# 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  
Models describing the relationship between antioxidant activity expressed as the ability to scavenge free radicals ABTS**+** or DPPH**+**, total polyphenol content (TPC), and selected physicochemical properties of honey samples from Poland and Slovakia were developed. In the first model, the dependent variable used in the regression analysis was TEAC\({}_{\text{ABTS}}\)**+**. The model (Supplementary Materials Table S2, Equation (S1)) was based on seven explanatory variables selected through variance inflation factor (VIF) analysis to detect and mitigate multicollinearity. Those selected variables (two color parameters _a_* and _b_* and the content of polyphenols: phloridzin, caffeic acid, quercetin, p-coumaric acid, and vanillic acid) represent various chemical components and factors influencing antioxidant activity. At a significance level of 5%, the statistically significant predictors were _a_*, _b_*, and content of p-coumaric acid and vanillic acid (Supplementary Materials Table S2) in honey samples. According to the model, a one unit increase in the _a_* parameter is associated with a decrease in ABTS**+** radical scavenging capacity by approximately 0.18 mmol/kg, assuming all other variables are held constant. Conversely, a one-unit increase in _b_* is associated with an increase in scavenging ability by approximately 0.03 mmol/kg. Regarding the phenolic compounds, a one-unit increase in p-coumaric acid is expected to decrease ABTS**+** scavenging capacity by approximately 0.09 mmol/kg, while a one-unit increase in vanillic acid is associated with an increase of approximately 0.05 mmol/kg, keeping all other variables at a constant level. The regression model demonstrates good explanatory power, with an adjusted R\({}^{2}\) value of 0.858. This means that 85.8% of the variability in the dependent variable is explained by the model, after accounting for the number of predictors. The above model was subsequently simplified. The revised version (Equation (3)) was constructed using four explanatory variables that influence antioxidant activity: the color parameters _a_* and _b_*, and content of p-coumaric acid and vanillic acid (Table 2). In this case, the simplified regression model equation was as follows:  
\[\mathrm{Y}=-0.2466-0.1588\cdot a^{*}+0.0377\cdot b^{*}-0.0800\cdot\mathrm{p}\text {-coumaric acid}+0.0435\cdot\text{vanillic acid} \tag{3}\]  
where: Y--ability to scavenge ABTS free cation radicals; \(a^{*}\)--color change from greenness, redness; \(b^{*}\)--color change from blueness to yellowness; p-coumaric acid--content of p-coumaric acid; vanillic acid--content of vanillic acid. Assuming a significance level of 5%, the statistically significant variables are \(a^{*}\), \(b^{*}\), and concentration of p-coumaric acid, and vanillic acid. According to the model, for every one-unit increase in \(a^{*}\), the antioxidant activity is expected to decrease by approximately 0.16 mmol/kg, assuming all other variables remain constant. Conversely, a one-unit increase in \(b^{*}\) is associated with an increase in antioxidant activity of approximately 0.04 mmol/kg, again holding all other variables constant. An increase in p-coumaric acid content leads to a decrease in the ABTS\({}^{*+}\) radical scavenging capacity by approximately 0.08 mmol/kg, while an increase in vanillic acid content results in an increase of approximately 0.04 mmol/kg, assuming all other variables are held constant. The regression model demonstrates good explanatory power, with an adjusted R\({}^{2}\) value of 0.858. This indicates that 85.8% of the variance in the dependent variable is explained by the independent variables, after adjusting for the number of predictors. Another model was developed to assess the scavenging activity against DPPH\({}^{*}\) free radicals (Supplementary Materials Table S3, Equation (S2)).