## 4 Discussion
### Quadratic Predictive Model
There is a good agreement between the prediction and the linear mathematical model for average values of laser power and gas pressure. The Kerf prediction graph contains the interaction effects of the laser power and the assist gas pressure. Kerf decreases sharply at average values of 5000 W of laser power compared to the average values of gas pressure, but also at minimum laser power with maximum gas pressure. The Kerf response surface contains several interaction effects due to input factors, and the surface area reaches the Kerf value. The prediction graph (Q) is a curved area at maximum values of laser power and gas pressure. The Kerf minimum is achieved at sensible variations compared to the average level of laser power and low gas pressure. The developed mathematical RSM (Q) model shows that the average gas pressure and the average laser power have a Kerf size reduction effect. The curve due to the effects of laser power is steeper than due to the effect of working gas pressure, which means that laser power had a greater effect in reducing Kerf, being the most significant parameter. The gas pressure had a lower effect in terms of Kerf size compared to laser power. These quadratic models of predictability and regression can reduce the cost of the experiment and the working time. The minimum Kerf < 0.32 mm is obtained at \(p\) = 5000 W and the pressure of 0.45 bar, and the maximum Kerf > 0.38 mm results at the maximum power of 5100 W and the cutting gas pressure equal to 0.45 bar. The quadratic model is more complete than the linear model because it contains quadratic interactions of process parameters, linear interactions, and interactions of each type, so it is possible to obtain a better cutting width for Kerf in the case of the straight cut profile. Square RSM (Q) graphs predict and estimate Kerf for average values of laser power and are significantly different for cutting gas pressure due to instability of cutting flow. In any case, maximised laser power and gas pressure damage Kerf due to the accumulation of caloric energy, and the increased gas flow maximises Kerf at minimum values of the energy received from the laser. Kerf is optimized when the technical characteristics chosen are the gas pressure in the range (0.44-0.52 bar) at the same time with the laser power around (4920-5080 W). The quadric model is a restricted mathematical analysis model that requires that the parameters of studied cutting, laser power and gas pressure tend to the average values used in the experiment. As there is relatively good comparative agreement between prediction (Q) and regression (Q), it is possible that other external factors influence the process: temperature in the material, heat gradient, state of the material and chemical composition. Statistical models were developed to validate the Kerf regression equations (linear and quadratic). The effect of each input parameter, the interaction between the parameters, the standard deviation, the Student's \(t\)-test and the probability of error are presented in Table 7.  
From Table 7 provided by the Statistics 7.0 program results: the coefficient of determination R\({}^{2}\) = 0.74211, the adjustment coefficient Adj = 0.16184 and the standard deviation STD = 0.01122. The average cutting width is 0.348 mm resulting from a complete factorial experiment with 27 trials. There is a 7421% chance that the influencing factors and their interactions will determine the cutting width. The adjustment coefficient helps to detail  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Factor**}} & \multicolumn{6}{c}{**Effect Estimates; Var: Kerf (mm); R\({}^{2}\) = 0.74211; Adj: 16184 (Spreadsheet 55) 3 \(\times\) 3-Level Factors. 1 Blocks;**} \\  & \multicolumn{6}{c}{**27 Runs; MS Residual = 0.001134; DV: Kerf (mm)**} \\ \cline{2-10}  & **Effect** & **Std.Err. ** & **t(8)** & \(p\) & \(-\)**95.00\%** & **95.00\%** & **Coeff. ** & **Std.Err.