## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{\(y_{3}\) (Final Wall Thickness of the Tube)} \\ \hline
**Source** & **MS** & **F** & \(p\)**-Value** \\ \hline Diameter of the pre-tube (\(A\)) & \(1.084\times 10^{-5}\) & \(4.802\times 10^{1}\) & \(0.036\times 10^{-5}\) \\ Wall thickness (\(B\)) & \(0.879\times 10^{-1}\) & \(3.891\times 10^{7}\) & \(0.00000\) \\ Diameter of the die (C) & \(2.183\times 10^{-3}\) & \(9.666\times 10^{3}\) & \(0.00000\) \\ \(A\,{}^{*}\,B\) & \(2.348\times 10^{-3}\) & \(1.040\times 10^{4}\) & \(0.00000\) \\ \(A\,{}^{*}\,C\) & \(8.972\times 10^{-4}\) & \(3.973\times 10^{3}\) & \(0.00000\) \\ \(B\,{}^{*}\,C\) & \(1.869\times 10^{-4}\) & \(8.274\times 10^{2}\) & \(0.00000\) \\ \(A\,{}^{*}\,B\,{}^{*}\,C\) & \(6.187\times 10^{-4}\) & \(2.739\times 10^{3}\) & \(0.00000\) \\ Error & \(2.258\times 10^{-7}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Summary of key ANOVA values for the response variable y\({}_{3}\). The following Figure 8 presents the plot for all main effects. The analysis of these graphs also helps in interpreting and/or contributing to the understanding of a key part of the results obtained with the ANOVA, and specifically the impact of the main terms involved on the studied variables. As mentioned before, given the size of the experimentation in this paper, the graphs are only presented for the case of the response variable \(y_{1}\), or the final roundness of the tube; however, a similar process of analysis indeed applies for the rest of the variables, and readers and reviewers of this paper are welcome to request access to these extra graphs if needed. From this figure, it is possible to see that there are main effects present in the case of all factors, leading the authors to confirm that the response mean is not the same across all of the factor levels. In more concrete terms, it is possible to see that the lower level of the diameter of the pre-tube (factor \(A\)) has the lowest effect on the response variable \(y_{1}\), or the final roundness of the tube, while its upper value behaves in the opposite manner. A similar analysis applies for the diameter of the die (factor \(C\)), while in the case of the remaining factor (factor \(B\)), its lower value influences the response variable the most. All of these analyses closely relate to those in Table 11, where it can be seen that the interactions of all these factors are significant as well. Another tool the authors decided to use for a better analysis of the results and data was the interaction plots. These plots allowed viewing and/or reaffirming how a given categorical factor and a continuous response depend on the value of the second categorical factor. Given the many pages that would be needed within the paper to show all of the interaction plots analyzed, the authors show an illustrative example of the interaction plot for \(y_{1}\) considering the factors \"diameter of the pre-tube\" and \"wall thickness of the tube\". As it can be appreciated in Figure 9, there is a lack of parallelism between both lines, which reaffirms the effects manifested by the respective \(p\)-value in Table 11. This, in practical terms, means that the relationship between the response variable \(y_{1}\) and the wall thickness also depends on the diameter of the pre-tube. Conclusions such as this are extremely important in the context of the specific cold tube drawing process under study and represent valuable information for either research teams or the end user of this research. Once more, the readers and reviewers of this paper are kindly invited to ask for any other proof of these results in case they find it necessary. Figure 8: Main effects plot for the variable y1, or the final roundness of the tube.