## 3 Results and Discussion
### Adsorption Efficiency in Batch System  
From Table 5, it is observed, from the values of _p_-value \(<\) 0.05, that temperature was the variable with the most significant influence on the removal of Cr (VI) when using the biomaterials under study, as well as the amount of adsorbent when using YSR and the initial concentration of contaminant when using YSR; this can be explained since these variables are determinants on the rate of diffusion from within the solution to the active sites available on the surface and pores of the adsorbent [60]. From Table 6, it is observed that the adsorbent dose and temperature are the relevant factors in the design used for the removal of Ni (II) on PSR. At the same time, such variables are not significant when using YSR. The above shows that the processes where there is an incidence of the variables in the metal removal may be due to the interaction of adsorbate-adsorbent bonding or the formation of new effective sites for adsorption [61]. Regression model equations in coded form for each adsorption system in the batch system are as follows: Equation (4) is for YSR-Cr (VI), Equation (5) is for YSR-Ni (II), Equation (6) is for PSR-Cr (VI), and Equation (7) is for PSR-Ni (II). Where \(T\) is the temperature \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Biomass** & \multicolumn{3}{c}{**PSR**} & \multicolumn{3}{c}{**YSR**} \\ \hline
**Source** & **Sum of Squares** & **F-Ratio** & _p_**-Value** & **Sum of Squares** & **F-Ratio** & _p_**-Value** \\ \hline A: Temperature & 1.9 & 0.09 & 0.8 & 1.6 & 0.06 & 0.8 \\ B: Adsorbent dose & 948.5 & 43.4 & 0.0012 & 59.3 & 2.3 & 0.3 \\ C: Initial concentration & 1490.7 & 68.2 & 0.0004 & 7.3 & 0.3 & 0.6 \\ AA & 38.3 & 1.8 & 0.2 & 7.0 & 0.3 & 0.7 \\ AB & 0.2 & 0.01 & 0.9 & 6.8 & 0.3 & 0.7 \\ AC & 1.52837 & & & 5.9 & 0.2 & 0.7 \\ BB & 124.6 & 5.7 & 0.06 & 28.6 & 1.1 & 0.4 \\ BC & 109.1 & 4.9 & 0.08 & 0.015 & 0.0 & 1.0 \\ CC & 207.7 & 9,5 & 0.03 & 0.02 & 0.0 & 1.0 \\ Total error & 109.4 & & & 50.6 & & \\ Total (corr.) & 2901.7 & & & 207.7 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Analysis of variance for Ni (II) adsorption in a batch system. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Biomass** & \multicolumn{3}{c}{**PSR**} & \multicolumn{3}{c}{**YSR**} \\ \hline
**Source** & **Sum of Squares** & **F-Ratio** & _p_**-Value** & **Sum of Squares** & **F-Ratio** & _p_**-Value** \\ \hline A: Temperature & 158.3 & 0.5 & 0.04 & 997.5 & 8.3 & 0.03 \\ B: Adsorbent dose & 1302.2 & 3.9 & 0.03 & 132,95 & 1.1 & 0.3 \\ C: Initial concentration & 126.2 & 0.4 & 0.6 & 743.5 & 6.2 & 0.05 \\ AA & 58.8 & 0.2 & 0.7 & 51.1 & 0.4 & 0.5 \\ AB & 113.2 & 0.3 & 0.6 & 299.6 & 2.5 & 0.2 \\ AC & 5.0 & 0.02 & 0.9 & 520.5 & 4.4 & 0.08 \\ BB & 456.7 & 1.4 & 0.3 & 1.2 & 0.01 & 0.9 \\ BC & 43.6 & 0.1 & 0.7 & 231.9 & 1.9 & 0.2 \\ CC & 41.5 & 0.1 & 0.7 & 12.6 & 0.1 & 0.8 \\ Total error & 1976.9 & & & 718.2 & & \\ Total (corr.) & 4190.4 & & & 3719.9 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Analysis of variance for Cr (VI) adsorption in a batch system. (\({}^{\circ}\)C), \(A\) the adsorbent amount (g), \(C\) is the initial concentration, and \(q_{t}\) is the adsorption capacity (mg/g). \[ \begin{array}{c}q_{t}=-6.01859-0.79674*T\ +98.0305*A\ -0.155557*C\ +0.0104372\\ *T^{2}-1.26502*T*A\ +0.00537723*T*C\ -3.49734\\ *A^{2}-0.166952*A*C\ +0.000116763*C^{2}\end{array}  \tag{4}\]  
\[ \begin{array}{c}q_{t}=-4.6956-23.224*A+0.6779*T+0.0484*C-6.6834*A^{2}+0.7036* M*T\\ +0.0146*A*C-0.0037*T^{2}-0.0029*T*C+0.0002*C^{2}\end{array}  \tag{5}\]  
\[ \begin{array}{c}q_{t}=325.826-68.131*A-6.8846*T-1.0124*C+153.937*A^{2}-3.775 1*A*T\\ +0.2585+A*C+0.6677*T^{2}+0.0129*T*C+0.00034*C^{2}\end{array}  \tag{6}\]  
\[ \begin{array}{c}q_{t}=63.7897-0.0362617*C-1.1754*T-60.2943*A+0.0006*C^{2}-0.0 003\\ *C*T-0.1145*C*A+0.0112*T^{2}-0.03176*T*A+43.6142*A^{2}\end{array}