## 3 Results and Discussion
### Factors Screening in a Full 2\({}^{5}\) Factorial Design for the Initial Regression Model  
Table 2 gives the experimental values of the two main responses in each experiment. The 2-level factorial was employed to improve the correlation between the five process variables, temperature, feed flow rate, amount of catalyst and the catalyst of Ni to Co ratio, and phenol concentration in the feed (coded as \(A\), \(B\), \(C\), \(D\), and \(E\), respectively) to responses of phenol conversion (\(Y_{1}\)) and hydrogen yield (\(Y_{2}\)). Thirty-two sets of experiments were performed to explore the effects of the reaction parameters on the phenol conversion and the generation of hydrogen in the phenol steam reforming process. It was found that the conversion of the phenol varied from 2.7% to 96.8% and H\({}_{2}\) yield was in the range of 21.4%-72.4%. The maximum catalyst activity for \(Y_{1}\) of 96.8 and \(Y_{2}\) of 72.4% was found to be at 800 \({}^{\circ}\)C, 0.16 mL/min feed flow rate, 0.3 g of catalyst, 0 ratio of Ni-Co (Co/ZrO\({}_{2}\)), and 10 wt % of phenol in the feed (run number 32). To identify whether the results are \"real\" or \"chance,\" a Normal plot (Figure 4) was used to display the estimates of the main effects among the factors as well as their interaction. To obtain this Normal plot, effects were ranked in ascending order and plotted against their corresponding cumulative probability [54]. All the effects that tended to fall along a straight line in the plot (distributed with mean zero and marked in black) do not demonstrate any significant effect on the responses. In comparison, the significant effects were located far from the straight line and had non-zero means. They appear in red. The significant effects get more distanced from the straight line as they become larger. From Figure 4, it can be seen that all of the main parameters (\(A\), \(B\), \(C\), \(D\), and \(E\)) and their interactions (\(AE\), \(BE\), \(CE\), and \(DE\)) are found to be \"real\" parameters for \(Y_{1}\) and \(Y_{2}\). The red marks, which lie to the left of the fitted line, had a negative effect on the responses [55]. Figure 3: TPR-H\({}_{2}\) profiles for the Ni/ZrO\({}_{2}\) and Co/ZrO\({}_{2}\) catalysts. The evaluation of the effect of each variable on the \(Y_{1}\) and \(Y_{2}\) may also be verified from the Pareto chart. A Pareto chart (Figure 5) visually represents the absolute values of the effects of main factors and the effects of \(n\)-way interaction of factors. The chart includes a vertical reference line at the critical \(t\)-value for an alpha of 0.05 (magnitude for a 95% confidence level) to indicate that the factors that extend past this line are potentially important. For a 95% confidence level and 32 degrees of freedom (DF), \(t\)-value is equal to 4.89 for \(Y_{1}\) and 3.04 for \(Y_{2}\). It can again be seen from the Pareto chart that all effects are statistically significant. The significance of the \(n\)-way interactions could also be compared from the Pareto charts. These results were in agreement with those obtained from the analysis of the Normal plot. These plots clearly indicate that the significance of the variables and their \(n\)-way interaction towards \(Y_{1}\) and \(Y_{2}\) decreased in this order: \(E>A>B>D>AE>C>DE>BE>CE\) and \(E>A>B>D>DE>AE>C>BE\). Based on the experimental data, regression models were fitted for \(Y_{1}\) and \(Y_{2}\), as shown in Equations (6) and (7), respectively. The adequacy of the initial model was tested a via parity plot for observed versus predicted values, as demonstrated in Figure 6. As seen in Figure 6, the high value of the correlation coefficient (\(R^{2}=1\)) demonstrates good correlation between the observed and the predicted responses by the initial models. The analysis of the regression coefficient for initial models \(Y_{1}\) and \(Y_{2}\) is shown in Tables 3 and 4. In such analysis, a modal term is considered significant if its \(p\)-value  
Figure 4: Normal plot for (**a**) \(Y_{1}\) and (**b**) \(Y_{2}\).