## 3 Results  
Descriptive statistics for the model outputs are shown in Table 3. Positive values for kinematics represent knee extension, adduction, internal rotation, and anterior translation. The combination of 0 N*m of internal rotation moment and 150 N*m of valgus moment resulted in the highest mean loading for both bundles (a: 667.0 \(\pm\) 99.1 N, p: 1382.1 \(\pm\) 168.5 N), while the combination of 90 N*m of rotation and 0 N*m of valgus resulted in the lowest mean loading for both bundles (a: 369.9 \(\pm\) 65.9 N, p: 921.1 \(\pm\) 118.1 N). The ACL was modeled as two bundles in OpenSim: the anterior and posterior bundles. There was no difference in magnitude or direction between each independent variable and the load on each respective bundle. For simplicity, results of the regression analysis are therefore presented only for the anterior bundle. The results of the generalized linear regression using only knee kinematics are presented in Table 4. The model R2 was 0.91 and of the kinematic variables the anterior tibial translation had the greatest partial correlation (0.86). The results of the generalized linear regression using only external moments are presented in Table 5. The model R2 was 0.37, and the rotation moment had a greater partial correlation than the valgus moment. The results of the generalized linear regression for all forces are presented in Table 6. The model R2 was 0.59, and the muscle with the highest partial correlation was the Vastus Lateralis muscle at \(-\)0.30. The results of the GBM are presented in Figure 1 and the last column of Table 6. The model R2 was 0.9. The most important variable (Table 6, last column) was the internal rotation moment followed by the Vastus Medialis muscle. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multirow{2}{*}{**Coefficient**} & \multicolumn{2}{c}{**Partial**} & \multirow{2}{*}{_p-Value_} & \multicolumn{2}{c}{**Root Mean**} \\  & & & **Correlation** & & **Square Loss** \\ \hline Valgus Moment & 0.82 & 0.41 & \(<\)2 \(\times\) 10\({}^{-16}\) & 55 \\ Int. Rotation & \(-\)3.16 & \(-\)0.64 & \(<\)2 \(\times\) 10\({}^{-16}\) & 122 \\ Moment & \(-\)0.05 & \(-\)0.15 & \(<\)2 \(\times\) 10\({}^{-16}\) & 51 \\ Biceps Femoris & \(-\)0.01 & \(-\)0.03 & \(<\)2 \(\times\) 10\({}^{-16}\) & 42 \\ Short & \(1.38\) & 0.13 & \(<\)2 \(\times\) 10\({}^{-16}\) & 57 \\ Rectus Femoris & \(-\)0.07 & \(-\)0.25 & \(<\)2 \(\times\) 10\({}^{-16}\) & 53 \\ Semimetandinosus & \(-\)0.11 & \(-\)0.18 & \(<\)2 \(\times\) 10\({}^{-16}\) & 46 \\ Vastus & \(0.68\) & 0.13 & \(<\)2 \(\times\) 10\({}^{-16}\) & 47 \\ Vastus Lateralis & \(-\)1.26 & \(-\)0.3 & \(<\)2 \(\times\) 10\({}^{-16}\) & 56 \\ Vastus Medialis & 0.25 & 0.04 & \(<\)2 \(\times\) 10\({}^{-16}\) & 63 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Regression table for a generalized linear model using hamstring and quadriceps muscles and externally applied knee moments to predict ACL loading. The final column of the table was calculated using the same predictor variables in a generalized boosted model (GBM). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Variable**} & \multirow{2}{*}{**Coefficient**} & \multicolumn{2}{c}{**Partial Correlation**} & \multicolumn{1}{c}{_p-Value_} \\ \hline Flexion & 28.92 & 0.78 & \(<\)2 \(\times\) 10\({}^{-16}\) \\ Rotation & \(-\)4.38 & \(-\)0.47 & \(<\)2 \(\times\) 10\({}^{-16}\) \\ Valgus & 4.3 & 0.11 & \(<\)2 \(\times\) 10\({}^{-11}\) \\ Anterior Translation & 46,300 & 0.86 & \(<\)2 \(\times\) 10\({}^{-16}\) \\ Medial Translation & \(-\)58,880 & \(-\)0.53 & \(<\)2 \(\times\) 10\({}^{-16}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Regression table for a generalized linear model using knee kinematics to predict ACL loading.