## 4 Analyses  
### Testing Accuracy of Statistical Model  
An F-test of ANOVA was used to evaluate the accuracy of the models formulated from the outcomes and the results are presented in Table 7. From the analyses, it was revealed that, at a 95% confidence level, \(\text{F}_{\text{calculated}}>\text{F}_{\text{tabulated}}\). Thus, these values reflected the best fit for the regression model, i.e., the adopted statistical models seemed to be accurate [27]. Table 8 shows the impact of the process variables on the outcomes (YS, UTS and % E). From Table 8 II,III, it is found that the \(p\)-value \(\leq\) 0.05, which means that the two welding variables have an outstanding impact on the outcomes of the experimental results (UTS, % E) [28].  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Outcomes**} & \multicolumn{2}{c}{**DF**} & \multicolumn{2}{c}{**SS**} & \multicolumn{2}{c}{**MS**} & \multicolumn{2}{c}{**Calculated F**} & \multicolumn{2}{c}{**Tabulated F**} \\ \cline{2-9}  & **Regression** & **Residual** & **Regression** & **Residual** & **Regression** & **Residual** & **Value** & **Value** & **Value** \\ \hline YS & 2 & 6 & 146.371 & 20.438 & 73.185 & 73.185 & 21.48 & 5.14 & Adequate \\ \hline UTS & 2 & 6 & 58.901 & 2.794 & 29.451 & 0.466 & 63.23 & 5.14 & Adequate \\ \hline \% E & 2 & 6 & 21.897 & 0.425 & 10.949 & 0.071 & 154.56 & 5.14 & Adequate \\ \hline \hline \end{tabular}
\end{table}
Table 7: Statistical model—ANOVA test results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**I For YS (MPa)**} \\ \hline
**Source** & **DF** & **SS** & **MS** & **F** & **P** \\ \hline Tool Rotation Speed & 2 & 120.429 & 60.2144 & 18.60 & 0.009 \\ \hline Weld Speed & 2 & 33.429 & 16.7144 & 5.16 & 0.078 \\ \hline Error & 4 & 12.951 & 3.2378 & & \\ \hline Total & 8 & 166.809 & & & & \\ \hline \hline \multicolumn{2}{c}{S = 1.799; R-Sq = 92.24\%; R-Sq (adj) = 84.47\%} & & \\ \hline
**II For UTS (MPa)** & & & & & \\ \hline
**Source** & **DF** & **SS** & **MS** & **F** & **P** \\ \hline Tool Rotation Speed & 2 & 47.1489 & 23.5744 & 94.51 & 0.000 \\ \hline Weld Speed & 2 & 13.5489 & 6.7744 & 27.16 & 0.005 \\ \hline Error & 4 & 0.9978 & 0.2494 & & \\ \hline Total & 8 & 61.6956 & & & & \\ \hline \multicolumn{2}{c}{S = 0.4994; R-Sq = 98.38\%; R-Sq (adj) = 96.77\%} & & \\ \hline
**III For \% Elongation** & & & & & \\ \hline
**Source** & **DF** & **SS** & **MS** & **F** & **P** \\ \hline Tool Rotation Speed & 2 & 15.4156 & 7.70778 & 86.17 & 0.001 \\ \hline Weld Speed & 2 & 6.5489 & 3.27444 & 36.61 & 0.003 \\ \hline Error & 4 & 0.3578 & 0.08944 & & \\ \hline Total & 8 & 22.3222 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 8: Analysis of variance for test results of tensile properties.  
Scatter diagrams further confirms the reliability of the regression model. The connection between the forecasted values derived from the models and the actual values of the FSW joint are reflected in the scatter diagrams. From Figure 7a-c, it can be seen that the actual values and the hypothetical values of the outcomes are widely dispersed and aligned along the 45\({}^{\circ}\) line. This orientation of the data reflects the adequacy of the formulated regression models [29].