## 3 Results and Discussion
### Regression Modeling and Statistical Analysis
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Response** & \multicolumn{3}{c}{**Model**} & \multicolumn{3}{c}{**Radj**  } \\ \hline Biomass productivity (mg.L\({}^{-1}\) d\({}^{-1}\)) & \(\mu\)=38.71 + 3.08 \(\times\) A + 8.69 \(\times\) B + 2.68 \(\times\) C + 17.74 \(\times\) D + 0.4950 \(\times\) E & 0.33 \\ Lipid content (\%) & \(\mu\)=+20.68 + 1.64 \(\times\) A + 4.64 \(\times\) B + 1.43 \(\times\) C + 9.48 \(\times\) D + 0.2645 \(\times\) E & 0.41 \\  & \(\mu\)=+12.18 + 0.074 \(\times\) A + 0.8357 \(\times\) B + 0.6287 \(\times\) C + 2.44 \(\times\) D + 0.4549 \(\times\) E + & \\ Chlorophyll a yield (\(\mu\)g.mL\({}^{-1}\)) & 0.6908 \(\pm\) AB + 0.9296 \(\times\) AC + 0.0032 \(\times\) AD + 0.5578 \(\times\) AE + 2.40 \(\times\) BC + & \\  & 0.4617 \(\times\) BD \(-\) 0.9000 \(\times\) BE + 0.4461 \(\times\) CD + 0.4023 \(\times\) CE \(-\) 0.2485 \(\times\) DE + & \\  & 0.1134 \(\times\) A\({}^{2}\) - 0.1134 \(\times\) B + 0.6203 \(\times\) C\({}^{2}\) - 6.10 \(\times\) D\({}^{2}\) + 0.1341 \(\times\) E & \\ Chlorophyll b yield (\(\mu\)g.mL\({}^{-1}\)) & \(\mu\)= + 4.34 \(\times\) 1.60\(\times\) A + 0.5636 \(\times\) D - 0.3356 \(\times\) C + 2.515 \(\times\) D + 0.0567 \(\times\) E & \\  & \(\mu\)=+4.87 \(\times\) 0.8053 \(\times\) A - 0.4848 \(\times\) B - 0.1982 \(\times\) C + 0.2919 \(\times\) D + 1.94 \(\times\) E + & \\ Total Carotenoid yield (\(\mu\)g.mL\({}^{-1}\)) & 0.2719 \(\times\) AB + 0.1836 \(\times\) AC + 1.91 \(\times\) AD + 3.14 \(\times\) AE + 0.6001 \(\times\) BC + & \\  & 2.82 \(\times\) BD \(-\) 0.1718 \(\times\) BE - 1.97 \(\times\) CD + 1.69 \(\times\) CE + 0.0983 \(\times\) DE & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accurate models and associated adjusted \(\mathrm{R^{2}}\) (\(\mathrm{R_{adj}}^{2}\)) of response surface methodology- central composite design (RSM-CCD) for biomass productivity (mg.L\({}^{-1}\)d\({}^{-1}\)), lipid content (%), chlorophyll a (ug.mL\({}^{-1}\)), chlorophyll b (ug.mL\({}^{-1}\)), and total carotenoids (ug.mL\({}^{-1}\)) in response to abiotic factors including A-Nitrogen (mg.L\({}^{-1}\)), B-Potassium and phosphorus (mg.L\({}^{-1}\)), C-Sulphur (mg.L\({}^{-1}\)), D- Light intensity (\(\mu\)mol.m\({}^{-2}\)s\({}^{-1}\)), and E-Photoperiod (h). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Response** & **Model Term** & **Coefficient Estimated** & **df** & **Standard Error** & **Mean Square** & **F-Value** & \(p\)**-Value** \\ \hline Biomass productivity & & & & & & & \\ (mg.L\({}^{-1}\) d\({}^{-1}\)) & Intercepts & 29.06 & 1 & 2.75 & 862.17 & 5.20 & 0.0010 \\  & A & 3.08 & 1 & 3.22 & 151.53 & 0.9135 & 0.3454 \\  & B & 2.68 & 1 & 3.22 & 114.96 & 0.6931 & 0.4105 \\  & C & 0.4950 & 1 & 3.22 & 3.92 & 0.0236 & 0.8786 \\  & D & 13.90 & 1 & 5.15 & 1207.42 & 7.28 & 0.0104 \\  & E & 13.31 & 1 & 3.22 & 2833.02 & 17.08 & 0.0002 \\ Lipid content (\%) & Intercepts & 15.53 & 1 & 1.47 & 246.07 & 5.20 & 0.0010 \\  & A & 1.64 & 1 & 1.72 & 43.25 & 0.9135 & 0.3454 \\  & B & 1.43 & 1 & 1.72 & 32.81 & 0.6931 & 0.4105 \\  & C & 0.2645 & 1 & 1.72 & 1.12 & 0.0236 & 0.8786 \\  & D & 7.43 & 1 & 2.75 & 344.61 & 7.28 & 0.0104 \\  & E & 7.11 & 1 & 1.72 & 808.58 & 17.08 & 0.0002 \\ Chlorophyll a yield (ug.mL\({}^{-1}\)) & Intercepts & 10.72 & 1 & 0.7372 & 22.69 & 10.69 & \(<\)0.0001 \\  & A & \(-\)0.3409 & 1 & 0.5689 & 0.7621 & 0.3591 & 0.5551 \\  & B & \(-\)0.9199 & 1 & 0.5689 & 5.55 & 2.61 & 0.1201 \\  & C & 0.1472 & 1 & 0.5689 & 0.1421 & 0.0670 & 0.7982 \\  & D & 1.37 & 1 & 1.25 & 2.55 & 1.20 & 0.2848 \\  & E & 3.91 & 1 & 0.5689 & 100.41 & 47.32 & \(<\)0.0001 \\  & AB & 0.9296 & 1 & 0.7284 & 3.46 & 1.63 & 0.2152 \\  & AC & 0.5578 & 1 & 0.7284 & 1.24 & 0.5865 & 0.4519 \\  & AD & 1.11 & 1 & 1.17 & 1.91 & 0.8995 & 0.3532 \\  & AE & 0.0024 & 1 & 0.7284 & 0.0000 & 0.0000 & 0.9974 \\  & BC & 0.4023 & 1 & 0.7284 & 0.6472 & 0.3050 & 0.5863 \\  & BD & 3.83 & 1 & 1.17 & 22.95 & 10.81 & 0.0034 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Analysis of variance (ANOVA) for the proposed most accurate regression model.