## 3 Results
### Visible Spectroscopy Analysis of Expired EBT3 Gafchromic Film
#### 3.3.3 Multiple Linear Regression (MLR) Analysis  
Multiple linear regression (MLR) analysis was performed to determine the correlation between two or more predicted variables with one response variable and to make predictions for the response using the relation. The multiple linear analysis was performed by selected wavelengths in the range from 520 nm to 700 nm. This range showed highly correlated color changes of the expired EBT3 films, which indirectly indicate radiation-absorbed dose. The best selected wavelength subset is which has the lowest value of Root Mean Square error (RMSE) and the highest coefficient of determination, R\({}^{2}\). Table 3 presents the best wavelength subsets using Minitab software version 19.  
From Table 3, the best wavelength subsets that presented the best MLR regression fitting for 90 kVp X-rays were 632.52 nm, 641.84 nm, and 678.11 nm where RMSE = 0.004 Gy and R\({}^{2}\) = 99.99% and were used to develop an algorithm as per Equation (1). \(A\lambda\) is the absorbance, A at wavelength, \(\lambda\).  
90-kVp X-ray absorbed dose (Gy) = \(-\)0.06626\(-\)12.5940 (A632.52) + 30.584 (A641.84)\(-\)55.44 (A678.11)  
For the 6-MV photon beam, the best wavelength subsets that presented the best MLR regression fitting were 600.28 nm, 624.50 nm, and 640.18 nm where RMSE = 0.021 Gy and R\({}^{2}\) = 99.99% and were used to develop an algorithm as per Equation (2).  
6-MV X-ray absorbed dose (Gy) = \(-\)0.9849\(-\)74.27 (A600.28) + 37.10 (A624.50) + 2.024 (A640.18)  
The best wavelength subsets that presented the best MLR regression fitting for the 6-MeV electron beam were 650.79 nm, 654.10 nm, 660.37 nm where RMSE = 0.040 Gy and R\({}^{2}\) = 99.99% and were used to develop an algorithm as per Equation (3).  
6-MeV electron beam absorbed dose (Gy) = \(-\)0.799\(-\)94.35 (A650.79) + 300.4 (A654.10)\(-\)274.3 (A660.37)  
To obtain the best set of wavelengths for this expired EBT3 film towards all radiation sources that provide high accuracy, all experimental data were combined and MLR was performed. The entire set of wavelengths is shown in Table 4 below.  
From Table 4, the best wavelength subsets that presented the best MLR regression fitting for the 90-kVp X-rays, 6-MV photon beam, and 6-MeV electron beam were 541.48 nm, 561.11 nm, and 600.28 nm where RMSE = 0.596 Gy and R\({}^{2}\) = 87.42% and were used to develop an algorithm as per Equation (4).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Energy and Source of Radiation** & \multicolumn{2}{c}{**90-kVp X-Rays**} & \multicolumn{2}{c}{**6-MV Photon Beam**} & \multicolumn{2}{c}{**6-MeV Electron Beam**} \\ \hline
**Wavelength (nm)** & \(R^{2}\) **(\%)** & **RMSE (Gy)** & \(R^{2}\) **(\%)** & **RMSE (Gy)** & \(R^{2}\) **(\%)** & **RMSE (Gy)** \\ \hline
521.00, 532.13, 600.28 & 95.2 & 0.496 & 99.1 & 0.280 & 98.4 & 0.406 \\
541.48, 561.11, 600.28 & 98.0 & 0.318 & 99.6 & 0.190 & 99.7 & 0.184 \\
561.11, 600.28, 640.18 & 96.5 & 0.425 & 99.9 & 0.113 & 99.9 & 0.087 \\
600.28, 624.50, 640.18 & 97.3 & 0.371 & 99.7 & 0.167 & 98.0 & 0.446 \\
600.28, 654.10, 650.79 & 99.6 & 0.147 & 99.3 & 0.251 & 98.8 & 0.350 \\
632.52, 641.84, 678.11 & 100.0 & 0.018 & 99.4 & 0.234 & 97.6 & 0.488 \\
635.85, 646.82, 664.00 & 99.4 & 0.174 & 99.1 & 0.277 & 97.3 & 0.521 \\
650.79, 654.10, 660.37 & 98.0 & 0.324 & 99.0 & 0.289 & 99.8 & 0.144 \\
655.09, 675.81, 678.11 & 99.8 & 0.101 & 98.8 & 0.324 & 97.7 & 0.477 \\ \hline \end{tabular}
\end{table}
Table 3: Results of Multiple Linear Regression Technique using the selected wavelengths.  
From Table 5, the best wavelength subsets that presented the best MLR regression fitting for the 6-MV photon beam and 6-MeV electron beam were 600.28 nm, 650.79 nm, 654.10 nm where RMSE = 0.354 Gy and R\({}^{2}\) = 96.52% and were used to develop an algorithm as per Equation (5).  
Radiation-absorbed dose (Gy) = 1.033 + 635(A600.28 nm)\(-\)49.0(A650.79 nm) + 78.5(A654.10 nm). (5)