & False \\ C & 0.9679 & \textless{}0.0001 & False \\ H & 0.9374 & \textless{}0.0001 & False \\ O & 0.9693 & \textless{}0.0001 & False \\ N & 0.9071 & \textless{}0.0001 & False \\ S & 0.7743 & \textless{}0.0001 & False \\ Temp & 0.9660 & \textless{}0.0001 & False \\ ER & 0.8717 & \textless{}0.0001 & False \\ SB & 0.8229 & \textless{}0.0001 & False \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Shapiro–Wilk test results. Figure 2: Violin Plots of the original dataset (**A**) and the normalized dataset (**B**). \[S_{i}=\frac{N_{i}}{\sum_{j-1}^{n}N_{j}} \tag{3}\]  
Here, \(f_{max}(x_{i})\) and \(f_{min}(x_{i})\) represent the maximum and minimum values of the \(i\)th prediction model output, respectively. The input values are held constant at their mean values. Ni provides the range of the \(i\)th input variable by calculating the difference between \(f_{max}(x_{i})\) and \(f_{min}(x_{i})\). The contribution of each input parameter to the predicted output for CO was measured using sensitivity analysis, and the results for both the original and normalized datasets are presented in Figure 3.  
Figure 3 compares the model's sensitivity to the inputs for both the original and normalized datasets. In the original dataset, the Temp (temperature) variable was identified as the most dominant parameter by far, and it was observed that the model was overly dependent on this variable. This issue arose from the uneven distribution of the data, which leads to limited effects from the other variables. For example, variables such as N, MC, and VM were found to have a sensitivity threshold below 0.05 and showed no significant impact on the model. When the dataset was normalized, the effects of all variables on the model were more evenly distributed. Variables such as N, SB, and MC showed the highest sensitivity, while Ash, ER, and VM exhibited the lowest sensitivity. However, even low-impact variables became more significant thanks to the normalization of the data. This demonstrates that normalization helps provide a fairer analysis by equalizing the effects of variables with different scales. Our study emphasizes the impact of normalization on sensitivity analysis. Although the Temp variable appeared to be the most important feature in the original dataset, the Sulfur (S) variable exhibited the highest sensitivity in the normalized dataset.