## 4 Discussion  
The decrease in the OIT index (OIT100, OIT120) and DPPH value, as well as the increase in the CD concentration in samples LWS and LWE, is proof that the oxidation of lipids has occurred while the wafers were being stored. However, in the case of the LWE samples, the process was slowed down by the fruit extract addition. To gain more insight into the data obtained, the cluster analysis (CA) and regression analysis were performed. The CA was applied to group samples as the unsupervised pattern recognition technique of multivariate analysis on the basis of similarities in clusters. The Ward method and Euclidean distance between centroids were applied. All data was standardized before analysis. The CA dendrogram enabled three distinct clusters at the Distance of Dlink/Dmax = 58% to be determined (Figure 5). Additionally, a heat map was obtained to show the levels of all parameters in the samples (Figure 5). The first cluster includes the LWE samples stored during the first 6 months: 0 LWE, 3 LWE, 6 LWE (0, 3, 6 months of storage, respectively). Those samples showed the highest OIT and DPPH values and the lowest CD concentration (based on the heat map). The second cluster includes LWS samples stored during the first 3 months (0 LWS, 3 LWS) and LWE samples after 8 months (8 LWE) and 10 months (10 LWE) of storage. All other samples were stacked in the third cluster and were characterized by low OIT and DPPH values and high CDs content (as seen from the heat map). Regression analysis was also applied to show the rate of changes of the parameters measured, as shown in Figure 6a-d.  
Figure 5: Heat map with the dendrogram of LWS (standard wafers) and LWE (wafers with fruit extract) samples classified using cluster analysis of similarities. Note: DPPH—antioxidant activity; CD—diene concentration; OIT—oxidation induction time 100 \({}^{\circ}\)C or 120 \({}^{\circ}\)C. Data was standardized. When showing the data as %, it enables comparison of the results between various parameters. For the OIT (OIT100 and OIT120) and DPPH values, segmented regression (piecewise regression) was applied. The breakpoint was set at 6 months. The regression coefficients are shown in Table 2.  
As can be seen from the figures (Figure 6a-d) and Table 2, the rate of changes is significantly higher in standard (LWS) samples than samples treated with extract (LWE) during the first 6 months of storage for the OIT (Figure 6a,b) and DPPH (Figure 6d) parameters or during the whole storage period for CD parameter (Figure 6c). Predicting changes in OIT after the first month of storage based on the equations in Table 2, it can be noticed the OIT100 value of LWS sample will decrease by 5.44% and OIT120 by 14.86%, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & \multicolumn{2}{c}{**LWS**} & \multicolumn{2}{c}{**LWE**} \\ \hline  & \(\beta\) & R\({}^{2}\) & \(\beta\) & R\({}^{2}\) \\ \hline OIT 100 & \(-\)5.44 (\(\leq\)13) & 0.98 & \(-\)2.86 (\(\leq\)6) & 0.98 \\  & & \(-\)6.78 (\(>\)6) & 0.96 \\ \hline OIT 120 & \(-\)14.86 (\(\leq\)6) & 0.91 & \(-\)6.99 (\(\leq\)6) & 0.85 \\  & 0 * (\(>\)6) & 1 & \(-\)0.75 * (\(>\)6) & 1 \\ \hline CDs & 63.03 (\(\leq\)13) & 0.67 & 35.57 (\(\leq\)13) & 0.87 \\ \hline DPPH & \(-\)11.32 (\(\leq\)6) & 0.96 & \(-\)7.85 (\(\leq\)6) & 0.68 \\  & \(-\)5.37 (\(>\)6) & 0.85 & 2.02 * (\(>\)6) & 0.98 \\ \hline \hline \end{tabular}  
* Non-significant coefficient at \(\alpha\) = 0.05.  
\end{table} 
Table 2: Regression coefficients (\(\beta\)) calculated for changes of the parameters (OIT100, OIT120, CD and DPPH) in time. Figure 6: Changes (in %) of (**a**) DSC OIT index measured at 100 \({}^{\circ}\)C, (**b**) DSC OIT index measured at 120 \({}^{\circ}\)C, (**c**) diene concentration (CD) and (**d**) the antioxidant activity (DPPH) in time. whereas for LWE this decrease will be only by 2.86% (OIT100) and 6.99% (OIT120). At the same time, the CDs will increase two times faster in the LWS sample than the LWE.