## 1 Introduction  
Polyphenols are secondary plant metabolites which in recent years showed many potentially positive bioactivities [1; 2; 3]. One of the polyphenol bioactivities not completely investigated yet is their interaction with various food constituents in the digestive tract [4; 5]. Interactions between polyphenols and food constituents can affect polyphenol's accessibility for absorption in the digestive tract (bioaccessibility) or the amount that is being absorbed. This might directly affect bioactivities of polyphenols. That is why the studies of interactions of polyphenols with different food constituents are the focus of present studies [4; 6; 7]. Interactions of polyphenols with food constituents like dietary fibers (cellulose, glucans, etc.) are especially interesting because fibers are resistant to digestion and absorption in the human small intestine. They ferment, completely or partially, in the large intestine [8]. This means that dietary fibers can interact with polyphenols in the digestive tract and potentially \"carry\" them to the lower parts of the digestive tract in non-metabolized form where they can potentially show some positive bioactivities. It has been already shown that polyphenols can interact with cellulose [9; 10; 11], cellulose based composites [7] or xylan [9]. Furthermore, \(\beta\)-glucan is one of common dietary fibers that can be found in certain cereals [12]. Many positive activities of \(\beta\)-glucan on human organism have been found [13; 14; 15], so there are many dietary supplements developed containing \(\beta\)-glucans. Moreover \(\beta\)-glucans can also interact with polyphenols [16; 17]. Better understanding of polyphenol-dietary fiber interactions can be obtained by studying the adsorption process. This is a process in which molecules of polyphenols adsorb onto the surface of dietary fibers. It is known that many factors affect adsorption, like the chemical structure of polyphenols or dietary fibers, the conditions in the environment (pH, temperature and ionic strength) or the food matrix [17; 18; 19; 20]. However, there is still much unknown about polyphenol-dietary fiber interactions (adsorptions). Specifically, there are only a few published papers dealing with \(\beta\)-glucan and polyphenols adsorptions [16; 17; 20; 21; 22; 23]. Since polyphenols are a large group of compounds, many of them have never been studied in the adsorption process with \(\beta\)-glucan. Quercetin derivatives, which belong to a subclass of flavonoids, can be found in plant foods like apples or onions [24; 25]. But, none of the papers have presented results for adsorption of quercetin derivatives onto \(\beta\)-glucan, to the best of our knowledge. Furthermore, when interactions between polyphenols and dietary fibers are studied using the adsorption process, differences in modeling methodology can lead to different results which could affect the explanation of the adsorption process, and consequently the polyphenol-dietary fiber interactions. Experimental results of the adsorption process are modeled with different adsorption isotherm equations [18; 19; 26; 27; 28; 29] to obtain parameters of isotherms and to assist in gaining a theoretical insight into the adsorption process. Depending on whether linear or non-linear modeling is applied, isotherm parameters can be different, which could lead to difficulties in explaining the adsorption process. Linear regression has already shown some usefulness in restricted situations [28]. Traditional non-linear least squares fitting is typically better than linear, depending on the error structure. Nevertheless, as we discuss, in the setting of adsorption measurements, traditional non-linear least squares can also lead to statistical inconsistency and potentially poor interpretation of adsorption and, consequently, potentially poor interpretation of interactions.