# Developing a Generalized Regression Forecasting Network for the Prediction of Human Body Dimensions
## 4 Experimental Results and Discussion
### Experimental Setup
#### 4.1.3 Performance Metrics  
To quantitatively compare the predictive accuracies of the models, this study employed the root mean square error (\(e_{RMSE}\)), mean absolute error (\(e_{MAE}\)), and coefficient of determination (\(R^{2}\)). The corresponding equations are presented as follows:  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Measurements** & **Abbr.** & **Min** & **Max** & **Mean** & **Median** & **SM** & **SD** & **CV (\%)** \\ \hline Waist Height & WH & 58.3 & 81.3 & 69.1 & 68.8 & 69.0 & 4.94 & 7.14 \\ Hip Circumference & HC & 78.0 & 101.8 & 92.2 & 92.5 & 92.4 & 4.75 & 5.15 \\ Thigh Circumference & TC & 42.4 & 60.8 & 52.9 & 52.6 & 52.7 & 3.75 & 7.09 \\ Knee Circumference & KC & 31.6 & 43.9 & 37.4 & 37.3 & 37.3 & 2.26 & 6.05 \\ Abdomen Circumference & AC & 65.0 & 91.2 & 79.2 & 79.2 & 79.2 & 5.35 & 6.75 \\ Total Crotch Length & TCL & 64.5 & 93.9 & 73.2 & 72.8 & 73.1 & 4.10 & 5.61 \\ Crotch Width & CW & 17.2 & 22.2 & 19.7 & 19.8 & 19.7 & 1.04 & 5.28 \\ \hline \hline \end{tabular}  
* Notes: Measurements are in centimeters (cm). Height (ST), waist circumference (WC), hip circumference (HC), crotch height (CH), waist height (WH), abdominal height (AH), hip height (HH), knee height (KH), total crotch length (TCL), thigh circumference (TC), abdomen circumference (AC), knee circumference (KC), and crotch width (CW). The sum mean (SM) is the average of the sums of the upper quartile, lower quartile, and overall mean. Standard deviation (SD) and the coefficient of variation (CV) are also listed.  
\end{table}
Table 1: _Cont._  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Measurements** & **Abbr.** & **Component 1** & **Component 2** \\ \hline
1 & Stature & ST & 0.970 & 0.209 \\
2 & Waist Height & WH & 0.964 & 0.215 \\
3 & Abdomen Height & AH & 0.958 & 0.223 \\
4 & Hip Height & HH & 0.960 & 0.198 \\
5 & Crotch Height & CH & 0.890 & \(-\)0.021 \\
6 & Knee Height & KH & 0.909 & 0.273 \\
7 & Waist Circumference & WC & 0.047 & 0.915 \\
8 & Hip Circumference & HC & 0.258 & 0.918 \\
9 & Thigh Circumference & TC & 0.163 & 0.927 \\
10 & Knee Circumference & KC & 0.232 & 0.794 \\
11 & Abdomen Circumference & AC & 0.220 & 0.920 \\
12 & Total Crotch Length & TCL & 0.445 & 0.553 \\
13 & Crotch Width & CW & 0.045 & 0.852 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Rotated component matrix.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & **Factor** & **Eigenvalues** & **\% of Variance** & **Cumulative \%** \\ \hline Factor 1 & Height Factor & 5.725 & 44.040 & 44.040 \\ Factor 2 & Circumference Factor & 5.302 & 40.787 & 84.827 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Sum of squares of rotated loadings.  
\[e_{RMSE}(\mathrm{Y}_{obs},\mathrm{Y}_{pred})=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n }{(y_{i}-\hat{y}_{i})}^{2}}, \tag{43}\]  
\[e_{MAE}(\mathrm{Y}_{obs},\mathrm{Y}_{pred})=\frac{1}{n}\sum\limits_{i=1}^{n}{ \left|y_{i}-\hat{y}_{i}\right|}, \tag{44}\]  
\[R^{2}(\mathrm{Y}_{obs},\mathrm{Y}_{pred})=1-\sum\
olimits_{i=1}^{n}{(y_{i}- \hat{y}_{i})}^{2}/{\sum\
olimits_{i=1}^{n}{(y_{i}-\overline{y})}^{2}}, \tag{45}\]  
where \(y_{i}\) and \(\hat{y}_{i}\) represent observed and predicted values, respectively, and the variable \(\overline{y}\) denotes the average of the predicted values derived from a collection of \(n\) samples.