# 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 \hline \multicolumn{2}{c}{**Model**} & \multicolumn{1}{c}{**Sum of Squares**} & \multicolumn{1}{c}{**df**} & \multicolumn{1}{c}{**Mean Square**} & \multicolumn{1}{c}{**F**} & \multicolumn{1}{c}{**Sig.**} \\ \hline \multirow{3}{*}{1} & Regression & 0.072 & 4 & 0.018 & 10.530 & 0.001 \\ \cline{2-6}  & Residual & 0.019 & 11 & 0.002 & & \\ \cline{2-6}  & Total & 0.091 & 15 & & & \\ \hline \multicolumn{6}{c}{1. Dependent Variable: X\({}_{\text{A}}\)} \\ \hline \multicolumn{6}{c}{2. Predictors: (Constant), X\({}_{\text{1}}\)X\({}_{\text{4}}\), X\({}_{\text{4}}^{2}\), X\({}_{\text{1}}^{2}\), X\({}_{\text{4}}\)} \\ \hline \hline \end{tabular}
\end{table} 
Table 16: ANOVA for 2 nd order polynomial with two predictors. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**R**} & \multirow{2}{*}{**Square**} & \multirow{2}{*}{**Adjusted R**} & \multicolumn{1}{c}{**Std. Error of**} & \multicolumn{1}{c}{**Change Statistics**} & \multirow{2}{*}{**Durbin-Watson**} \\  & & & & & & & & & & \\  & & & & & & & & & & \\ \cline{1-1} \cline{6-10}  & \multirow{2}{*}{**R**} & \multirow{2}{*}{**Square**} & \multirow{2}{*}{**Adjusted R**} & \multirow{2}{*}{**Std. Error of**} & \multicolumn{1}{c}{**the Estimate**} & \multicolumn{1}{c}{**R square**} & \multirow{2}{*}{**F Change**} & \multirow{2}{*}{**df1**} & \multirow{2}{*}{**df2**} & \multicolumn{1}{c}{**Sig. F Change**} & \multirow{2}{*}{**[PERSON]**} \\  & & & & & & & & & & & \\ \hline \(1\) & 0.890 & 0.793 & 0.718 & 0.0414313 & 0.793 & 10.530 & 4 & \(11\) & 0.001 & 0.914 \\ \hline \multicolumn{6}{c}{1. Predictors: X\({}_{\text{1}}\), X\({}_{\text{1}}\)X\({}_{\text{4}}\), X\({}_{\text{4}}^{2}\), X\({}_{\text{1}}^{2}\), X\({}_{\text{4}}\)} \\ \multicolumn{6}{c}{2. Dependent Variable: X\({}_{\text{A}}\)} \\ \hline \hline \end{tabular}
\end{table} 
Table 15: 2 nd order polynomial model summary with two predict. The regression standardized residual to determine the steady-state conversion of NaOH mechanism is depicted in Figure 1a. An equivalent variance is witnessed for the experiment as revealed. No substantial difference between an observed and expected values of predicted response (X\({}_{\text{A}}\)) in terms of conversion of NaOH was found. Figure 1b exemplifies a plot (scatter) of NaOH conversion and validates that the values (experimental data) of reaction conversion lie on the straight line, and this shows that the random error is at a minimal and acceptable level. The curve also signifies outlier number for determining the best conversion. As depicted in the graph, the optimum level of reaction conversion is 0.63 (63%). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Unstandardized**} & \multicolumn{2}{c}{**Standardized**} & \multirow{2}{*}{**t**} & \multirow{2}{*}{**Sig.**} & \multicolumn{2}{c}{**95.0\% Confidence Interval for B**} \\ \cline{3-4} \cline{6-7}  & **B** & **Std. Error** & & & **Lower bound** & **Upper Bound** \\ \hline \multirow{5}{*}{1} & (Constant) & \(-2.189\) & 0.706 & \(-3.101\) & 0.010 & \(-3.742\) & \(-0.635\) \\ \cline{2-7}  & \(\text{X}_{1}\) & 0.021 & 0.006 & 1.235 & 3.125 & 0.037 & 0.258 & 0.485 \\ \cline{2-7}  & \(\text{X}_{4}\) & 3.480 & 1.050 & 6.909 & 3.316 & 0.007 & 1.170 & 5.791 \\ \cline{2-7}  & \(\text{X}_{1}\)\({}^{2}\) & 0.001 & 0.001 & 2.142 & 1.247 & 0.238 & \(-0.001\) & 0.002 \\ \cline{2-7}  & \(\text{X}_{4}\)\({}^{2}\) & \(-0.862\) & 0.260 & \(-4.616\) & \(-3.311\) & 0.007 & \(-1.435\) & \(-0.289\) \\ \cline{2-7}  & \(\text{X}_{1}\text{X}_{4}\) & \(-0.029\) & 0.029 & \(-2.523\) & \(-1.017\) & 0.331 & -0.093 & 0.034 \\ \hline \hline \end{tabular} \(1\). Dependent Variable: X\({}_{\text{A}}\)  
\end{table} 
Table 17: Coefficients for 2 nd order polynomial with two predictors. Figure 1: (a) Expected versus observed probability of reaction conversion; (b) Scatter plot of optimizing reaction conversion.