## 3 Results
### Analysis of Covariance  
Subsequently, an analysis of covariance (ANCOVA) was conducted to determine whether there were statistically significant differences between the sample groups, considering the covariate's effect corresponding to the raw material's initial parameters. Thus, the analysis was configured to ascertain whether the covariate considerably affected the outcome of the processed final product for each considered variable. This process began by verifying several assumptions (the existence of a dependent linear relationship, the homogeneity of regression slopes, and that the covariate (in this context, the initial value for each initial parameter) was not correlated with the effects of the administered treatments). Accordingly, all these assumptions were verified and accepted, which aligned with expectations as the raw material comes from different sources, constituting entirely independent samples, and the treatments are distinct. The results of the ANCOVA tests applied to each variable comprising the database are presented in Table 2 and Figure 3. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Variety** & **\% Moisture** & **\% Protein** & **\%Starch** & **\% Fiber** & **\% Ash** & **\% Fat** \\ \hline \hline
\begin{tabular}{c} \(\mathrm{Ssn}\) \\ S\(\mathrm{sd}\) \\ \(\mathrm{r}\)-\(\mathrm{\textit{Statistics}}\) \\ \end{tabular} & 0.012 & 0.283 & 0.000287 & 0.298 & 0.006 & 0.017 \\ \(\mathrm{\textit{F}}\)-\(\mathrm{\textit{Statistics}}\) & 0.359 & 0.205 & 0.003 & 5.671 & 0.054 & 0.119 \\ \(\mathrm{\textit{F}}\)-\(\mathrm{\textit{Statistics}}\) & 0.229 & 9.672 & 0.756 & 0.368 & 0.793 & 1.028 \\ \(\mathrm{\textit{p}}\)-value & 0.647 & 0.017 \({}^{*}\) & 0.414 & 0.563 & 0.403 & 0.344 \\ \(\mathrm{\textit{Not\,significant}}\) & \(\mathrm{\textit{Significant}}\) & \(\mathrm{\textit{Not\,significant}}\) & \(\mathrm{\textit{Not\,significant}}\) & \(\mathrm{\textit{Not\,significant}}\) & \(\mathrm{\textit{Not\,significant}}\) \\ \hline \end{tabular} \({}^{*}\) Significant contrasts. Columns for non-significant contrasts are shaded in gray.  
\end{table} 
Table 2: ANCOVA tests for each variable using each parameter of the raw material as a covariate. As can be seen in Table 2, the effect of the covariate related to the initial value of each parameter on the final value obtained in the chips was analyzed using the ANCOVA test. This allowed for the verification of the fact that the initial effect of each covariate was not significant for the variables moisture, starch, fiber, ash, and fat. Therefore, it cannot be asserted that the initial values of each of these parameters had an impact on the final result. Additionally, in Figure 3, it can be observed that there are significant differences between the various treatments for each evaluated variable. However, as the significance level was not reached, these effects are analyzed in Section 3.3. On the other hand, the only variable that showed a significant effect from its covariate was the percentage of protein. Therefore, the post-hoc test known as the Least-Square means test, also known as the Estimated Marginal Means test, was conducted using the _emmeans_ package in R. The results of this test for the protein percentage variable are presented in Table 3 and Figure 4.  
Figure 3: Regression graphs obtained for the ANCOVA tests for the final product parameters based on the raw material parameters. The variables used were (**a**) moisture, (**b**) protein, (**c**) starch, (**d**) fiber, (**e**) ash, and (**f**) fat. As can be seen in Table 3, the protein content of the chips showed significant differences. When comparing the four designed treatments, it was identified that treatments T2 (Dominico + Baked) and T4 (Dominico + Fried) were significantly higher compared with treatment T1 (Barraganate + Baked), with \(p\)-values of 0.0364 and 0.0334, respectively. Additionally, it is noted that, although descriptive differences were observed concerning the other treatments, these were not significant.