## 3 Results
Previous research carried out on prints made on paper substrates with triticale pulp using the UV inkjet printing process showed a correlation between the penetration depth of the ink and the print-through parameters. Therefore, the analysis of the behavior of these two qualitative parameters together with the integral optical density in this study is based on testing the interdependence of the variables using multiple regression analysis [18]. For the cyan prints, a linear regression analysis was conducted with two independent variables, _Density C_ and _Penetration C_, to evaluate their impact on the dependent variable _Print-through C_ (Table 5). The correlation coefficient (\(R\)) is 0.19670, indicating a very weak negative linear correlation between the independent variables and the dependent variable. However, it still exists, albeit with a very low coefficient of determination (\(R^{2}\)) of 0.03881, explaining only about 3.88% of the variance of the dependent variable. Furthermore, the adjusted \(R^{2}\) is negative, which may be indicative of the model lacking predictive value, as suggested by the \(F\)-test value of 0.74693 with a \(p\)-value of 0.48083, meaning the model as a whole is not statistically significant (\(p>\) 0.05). The intercept coefficient is 12.23850, with a large standard error of 41.73720 and a high \(p\)-value, further confirming the model's lack of statistical significance. The observed independent variable, _Density C_, has a regression coefficient (\(b^{*}\)) of 0.00225 with a high standard error relative to the coefficient itself and a very high \(p\)-value of 0.98908, indicating that _Density C_ is not a statistically significant predictor. Similarly, the independent variable _Penetration C_ is not a statistically significant predictor, having a regression coefficient (\(b^{*}\)) of 0.19659 with a relatively small standard error and a \(p\)-value of 0.23729. The model demonstrates a very low capacity to explain the variability of the dependent variable, and none of the predictors are statistically significant. However, additional predictors (different types of printing substrates) could improve the explanation of the dependent variable. The regression results indicate that none of the variables individually provide a statistically significant contribution to predicting the dependent variable within a linear context. Given the very low \(R^{2}\) and high \(p\)-values for the coefficients, it can be concluded that the linear model is inadequate in explaining the relationship between the independent variables (_Density C_ and _Penetration C_) and the dependent variable (_Print-through C_). Therefore, a non-linear spline model was used for data visualization. Spline models can capture more complex patterns of relationships that are not strictly linear, offering greater flexibility in data modeling. This is because spline interpolation can provide a smoother and potentially more informative representation of the relationships among variables by allowing adjustments to local variations in the data without assuming a specific functional form of the relationship between the variables. The spline model is formulated as follows:  
\[PT=a-b\times x_{1}+c\times{x_{1}}^{2}+d\times x_{2}-e\times{x_{2}}^{2}+f\times x _{1}\times x_{2} \tag{5}\]  
where \(PT\) is the dependent variable _Print-through_; \(x_{1}\) is the independent variable _Density_; \(x_{2}\) is the independent variable _Penetration_; and \(a\), \(b\), \(c\), \(d\), \(e\), and \(f\) are coefficients that are specific to each _Print-through_ variable.