Wine Chemistry and Biochemistry

13 Statistical Techniques for the Interpretation of Analytical Data 709

dure (RMSEP), which are defined by the equationsRMSEC=

√

∑n

i= 1

(yi−ˆyi)^2 /n

andRMSEP=

√

∑n

i= 1

(yi−ˆy(i))^2 /n,whereyiis the observed value ofY,ˆyi,is

the predicted value, and ˆy(i)is the predicted value when the regression model is

constructed without the samplei,andnis the number of samples.RMSEPis a

measure of the model’s ability to predict the values of the response variables in new

samples.

In many cases, it is possible to use only a subset of thepvariablesXwithout

a serious loss predictive ability with theforward stepwise regression(SWMLR)

procedure, which, in each step, selects the predictor that more increases the variation

explained and verifies if a previously selected predictor can be removed (values for

F-statistics to enter and to remove variables should be fixed); or with thebest subsets

regressionprocedure.

Applications

MLR was used to investigate the factors influencing growth and tyramine production

(Marcobal et al. 2006a); SWMLR, PCR and PLS regression have been used to pre-

dict the aging time of the wine samples from the volatile composition (P ́erez-Coello

et al. 1999), and from the nitrogenous fraction (Moreno-Arribas et al. 1998). MLR
was applied to detect the proportion of eachfruit present in mixtures of grape and

apple juices (Dizy et al. 1992). SWMLR has been used: to predict the CIELAB

variables using the colorimetric indices as possible predictor variables (Monagas

et al. 2006b), to predict the foam characteristics of sparkling wines (Moreno-Arribas

et al. 2000), and to find out the phenolic compound that provided the best predictive

model of the antioxidant capacity (Monagas et al. 2005). PLS was used to model

quantitative relationships between foam characteristics and chemical composition

of cava samples (Pueyo et al. 1995). Table 13.24 shows the results of the applica-

tion of PLS regression for the prediction of aging times in wines from five amino

acids in peptides<700-Da fraction (Moreno-Arribas et al. 1998), obtained with The

Unscrambler program version 7.8 (CAMO PROCESS AS, http://www.camo.no/)..)

Figure 13.7 shows the predicted values obtained using the fitted regression equation

Table 13.24Results of PLS regression for prediction of the aging times in wines from five amino
acids in peptides<700 Da fraction

Regresi ́on coefficients: Statistics:

Intercept Aspartic
acid +
asparagine

Threonineα-Alanineγ-Amino

butyric

acid

Ornithine NC R^2 RMSEC RMSEP

4.13513 1.14990 –.77765 –.89973 –.69257 1.07405 2 .968 1.67 1.94

NC=number of components selected by cross-validation, R^2 =determination coefficient,
RMSEC=Root Mean Square Error of Calibration, RMSEP=Root Mean Square Error of Predic-
tion