## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**CD**} & \multicolumn{4}{c}{**SpEn**} & \multicolumn{4}{c}{**LyE\({}_{\text{w}}\)**} \\ \hline \multicolumn{2}{c}{**Coefficient of**} & \multicolumn{4}{c}{0.42} & \multicolumn{4}{c}{0.41} & \multicolumn{4}{c}{0.25} \\
**Determination (R\({}^{2}\)\({}_{\text{MLR}}\))** & & & & & & & & \\ \hline
**Variable** & **Estimate** & **SE (W/Kg)** & \(p\)**-value** & **Estimate** & **SE (W/Kg)** & \(p\)**-value** & **Estimate** & **SE (W/Kg)** & \(p\)**-value** \\ \hline \(\beta\)0 (Intercept) & 0.2221 & 0.1192 & 0.0652 & 0.0391 & 0.0449 & 0.3853 & **0.0491** & **0.0077** & **<0.0001** \\ \(\beta\)1 (Hip angle) & 0.0358 & 0.0375 & 0.3421 & \(-\)0.0440 & 0.1040 & 0.6733 & 0.0039 & 0.0043 & 0.3687 \\ \(\beta\)2 (Hip velocity) & \(-\)0.0344 & 0.0395 & 0.3853 & \(\mathbf{-0.2262}\) & **0.0662** & **0.0009** & \(-\)0.0030 & 0.0085 & 0.7245 \\ \(\beta\)3 (Hip moment) & 0.0553 & 0.0440 & 0.2120 & **0.1801** & **0.0538** & **0.0011** & \(-\)0.0006 & 0.0034 & 0.8569 \\ \(\beta\)4 (Knee angle) & 0.0105 & 0.0425 & 0.8048 & 0.0864 & 0.0786 & 0.2744 & \(-\)0.0198 & 0.0108 & 0.0688 \\ \(\beta\)5 (Knee velocity) & \(-\)0.0765 & 0.0399 & 0.0577 & 0.0935 & 0.0787 & 0.2375 & **0.0339** & **0.0106** & **0.0019** \\ \(\beta\)6 (Knee moment) & \(-\)0.0246 & 0.0282 & 0.3846 & \(\mathbf{-0.0992}\) & **0.0382** & **0.0107** & \(-\)0.0009 & 0.0030 & 0.7668 \\ \(\beta\)7 (Arkle angle) & \(-\)0.0448 & 0.0297 & 0.1340 & \(-\)0.0899 & 0.0460 & 0.0816 & \(-\)0.0047 & 0.0074 & 0.5249 \\ \(\beta\)8 (Ankle velocity) & \(-\)0.0557 & 0.0374 & 0.1388 & \(-\)0.0547 & 0.0437 & 0.2133 & **0.0199** & **0.0082** & **0.0168** \\ \(\beta\)9 (Ankle moment) & **0.0827** & **0.0337** & **0.0156** & 0.1742 & 0.1519 & 0.2539 & \(-\)0.0010 & 0.0027 & 0.7053 \\ \(\beta\)10 (GRF Ver) & \(-\)**0.9418** & **0.2991** & **0.0021** & **0.6748** & **0.3341** & **0.0460** & 0.0002 & 0.0006 & 0.7892 \\ \(\beta\)11 (GRF AP) & **0.1864** & **0.0871** & **0.0346** & \(-\)**0.7148** & **0.1911** & **0.0003** & \(-\)0.0036 & 0.0055 & 0.5216 \\ \(\beta\)12 (COM position) & 0.0127 & 0.0290 & 0.6623 & \(-\)0.1050 & 0.0788 & 0.1858 & \(\mathbf{-0.0281}\) & **0.0086** & **0.0015** \\ \(\beta\)13 (COM velocity) & \(-\)0.0122 & 0.0361 & 0.7354 & 0.2258 & 0.1240 & 0.0714 & 0.0081 & 0.0075 & 0.2793 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of multiple linear regression (MLR) analysis for gait nonlinearity measures. This table presents the results of multiple linear regression analyses for the correlation dimension (CD), Sample Entropy (SpEn), and Lyapunov Exponent based on [PERSON]’s algorithm (LyE\({}_{\text{w}}\)) as predictors of the metabolic cost. The table includes the coefficient of determination (R\({}^{2}\)\({}_{\text{MLR}}\)) values, which indicate the proportion of variance in the metabolic cost that is predictable from the nonlinearity measures. Regression coefficients (\(\beta\) values = estimates), Standard Errors (SE), and \(p\)-values are listed for each predictor variable, including joint angles, velocities, moments, ground reaction forces (GRFs), and the center of mass (COM) position and velocity, providing insight into their statistical significance and impact on the predicted metabolic cost. Values with statistically significant \(p\)-values are highlighted in bold font.