# Effect of Formation Size on Flocking Formation Performance for the Goal Reach Problem
## Appendix B
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multicolumn{10}{c}{**Localization Time**} \\ \hline
**Equation** & \(\mathbf{R^{2}}\) & \multicolumn{4}{c}{**Model Summary**} & \multicolumn{4}{c}{**Parameter Estimates**} \\ \hline  & & **F** & \(\mathbf{df_{1}}\) & \(\mathbf{df_{2}}\) & **Sig** & **Constant** & \(\mathbf{b_{1}}\) & \(\mathbf{b_{2}}\) & \(\mathbf{b_{3}}\) \\ \hline Linear & 0.008 & 1.551 & 1 & 198 & 0.21 & 596.80 & 1.064 & & \\ Logarithmic & 0.003 & 0.621 & 1 & 198 & 0.432 & 593.036 & 27.878 & & \\ Inverse & 0.000 & 0.092 & 1 & 198 & 0.762 & 663.673 & \(-\)284.653 & & \\ Quadratic & 0.018 & 1.819 & 2 & 197 & 0.165 & 133.633 & \(-\)4.277 & 0.049 & 0.049 \\ Cubic & 0.019 & 1.257 & 3 & 196 & 0.290 & 6572.206 & \(-\)1.160 & \(-\)0.041 & 0.001 \\ Exponential & 0.032 & 6.595 & 1 & 198 & 0.011 & 517.037 & 0.003 & & \\ \hline \multicolumn{10}{c}{**Distance to Center of Mass**} \\ \hline
**Equation** & \(\mathbf{R^{2}}\) & \multicolumn{4}{c}{**Model Summary**} & \multicolumn{4}{c}{**Parameter Estimates**} \\ \hline  & **F** & \(\mathbf{df_{1}}\) & \(\mathbf{df_{2}}\) & **Sig** & **Constant** & \(\mathbf{b_{1}}\) & \(\mathbf{b_{2}}\) & \(\mathbf{b_{3}}\) \\ \hline Linear & 0.404 & 134.127 & 1 & 198 & \(<\)0.001 & 5.766 & \(-\)0.011 & & \\ Logarithmic & 0.601 & 298.740 & 1 & 198 & \(<\)0.001 & 7.239 & \(-\)0.541 & & \\ Inverse & 0.697 & 455.018 & 1 & 198 & \(<\)0.001 & 4.724 & 154.01 & & \\ Quadratic & 0.661 & 192.028 & 2 & 197 & \(<\)0.001 & 6.511 & \(-\)0.048 & \(<\)0.000 & \(<\)0.000 \\ Cubic & 0.711 & 160.586 & 3 & 196 & \(<\)0.001 & 7.040 & \(-\)0.095 & 0.001 & \(-\)6.17 \(\times\) 10\({}^{6}\) \\ Exponential & 0.426 & 146.981 & 1 & 198 & \(<\)0.001 & 5.733 & \(-\)0.002 & & \\ \hline \multicolumn{10}{c}{**Collisions per Member**} \\ \hline
**Equation** & \(\mathbf{R^{2}}\) & \multicolumn{4}{c}{**Model Summary**} & \multicolumn{4}{c}{**Parameter Estimates**} \\ \hline  & **F** & \(\mathbf{df_{1}}\) & \(\mathbf{df_{2}}\) & **Sig** & **Constant** & \(\mathbf{b_{1}}\) & \(\mathbf{b_{2}}\) & \(\mathbf{b_{3}}\) \\ \hline Linear & 0.221 & 56.250 & 1 & 198 & \(<\)0.001 & \(-\)0.185 & 0.006 & & \\ Logarithmic & 0.140 & 32.215 & 1 & 198 & \(<\)0.001 & \(-\)0.603 & 0.195 & & \\ Inverse & 0.069 & 14.672 & 1 & 198 & \(<\)0.001 & 0.248 & \(-\)3.628 & & \\ Quadratic & 0.315 & 45.34 & 2 & 197 & \(<\)0.001 & 