# Comprehensive Evaluation of Conveyor Belt Impact Resistance Using Canonical Correlation Analysis
## 4 Results and Discussion
### Canonical Correlation Analysis  
First, let us see if there is any correlation between the original variables. Since the variables were measured in different units, the relationships between them were identified using a correlation matrix (Table 6), where the relationship between the two variables was determined through the Pearson correlation coefficient \(r\). We used a scale to determine the degree of dependence: no correlation (\(\left.\left|\left.r\right|\right.<0.29\right)\), moderate correlation (\(0.30<\left.\left|\left.r\right|\right.<0.49\right)\), medium correlation (\(0.50<\left.\left|\left.r\right|\right.<0.79\right)\), and strong correlation (S, \(0.80<\left.\left|\left.r\right|\right.<1\right)\). If the correlation coefficient \(r\) is positive (or negative), there is a positive (or inverse) linear dependence between the variables. The results of the correlation matrix show that there is a strong inverse correlation between the variables \(E_{relatt}\) and Type (\(r=-0.787\)) and also \(E_{relatt}\) and \(F_{impatt}\) (\(r=-0.615\)). For the Type variable, the reference category was the steel cord conveyor belt. If the correlation coefficient is \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & **Weight** & **Height** & **Strength** & **Type \({}^{*}\)** & \(F_{impact}\) & \(\Delta F_{tension}\) & \(E_{relatt}\) & **Damage** \\ \hline Weight & \(1\) & & & & & & & \\ Height & \(-0.050\) & \(1\) & & & & & & \\ Strength & \(0.057\) & \(0.0650\) & \(1\) & & & & & \\ Type \({}^{*}\) & \(0.057\) & \(0.0650\) & \(-0.065\) & \(1\) & & & & \\ \(F_{impact}\) & \(0.575\) & \(0.6042\) & \(0.274\) & \(0.332\) & \(1\) & & & \\ \(\Delta F_{tension}\) & \(0.569\) & \(0.4985\) & \(-0.154\) & \(-0.347\) & \(0.585\) & \(1\) & & \\ \(E_{relatt}\) & \(-0.296\) & \(-0.1046\) & \(-0.411\) & \(-0.787\) & \(-0.615\) & \(0.107\) & \(1\) & \\ Damage & \(0.247\) & \(0.1418\) & \(-0.175\) & \(-0.397\) & \(0.065\) & \(0.456\) & \(0.246\) & \(1\) \\ \hline \hline \end{tabular} \({}^{*}\) Reference category: Steel cord conveyor belt.  
\end{table} 
Table 6: Correlation matrix of original variables. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & **Coefficients** & \multicolumn{2}{c}{**Standardized**} & \multirow{2}{*}{**t State**} & \multirow{2}{*}{\(p\)-Value**} & \multirow{2}{*}{**Lower 95\%**} & \multirow{2}{*}{**Upper 95\%**} \\  & & & & & & & \\ Model IV, Output variable Damage (\(p\)-value \(<\) 2\(\times\)10\({}^{-10}\)) & & & & & & \\ Intercept & \(-0.8615\) & & \(-3.006\) & \(3\times 10^{-3}\) & \(-1.4286\) & \(-0.2943\) \\ Weight & \(0.0115\) & \(0.295\) & \(4.008\) & \(1\times 10^{-4}\) & \(0.0058\) & \(0.0171\) \\ Height & \(0.2765\) & \(0.201\) & \(2.717\) & \(7\times 10^{-3}\) & \(0.0751\) & \(0.4779\) \\ Strength & \(-0.0002\) & \(-0.234\) & \(-3.170\) & \(1\times 10^{-3}\) & \(-0.0003\) & \(-0.0001\) \\ Type \({}^{*}\) & \(0.4848\) & \(0.442\) & \(5.998\) & \(2\times 10^{-8}\) & \(0.3249\) & \(0.6447\) \\ \hline \hline \end{tabular} \({}^{*}\) Reference category: Steel cord conveyor belt.  
\end{table} 
Table 5: _Cont._negative, the rubber textile conveyor belt acquires a value of the examined variable that is lower than that for the reference category, i.e., a steel cord conveyor belt (for example, in \(\Delta F_{n}\), \(E_{relat}\), Damage). On the other hand, if the correlation coefficient is positive, the rubber textile conveyor belt acquires a value of the examined variable (for example, \(F_{impact}\)) that is higher than that of the reference category. It turns out that there are moderate to medium correlations between many pairs of variables, which is enough for the data to be processed using the CCA method. All the variables are divided into two groups. The first group of the original variables called Properties (Weight, Height, Strength, Type) describes the properties of the conveyor belt or the conditions of the experiment.