## 3 Results and Discussion
### Regression Modeling and Statistical Analysis  
The results on the improved production of biomass, lipids, and carotenoids under different abiotic factors were presented based on the design of RSM-CCD. Design Expert was used to determine the anticipated and actual values in Table 1. The data on augmented biomass, lipids, and carotenoids production under distinct abiotic factor optimization scenarios are shown in Table 1, and the obtained yields of chlorophyll a and b are provided in Table S1. The relationship between the growth and biochemical parameters (biomass, lipid, chlorophyll a, chlorophyll b, and total carotenoids) and the factor variables (nitrogen, potassium and phosphorus, sulphur, light intensity, and photoperiod) was obtained by performing regression analysis and curve fitting of the data using RSM-CCD. The relationships were expressed by the polynomial equations presented in Table 2. The equations were developed by the Design Expert and their corresponding R\({}_{\text{adj}}\)2 values are also included in the table. Figure 1: Bright field light microscopy with a magnification of 60\(\times\) and a scale bar of 10 μm was used to analyze the morphology of _Monoraphidium_ sp. Figure 2: Diagrammatic representation of the biochemical evaluation of _Monoraphidium_ sp. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & & & \\ \multirow{2}{*}{**Run**} & \multirow{2}{*}{**Nirogen**} & \multirow{2}{*}{**Potassium +**} & \multirow{2}{*}{**Sulphur (mg L\({}^{-1}\))**} & \multirow{2}{*}{**Sulphur (mg L\({}^{-1}\))**} & \multirow{2}{*}{**Light Intensity**} & \multirow{2}{*}{**Photoperiod (h)**} & \multirow{2}{*}{**Biomass**} & \multirow{2}{*}{**Lipid**} & \multirow{2}{*}{**Contected**} & \multirow{2}{*}{**Biomass**} & \multirow{2}{*}{**Total**} \\  & & & & & & & & & & & & &  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Run**} & \multirow{3}{*}{\ \begin{tabular}{c} **Nitrogen** \\ **(mg I\({}^{-1}\))** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Potassium +** \\ **Phosphorus (mg I\({}^{-1}\))** \\ \end{tabular}  } & \multirow{3}{*}{**Sulphur (mg I\({}^{-1}\))**} & \multirow{3}{*}{**Sulphur (mg I\({}^{-1}\))**} & \multirow{3}{*}{**Pot photoperiod (h)**} & \multirow{3}{*}{**Biomass**} & \multirow{3}{*}{**Total**} & \multirow{3}{*}{**Cantenold**} & \multirow{3}{*}{**Biomass**} & \multirow{3}{*}{**Capationation**} \\  & & & & & & & & & & & \\  & & & & & & & & & & & & \\  & & & & & & & & & & & & \\  & & & & &  
Figures S1-S5 depict 3D surface response plots of the association between factors and the response value achieved. As illustrated in the 3D surface response plots, the regression equation generated by the RSM Design Expert Software was subjected to analysis of variance (ANOVA) to assess the efficacy of the selected model and the accuracy of the anticipated results. The fitted model appeared to be accurate and could offer recommendations for enhancing productivity by employing suitable conditions. Table 3 presents the F value and \(p\)-value of the model for the responses' correspondence to the influence of factors. The combined effect of five distinct abiotic factors showed the greatest impact. The reliability of the model was indicated by the obtained \(\mathrm{R_{adj}}^{2}\) coefficient values. The regression model and actual values showed a strong correlation, as evidenced by the \(\mathrm{R_{adj}}^{2}\) value, and the model had a high probability of accurately predicting the outcome of the experimental setup. The test demonstrated great reliability and precision, as indicated by the low coefficient of variation, which reflected the repeatability of the test. The overall consistency was significant, indicating that the experimental design was effectively executed and the regression model was significant.