# Statistical Analysis Applied to the Production of Mirto Liqueur
## 3 Results
### Multivariate Analysis
#### 3.1.1 Anthocyanin  
The multivariate analysis relative to the variation of the anthocyanin content shows some interesting aspects. From the analysis of variance (ANOVA), three factors were statistically significant with a \(p\)-value \(<\) 0.05 (Table 3). For the considered system, there is an R-squared of 91.6858%, and a R-squared (adjusted for d.f.) of 75.0573%. The standard error of the estimates corresponds to 0.794119. The mean absolute error (MAE) is 0.360938, with a Durbin-Watson (DW) statistic value of 3.28444 (\(p=0.9963\)). The ANOVA table partitions the variability in anthocyanin into separate pieces for each of the effects. It then tests the statistical significance of each effect by comparing the mean square against an estimate of the experimental error. In this case, three effects have \(p\)-values less than 0.05, indicating that they are significantly different from zero at the 95.0% confidence level. The R-squared statistic indicates that the model as fitted explains 91.6858% of the variability in anthocyanin. The adjusted R-squared statistic, which is more suitable for comparing models with different numbers of independent variables, is 75.0573%. The standard error of the estimate shows the standard deviation of the residuals to be 0.794119. The MAE of 0.360938 is the average value of the residuals. The Durbin-Watson DW statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in the data file. Since the \(p\)-value is greater than 5.0%, there is no indication of serial autocorrelation in the residuals at the 5.0% significance level. The Pareto plot (Figure 1) reports such results in terms of the horizontal bars, indicating which one is statistically relevant for the variation of the anthocyanin content (\(p\)-value textless 0.05 indicated by the vertical line, Figure 1). Looking at the Pareto plot, as expected, the anthocyanin content is affected by the temperature, the ethanol percentage, and the ratio between ethanol and _Myrtus_. It is interesting to notice that the time of extraction has no relevant effect on the anthocyanin content. This represents very useful information for industrial production as it indicates that 20 days should be fine for the complete extraction of anthocyanin, with no advantage of prolonging the extraction protocol to 40 days. The specific effect of each relevant factor can be observed in the so-called main effect plot (Figure 2). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Source** &
\begin{tabular}{c} **Sum of** \\ **Squares** \\ \end{tabular} & **Df** & **Mean Square** & **F-Ratio** & \(p\)**-Value** \\ \hline A: Time & 0.330625 & 1 & 0.330625 & 0.52 & 0.5015 \\ B: v \(\times\) w & 13.8756 & 1 & 13.8756 & 22.00 & 0.0054 \\ C: Temperature & 8.85063 & 1 & 8.85063 & 14.03 & 0.0133 \\ D: \% EtOH & 4.51563 & 1 & 4.51563 & 7.16 & 0.0440 \\ AB & 0.005625 & 1 & 0.005625 & 0.01 & 0.9284 \\ AC & 0.180625 & 1 & 0.180625 & 0.29 & 0.6155 \\ AD & 3.70563 & 1 & 3.70563 & 5.88 & 0.0598 \\ BC & 0.455625 & 1 & 0.455625 & 0.72 & 0.4341 \\ BD & 0.525625 & 1 & 0.525625 & 0.83 & 0.4031 \\ CD & 2.32563 & 1 & 2.32563 & 3.69 & 0.1129 \\ \hline \end{tabular}
\end{table} 
Table 3: Analysis of variance for the anthocyanin content. Figure 1: Pareto plot for the considered factors and their combinations. The main effects plot shows that to higher ethanol content corresponds an increase of the anthocyanin amount. This is related to the ratio between ethanol and myrtle berries' weight according to the Equation (1). Also, low temperatures guarantee a better outcome. This counterintuitive evidence suggests that elevated temperature could promote with time some kind of decomposition of the anthocyanins. Considering the behavior of the factors and their influence on the anthocyanin content, it is possible to conduct a multiple regression and to extract a mathematical equation that describes the system (Equation (1)). \[