## 3 Results and Discussion
### Statistical Analysis
#### 3.2.2 Regression Models: Generation, Calibration and Analysis of Variance  
Equations (3) and (4) show the generated second-order polynomial models with respect to the turbidity removal, and coagulation activity as a function of deshelled _Caraic papaya_ seeds dosage, pH and initial turbidity, respectively. Table 5 shows the analysis of variance (ANOVA), as well as the adjustment indicator coefficients. Based on the table, ANOVA for the turbidity removal shows that most terms are significant (\(p\leq 0.05\)) excluding square term of bio-coagulant dosage and initial turbidity, as well as interaction square term of bio-coagulant dosage and pH. Meanwhile, for the coagulation activity, ANOVA results also show that almost all terms are significant (\(p\leq 0.05\)) except for square  
Figure 3: Pareto effects that correspond to regression performed for (**a**) turbidity removal and (**b**) coagulation activity from the synthetic kaolin water, \(p\)-value = 0.05.  
term of bio-coagulant dosage and pH. The lack of fit (LOF) for turbidity removal and coagulation activity are 0.2319 and 0.0648, respectively. The LOF for all models obtained is not significant (\(p\) > 0.05) thus, indicating that the models fit well with the data. \[ \begin{split}\text{Turbidity removal (\%)}=876.47738-4.4455\text{-A}-292.89066\text{-B}-0. 20255\text{-C}+1.4685\text{-AB}+(4.1124\text{-}10^{-3})\text{-AC}\\ +0.03401\text{-BC}+23.9838\text{-B}^{2}-(4.38267\text{-}10^{-4}) \text{-ABC}-(4.52659\text{-}10^{-6})\text{-A}^{2}\text{C}-0.11940\text{-AB}^{2} \end{split}  \tag{3}\]  
\[ \begin{split}\text{Coagulation activity (\%)}=227.95931-1.44168\text{-A}-26.09152\text{-B}-0.4 9899\text{-C}+0.022251\text{-AB}+(6.97200\text{-}10^{-3})\text{-AC}\\ +0.034482\text{-BC}+(2.62032\text{-}10^{-4})\text{-C}^{2}-(4.4072 1\text{-}10^{-4})\text{-ABC}-(1.01590\text{-}10^{-3})\text{-A}^{2}\text{B}-(1.58 877\text{-}10^{-5})\text{-A}^{2}\text{C}-(5.79928\text{-}10^{-3})\text{-AB}^{2} \end{split}  \tag{4}\]  
where,  
A = Deshelled _Carica papaya_ seeds bio-coagulant dosage  
B = pH  
C = Initial turbidity of the Synthetic Kaolin Water  
The determination coefficients (\(R^{2}\)) values were shown to be 96.9% and 95.3% for turbidity removal and coagulation activity, respectively. The values of the adjusted determination coefficients (adjusted \(R^{2}\)) were 94.7%, and 92.1% for turbidity removal, and coagulation activity, respectively. An adjusted \(R^{2}\) indicates the percentage of variation in response to an adjusted model for the number of predictors relative to the number of observations. According to [PERSON] et al. [40], when evaluating the model adequacy, the discrepancy between \(R^{2}\) and adjusted \(R^{2}\) should be less than 20%. Response Surface: Effect of Deshelled Carica Papaya Seeds Bio-Coagulant Dosage, pH and Initial Turbidity  
Mathematical models (Equations (3) and (4)) have generated response surfaces (Figures 4 and 5), which show the effect of deshelled _Carica papaya_ seeds bio-coagulant dosage, pH and initial turbidity for turbidity removal and coagulation activity. Figure 4a shows the response surface between significant interaction of bio-coagulant dosage and pH towards the turbidity removal at fixed initial turbidity of 300 NTU. Based on Figure 4a, as the dosage increased from 50 mg/L to 200 mg/L, the turbidity removal was slightly increased. Contrary, as the pH decreased from 6.5 to 4.0, the turbidity removal was greatly increased, more significantly compared to the effect by the increased dosage. By examining the impact of pH, it is confirmed that the adjustment was crucial in order to achieve high turbidity removal performance. Since no floc formation was observed in the alkaline medium, the turbidity in the synthetic kaolin water remained nearly constant.