0.152 & \(-\)0.011 & 0.000 & \\ Cubic & 0.337 & 33.213 & 3 & 196 & \(<\)0.001 & \(-\)0.110 & 0.012 & 0.000 & 3.054 \(\times\) 10\({}^{6}\) \\ Exponential & & & & & & & & \\ \hline \multicolumn{10}{c}{**Separations per Member**} \\ \hline
**Equation** & \(\mathbf{R^{2}}\) & \multicolumn{4}{c}{**Model Summary**} & \multicolumn{4}{c}{**Parameter Estimates**} \\ \hline  & **F** & \(\mathbf{df_{1}}\) & \(\mathbf{df_{2}}\) & **Sig** & **Constant** & \(\mathbf{b_{1}}\) & \(\mathbf{b_{2}}\) & \(\mathbf{b_{3}}\) \\ \hline Linear & 0.650 & 368.184 & 1 & 198 & \(<\)0.001 & \(-\)71.942 & 2.758 & & \\ Logarithmic & 0.452 & 163.134 & 1 & 198 & \(<\)0.001 & \(-\)282.284 & 94.948 & & \\ Inverse & 0.246 & 64.762 & 1 & 198 & \(<\)0.001 & 134.062 & \(-\)1854.17 & & \\ Quadratic & 0.795 & 382.765 & 2 & 197 & \(<\)0.001 & 41.334 & \(-\)2.906 & 0.051 & \\ Cubic & 0.814 & 286.573 & 3 & 196 & \(<\)0.001 & \(-\)24.798 & 2.960 & \(-\)0.076 & 0.001 \\ Exponential & & & & & & & & \\ \hline \multicolumn{10}{c}{**Aigments per Member**} \\ \hline
**Equation** & \(\mathbf{R^{2}}\) & \multicolumn{4}{c}{**Model Summary**} & \multicolumn{4}{c}{**Parameter Estimates**} \\ \hline  & **F** & \(\mathbf{df_{1}}\) & \(\mathbf{df_{2}}\) & **Sig** & **Constant** & \(\mathbf{b_{1}}\) & \(\mathbf{b_{2}}\) & \(\mathbf{b_{3}}\) \\ \hline Linear & 0.015 & 3.001 & 1 & 197 & 0.085 & 692.039 & \(-\)1.389 & & \\ Logarithmic & 0.015 & 2.954 & 1 & 197 & 0.087 & 832.665 & \(-\)56.934 & & \\ Inverse & 0.013 & 2.507 & 1 & 197 & 0.115 & 574.867 & 1388.522 & & \\ Quadratic & 0.015 & 1.498 & 2 & 196 & 0.226 & 699.440 & \(-\)1.760 & 0.003 & \\ Cubic & 0.015 & 0.999 & 3 & 195 & 0.394 & 713.458 & \(-\)3.003 & 0.030 & 0.00 \\ Exponential & 0.008 & 1.660 & 1 & 197 & 0.199 & 604.031 & \(-\)0.001 & & \\ \hline \multicolumn{10}{c}{**Cohesions per Member**} \\ \hline
**Equation** & \(\mathbf{R^{2}}\) & \multicolumn{4}{c}{**Model Summary**} & \multicolumn{4}{c}{**Parameter Estimates**} \\ \hline  & **F** & \(\mathbf{df_{1}}\) & \(\mathbf{df_{2}}\) & **Sig** & **Constant** & \(\mathbf{b_{1}}\) & \(\mathbf{b_{2}}\) & \(\mathbf{b_{3}}\) \\ \hline Linear & 0.725 & 521.941 & 1 & 198 & \(<\)0.001 & \(-\)6.625 & 0.802 & & \\ Logarithmic & 0.536 & 228.370 & 1 & 198 & \(<\)0.001 & \(-\)58.871 & 28.490 & & \\ Inverse & 0.322 & 94.027 & 1 & 198 & \(<\)0.001 & 69.866 & \(-\)583.987 & & \\ Quadratic & 0.840 & 517.244 & 2 & 197 & \(<\)0.001 & 36.426 & \(-\)0.588 & 0.013 & & \\ Cubic & 0.872 & 4