## 3 Results
The \(F\)-test value of 0.39768 with a \(p\)-value of 0.67472 indicates that the model as a whole is not statistically significant, which once again confirms that the independent variables _Density Y_ and _Penetration Y_ do not explain the variability of _Print-through Y_ any better than a model that does not include these variables. Given that none of the regression coefficients (\(b^{\star}\)) are statistically significant, it can be concluded that there is no statistically significant linear relationship between the independent variables and the dependent variable in the model, that is, the regression model does not provide a significant predictive utility for the dependent variable. Considering the very low \(R^{2}\) and adjusted \(R^{2}\), which suggest that the current linear model does not adequately explain the variability of the dependent variable, a 3D surface plot, specifically a non-linear spline model (Figure 5), has been selected again for the visualization of the relationship between the independent and dependent variables. This 3D surface plot illustrates the complex relationship between two independent variables, _Density Y_ on the X-axis and _Penetration Y_ on the Y-axis, and the dependent variable _Print-through Y_ on the Z-axis. The shape of the surface and its smoothness indicate a non-linear interaction between the variables and the specific conditions under which the dependent variable reaches local extremes and changes in gradient. Considering the results of the regression analysis and the visualization of the relationship between the independent and dependent variables, the model will be further examined with additional independent variables (types of substrates) to assess its predictive power. To compare three alternative types of paper with a 100% wood-based paper as the standard, the paper was used as the reference category in the model, which means that all effect estimates were made in relation to this paper. For this purpose, dummy coding of the categorical variable 'type of paper' was performed in such a way that for reference paper (\(R\)), the dummy variable was assigned a value of 0 to serve as the reference value. Figure 5: 3D surface plot of _Print-through Y_ against _Density Y_ and _Penetration Y_. The Wald test was used because it can be applied to both linear and non-linear models; this test evaluates the significance of individual coefficients (parameters) of the model by squaring the ratio of the estimated parameter to its standard error. Regression analysis of measurement results obtained for cyan (C), magenta (M), and yellow (Y) prints is presented in Table 8.  
The results of the multiple regression analysis for samples printed in each ink (cyan, magenta, and yellow) show the impact of each variable on the print-through (_Print-through C_, _Print-through M_, and _Print-through Y_) using a logarithmic transformation (log link function) due to the normal distribution of responses. By observing the obtained values of the Wald statistics and \(p\)-values, it can be concluded that for the alternative paper 70R30W (Wald statistics = 46.06860 and \(p\) < 0.0001), there is a statistically significant influence of the paper substrate composition on the print-through (_Print-through C_) in comparison to the reference category, that is, the reference paper R. Given the low \(p\)-value, the impact is significant. Furthermore, for the alternative paper 70R30B, the values of Wald statistics (42.59720) with a \(p\)-value < 0.0001 indicate that there is also a statistically significant influence of the paper composition on the print-through (_Print-through C_) in comparison to the reference category. For the third alternative paper 70R30T, by observing the values of Wald statistics and \(p\)-values (Wald statistics = 100.59890 and \(p\) < 0.0001), it has been determined that there is a pronounced statistically significant influence of the paper on the print-through (_Print-through C_) compared to the reference category.