# 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 c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Standardized**} & \multirow{2}{*}{**Stg.**} & \multirow{2}{*}{**95.0\% Confidence Interval for B**} \\ \cline{3-3} \cline{8-8}  & & & **B** & **Std. Error** & & **Beta** & & **Lower Bound** & **Upper Bound** \\ \hline \multirow{4}{*}{\(1\)} & (Constant) & \(-0.240\) & 0.277 & & \(-0.867\) & 0.405 & \(-0.851\) & 0.370 \\ \cline{2-8}  & X\({}_{1}\) & 0.011 & 0.005 & 0.417 & 2.065 & 0.043 & \(-0.001\) & 0.022 \\ \cline{1-1} \cline{2-8}  & X\({}_{4}\) & 0.295 & 0.102 & 0.585 & 2.894 & 0.015 & 0.070 & 0.519 \\ \cline{1-1} \cline{2-8}  & X\({}_{3}\) & \(-0.001\) & 0.003 & \(-0.083\) & \(-0.411\) & 0.689 & \(-0.007\) & 0.005 \\ \cline{1-1} \cline{2-8}  & X\({}_{2}\) & 0.000 & 0.001 & 0.099 & 0.492 & 0.632 & \(-0.001\) & 0.002 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Determination of coefficients with four predictors. The regression Equation (7) was formulated to augment the steady-state NaOH conversion. \[X_{A}=\beta_{o}+\beta_{1}X_{1}+\beta_{2}X_{2}+\beta_{4}X_{4}+e \tag{7}\]  
The coefficient of correlation with only three predictors declined slightly as compared to the four predictors, which is shown in Table 7. Fitness of model and contribution of extraneous variable also declined slightly with three predictors. F value is still significant with three predictors as stated in Table 8, which explain that the impact of three independent variables varies considerably. The coefficient of predictors are summarized in Table 9. \(p\) value is statistically significant for \(X_{1}\) and \(X_{4}\) while insignificant for \(X_{2}\). Equation (8) is formulated using the coefficient presented in Table 9. As reported in Equation (8), the stirrer rate's contribution is marginal amongst all three predictors in forecasting the conversion with respect to sodium hydroxide (response variable). \[X_{A}=-0.305+0.011X_{1}+0.001X_{2}+0.293X_{4}+e \tag{8}\] \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Minimal** & **Maximal** & **Mean** & **Std. deviation** & **N** \\ \hline Predicted value & 0.350127 & 0.602460 & 0.493438 & 0.0579618 & 16 \\ \hline Residual & \(-\)0.1370079 & 0.0531587 & 0.0000001 & 0.0521474 & 16 \\ \hline Std. predicted value & \(-\)2.472 & 1.881 & 0.000 & 1.000 & 16 \\ \hline Std. residual & \(-\)2.250 & 0.873 & 0.000 & 0.856 & 16 \\ \hline \end{tabular}
\end{table} 
Table 6: Statistics- residuals with four predictors. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & **Model** & **Sum of Squares** & **df** & **Mean Square** & **F** & **Sig.** \\ \hline \multirow{4}{*}{1} & Regression & 0.050 & 3 & 0.017 & 4.806 & 0.020 \\ \cline{2-10}  & Residual & 0.041 & 12 & 0.003 & & & \\ \cline{1-1} \cline{2-10}  & Total & 0.091 & 15 & & & & \\ \hline \multicolumn{10}{c}{1. Dependent variable: \(X_{A}\)} \\ \hline \end{tabular}
\end{table} 
Table 8: ANOVA with three predictors. Table 10 signifies the highest and lowest steady state conversion for NaOH applying residual analysis predicted by model Equation (8). As stated in the Table, the highest NaOH conversion is 0.6019, which signifies that predicted conversion is not very good. The conversion can be further enhanced by the deletion or addition of some independent variables. There is not much difference on maximum and minimum conversion observed with four predictors and three predictors as indicated through Tables 6 and 10, respectively. On the basis of a highly insignificant predictor as depicted in Table 9, X\({}_{2}\) (stirrer rate) was removed in the second step for further analysis to optimize the reaction conversion. Regression Equation (9) was formulated to augment the NaOH conversion with only two predictors.