# Assessment of a Patient Dose Monitoring System for Average
## 3 Results
In Figure 4, both the polynomial regression curve (a) and its corresponding residual plot (b) are shown. The regression model facilitated the calculation of g factors for each patient in the dataset and demonstrated a good fit to the data. The F test revealed an F value significantly exceeding the critical F value at a 0.05 significance level (F >> F\(\alpha\) = 0.05), indicating the statistical significance of the polynomial model in effectively capturing and explaining the nuances of the data. The residual plots (b) show a random distribution, indicating that the regression model is appropriate. Similarly, c factors were determined for each patient through polynomial regression (4), incorporating HVL, thickness, and glandularity values from [PERSON]'s Table 6 (reference [2]). Figure 5 displays both the third-degree polynomial regression curve (a) and its corresponding residual plot (b) for HVL = 0.50 mm Al. Similar results were observed for other HVL values; hence, only one example is presented for clarity. Once again, the F test showed F >> F\(\alpha\) = 0.05, affirming the statistical significance of the c factor regression model, analogous to the considerations for the g factor regression model. Figure 3: LIBRA segmentation algorithm. (**a**) Original DICOM image of the mammogram; (**b**) clustering representing regions of the image with similar gray-level intensity (i.e., similar X-ray attenuation properties); (c) final dense-tissue segmentation output image. Figure 2: Comparison of DoseWatch and calculated AGD values with acceptable and achievable dose levels for (**left**) Dimensions 1 and (**right**) Dimensions 2 mammographic units. Calculated values refer to [PERSON]’s method. Figures 4 and 5 display the results of the third-degree polynomial regressions (3) and (4) for the g and c factors, respectively, using HVL, thickness, and glandularity data from [PERSON]'s tables (reference [2]). The polynomial regression was used to model the behavior of the g and c factors in relation to these variables. The model demonstrated a good fit to the data, as evidenced by the F value significantly exceeding the critical value, confirming the statistical validity of the results. The residual plots (b) showed a random distribution, indicating that the regression models were appropriate. The mean AGD values and corresponding standard deviations (SDs) for the values displayed by the mammographic units and extracted from DoseWatch, as well as for the values independently calculated using the Dance and Boone methods (with breast density estimates from LIBRA or the multivariable fitting process based on [PERSON]'s Table 5 [2] and [PERSON]'s tables in the Supplemental Material [27]), are shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Unit**} & \multicolumn{5}{c}{**Mean AGD, SD (mGy)**} \\ \cline{2-6}  & **DoseWatch** & **Dance** & **Dance-LIBRA** & **Boone** & **Boone-LIBRA** \\ \hline Dim1 & 1.28, 0.43 & 1.21, 0.41 & 1.29, 0.39 & 1.13, 0.44 & 1.22, 0.38 \\ \hline Dim2 & 1.29, 0.42 & 1.23, 0.40 & 1.29, 0.36 & 1.14, 0.43 & 1.22, 0.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean AGD of the images of the two subgroups of patients acquired with Dim1 and Dim2 units and corresponding standard deviations (SDs) for displayed values (DoseWatch) and for AGD calculated with Dance and Boone methods using the glandularity calculated by polynomial fits (Dance and Boone, respectively) or using the glandularity estimated by LIBRA software (Dance-LIBRA and Boone-LIBRA, respectively). Figure 4: Polynomial regression curve (**a**) for the g factor and associated residual plot (**b**). The F test reveals a notably high F value, exceeding the critical F value at a 0.05 significance level (F >> F\({}_{\alpha}\) = 0.05). Figure 5: Polynomial regression curve (**a**) for the c factor and its corresponding residual plot (**b**), specifically for HVL equal to 0.50 mm Al.