## 4 Discussion  
Recent advances in X-ray fluorescence instrumentation allow for quick measurements of a range of elements that some time ago were available only through complicated and often destructive means of analytical chemistry (ICP (ICP-OES, ICP-MS)) methods for the analysis of heavy metals. XRF is a simple, fast, and safe method for sample preparation without chemical waste and with a non-destructive analytical technique, whereas ICP requires a long time for sample pretreatment. Further, the original state of samples is destroyed due to the complexity of preprocessing. These are usually used as a precision analysis process to determine confidence of the result from XRF [41]. On the other hand, on top of being easy-to-manage and easy-to-use, XRFs are widely used because of their sufficient reliability [42; 43]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Summary of Simple Regression Analysis**} \\ \hline \multicolumn{5}{c}{**Institute \#1–Institute \#2**} & \multicolumn{3}{c}{**Institute \#1–Institute \#3**} \\ \hline  & **Intercept** & **Slope** & **R\({}^{2}\)** & **Intercept** & **Slope** & **R\({}^{2}\)** \\ \hline S & 4300 & 0.40 \({}^{\star}\) & 0.999 & 3800 & 0.87 \({}^{\star}\) & 0.999 \\ Mn & \(-\)0.9 & 0.36 & 0.998 & 11.6 & 0.69 & 0.996 \\ Pb & 52.9 & 0.37 \({}^{\star}\) & 0.997 & \(-\)2.2 & 0.55 & 0.990 \\ Zn & 156.3 & 0.38 \({}^{\star}\) & 0.996 & 170 & 0.63 \({}^{\star}\) & 0.995 \\ K & 395.9 & 0.54 \({}^{\star}\) & 0.992 & 487.7 & 0.97 \({}^{\star}\) & 0.990 \\ Fe & 4800 & 0.34 \({}^{\star}\) & 0.987 & 334.0 & 0.59 \({}^{\star}\) & 0.988 \\ V & 19.1 & 0.42 \({}^{\star}\) & 0.985 & 38.2 & 0.71 \({}^{\star}\) & 0.982 \\ Cu & 38.3 & 0.26 \({}^{\star}\) & 0.967 & 64.7 & 0.26 \({}^{\star}\) & 0.930 \\ Sn & \(-\)140.5 & 0.24 \({}^{\star}\) & 0.945 & \(-\)276.3 & 1.63 \({}^{\star}\) & 0.798 \\ Ba & \(-\)235.7 & 0.87 \({}^{\star}\) & 0.932 & 196.6 & 3.41 & 0.682 \\ Cr & \(-\)47.3 & 1.68 & 0.921 & \(-\)12.9 & 2.38 & 0.971 \\ Cs & \(-\)50.0 & 0.39 \({}^{\star}\) & 0.913 & 29.7 & 0.18 \({}^{\star}\) & 0.974 \\ Sr & 3.9 & 0.34 \({}^{\star}\) & 0.881 & 4.2 & 0.13 \({}^{\star}\) & 0.909 \\ Ti & \(-\)540.9 & 5.99 & 0.878 & \(-\)334.6 & 5.92 & 0.942 \\ Cd & 52.4 & 0.07 \({}^{\star}\) & 0.816 & 113.9 & \(-\)0.10 \({}^{\star}\) & 0.001 \\ Al & \(-\)2747.4 & 5.04 & 0.807 & \(-\)2140.3 & 6.09 & 0.841 \\ Ca & 533.7 & 0.19 \({}^{\star}\) & 0.767 & 196.6 & 0.29 & 0.737 \\ Se & \(-\)15.2 & 0.79 \({}^{\star}\) & 0.753 & 11.4 & 0.15 \({}^{\star}\) & 0.921 \\ As & 4.9 & 0.64 & 0.668 & 35.3 & \(-\)0.03 \({}^{\star}\) & 0.000 \\ Cl & \(-\)1136.4 & 3.82 & 0.641 & 565.3 & 5.40 & 0.521 \\ Br & 45.3 \(\pm\) SE & 0.46 & 0.543 & 84.4 & 0.14 & 0.642 \\ Sb & 45.2 \(\pm\) SE & 0.03 & 0.443 & 70.1 & 1.05 & 0.215 \\ Ni & 3.2 \(\pm\) SE & 0.01 & 0.024 & 2.1 & 0.02 & 0.003 \\ Rb & 3.9 \(\pm\) SE & \(-\)0.01 \({}^{\star}\) & 0.009 & 3.5 & 0.08 \({}^{\star}\) & 0.007 \\ Si & 11,000 \(\pm\) SE & \(-\)0.07 \({}^{\star}\) & 0.006 & 11,000 & \(-\)0.10 \({}^{\star}\) & 0.012 \\ \hline \hline \end{tabular} \({}^{\star}\): \(p<0.05\).  
\end{table} 
Table 2: Coefficients of determination obtained from a simple regression between institutions. This study compared and evaluated the correlation and determination coefficients of the obtained results, using the same filter samples, across three global analytical institutes, using XRF. Since ED-XRF measured all the emitted X-rays simultaneously, based on the principle of multi-channel energy dispersion, both qualitative and quantitative analyses of the composition of heavy metals collected in a PTFE filter were possible within a short time. Moreover, since ED-XRF could, theoretically, infinitely measure, owing to minimization of the damage caused by heat generated by the filter, each institution in this study conducted heavy metal analysis using ED-XRF. In this study, XRF was used to analyze the elemental composition of the measured 25 metals contained in PM2.5.