## 3 Experimental Results
### Size-Specific Dose Estimate (SSDE) Correlations  
In this section, linear and multiple linear regression is performed to investigate the relationship between SSDE as an output variable and BMI, weight and age as input variables. Table 6 shows the results of the regression and correlation analysis.  
As can be seen in Table 6, for both BMI and weight, SSDE exhibited a positive linear relationship across the given exams as indicated by the evaluation metrics (the \(p\)-value \(<0.05\)). As observed with the other dose indices, age did not show any linear relationship with SSDE in any of the given exams.  
Using multiple regression models resulted in a higher correlation with the output variables than when using simple regression in both CT exams. This increase is noticed in the resulting R\({}^{2}\), MAPE and \(r\) values of the multiple linear regression models compared to those of the respective best simple linear regression models.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**SSDE (mGy)**} \\ \cline{3-6} \multirow{4}{*}{**Model**} & \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Linear**} & \multicolumn{2}{c}{**Multiple Linear**} \\ \cline{3-6}  & & \multicolumn{2}{c}{**X\({}_{\text{i}}\): BMI**} & \multicolumn{2}{c}{**X\({}_{\text{i}}\): Weight**} & \multicolumn{2}{c}{**X\({}_{\text{i}}\): Age**} & \multicolumn{2}{c}{**All Parameters**} \\  & & & & & **(X\({}_{\text{i}}\): BMI, X\({}_{\text{i}}\): Age)** & \multicolumn{2}{c}{**X\({}_{\text{i}}\): Weight, X\({}_{\text{i}}\): Age**} \\ \hline \multirow{4}{*}{**Model**} & R\({}^{2}\) & 0.30 & 0.28 & 0.01 & 0.40 \\  & RMSE & 18.02 & 59.88 & 60.94 & 1.92 \\  & MAE & 17.32 & 57.91 & 57.36 & 1.63 \\  & MAPE & 67.79 & 87.49 & 86.01 & 20.35 \\  & Eq. & \(g=1.30\) X\({}_{\text{i}}\) + 1487 & \(g=3.55\) X\({}_{\text{i}}\) + 37.38 & \(g=0.98\) X\({}_{\text{i}}\) + 57.49 & \(g=0.7\) + 0.12 X\({}_{\text{i}}\) + 0.04 X\({}_{\text{i}}\) + 0.02 X\({}_{\text{i}}\) \\  & \(r\) & 0.55 & 0.53 & 0.12 & 0.63 \\  & \(p\)-value & \(1.23\times 10^{-5}\) & \(2.30\times 10^{-5}\) & \(3.40\times 10^{-1}\) & \(1.57\times 10^{-7}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Regression and correlation analysis between SSDE as output variable and BMI, weight and age as input variables.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**ED (mSv)**} \\ \cline{3-6} \multirow{4}{*}{**Model**} & \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Linear**} & \multicolumn{2}{c}{**Multiple Linear**} \\ \cline{3-6}  & & & \multicolumn{2}{c}{**X\({}_{\text{i}}\): BMI**} & \multicolumn{2}{c}{**X\({}_{\text{i}}\): Weight**} & \multicolumn{2}{c}{**X\({}_{\text{i}}\): Age**} & \multicolumn{2}{c}{**All Parameters**} \\  & & & & & **(X\({}_{\text{i}}\): BMI, X\({}_{\text{i}}\): Age)** & \multicolumn{2}{c}{**(X\({}_{\text{i}}\): Age)**} \\ \hline \multirow{4}{*}{**Model**} & R\({}^{2}\) & 0.28 & 0.17 & 0.01 & 0.30 \\  & RMSE & 23.01 & 64.97 & 66.44 & 1.03 \\  & MAE & 22.39 & 62.97 & 63.64 & 0.86 \\  & MAPE & 88.14 & 95.35 & 94.90 & 28.79 \\  & Eq. & \(g=2.51\) X\({}_{\text{i}}\) + 17.88 & \(g=5.48\) X\({}_{\text{i}}\) + 49.58 & \(g=1.85\) X\({}_{\text{i}}\) + 60.15 & \(g=0.18\) + 0.12 X\({}_{\text{i}}\) = 0.01 X\({}_{\text{i}}\) = 0.01 X\({}_{\text{i}}\) = 0.03 X\({}_{\text{i}}\) \\  & \(r\) & 0.52 & 0.41 & 0.12 & 0.54 \\  & \(p\)-value & \(3.28\times 10^{-5}\) & \(1.70\times 10^{-3}\) & \(3.40\times 10^{-1}\) & \(1.48\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Regression and correlation analysis between ED as output variable and BMI, weight and age as input variables.