## 3 Results and Discussion
### Analysis of Variance and Regression Analysis
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Response** & **WKU* & **WHAZU* & **WKD* & **WHAZD* & **WKR* & **B* \\ \hline Factor & Coeff. & Coeff. & Coeff. & Coeff. & Coeff. & Coeff. \\ AR & 0.0031 & 0.0021 & \(-\)0.0112 & 0.0003 & \(-\)0.0177 & 0.00487 \\ P & 0.1762 & 0.0451 & 0.3501 & 0.2583 & 0.2847 & \(-\)0.05437 \\ V & \(-\)0.0586 & 0.0168 & \(-\)0.061 & \(-\)0.0110 & \(-\)0.0304 & \(-\)0.00415 \\ Constant & 0.9691 & 0.5613 & 0.6486 & 0.5189 & 0.5699 & 0.22126 \\ R\({}^{2}\) & 71.76\% & 49.14\% & 84.65\% & 46.51\% & 46.74\% & 2.73\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of linear models without interactions (e.g., WKU* = 0.9691 + 0.0031\(\cdot\)AR + 0.1762\(\cdot\)P - 0.0586\(\cdot\)V). Background color was used for statistically significant values for 99% confidence interval. Figure 3: Influence of the main factors: First line (left) WKU* and (right) WHAZU*; second line (left) WKD* and (right) WHAZD*; and last line (left) WKR* and (right) B*. and the width of the cutting kerf WKU\({}^{*}\) decreases with an increasing cutting speed. We can explain this phenomenon by the decreasing amount of energy interacting with the board material per unit time. For this reason, it is necessary to include the interactions between the investigated factors in the model, which correlates with the results of [PERSON] [65] in the case of Scots pine, with [PERSON] [81] in the case of Silver fir, and with [PERSON] et al. [82] in case of cherry wood. On the contrary, the width of the cutting kerf increases with an increasing laser power, which was confirmed in the work of [PERSON] et al. [53] in their research on selected Malaysian wood cutting. If we consider the factor AR, then its effect on WKU\({}^{*}\), although negligible, is directly proportional. In the case of the interaction model of factors for WKU\({}^{*}\), in addition of the factors P and V, the interactions P\({}^{*}\)V and V\({}^{2}\) are also statistically significant. This confirmed the assumption of the mutually important influence of V and P on the cutting kerf width, so these factors significantly affect the amount of absorbed and reflected energy in the board structure, as pointed out by [PERSON] in his work [65] on pine wood cutting, as well as [PERSON] [48]. A statistically significant factor AR in the form of the self-interaction AR\({}^{2}\) already appeared in the interactions model. This is indicated by the fact that the wood density affects the properties of the cutting kerf, which is also stated in the work of [PERSON] [83]. It follows from the results of the analysis of variance for the transformed values of WHAZU\({}^{*}\) that the influence of the cutting speed factor V and the laser power factor P is statistically significant. The influence of the factor AR, which is related to the wood density, was not confirmed by the mathematical-statistical analysis. The significant influence of the speed factor V points to the fact that the cutting speed significantly affects the energy distribution in the cutting process by the radiation beam on the workpiece surface at the point of energy interaction with the material. This is consistent with [PERSON]'s results [65]. This follows from a detailed analysis showing that the cutting speed V and laser power P have the greatest influence on the width value of the heat-affected area on the upper board's surface in comparison with the other investigated factors. In the case of the cutting speed V, the effect is directly proportional, and the width of the heat-affected area WHAZU\({}^{*}\) increases with an increasing cutting speed. The result obtained is in contrast to the findings published in the work of [PERSON] [83], [PERSON] [7], and [PERSON] [45]. The reason for this is that these authors examined the heat-affected area below the surface of cut wood, while the subject of our research was the size of the heat-affected area on the board surface.