Group Equation Fitted Equations RMSE ${\beta }_{0}$ ${\beta }_{1}$ ${\beta }_{2}$ ${\beta }_{3}$ Group 1 with $D$ and $\rho$ (a) $\mathrm{ln}\left(AGB\right)={0.136}^{ns}+2.205×\mathrm{ln}\left(D×\rho \right)$ 0.426 1.255 2.205 0 2.205 (b) $\mathrm{ln}\left(AGB\right)=-1.272+2.421×\mathrm{ln}\left(D\right)+\mathrm{ln}\left(\rho \right)$ 0.305 0.294 2.421 0 1.000 (c) $\mathrm{ln}\left(AGB\right)=-1.228+2.418×\mathrm{ln}\left(D\right)+1.071×\mathrm{ln}\left(\rho \right)$ 0.305 0.307 2.418 0 1.071 (d) $\mathrm{ln}\left(AGB\right)=-1.108+1.202×\mathrm{ln}\left({D}^{2}×\rho \right)$ 0.306 0.346 2.404 0 1.202 Group 2 with $D$ , $\rho$ and $H$ (e) $\mathrm{ln}\left(AGB\right)=-2.250+0.925×\mathrm{ln}\left(\rho ×{D}^{2}×H\right)$ 0.338 0.112 1.850 0.925 0.925 (f) $\mathrm{ln}\left(AGB\right)=-2.226+0.926×\mathrm{ln}\left({D}^{2}×H\right)+\mathrm{ln}\rho$ 0.340 0.114 1.852 0.926 1.000 (g) $\mathrm{ln}\left(AGB\right)=-2.362+0.930×\mathrm{ln}\left({D}^{2}×H\right)+0.808×\mathrm{ln}\rho$ 0.337 0.100 1.860 0.930 0.808 (h) $\mathrm{ln}\left(AGB\right)=-1.581+2.273×\mathrm{ln}\left(D\right)+0.259×\mathrm{ln}\left(H\right)+\mathrm{ln}\left(\rho \right)$ 0.299 0.215 2.273 0.259 1.000 (i) $\mathrm{ln}\left(AGB\right)=-1.586+2.273×\mathrm{ln}\left(D\right)+0.260×\mathrm{ln}\left(H\right)+0.995×\mathrm{ln}\left(\rho \right)$ 0.299 0.214 2.273 0.260 0.995 Group 3 with ( $D$ and $\rho$ ) not on power function (j) $\mathrm{ln}\left(AGB\right)=3.241+0.316×{\left(\mathrm{ln}\left(D\right)\right)}^{2}+\mathrm{ln}\left(\rho \right)$ 0.344 27.123 NA 0 1.000 (k) $\mathrm{ln}\left(AGB\right)=3.258+0.316×{\left(\mathrm{ln}\left(D\right)\right)}^{2}+1.031×\mathrm{ln}\left(\rho \right)$ 0.344 27.592 NA 0 1.031 (l) $\mathrm{ln}\left(AGB\right)=4.789+0.053×{\left(\mathrm{ln}\left(D\right)\right)}^{3}+\mathrm{ln}\left(\rho \right)$ 0.421 131.277 NA 0 1.000 (m) $\mathrm{ln}\left(AGB\right)=-1.840+2.729×\mathrm{ln}\left(D\right)-{0.041}^{n.s}×{\left(\mathrm{ln}\left(D\right)\right)}^{2}+\mathrm{ln}\left(\rho \right)$ 0.305 0.166 NA 0 1.000 (n) $\mathrm{ln}\left(AGB\right)=-1.619+2.562×\mathrm{ln}\left(D\right)-{0.003}^{n.s}×{\left(\mathrm{ln}\left(D\right)\right)}^{3}+\mathrm{ln}\left(\rho \right)$ 0.305 0.208 NA 0 1.000 (o) $\mathrm{ln}\left(AGB\right)=-5.783+6.010×\mathrm{ln}\left(D\right)-{0.929}^{n.s}×{\left(\mathrm{ln}\left(D\right)\right)}^{2}+{0.079}^{n.s}×{\left(\mathrm{ln}\left(D\right)\right)}^{3}+\mathrm{ln}\left(\rho \right)$ 0.303 0.003 NA 0 1.000 (p) $\mathrm{ln}\left(AGB\right)=1.517+0.682×{\left(\mathrm{ln}\left(D\right)\right)}^{2}-0.063×{\left(\mathrm{ln}\left(D\right)\right)}^{3}+\mathrm{ln}\left(\rho \right)$ 0.307 4.779 NA 0 1.000