## 3 Results  
The average scores for the deep squat, hurdle step, in-line lunge, active straight leg, raise, trunk stability pushup, and rotary stability tests, as graded by the professional athletic trainer and the automatic grading system, were 1.83 \(\pm\) 0.85 and 1.79 \(\pm\) 0.85, 1.81 \(\pm\) 0.55 and 1.93 \(\pm\) 0.43, 2.03 \(\pm\) 0.48 and 1.96 \(\pm\) 0.32, 2.33 \(\pm\) 0.74 and 2.44 \(\pm\) 0.69, 1.80 \(\pm\) 0.93 and 1.86 \(\pm\) 0.95, and 1.61 \(\pm\) 0.49 and 1.69 \(\pm\) 0.47 points, respectively (Table 3). Differences in scores were within 1 point, ranging from 0.04 to 0.12. Table 3 shows the number and classification rate for each class. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Confusion Matrix**}} & \multicolumn{4}{c}{**Actual Class**} \\ \cline{3-5}  & & **Y1** & **Y2** & **Y3** \\ \hline \multirow{3}{*}{Predicted Class} & Y1 & T1 & F1 & F2 \\  & Y2 & F4 & T2 & F3 \\  & Y3 & F5 & F6 & T3 \\ \hline \multicolumn{5}{c}{T: Truth; F: False.} \\ \multirow{3}{*}{Accuracy = T1 + T2 + T3/(T1 + T2 + T3 + F1 + F2 + F3 + F4 + F5 + F6)} \\  & Recall & Recall1 = T1/(T1 + F4 + F5) \\  & Recall2 = T2/(T2 + F1 + F6) \\  & Recall3 = T3/(T3 + F2 + F3) \\ \multirow{3}{*}{Precision} & Precision1 = T1/(T1 + F1 + F2) \\  & Precision2 = T2/(T2 + F4 + F3) \\  & Precision3 = T3/(T3 + F5 + F6) \\ \multirow{3}{*}{F-Score = (2 \(\times\) Precision \(\times\) Recall)/(Precision + Recall)} \\ \cline{2-5}  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ \end{tabular}
\end{table} 
Table 2: Confusion matrix for three classes. As demonstrated in Table 4, the Nagelkerke R\({}^{2}\) values from the ordinal logistic regression analysis for the deep squat, hurdle step, in-line lunge, active straight leg raise, trunk stability pushup, and rotary stability tests were 82.5%, 18.9%, 44.1%, 78.6%, 40.1%, and 34.3%, respectively. Higher R\({}^{2}\) values indicate better goodness of fit. The deep squat and hurdle step tests had the highest and lowest R\({}^{2}\) values and were thus the best and worst models, respectively. In addition, the regression models, each of which contained 1-4 variables, determined the best predictor variables for each exercise. Table 4 presents the given subsets of predictor variables in each model. For the deep squat, hurdle step, in-line lunge, active straight leg raise, trunk stability pushup, and rotary stability tests, the best classifiers after feature selection were trained using the reduced feature sets of the selected M = 4 joint angles (shoulder horizontal abduction (S-SHAB), pelvic tilt (PT), scoring side thigh flexion (S-ThF), and trunk rotation (TR); Table 5), the M = 1 joint angle (head rotation (HR)), the M = 1 joint angle (trunk flexion (TF)), the M = 2 joint angles (S-ThF, PT), the M = 2 joint angles (TF and scoring shoulder rotation (S-SR)), and the M = 3 joint angles (non-scoring shoulder rotation (NS-SR), scoring side shoulder flexion (S-SF), and scoring thigh flexion (S-ThF)), respectively. The ROM parameters presented in bold in Table 4 indicate that the regression model coefficients are negative. A negative coefficient suggests that as the value of the independent variable increases, that of the dependent variable decreases as well. A positive coefficient indicates that as the value of the independent variable increases, the mean of the dependent variable also increases. Table 4 also presents the stepwise regression analysis of the ROM data (means \(\pm\) standard deviations) for all participants who scored 1, 2, or 3 points on each test.