## 3 Results
### Nanomaterials
\begin{split}\text{$Y$Zine\;oxide}=302.751-0.577x_{1}+1.625x_{2} -0.712x_{3}+0.000348x_{1}\text{${}^{2}$}-0.00438x_{2}\text{${}^{2}$}\\ (0.629)\;(0.970)\;(0.985)\;(0.565)\;(0.997)\\ -0.432x_{3}\text{${}^{2}$}-0.00871x_{1}x_{2}+0.0113x_{1}x_{3}+0.0897 x_{2}x_{3}\\ (0.739)\;(0.733)\;(0.566)\;(0.932)\\ R^{2}=0.768,R^{2}_{\text{adj}}=0.351,\text{s}=7.154,\text{ PRESS}=6124.736\end{split}  \tag{36}\]In our study, the adequate equation evaluated by complete regression analysis is  
\[ \begin{array}{c}\text{$Y${\rm{Zine\,oxide}}}=129.859\,-\,2.526x_{2}\,-\,3.663x _{3}\\ \text{R}^{2}=0.651,\,\text{R}^{2}_{\text{adj}}=0.592,\,\text{s}=5.668,\,\text{ PRESS}=639.412\end{array}  \tag{37}\]  
The normality and constant variance tests are passed, and two suspicious data points are found. The PRESS values for the adequate and complete equation are 639.432 and 6124.736. The adequate equation offers a significant improvement in the predictive ability. [PERSON] et al. [38] investigated the optimization of a photovoltaic/thermal system using a Mxene/water nanofluid as the heat transfer fluid via CCD. The four influencing variables were \(x_{1}\), nanofluid concentration; \(x_{2}\), nanofluid flow rate; \(x_{3}\), solar radiation; and \(x_{4}\), inlet temperature. The four responses were \(y_{nth}\), thermal efficiency; \(y_{nole}\), electrical efficiency; \(y_{nex}\), thermal exergy efficiency; and \(y_{nex}\), electrical exergy efficiency. The author proposed full equations for four responses, which were used to produce curve surface plots of contour and 3D response surface plots [38]. The coefficients of variables and their corresponding \(p\)-values for four responses (\(y_{nth}\), \(y_{ncle}\), \(y_{nex,th}\), and \(y_{nex,dc}\)) are presented in the table from the study [38]. In this table, many \(p\)-values of each parameter in the full equations are >0.05. This indicates that these parameters did not significantly affect the response. However, the complete equations were adopted [38]. The complete regression technique evaluated the adequate equation of the four responses. \[ \begin{array}{c}y_{nth}=51.078+29.749x_{1}+0.257x_{2}\,-\,0.631x_{4}\\ \text{R}^{2}=0.814,\,\text{R}^{2}_{\text{adj}}=0.789,\,\text{s}=4.017,\,\text{ PRESS}=515.04\end{array}  \tag{38}\]  
The normality and constant variance tests are passed. One suspicious data point is found. \[ \begin{array}{c}y_{ncle}=19.452\,-\,0.462x_{1}+0.00935x_{2}\,-\,0.00438x_{3} \,-\,0.0539x_{4}+0.0000238x_{2}x_{3}\\ \,-\,0.000406x_{2}x_{4}\\ \text{R}^{2}=0.984,\,\text{R}^{2}_{\text{adj}}=0.979,\,\text{s}=0.171,\, \text{PRESS}=1.419\end{array}  \tag{39}\]  
The normality and constant variance tests are passed. Three suspicious data points are found. \[ \begin{array}{c}y_{nex,th}=0.601\,-\,3.364x_{1}\,-\,0.00775x_{2}\,+\,0.0035 3x_{3}\,-\,0.0271x_{4}+19.391x_{1}{}^{2}\\ \,-\,0.0000171x_{2}x_{3}\,+\,0.000328x_{2}x_{4}\,-\,0.0000258x_{3}x_{4}\\ \,\text{R}^{2}=0.979,\,\text{R}^{2}_{\text{adj}}=0.970,\,\text{s}=0.119,\, \text{PRESS}=0.666\end{array}  \tag{40}\]  
The normality and constant variance tests are passed. Two suspicious data points are found. \[ \begin{array}{c}y_{nex,de}=20.366\,-\,0.175x_{1}+0.0225x_{2}\,-\,0.00427x_{3} \,-\,0.0748x_{4}\,-\,0.000192x_{2}{}^{2}\\ \,-\,0.00158x_{1}x_{3}+0.0000196x_{2}x_{3}\\ \,\text{R}^{2}=0.998,\,\text{R}^{2}_{\text{adj}}=0.997,\,\text{s}=0.068,\, \text{PRESS}=0.175\end{array}  \tag{41}\]  
The normality test is passed. However, the constant variance test is failed (\(p=0047\)). Two suspicious data points are found. For \(y_{nth}\) and \(y_{ncle}\), only the linear relationship is valid. No quadratic terms (\(x_{1}{}^{2}\), \(x_{2}{}^{2}\), or \(x_{4}{}^{2}\)) significantly affect \(y_{nth}\) and \(y_{ncle}\). So, the curve surface plots were inappropriate. For \(y_{nex,th}\), only \(x_{2}{}^{2}\) has a significant effect on response. For \(y_{nex,de}\), only the \(x_{2}{}^{2}\) term exists in the adequate equation. The constant variance test is failed for \(y_{nex}\) and \({}_{ele}\).