# Physicochemical and Antioxidant Properties of Selected Polish and Slovak Honeys
## 3 Results and Discussion
### Statistical Discrimination of Honeys
#### 3.2.2 Assessment of OLS Regression Model Fit
The model was constructed using five explanatory variables found to influence antioxidant activity: color parameters \(a^{*}\) and Browning Index (\(BI\)) as well as contents of phloridzin, caffeic acid, and vanillic acid. These variables were selected based on the results of the variance inflation factor (VIF) analysis, which identify and mitigate multicollinearity. Assuming a significance level of 5%, the only statistically significant variable in this model is the Browning Index (\(BI\)). Specifically, a one-unit increase in \(BI\) is associated with an increase in antioxidant activity against DPPH\({}^{*}\) radical of approximately 0.018 mmol/kg, holding all other variables constant. This regression model also shows a strong fit, with an adjusted R\({}^{2}\) value of 0.927. This indicates that 92.7% of the variability in the dependent variable is explained by the independent variables, after accounting for the number of predictors. Based on these findings, the model was simplified using \(BI\) as a single explanatory variable to evaluate its influence on antioxidant activity (Table 3, Equation (4)). \[\mathrm{Y}=0.1590+0.0163\cdot BI \tag{4}\]  
where: Y--ability to scavenge DPPH free radicals; \(BI\)--browning index change. A simplified regression model was developed, indicating that for every one-unit increase in the Browning Index (\(BI\)), antioxidant activity is expected to increase by approximately 0.016 mmol/kg, assuming all other variables remain constant. This model exhibits a strong fit, with an adjusted R\({}^{2}\) value of 0.926, suggesting that 92.6% of the variance in the de \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variable** & **Coefficient** & **Standard Error** & **t-Statistic** & \(p\)**-Value** & **95\% Confidence Interval** \\ \hline const & \(-0.2466\) & 0.1500 & \(-1.6410\) & 0.1100 & \(-0.5520\) & 0.0590 \\ \(a^{*}\) & \(-0.1588\) & 0.0570 & \(-2.8090\) & 0.0080 & \(-0.2740\) & \(-0.0440\) \\ \(b^{*}\) & 0.0377 & 0.0030 & 12.8410 & 0.0000 & 0.0320 & 0.0440 \\ p-coumaric acid & \(-0.0800\) & 0.0180 & \(-4.4140\) & 0.0000 & \(-0.1170\) & \(-0.0430\) \\ vanillic acid & 0.0435 & 0.0160 & 2.6660 & 0.0120 & 0.0100 & 0.0770 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the simplified ABTS\({}^{*+}\) free radical scavenging model as a function of selected variables. pendent variable is explained by the independent variables, even after accounting for model complexity. The final model (Supplementary Materials Table S4, Equation (S3)) was developed to examine the relationship between total polyphenol content (TPC) and specific physicochemical properties of honeys. The model includes six explanatory variables that may influence TPC: the colour parameters \(a^{\star}\) and \(b^{\star}\), and the contents of four polyphenols like phlorlorlain, caffeic acid, quercetin, and vanillic acid, selected based on a Variance Inflation Factor (VIF) analysis to mitigate multicollinearity. At a 5% significance level, the statistically significant variables are the colour parameter \(b^{\star}\) and content of caffeic acid in honey samples. According to the model, a one-unit increase in \(b^{\star}\) is associated with an increase in TPC of approximately 8 mg GAE/kg, holding all other variables constant. An increase in caffeic acid content results in a TPC increase of approximately 15 mg GAE/kg assuming all other variables are held constant. The regression model demonstrates a very strong fit, with an adjusted R\({}^{2}\) value of 0.925. This indicates that 92.5% of the variability in the dependent variable is explained by the independent variables, even after adjusting for the number of predictors. This model was subsequently simplified. The final model (Table 4, Equation (5)) was constructed using two explanatory variables like colour parameter \(b^{\star}\) and content of caffeic in honey samples.