## 4 Results  
For predicting Ethanol Steam Reforming (ESR) products including CO conversion (%), CO\({}_{2}\) yield and H\({}_{2}\) conversion (%) the Au-Cu supported over nano-shaped CeO\({}_{2}\) is used where three morphologies including polyhedral, rods and cubes are considered. The description of these ESR products is summarized in Table 2. This indicates that the CO conversion is highest with cube morphology and lowest with rods morphology. The CO\({}_{2}\) yield is highest with cubes and polyhedral morphologies, and lowest with rods morphology. Similarly, with cube morphology, the H\({}_{2}\) conversion is at its highest level, while with polyhedral morphology, it is at its lowest. Since ESR products such as CO conversion (%), CO\({}_{2}\) yield and H\({}_{2}\) conversion (%) are temperature dependent, the catalyst activity and characterization spectrum are also temperature dependent. We used an interpolation technique because both catalyst activity \begin{table}
\begin{tabular}{l l c c c c} \hline
**ESR Product** & **Morphology** & **Min** & **Max** & **Mean** & **SD** \\ \hline CO Conversion (\%) & Cubes & 15.22 & 51.61 & 37.09 & 13.81 \\  & Polyhedral & 11.11 & 37.42 & 30.00 & 8.15 \\  & Rods & 6.56 & 34.31 & 25.65 & 8.87 \\ CO\({}_{2}\) yield (\%) & Cubes & 0.11 & 0.29 & 0.24 & 0.07 \\  & Polyhedral & 0.02 & 0.32 & 0.24 & 0.10 \\  & Rods & 0.05 & 0.25 & 0.19 & 0.06 \\ H\({}_{2}\) conversion (\%) & Cubes & 10.90 & 18.45 & 13.44 & 2.54 \\  & Polyhedral & 7.90 & 17.20 & 10.63 & 3.15 \\  & Rods & 6.26 & 13.33 & 11.18 & 2.27 \\ \hline \end{tabular}
\end{table} 
Table 2: The summary statistics include the average, minimum, maximum, and standard deviation (SD) of ESR products with various morphologies. Figure 1: The left panel shows the reference measures loading weights (\(W\)), variable importance on projection (\(V\)), and significance multivariate correlation (\(C\)) extracted from the simulation study, while the right panel shows the proposed measures, which are the Johnsen index as a combination of \(W\), \(V\), and C. The data was generated using a simulation. \(R_{1}=(0.75,0.95,0.50,0,0,0,0,0,0,0)\) and with the correlation between x and y \(C_{xy}=(0.6,-0.5,0.2,0,0,0,0,0,0,0)\), \(p=1000\) and \(n=100\). and catalyst characterization are performed at different temperatures. First, the polynomial equation of degree two was used to fit catalyst activity as a function of temperature one by one. The temperature measured against the spectrum is then used in conjunction with the fitted polynomial to estimate the catalyst activity. The interpolation of CO conversion (%), CO\({}_{2}\) yield and H\({}_{2}\) conversion (%) through polynomial equation of degree two is exemplified for cube morphology is presented in Figure 2.  
For ESR product prediction, we have proposed the Johnsen index based \(PLS_{WV}\), \(PLS_{WC}\), \(PLS_{CV}\) which will be compared with the reference method \(PLS_{W}\), \(PLS_{V}\), \(PLS_{C}\). Hence for each EST product prediction we have to fit 06 \(PLS\) models. Since, we have considered 03 ESR products CO conversion (%), CO\({}_{2}\) yield and H\({}_{2}\) conversion (%) the Au-Cu supported over nano-shaped CeO\({}_{2}\) with three morphologies including polyhedral, rods and cubes, hence we have fitted \(6\times 3\times 3=54\) models. Each optimal PLS model is subject to tuning model parameters such as the number of components and the threshold that defines the number of selected variables, that is, the number of wavenumbers. We considered the number of \(PLS\) components as well as the threshold levels. Tuning is required for the number of components and the threshold. For this, we divided the data into 70 percent training and 30 percent test, that is, ESR product response \(y\) and spectroscopic data \(X\). The training model is used to construct the model, and the performance of the fitted model is evaluated using test data.