## 2 Experimental Research
### Main Experiment and Analysis of Obtained Results
The coefficient of determination \(\mathrm{R}^{2},0.9557\), is the proportion of explained variability to the total variability. However, a higher value of the coefficient of determination does not necessarily mean that the regression model is good. If new terms are added to the model, the \(\mathrm{R}^{2}\) value will increase, regardless of whether the added term is statistically significant or not. Therefore, there is a possibility that models  
Figure 4: Measuring the thickness of the applied protective layer. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Mean Square** & **Deviation from** & \multirow{2}{*}{**Coefficient of**} & **Adjusted** & **Predicted** \\  & **Deviation,** & **the Model,** & **Determination** & **Coefficient of** & **Coefficient of** \\  & \(p\)**-Value** & \(p\)**-Value** & & **Determination** & **Determination** \\ \hline Linear & \textless{}0.0001 & 0.0039 & 0.7632 & 0.7294 & 0.6826 \\
2 FI & 0.9600 & 0.0023 & 0.7730 & 0.6842 & 0.5764 \\ Quadratic & \textless{}0.0001 & 0.1275 & 0.9557 & 0.9325 & 0.8823 \\ Cubic & 0.0376 & 0.3634 & 0.9845 & 0.9618 & 0.8748 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation of four models in the Design-Expert software—coating thickness. with a high coefficient of determination poorly express the estimate of the new value or the arithmetic mean of the response. Because the R\({}^{2}\) value increases with the addition of new terms to the model, the adjusted coefficient of determination R\({}^{2}_{\text{adj}}\) is also used, which is adjusted for the number of model terms in relation to the number of experimental conditions [22]. The adjusted coefficient of determination R\({}^{2}_{\text{adj}}\), adjusted for the number of model terms in relation to the number of experimental conditions, is 0.9325. The value of the adjusted coefficient of determination will not always increase with the inclusion of new variables in the model. On the contrary, the addition of new insignificant variables will decrease the aforementioned value. A significant difference between R\({}^{2}\) and R\({}^{2}_{\text{adj}}\) indicates that insignificant terms are very likely included in the model [22]. The predicted coefficient of determination R\({}^{2}_{\text{pred}}\) is 0.8823. Since, with the largest coefficient of determination R\({}^{2}\), the difference between R\({}^{2}_{\text{adj}}\) and R\({}^{2}_{\text{pred}}\) is not greater than 0.2, the choice of this quadratic model is justified. Table 6 contains a report obtained from the Design-Expert software for the quadratic model. The dependence of the coating thickness on the input variables in the experiment is shown by the quadratic model. The sum of squares total is the total variation of the value 7331.01. The number of degrees of freedom (df) is 32 (number of data in the experiment: 33 \(-\) 1 = 32). The sum of squares residual is the unexplained variance, a random error, with a residual of 323.79. The number of degrees of freedom for the residual is 21 (number of data minus the number of model members minus 1: 33 \(-\) 11 \(-\) 1 = 21). The mean square residual is 15.42. The sum of squares model is the explained variance, which is 6987.22. The number of degrees of freedom for the model is 11 (11 regression variables). The mean square deviation for the regression model has a value of 635.20. The members of the model A, B, C, A\({}^{2}\) and B\({}^{2}\) are significant in the model (the probabilities for the F variables whose values are 20.65, 263.21, 39.02, 16.14 and 84.75 have \(p\)-values less than 0.05). The other members of the model AB, AC and BC are not significant (the probabilities for the F variables whose values are 0.6877, 1.72 and 0.2502 have \(p\)-values greater than 0.05). The value of the model deviation (lack of fit) is presented here with a probability for the F variable of 0.1275, which indicates that the model's estimate of reality is good.