# Comprehensive Evaluation of Conveyor Belt Impact Resistance Using Canonical Correlation Analysis
## 4 Results and Discussion
### Regression and Correlation Analysis  
When observing the influence of selected input variables (weight, impact from height, conveyor belt strength, conveyor belt type) on the output variables (impact force, relative absorption, tension force, degree of damage), we commence from the following model:  
\[Y_{z}=f(\text{Weight},\text{Height},\text{Strength},\text{Type}),\text{ for}=1,2,3,4 \tag{6}\]  
where \(Y_{1}=F_{impact}\), \(Y_{2}=\Delta F_{tension}\),\(Y_{3}=E_{relat}\), and \(Y_{4}=\text{Damage}\). The best regression model of dependence in all cases is the model of the following form:  
\[Y_{z}=\beta_{0,z}+\beta_{1,z}X_{1}+\beta_{2,z}X_{2}+\beta_{3,z}X_{3}+\beta_{4, z}X_{4}+\varepsilon_{z}, \tag{7}\]  
where \(\beta_{0,z}\), \(\beta_{i,z}\)\(i=1,\ 2,\ 3,\ 4\), \(z=1,\ 2,\ 3,\ 4\) are the parameters of the models; \(X_{1}\) is the weight of hammer (Weight, kg); \(X_{2}\) is the height from which the impactor falls (Height, m); \(X_{3}\) is the conveyor belt strength type and (Strength); and \(X_{4}\) is the type of conveyor (Type). Due to the sensitivity of the least squares method to outliers, samples in which a puncture occurred (simultaneous complete damage to the upper covering layer, carcass, and lower covering layer, classed as Damage 3) causing the conveyor belt to be decommissioned were excluded from the experiment. All the parameters of the regression model and the regression models themselves are statistically significant (\(p\)-value < \(\alpha\)). Point and interval estimates of the parameters of the regression model together with the statistical significance of the parameters (\(p\)-value) for each model are in Table 5. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multicolumn{1}{c}{**Coefficients**} & \multicolumn{1}{c}{**Standardized**} & \multicolumn{1}{c}{**t State**} & \multicolumn{1}{c}{**\(p\)-Value**} & \multicolumn{1}{c}{**Lower 95\%**} & \multicolumn{1}{c}{**Upper 95\%**} \\ \hline Model I, Output variable \(F_{impact}\) (\(p\)-value \textless{}2 \(\times\)\(10^{-10}\)) & & & & & \\ Intercept & \(-\)11,890.00 & & \(-\)9.424 & \(<\)2 \(\times\)\(10^{-16}\) & \(-\)14,387.10 & \(-\)9393.52 \\ Weight & 206.820 & 0.576 & 16.408 & \(<\)2 \(\times\)\(10^{-16}\) & 181.88 & 231.76 \\ Height & 7654.957 & 0.601 & 17.086 & \(<\)2 \(\times\)\(10^{-16}\) & 6768.41 & 8541.50 \\ Strength & 1.776 & 0.219 & 6.238 & \(6\times\)\(10^{-9}\) & 1.2123 & 2.3389 \\ Type * & \(-\)2771.9 & \(-\)0.274 & \(-\)7.790 & \(2\times\)\(10^{-12}\) & \(-\)3479.01 & \(-\)2067.79 \\ \hline Model II, Output variable \(\Delta F_{tension}\) (\(p\)-value \textless{}2 \(\times\)\(10^{-10}\)) & & & & \\ Intercept & \(-\)7964.87 & \(-\)3.975 & \(1\times\)\(10^{-4}\) & \(-\)11,930.36 & \(-\)3999.38 \\ Weight & 358.63 & 0.637 & 17.914 & \(<\)2 \(\times\)\(10^{-16}\) & 319.02 & 398.25 \\ Height & 11,489.97 & 0.575 & 16.148 & \(<\)2 \(\times\)\(10^{-16}\) & 10,081.94 & 12,898.01 \\ Strength & \(-\)3.25 & \(-\)0.258 & \(-\)7.178 & \(5\times\)\(10^{-11}\) & \(-\)4.14 & \(-\)2.35 \\ Type * & 6940.99 & 0.438 & 12.282 & \(<\)2 \(\times\)\(10^{-16}\) & 5822.70 & 8059.28 \\ \hline Model III, Output variable \(E_{relat}\) (\(p\)-value \textless{}2 \(\times\)\(10^{-10}\)) & & & & \\ Intercept & 0.9047 & 30.724 & \(<\)2 \(\times\)\(10^{-16}\) & 0.8464 & 0.9629 \\ Weight & \(-\)0.0022 & \(-\)0.226 & \(-\)7.445 & \(1\times\)\(10^{-11}\) & \(-\)0.0028 & \(-\)0.0016 \\ Height & \(-\)0.0119 & \(-\)0.346 & \(-\)1.139 & 0.0256 & \(-\)0.0326 & 0.0088 \\ Strength & \(-\)0.0001 & \(-\)0.448 & \(-\)14.725 & \(<\)2 \(\times\)\(10^{-16}\) & \(-\)0.00008 & \(-\)0.00011 \\ Type * & 0.2187 & 0.801 & 26.334 & \(<\)2 \(\times\)\(10^{-16}\) & 0.2022 & 0.2351 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Regression model parameters (\(\alpha\) = 0.05). The analysis of regression models shows that all input variables significantly influence the output variables observed.