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In recent years, due to environmental awareness regarding the harmfulness of polymeric materials, there has been a growing interest in using papers, especially those from alternative raw materials. The importance of using all available raw materials is imperative today. Raw materials that were once viewed as waste are now of great importance because they have the ability to replace raw materials that are used irrationally or are lacking. Cereal straw is a lignocellulosic material that could be used in the paper industry and in the production of increasingly prevalent paper packaging. The aim of this research was to analyze the relationships between the qualitative parameters of straw-based printed papers containing 30% agricultural residues (wheat, barley, or triticale). The influence of two qualitative parameters (ink penetration depth and optical ink density) on the print-through was observed using multiple regression analysis on straw-based papers produced at the laboratory level. Throughout the research, 100% recycled wood paper was used as a reference sample. The results of the regression analysis showed that none of the variables individually make a statistically significant contribution to the prediction of the dependent variable in a linear context, that is, they indicate a non-linear interaction between the variables and the specific conditions under which the dependent variable reaches local extremes and changes in the gradient. Considering the results of the regression analysis and the visualization of the relationship, the model was additionally tested with other independent variables (paper type). From the results obtained, it can be concluded that the alternative straw-based paper with 30% barley pulp has the best interaction between ink and paper, which is the most similar to the reference sample in terms of printability, while the alternative straw-based paper with 30% wheat generally differs significantly from the reference paper when all three prints are considered. [ABSTRACT FROM AUTHOR]