# Functional Characterization of _Saccharomyces_ Yeasts from Cider Produced in Hardanger
## 3 Results and Discussion
### Relationships between Aroma Compounds and Variables
#### 3.6.2 Partial Least Squares (PLS) Regression Analysis
As can be seen in Figure 6, the aroma attributes of ethyl esters of fatty acids, ethyl esters of branched acids, volatile phenols, and C6 alcohols can be used to distinguish the aroma of ciders produced with yeast strains _S. uvarum_ 2401, 2216, 2176, and others in the same cluster. Similarly, the aroma properties of acetate esters can be used to discriminate the aroma of ciders produced with yeast strains _S. cerevisiae_ 2349, _S. uvarum_ 2186, and others in the same cluster. At the same time, yeast strain 2349 was well associated not only with acetate esters but also with the amino acids glutamic acid and glycine, the biogenic amine putrescine, and the sugars fructose and glucose. The ciders of _S. uvarum_ 2046 and _S. cerevisiae_ 2265 showed a high correlation with some attributes, such as the amino acids tyrosine, serine, and glutamine. The analysis showed that the amino acids aspartic acid, tryptophan, and histidine were highly correlated, with tryptophan having greater importance in the model because it had greater (positive) loadings in the first component. It was also observed that for CO\({}_{2}\) release, the amino acids asparagine and methionine were also strongly correlated, with asparagine being of greater importance in the model as it had greater (negative) loadings in the first component. In addition, glucose, tyramine, and malic acid were correlated, but only malic acid was important in the model. On the first component, predictors such as aspartic acid, malic acid, and serine had similar absolute loadings, suggesting that they were equally important. On the second component, H\({}_{2}\)S production, glutamic acid, valine, tartaric acid, and citric acid had similar absolute loadings, indicating that they were equally important (see Figure A4). In addition, the values for the importance of the variables in the projection (VIP) were also obtained in the PLS regression model and shown in Figure 6. These values are a good measure of the importance of each predictor variable in our PLS regression model. They are calculated by considering both the amount of variation in the response variable (five chemical groups of aroma compounds) explained by each latent variable (LV) and the importance (i.e., loading) of each predictor variable in this LV. The VIP values for the 16 predictor variables were \(\geq\)1, including H\({}_{2}\)S production, phenylalanine, asparagine, aspartic acid, tryptophan, histidine, valine, methionine, malic acid, serine, tartaric acid, citric acid, glutamic acid, glutamine, CO\({}_{2}\) release, and proline. These predictor variables with high VIP scores are more important to us than those with low VIP scores. Moreover, these VIP scores are also used for variable selection by selecting only the variables with the highest VIP scores for inclusion in the model (namely, those with VIP \(\geq\) 1). Finally, we proceeded with error analysis of our PLS model using the x-residual matrix plot. To this aim, we examined general patterns in the residuals and identified areas where problems exist. We then examined the x-residuals displayed in the output to determine which observations and predictors the model may be poorly describing. As can be seen in Figure 7, the PLS residual X-plot shows that the residuals are close to zero, indicating that our model does a good job of describing most of the variance in the predictors in our experimental analysis with cider made with 19 _Saccharomyces_ strains. There is no specific line on the graph that deviates dramatically from the other lines; therefore, the model describes all observations/yeast strains (represented by lines) very well. At both points 16 and 28, which correspond to the two predictors lysine and H\({}_{2}\)S, respectively, the lines are far apart. At point 16, the lines are slightly apart at the same point on the x-axis. Therefore, the model can still be considered a good statistical tool to describe the predictor at this point (i.e., lysine).