**4.7 Principal component analysis**

The antioxidant activity is given for 0.075 μM DPPH. Level of significance of the correlations (p < 0.01).

For the variables analyzed (proteolytic activity, total peptide concentration, and antioxidant activity) of the fermented beverages during their shelf life, a correlation coefficient was performed as shown in **Table 4**. The Pearson correlation coefficient is an index that measures the degree of covariation between different linearly related variables, where the correlation between directly proportional variables is positive and inversely proportional negative [38].

In this analysis, it is observed that the correlation between equal variables is positive, because exactly as one variable increases, the other increases [39] because the same data is analyzed in the two axes. The proteolytic activity and the total peptide concentration showed a negative correlation with a value of −0.787, since there is a tendency between the increase in proteolysis and the decrease in the peptide concentration.

### **5. Conclusion**

The analyzed physicochemical parameters of cow and goat milk showed values of a good quality product. The beverages fermented with *Lactobacillus acidophilus*, as well as the controls, presented an acidity higher than the minimum required for commercial yogurts; in addition, no significant variations were observed in the titratable acidity for the two types of milk. Regarding the proteolytic activity, this was significantly augmented during the shelf life of the beverages compared to the antioxidant activity and the peptide concentration, which were decreasing. For the proteolytic activity and the peptide concentration, goat's milk-based beverages had the highest values; however, in the antioxidant activity, cow's milk beverages had the highest percentages of radical inhibition. In the peptide concentration, the controls showed the highest concentration, confirming the effect of the addition of lactobacilli to transform the proteins into different compounds, for which a continuation study is suggested where the volatile compounds that are suggested are quantified they have formed.
