## 4 Results  
Table 8 shows the different regression models for stem volume estimation. The models were derived using all 178 identified pine trees. In addition to unstandardized regression coefficients also standardized coefficients are listed to analyze the relative importance of the predictors. Moreover the \(t\)-statistic is shown to determine if a variable is making a significant contribution to the model for stem volume estimation (if the value for significance is less than 0.05). The goodness-of-fit of the regressions is given in Table 9 by the coefficient of determination (R2) in addition to the adjusted R2:  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Model**} & **Regression coefficients** & **Unstandardized coefficients** & **Standardized coefficients** & \(t\) & **Significance** \\ \cline{2-6}  & \(\log(\beta_{{}_{0}})\) & \(-\)4.969 & & \(-\)42.141 & 0.000 \\ \cline{2-6}  & \(\log(h)\) & 3.575 & 0.951 & 40.799 & 0.000 \\ \hline \multirow{2}{*}{2} & \(\log(\beta_{{}_{0}})\) & \(-\)2.027 & & \(-\)14.409 & 0.000 \\ \cline{2-6}  & \(\log(cd)\) & 2.686 & 0.709 & 13.327 & 0.000 \\ \hline \multirow{2}{*}{3} & \(\log(\beta_{{}_{0}})\) & \(-\)2.441 & & \(-\)13.911 & 0.000 \\ \cline{2-6}  & \(\log(cv)\) & 1.206 & 0.700 & 13.020 & 0.000 \\ \hline \multirow{2}{*}{4} & \(\log(\beta_{{}_{0}})\) & \(-\)4.876 & & \(-\)48.487 & 0.000 \\ \cline{2-6}  & \(\log(h)\) & 3.101 & 0.825 & 33.162 & 0.000 \\ \cline{2-6}  & \(\log(cd)\) & 0.788 & 0.208 & 8.360 & 0.000 \\ \hline \multirow{2}{*}{5} & \(\log(\beta_{{}_{0}})\) & \(-\)5.011 & & \(-\)49.641 & 0.000 \\ \cline{2-6}  & \(\log(h)\) & 3.119 & 0.830 & 33.279 & 0.000 \\ \cline{2-6}  & \(\log(cv)\) & 0.348 & 0.202 & 8.109 & 0.000 \\ \hline \multirow{2}{*}{6} & \(\log(\beta_{{}_{0}})\) & \(-\)2.257 & & \(-\)12.247 & 0.000 \\ \cline{2-6}  & \(\log(cd)\) & 1.636 & 0.432 & 2.796 & 0.006 \\ \cline{2-6}  & \(\log(cv)\) & 0.507 & 0.295 & 1.910 & 0.058 \\ \hline \multirow{2}{*}{7} & \(\log(\beta_{{}_{0}})\) & \(-\)4.928 & & \(-\)46.315 & 0.000 \\ \cline{2-6}  & \(\log(h)\) & 3.086 & 0.821 & 32.900 & 0.000 \\ \cline{2-6}  & \(\log(cd)\) & 0.499 & 0.132 & 2.258 & 0.025 \\ \cline{2-6}  & \(\log(cv)\) & 0.144 & 0.084 & 1.443 & 0.1 Leave-One-Out Cross-Validation (LOOCV) was used to compare the prediction accuracy of the different regression models. Each single observation (here a tree crown segment) from the original sample was selected as \"validation data\" and the remaining observations (\(n\)-1 out of \(n\) trees) as \"training data\". The prediction accuracy was computed as the absolute and relative root mean square error (RMSE) and Bias. The results are given in Table 10.  
\[RMSE_{CV}\left[m^{3}\right]=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(y_{i}-\hat{y }_{i}^{-1}\right)^{\overline{y}}} \tag{4}\]  
\[Bias_{CV}\left[m^{3}\right]=\frac{1}{n}\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}^{ -1}\right) \tag{5}\]  
\[RMSE_{CV}\left[\%\right]=\frac{RMSE_{CV}}{\overline{y}} \tag{6}\]  
\[Bias_{CV}\left[\%\right]=\frac{Bias_{CV}}{\overline{y}} \tag{7}\]  
\(\hat{y_{i}}^{-I}=\) predicted value of the LOOCV;  
\(y_{i}=\) observed value;  
\(\overline{y}=\) mean of the observed values.  
With respect to the RMSE and Bias model 4 with the tree height and crown diameter as the predictors has shown best performance.