## 3 Results  
Twenty active college students, 7 males and 13 females (age: 22.1 \(\pm\) 0.2 years old, body mass: \(75.8\pm 3.5\) kg, height: 1.72 \(\pm\) 0.02 m), were recruited for the study. Countermovement jump (CMJ) heights with and without arm-swing were \(38.2\pm 2.0\) and \(31.9\pm 1.8\) cm, respectively.  
Table 1 presents the descriptive results of the mean \(\pm\) standard error of the mean (SE) for 12 core strength measurements and CMJ height.  
\begin{table}
\begin{tabular}{c c} \hline
**Variables** & **Mean \(\pm\) SE** \\ \hline NPDE\({}_{60}\) (Nm/Kg) & 3.85 \(\pm\) 0.18 \\ NPDF\({}_{60}\) (Nm/Kg) & 2.20 \(\pm\) 0.11 \\ NPDE\({}_{120}\) (Nm/Kg) & 3.72 \(\pm\) 0.18 \\ NPDF\({}_{120}\) (Nm/Kg) & 2.21 \(\pm\) 0.12 \\ NPDE\({}_{180}\) (Nm/Kg) & 3.52 \(\pm\) 0.21 \\ NPDF\({}_{180}\) (Nm/Kg) & 2.08 \(\pm\) 0.14 \\ NPSE\({}_{60}\) (Nm/Kg) & 3.86 \(\pm\) 0.24 \\ NPSF\({}_{60}\) (Nm/Kg) & 1.70 \(\pm\) 0.10 \\ NPSE\({}_{60}\) (Nm/Kg) & 3.62 \(\pm\) 0.21 \\ NPSF\({}_{90}\) (Nm/Kg) & 2.04 \(\pm\) 0.10 \\ NPSE\({}_{120}\) (Nm/Kg) & 3.51 \(\pm\) 0.21 \\ NPSF\({}_{120}\) (Nm/Kg) & 1.96 \(\pm\) 0.12 \\ \hline \end{tabular}
\end{table}
Table 1: Descriptive statistics for core strength measurements (n = 20).  
Figure 3: Exemplar vertical force–time profile during quiet standing and takeoff of CMJ without arm-swing.  
Normality was confirmed before the regression analysis. Table 2 shows the shared variance (R2) between CMJ height and 12 core strength measurements. All dynamic core strength at three speeds and static core strength at three positions have shared significant variance with CMJ height with/without arm-swing.  
Figure 4 shows the results of the linear regressions of CMJ height with arm-swing (H\({}_{\text{AS}}\)) and 12 core strength measurements. The regression model demonstrated that variation in peak torque during dynamic flexion at 180\({}^{\circ}\) per second (NPDF\({}_{180}\)) and variation in normalized peak torque during static flexion at 120\({}^{\circ}\) (NPSF\({}_{120}\)) explained 72% of variation in performance in CMJ with arm swing. The possibility of colinearlarity was low since the variance inflation factor for both independent variables was at 1.140.  
Figure 5 shows the results of the linear regression analyses of CMJ height without arm-swing (H\({}_{\text{NAS}}\)) and 12 core strength measurements. Normalized peak torque during static flexion at 120\({}^{\circ}\) (NPSF\({}_{120}\)) was the only variable left in the regression analysis, and it explained 57% of the variance observed in H\({}_{\text{NAS}}\) (\(p<0.01\), VIF = 1.000).  
\begin{table}
\begin{tabular}{c c c} \hline  & **H\({}_{\text{AS}}\)** & **H\({}_{\text{NAS}}\)** \\ \hline NPDE\({}_{60}\) & 0.494 \({}^{**}\) & 0.460 \({}^{**}\) \\ NPDF\({}_{60}\) & 0.366 \({}^{**}\) & 0.412 \({}^{**}\) \\ NPDE\({}_{120}\) & 0.244 \({}^{**}\) & 0.295 \({}^{*}\) \\ NPDF\({}_{120}\) & 0.521 \({}^{**}\) & 0.446 \({}^{**}\) \\ NPDE\({}_{180}\) & 0.182 \({}^{*}\) & 0.208 \({}^{*}\) \\ NPDF\({}_{180}\) & 0.331 \({}^{*}\) & 0.270 \({}^{*}\) \\ NPSE\({}_{60}\) & 0.407 \({}^{**}\) & 0.336 \({}^{**}\) \\ NPSF\({}_{60}\) & 0.235 \({}^{*}\) & 0.231 \({}^{*}\) \\ NPSE\({}_{90}\) & 0.484 \({}^{**}\) & 0.469 \({}^{*}\) \\ NPSF\({}_{90}\) & 0.482 \({}^{**}\) & 0.503 \({}^{**}\) \\ NPSE\({}_{120}\) & 0.332 \({}^{*}\) & 0.326 \({}^{*}\) \\ NPSF\({}_{120}\) & 0.613 \({}^{**}\) & 0.570 \({}^{**}\) \\ \hline \end{tabular} \({}^{*}\) Significant at \(p<0.05\), \({}^{**}\) Significant at \(p<0.01\).  
\end{table}
Table 2: Shared variance (R2) between CMJ height and core strength measurements (n = 20).  
Figure 4: Results of linear regression analyses of CMJ height with arm-swing (H\({}_{\text{AS}}\)) with 12 core strength measurements (n = 20), which were tested on a dynamometer and included normalized (with body mass) peak torque during dynamic extension/flexion at 60, 120, and 180\({}^{\circ}\) per second and normalized peak torque during static extension/flexion at 60, 90, and 120\({}^{\circ}\).