## 3 Results
### Selecting Optimal Cluster Number for Sewage Pollution Analysis  
Multivariate regression analysis (Table 4a) further elucidated the disparities between sewage from different treatment stages. A statistically significant difference was found between raw sewage and mechanically treated sewage, with a high R\({}^{2}\) value of 0.88 indicating a strong relationship (Table 4b). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multicolumn{2}{c}{**Sulfates**} & \multicolumn{2}{c}{**Chlorides**} & \multicolumn{2}{c}{**Phenols**} & \multicolumn{2}{c}{**Ether Extract**} & \\ \hline \(\eta_{STD}\) & \(\eta_{Avg}\) & \(\eta_{STD}\) & \(\eta_{Avg}\) & \(\eta_{STD}\) & \(\eta_{Avg}\) & \(\eta_{STD}\) & \(\eta_{Avg}\) & **Treatment Stage** \\ \hline \multicolumn{8}{c}{**(\%)**} \\ \hline N/A & N/A & N/A & N/A & 12.87 & 23.97 & 5.64 & 27.98 &
\begin{tabular}{c} Mechanically \\ treated sewage \\ \end{tabular} \\ \hline
11.90 & 22.10 & 11.36 & 13.02 & 3.83 & 91.81 & 0.73 & 91.31 &
\begin{tabular}{c} Totally \\ treated sewage \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 3: Percentage reduction of pollutants in mechanically treated sewage and in totally treated sewage. Figure 3: Concentrations of pollutants noted in sewage at the various treatment stages along with permissible levels: (**a**) ether extract; (**b**) phenols; (**c**) chlorides; (**d**) sulfates. A Principal Component Analysis (PCA) was conducted to discern underlying patterns among various types of polluting substances in sewage. The analysis revealed correlations between the ether extract and phenols, while chlorides and sulfates exhibited close proximity. The scatter plot in Figure 4 depicts the results of sewage analysis. The plot's axes represent two principal components: Component 1 (80.99%) on the \(x\)-axis and Component 2 (17.89%) on the \(y\)-axis. The plot reveals distinct clusters, with the ether extract spreading out significantly along Component 2, suggesting substantial variance in this compound compared to others. Phenols and sulfates cluster more tightly near the origin, indicating that they share similar characteristics. Chlorides are also distinct, with some spread along both substances. The Kaiser-Meyer-Olkin (KMO) measure was 0.48172, which was considered unacceptable for factor analysis. The Detrended Correspondence Analysis (DCA) plot (Figure 5) showed the relationships between sewage pollutants. The distances between points on the plot reflect the similarity or dissimilarity of the sewage pollutants. Points closer together share more similar properties, while points farther apart have more distinct differences. This is measured using Bray-Curtis distance, a metric that quantifies the dissimilarity between two samples based on the presence and abundance of various substances. The ether extract varied across samples; phenols clustered together, indicating similar properties; chlorides also formed a distinct group, while sulfates either spread out or clustered, highlighting their variability. Distinct clustering and dispersion patterns were observed for the ether extract, phenols, chlorides and sulfates. Phenols were related to sulfates, while ether extract aligned closely with chlorides. Figure 5 highlights the unique and shared properties of these substances within the sewage samples. This analysis helps in identifying key trends and outliers, which can guide further research or inform management strategies in sewage treatment and water quality monitoring. Grasping the variability and consistency of sewage pollutant substances is important for targeted interventions and better treatment processes. Variability in the