## 3 Results
### Outcomes of the Multiple Linear Regression Model
* Models for deceleration behavior  
In these models, negative values of instantaneous acceleration (\(a_{i}(t+\tau)\)), i.e., decelerations, were considered without the negative sign. Four models were developed for the considered density levels. All four multiple linear regression models of deceleration behaviors corresponding to the four different density levels were significant, as indicated by the ANOVA results (see Table 3). The R-squared values were 0.244, 0.343, 0.254, and 0.225 for N = 14, N = 20, N = 24, and N = 30 cases, respectively. All the predictor variables were found to be significant for all the density levels except spacing, which was only significant for N = 24 cases (global density = 1.38 m\({}^{-1}\)). Further, gender was found to be significant for all the density levels. Table 4 shows the unstandardized coefficients for all the significant predictors. For all four density levels, relative speed had a negative association with instantaneous deceleration. Moreover, deceleration increases with decreasing relative speed. Decreasing relative speed means that the speed of the following pedestrian or the one under consideration is higher than the speed of the leading pedestrian. In such circumstances, pedestrians tend to decelerate or decrease their speed to avoid a collision with the leading pedestrian. The negative sign of the coefficient of the gender indicated that males were likely to decelerate significantly more than females for all the density levels (note: males were coded as \"0\" and females were coded as \"1\"). Gender had the greatest significant effect for N = 20 cases (global density = 1.16 m\({}^{-1}\)). The spacing was significant (at 0.05 level) only for N = 24 cases, and the sign is negative, which indicates that pedestrians tend to decelerate more when the spacing is decreasing. However, it can be noted that the spacing is not significant for other density levels, and the influence is weak even for N = 24 cases as compared to other variables. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Model**}} & \multicolumn{3}{c}{**Coefficients**} & \multirow{2}{*}{**t**} & \multirow{2}{*}{**Sig.**} \\ \cline{3-3} \cline{5-6}  & & **B** & & **Std. Error** & \\ \hline \multirow{4}{*}{N = 14} & (Constant) & 0.048 & 0.014 & 3.480 & 0.001 \\  & DS & 0.067 & 0.011 & 6.295 & 0.000 \\  & DV & 1.072 & 0.027 & 39.274 & 0.000 \\  & gender & \(-\)0.050 & 0.005 & \(-\)9.214 & 0.000 \\ \hline \multirow{4}{*}{N = 20} & (Constant) & 0.085 & 0.010 & 8.539 & 0.000 \\  & DS & 0.088 & 0.012 & 7.607 & 0.000 \\  & DV & 0.791 & 0.017 & 46.529 & 0.000 \\  & gender & \(-\)0.027 & 0.004 & \(-\)7.418 & 0.000 \\ \hline \multirow{4}{*}{N = 24} & (Constant) & 0.134 & 0.005 & 24.581 & 0.000 \\  & DS & 0.009 & 0.007 & 1.286 & 0.198 \\  & DV & 0.706 & 0.011 & 64.663 & 0.000 \\  & gender & \(-\)0.010 & 0.002 & \(-\)4.539 & 0.000 \\ \hline \multirow{4}{*}{N = 30} & (Constant) & 0.110 & 0.003 & 42.342 & 0.000 \\  & DS & 0.036 & 0.004 & 9.916 & 0.000 \\ \cline{1-1}  & DV & 0.523 & 0.008 & 69.504 & 0.000 \\ \cline{1-1}  & gender & \(-\)0.003 & 0.002 & \(-\)1.960 & 0.050 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coefficients in the multiple regression models for acceleration.