# Stochastic Models to Qualify Stem Tapers
## 3 Results
### Stem Taper and Volume Models
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & **B** & **AB** & **RMSE** & **B** & **AB** & **RMSE** & **RMSE** & **B** & **AB** & **RMSE** & **R2** \\
**Model** & (\%) & (\%) & (\%) & (\%) & (\%) & (\%) & (\%) & **R2** & (\%) & (\%) & (\%) & **(\%)** & **R2** \\ \hline \multirow{2}{*}{**6**} & \(-\).085 & 0.827 & 1.254 & 0.978 & \(-\).054 & 0.837 & 1.182 & 0.976 & \(-\)**0.100** & **0.957** & **1.476** & **0.980** \\  & \((-\).55) & (0.52) & (0.07) & 0.978 & \(-\)(\(-\).49) & 0.837 & 1.182 & 0.976 & \(-\)**(-\(\)**0.600** & **0.570** & **0.892** & **0.980** \\ \hline \multirow{2}{*}{**7**} & \(-\).079 & 0.679 & 1.047 & 0.985 & \(-\)0.150 & 0.705 & 1.012 & 0.983 & \(-\)0.377 & 0.849 & 1.246 & 0.986 \\  & \((-\).051) & (4.37) & (6.47) & (-\(-\).124) & (5.820) & (8.340) & (-\(-\).228) & (5.13) & (7.533) & & \\ \hline \multirow{2}{*}{**8**} & \(-\).085 & 0.834 & 1.273 & 0.978 & \(-\)0.115 & 0.837 & 1.193 & \(-\)0.376 & 1.041 & 1.535 & 0.979 \\  & \((-\).055) & (5.36) & (0.18) & (\(-\)0.95) & (6.82) & (9.86) & (-\(-\).228) & (6.29) & (9.28) & 0.979 \\ \hline \multirow{2}{*}{**9**} & \(-\).017 & 0.850 & 1.200 & 0.977 & \(-\)0.184 & 0.844 & 1.207 & 0.975 & \(-\)0.485 & 1.077 & 1.558 & 0.978 \\  & \((-\).110) & (5.47) & (0.33) & (-\(-\).152) & (6.97) & (9.97) & (-\(-\).250) & (6.51) & (9.41) & 0.978 \\ \hline \multirow{2}{*}{**10**} & \(-\).010 & 0.830 & 1.253 & \(\phantom{-}\)**0.078** & **\(\phantom{-}\)0.084** & **1.199** & **0.975** & \(\phantom{-}\)**-0.231** & **1.019** & **1.490** & **0.980** \\  & \((-\).064) & (5.34) & (8.06) & (\(-\)**0.564**) & (\(\phantom{-}\)**0.700**) & (**0.931**) & **0.975** & \(\phantom{-}\)**  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **B** & **AB** & **RMSE** & **R2** & **B** & **AB** & **RMSE** & **B** & **AB** & **RMSE** & **R2** \\  & **(”s)** & **(”s)** & **(”s)** & **(”s)** & **(”s)** & **(”s)** & **(”s)** & **R2** & **(”s)** & **(”s)** & **(”s)** & **(”s)** & **R2** \\ \hline \multicolumn{11}{c}{**Ash**} & \multicolumn{1}{c}{**Binch**} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ \hline
**1** & **-0.002** & **0.040** & **0.064** & **0.977** & \(-\)0.002 & 0.023 & 0.030 & 0.9  
In Tables 2 and 3, when the validation dataset was used, the values of R\({}^{2}\) and the RMSE were obtained with all three modeling techniques (1. Models 1, 2, 4, 5, 7; 2. Models 3, 6, 8; 3. Models 9-11), show model fitness that is very similar for the both diameter and volume predictions. With the division of the models into three groups, overall, the values of the statistical measures were similar among the SDE models (M3, M6, and M8) and the regression models (M9 to M11), while the SDE models (M1, M2, M4, M5, M7) led to larger R\({}^{2}\) and smaller RMSE values (Tables 2 and 3). With the division into three model groups, the optimal models, M1, M3, and M10 (optimal within each group), were selected based on all statistical measures, the visualization of residuals, and the model simplicity. The volume predictions by the stem taper models had very similar statistical measures (see Table 3). However, the diameter predictions by the SDE taper models that use the additional measurement of the fixed tree diameter at stem height \(h=0\) were superior to the others.