## 3 Results
### Frap  
The antioxidant activity of the extracts measured with the FRAP test was determined at the level from 29.57 to 107.76 \(\upmu\)M TE\(\cdot\)g\({}^{-1}\). In the literature, only [PERSON] and [PERSON] [54] conducted studies to assess the antioxidant activity using the FRAP reagent, but only in relation to hemp seed cake. The antioxidant activity increased as the particle size increased from 0.25 mm to 0.75 mm, and went down as the particle size increased from 0.75 mm to 1.25 mm. The antioxidant activity determined by the FRAP test increased with the rise of the extraction time. A similar tendency was observed as regards the intensity of the applied ultrasound, namely the antioxidant activity by means of the FRAP test increased with the increase of the intensity of the ultrasound during the extraction process (Figure 4). Figure 4: _Cont._  
The highest antioxidant activity was obtained for particle size of 0.75 mm, extraction time of 15 min and ultrasound intensity of 8.6 W\(\cdot\)cm\({}^{-2}\), while the lowest value for particle size of 1.25 mm, time of 5 min and ultrasonic intensity of 8.6 W\(\cdot\)cm\({}^{-2}\). The result of ANOVA analysis showed that the linear effects of particle size, time and intensity, the quadratic term of particle size and the two-level interaction of time and intensity were significant terms for the response FRAP test. However, similar to the case of the DPPH test the quadratic term of this variable demonstrated a negative correlation resulting in a decrease in antioxidant activity after overcoming a certain value. Changes in antioxidant activity determined by the FRAP test can be explained analogously as in the case of the DPPH test. A larger contact surface of the solvent with a particle of plant material is conducive to better extraction of bioactive substances, and thus their higher antioxidant activity of the extracts. A statistically significant effect of particle size on the antioxidant activity determined by the FRAP test was also observed during the extraction of phenolic compounds and _Celosia cristata_ seeds. The growth in particle size from 80 to 100 mesh caused a rise in the FRAP variable by 16.48% [50]. Based on the regression analysis, the equation was adjusted to the empirical data, as shown in Equation (5):  
\[FRAP=-31.79+127.50X_{1}+4.84X_{2}+9.52X_{3}-0.43X_{2}X_{3}-100.92X_{1}^{2} \tag{5}\]  
Equation (5) was verified with ANOVA, as was pointed in Table 3.  
Figure 4: Response surfaces for the FRAP test (uM TE:g\({}^{-1}\)) in hemp extracts depending on the (a) time and size particle, (b) size particle and intensity, (c) intensity and time. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **\(F\)-Value** & **\(p\)-Value** & **Coefficient** \\ \hline Model & 7754.84 & 5 & 1550.97 & 11.44 & 0.0011 & significant \\ X\({}_{1}\) & 1139.76 & 1 & 1139.76 & 8.40 & 0.0176 & +127.50213 \\ X\({}_{2}\) & 1383.28 & 1 & 1383.28 & 10.20 & 0.0109 & +4.84345 \\ X\({}_{3}\) & 2624.75 & 1 & 2624.75 & 19.35 & 0.0017 & +9.51553 \\ X\({}_{2}\)X\({}_{3}\) & 230.77 & 1 & 230.77 & 1.70 & 0.0244 & \(-\)0.434029 \\ X\({}_{1}\)\({}^{2}\) & 2376.28 & 1 & 2376.28 & 17.52 & 0.0024 & \(-\)100.91616 \\ \hline Residual & 1220.51 & 9 & 135.61 & & & \\ \hline Lack of Fit & 1167.95 & 7 & 166.85 & 6.35 & 0.1428 & not significant \\ \hline Pure Error & 52.56 & 2 & 26.28 & & & \\ \hline Cor Total & 8975.35 & 14 & & & & \\ \hline \hline \end{tabular} \({\rm R}^{2}=0.8640\). adj-\({\rm R}^{2}=0.7885\). CV = 17.02. Adeq Precision 10.7189.  
\end{table} 
Table 3: ANOVA results for response: FRAP test. Equation (5) is statistically significant (\(p\) < 0.0011), and the lack of model fit is statistically insignificant (\(p\) > 0.1482), which indicates that the equation was verified correctly. The determination coefficient (0.8640) and adjusted coefficient (0.7885) are rather low and the CV value (17.02%) is quite high, which means that the differences between the empirical and estimated values are not enough satisfactory.