# Optimizing the Sodium Hydroxide Conversion Using Regression Analysis in CSTR
## 3 Results and Discussion
### Experimental Findings
\begin{table}
\begin{tabular}{c c c c c c} \hline  & & **X\({}_{\text{A}}\)** & **X\({}_{\text{1}}\)** & **X\({}_{\text{2}}\)** & **X\({}_{\text{3}}\)** & **X\({}_{\text{4}}\)** \\ \hline \multirow{4}{*}{X\({}_{\text{A}}\)} & Pearson Correlation & 1 & 0.446 & 0.099 & \(-\)0.076 & 0.599 * \\  & Sig. (2-tailed) & & 0.083 & 0.715 & 0.780 & 0.014 \\  & N & 16 & 16 & 16 & 16 & 16 \\  & Pearson Correlation & 0.446 & 1 & 0.000 & \(-\)0.043 & 0.043 \\  & Sig. (2-tailed) & 0.083 & & 1.000 & 0.873 & 0.873 \\  & N & 16 & 16 & 16 & 16 & 16 \\  & Pearson Correlation & 0.099 & 0.000 & 1 & 0.000 & 0.000 \\  & Sig. (2-tailed) & 0.715 & 1.000 & & 1.000 & 1.000 \\  & N & 16 & 16 & 16 & 16 & 16 \\  & Pearson Correlation & \(-\)0.076 & \(-\)0.043 & 0.000 & 1 & 0.043 \\  & Sig. (2-tailed) & 0.780 & 0.873 & 1.000 & & 0.873 \\  & N & 16 & 16 & 16 & 16 & 16 \\  & Pearson Correlation & 0.599 * & 0.043 & 0.000 & 0.043 & 1 \\ X\({}_{4}\) & Sig. (2-tailed) & 0.014 & 0.873 & 1.000 & 0.873 & \\  & N & 16 & 16 & 16 & 16 & 16 \\ \hline \end{tabular}
* Significant correlation at 0.05 level. X\({}_{\text{A}}\) = Conversion, X\({}_{\text{1}}\) = Temperature, X\({}_{\text{2}}\) = Agitation Rate, X\({}_{\text{3}}\) = Feed Rate, X\({}_{\text{4}}\) = Volume.  
\end{table} 
Table 2: Correlation analysis with four predictors. Table 5 illustrates the impact of all independent variables on steady-state conversion of NaOH. The calculated \(p\) value is statistically significant for X\({}_{1}\) and X\({}_{4}\), while insignificant for X\({}_{2}\) and X\({}_{3}\). Furthermore, the \(p\) value demonstrates that X\({}_{3}\) is highly insignificant but X\({}_{2}\) is lowly insignificant as compared to X\({}_{3}\). Equation (6) was formulated using the coefficients shown in Table 5. As stated in Equation (6), the impact of agitation rate and feed flow rate is insignificant amongst all predictors in calculating steady state reaction conversion X\({}_{\text{A}}\). \[\text{X}_{\text{A}}=-0.240+0.011\text{X}_{1}+0.001\text{X}_{2}-0.001\text{X}_{ 3}+0.295\text{X}_{4}+\text{e} \tag{6}\]  
The investigation of residual described through Table 6 characterizes the highest and lowest steady state NaOH conversion expected by the model of Equation (7). As observed, maximal X\({}_{\text{A}}\) equals 0.6024, minimal X\({}_{\text{A}}\) = 0.3501, which specifies that the conversion predicted by the model is not very good and may be further amended for predicting higher reaction conversion. Relying on a highly insignificant predictor as depicted in Table 5, X\({}_{3}\) (Feed flow rate) was removed in the first step for further analysis. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**R**} & \multirow{2}{*}{**Adjusted R**} & \multirow{2}{*}{**Std. Error of**} & \multicolumn{5}{c}{**Change Statistics**} & \multirow{2}{*}{**Durbin-Watson**} \\ \cline{3-3} \cline{8-10}  & & & & **Square** & & & **Square** & & **Change** \\ \hline \(1\) & 0.743 & 0.553 & 0.390 & 0.0608951 & 0.553 & 3.397 & 4 & 11 & 0.048 & 0.304 \\ \hline \multicolumn{10}{c}{1. Independent variables: X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), X\({}_{4}\)} & \multicolumn{5}{c}{2. Predicted variable: X\({}_{\text{A}}\)} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of developed model with four predictors.