## 3 Results  
### Reduction of Particle Geometry Parameters Using Correlation, PCA and CA Analysis  
Correlation analysis is applied to assess the degree of association between two variables within a group of investigated parameters. It was conducted on 14 geometric parameters (6 describing size and 8 morphology of the particle). All correlation coefficients at the significance threshold of 0.05 (\(p<0.05\)) indicate exceptional associations among variables (Table 2). When determining the number of components for principal component analysis, the criterion of the latent root was taken into account, according to which only those factors with eigenvalues greater than 1 are considered. Based on this criterion, three components should be considered, which account for 94.2% of the total variance (Table 3). The scree test--graph (Figure 9) looks for the point where the line abruptly changes direction, and up to that point, the number of components to be included in the analysis is counted. By applying this test to determine the number of components, one additional component could potentially be included. However, considering that the eigen \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Particle Size Parameters**} & \multicolumn{6}{c}{**Particle Shape Parameters**} \\ \cline{2-13}  & \(A\) & \(P\) & \(\overline{D}_{F}\) & \(L\) & \(W\) & \(D_{CE}\) & \(EI\) & \(RT\) & \(CVX\) & \(Circ\) & \(AR\) & \(RD\) & \(SLD\) & \(CP\) \\ \hline \(A\) & 1.000 & & & & & & & & & & & & & \\ \(P\) & 0.693 & 1.000 & & & & & & & & & & & & \\ \(\overline{D}_{F}\) & 0.755 & 0.982 & 1.000 & & & & & & & & & & & \\ \(L\) & 0.777 & 0.968 & 0.987 & 1.000 & & & & & & & & & & \\ \(W\) & 0.665 & 0.943 & 0.955 & 0.908 & 1.000 & & & & & & & & & \\ \(D_{CE}\) & 0.767 & 0.961 & 0.989 & 0.972 & 0.968 & 1.000 & & & & & & & & \\ \(EI\) & \(-\)0.081 & 0.244 & 0.231 & \(-\)0.311 & \(-\)0.056 & \(-\)0.181 & 1.000 & & & & & & & \\ \(RT\) & 0.118 & 0.531 & 0.493 & 0.486 & 0.508 & 0.431 & \(-\)0.244 & 1.000 & & & & & & \\ \(CVX\) & \(-\)0.143 & \(-\)0.589 & \(-\)0.489 & \(-\)0.471 & \(-\)0.516 & \(-\)0.452 & \(-\)0.220 & \(-\)0.732 & 1.000 & & & & & \\ \(Circ\) & \(-\)0.138 & \(-\)0.567 & \(-\)0.506 & \(-\)0.509 & \(-\)0.472 & \(-\)0.453 & 0.501 & \(-\)0.789 & 0.851 & 1.000 & & & & \\ \(AR\) & 0.103 & 0.338 & 0.319 & 0.399 & 0.133 & 0.253 & \(-\)0.850 & 0.322 & \(-\)0.283 & \(-\)0.576 & 1.000 & & & \\ \(RD\) & \(-\)0.101 & \(-\)0.328 & \(-\)0.309 & \(-\)0.376 & \(-\)0.149 & \(-\)0.255 & 0.932 & \(-\)0.357 & 0.326 & 0.617 & \(-\)0.905 & 1.000 & & & \\ \(SLD\) & \(-\)0.036 & \(-\)0.329 & \(-\)0.269 & \(-\)0.284 & \(-\)0.220 & \(-\)0.191 & 0.402 & \(-\)0.703 & 0.608 & 0.793 & 0.470 & 0.514 & 1.000 & \\ \(CP\) & \(-\)0.140 & \(-\)0.552 & \(-\)0.512 & \(-\)0.511 & \(-\)0.501 & \(-\)0.476 & 0.444 & \(-\)0.823 & 0.827 & 0.940 & \(-\)0.513 & 0.554 & 0.689 & 1.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Pearson correlation coefficient of geometric parameters. explained only 2.3% of the total variance, and based on the criterion of the latent root, it can be seen that the first three components were optimal for defining the sample using this method. The eigenvalue indicated the proportion of total variance associated with a particular principal component. The proportion of the first principal component in the total variance was 63.8%, defining the variation in data due to the first principal component. The other components accounted for 19.5% and 10.9%, respectively. It was observed that the proportion of components gradually decreased. The first component was, of course, far more important and influential than the others. With statistical significance of component loading at a 95% probability level, for a sample consisting of 1517 particles and an equal amount of quantitative data per parameter, a level of 0.3 loading was considered significant in interpreting the results.