## 3 Results and Discussion
### Analysis of Variance and Regression Analysis  
A three-factor experimental model without interactions was used to primarily determine the influence of the investigated factors AR, P, and V for responses WKU*, WHAZU*, WKD*, WHAZD*, WKR*, and B*, with an evaluation of the variability degree of the investigated response (Table 4). Additional information on the influence of interactions between factors was analyzed by a second-degree polynomial model with first-order interactions (Table 5). The coefficients of the factors of the examined responses are marked in gray, which are significant in terms of impact at the significance level of 0.05. The force measures of the models are also marked in gray, which can be considered as sufficiently explanatory of the spruce board cutting process. The coefficients of the regression function were determined by the least squares method. The significance of the investigated factors was evaluated by analysis of variance (F test, \(p\) test, R\({}^{2}\), standard deviation, PACH analysis, and percentage error of the model were performed in all cases), graphically by a Pareto diagram, and by a graphical analysis of their influence (Figure 3). \begin{table}
\begin{tabular}{c c} \hline
**Reaction** & **Box-Cox Transformation** \\ \hline WKU* & 1 + (WKU\({}^{-0.569}-1\))/(\(-0.569\cdot 0.847226^{-1.569}\)) \\ WHAZU* & 1 + (WHAZU\({}^{0.134}-1\))/(0.134\(\cdot 0.172185^{-0.866}\)) \\ WKD* & 1 + (WKKD\({}^{0.206}-1\))/(0.206\(\cdot 0.460085^{-0.794}\)) \\ WHAZD* & 1 + (WHAZD\({}^{-0.605}-1\))/(\(-0.605\cdot 0.169228^{-1.605}\)) \\ WKR* & 1 + (WKR\({}^{0.372}-1\))/(0.372\(\cdot 0.543049^{-0.628}\)) \\ B* & 1 + (B\({}^{2.049}-1\))/(2.049\(\cdot 46.4258^{1.049}\)) \\ \hline \end{tabular}
\end{table} 
Table 2: Box-Cox transformation. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **WKU*** & **WHAZU*** & **WKD*** & **WHAZD*** & **WKR*** & **B*** \\ \hline Average & 0.8566 & 0.1741 & 0.5524 & 0.2192 & 0.6337 & 0.4688 \\ Standard deviation & 0.1761 & 0.0657 & 0.2093 & 0.1471 & 0.1709 & 0.0079 \\ Variation coefficient & 20.55\% & 37.75\% & 37.88\% & 67.14\% & 26.97\% & 16.74\% \\ Displacement coefficient & \(-0.42\) & 2.344 & 1.964 & 4.685 & 1.452 & \(-1.328\) \\ Peak coefficient & \(-1.256\) & \(-0.1885\) & \(-0.5222\) & 2.288 & \(-1.079\) & \(-0.657\) \\
95\% confidence interval for the & \(<\)0.8085; & \(<\)0.1561; & \(<\)0.4953; & \(<\)0.1179; & \(<\)0.5870; & \(<\)0.4474; \\ average & 0.9046\(>\) & 0.1920\(\cdot\) & 0.6095\(\cdot\) & 0.2593\(\cdot\) & 0.6803\(\cdot\) & 0.4902\(\cdot\) \\
95\% confidence interval for the & \(<\)0.148; & \(<\)0.0553; & \(<\)0.1759; & \(<\)0.1237; & \(<\)0.1437; & \(<\)0.0660; \\ standard deviation & 0.2174\(\cdot\) & 0.0811\(\cdot\) & 0.2583\(\cdot\) & 0.1816\(\cdot\) & 0.2110\(\cdot\) & 0.0969\(\cdot\) \\ \hline \end{tabular}
\end{table} 
Table 3: Descriptive statistics for transformed values of all parameters. It follows from the table of results on the analysis of variance for WKU* for the transformed values of the cutting kerf width (Table 4) that the influence of the cutting speed factor V and the laser power P is statistically significant. The influence of the AR factor was not confirmed by the mathematical-statistical analysis, which is related to the wood density. The reason for this may be the fact that the thermal conductivity of wood only plays a major role in heat transfer in the phase of penetration of the energy beam into the material, while on the surface, respectively in the phase of energy contact with the board surface, the surface properties of wood are more pronounced, e.g., color, roughness, reflectivity, and the properties of the laboratory environment. The cutting speed has the greatest influence on the value of the width size of the cutting kerf on the upper board's surface. However, this effect is disproportionate,