# Determination of Seed Volume Based on Selected Seed Dimensions
## 3 Results and Discussion
### Correlation Coefficients  
The correlation coefficients describing the relationship between seed volume coefficient vs. seed dimensions and shape factors are presented in Table 4. The calculated correlation coefficients were statistically significant (minimum 0.666) in 22 out of 60 comparisons, and the absolute value of the correlation coefficient was highest in a comparison of seed volume coefficient \(k_{7}\) and the sphericity index. In turn, the correlation coefficient was lowest in a comparison of seed volume coefficient \(k_{8}\) and the geometric mean diameter. In the group of basic dimensions, seed volume coefficients were most strongly correlated with average seed thickness. However, in most cases (8 out of 10), significant correlations were found between seed volume coefficients and the sphericity index. The sphericity index was the  
Figure 2: Errors in seed volume calculated with simplified formulas.  
only parameter that was significantly correlated with seed volume coefficients \(k_{0}\) and \(k_{4}\). This suggests that formulas based on the sphericity index should be used in calculations when the seed volume coefficient in a given plant species is unknown.  
The relationships between the sphericity index, the volume coefficients of seeds, and linear regression equations are presented in Figure 3. The coefficient of determination was highest for seed volume coefficient \(k_{7}\), followed by seed volume coefficient \(k_{1}\), although high values of this parameter were also noted for seed volume coefficients \(k_{2}\) and \(k_{6}\). These observations suggest that the seed volume coefficient of a new species can be predicted based on the average seed shape factor. Seed volume coefficient \(k_{8}\) will be predicted least accurately. Very strong correlations in the range of 0.9 < r < 0.96 were observed in only 3 out of 10 cases, which confirms the high natural variability of seeds belonging to different plant species [18; 34].  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Indicators**} & \multicolumn{10}{c}{**Seed Volume Coefficient**} \\ \cline{2-11}  & \(k_{0}\) & \(k_{1}\) & \(k_{2}\) & \(k_{3}\) & \(k_{4}\) & \(k_{5}\) & \(k_{6}\) & \(k_{7}\) & \(k_{8}\) & \(k_{9}\) \\ \hline \(L\) & \(-0.627\) & \(-0.374\) & \(-0.429\) & \(-0.452\) & \(0.118\) & \(0.098\) & \(0.431\) & \(-0.301\) & \(-0.277\) & \(0.529\) \\ \(W\) & \(0.167\) & \(0.597\) & \(0.535\) & \(0.454\) & \(-0.512\) & \(-0.352\) & \(-0.571\) & \(0.643\) & \(-0.033\) & \(-0.479\) \\ \(T\) & \(0.528\) & \(\mathbf{0.923}\) & \(\mathbf{0.816}\) & \(\mathbf{0.788}\) & \(-0.608\) & \(-0.501\) & \(\mathbf{-0.823}\) & \(\mathbf{0.946}\) & \(0.124\) & \(\mathbf{-0.761}\) \\ \(D\) & \(0.214\) & \(\mathbf{0.684}\) & \(0.586\) & \(0.524\) & \(-0.541\) & \(-0.405\) & \(-0.604\) & \(\mathbf{0.735}\) & \(-0.022\) & \(-0.503\) \\ \(R\) & \(0.549\) & \(\mathbf{0.851}\) & \(\mathbf{0.805}\) & \(\mathbf{0.762}\) & \(-0.600\) & \(-0.465\) & \(\mathbf{-0.878}\) & \(\mathbf{0.845}\) & \(0.161\) & \(\mathbf{-0.850}\) \\ \(\phi\) & \(\mathbf{0.698}\) & \(\mathbf{0.969}\) & \(\mathbf{0.951}\) & \(\mathbf{0.822}\) & \(\mathbf{-0.711}\) & \(-0.404\) & \(\mathbf{-0.929}\) & \(\mathbf{0.979}\) & \(\mathbf{0.070}\) & \(\mathbf{-0.864}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Correlations between seed volume coefficients vs. dimensions and indicators describing seed shape.