13 Statistical Techniques for the Interpretation of Analytical Data 689
Table 13.10Pearson’s correlation coefficients between the color parameters and phenolic
components
Phenolic components CI %yellow %red %blue %dA Tint
Anthocyanin glucosides –0.89∗ –0.96∗ 0.95∗ –0.78∗ 0.95∗ –0.95∗
Acetyl glucoside anthocyanins –0.94∗ –0.94∗ 0.91∗ –0.72 0.91∗ –0.93∗
Cinnamoyl-glucoside anthocyanins –0.89∗ –0.97∗ 0.94∗ –0.75 0.94∗ –0.96∗
Anthocyanin-piruvic acid adducts –0.89∗ –0.99∗ 0.98∗ –0.82∗ 0.98∗ –0.99∗
Anthocyanin-vinylflavanol adducts 0.79∗ 0.80∗ –0.77∗ 0.58 –0.78∗ 0.79∗
Hydroxybenzoic acids –0.80∗ –0.91∗ 0.88∗ –0.69∗ 0.89∗ –0.90∗
Hydroxycinnamic acids 0.87∗ 0.90∗ –0.86∗ –0.62 –0.86∗ 0.88∗
Flavanols –0.80∗ –0.92∗ 0.91∗ –0.76∗ 0.91∗ –0.92∗
Flavonols –0.56 –0.74 0.77∗ –0.74 0.77∗ –0.77∗
CI=Color intensity
∗Correlation significantly different from zero (p<0.05).
acids (Marcobal et al. 2006b), to correlate the autolytic capacity of the strains and
isobutanol production levels (Barcenilla etal. 2003), to examine the linear relation-
ships between chemical composition and foam characteristics in sparkling wines
(Moreno-Arribas et al. 2000), or to confirm the relationship between the wine color
and the phenolic composition during aging time in bottle (Monagas et al. 2006a).
In Table 13.10, Pearson’s correlation coefficients between the color parameters and
phenolic components during aging time inbottle in Tempranillo wines are shown.
Color parameters were significantly correlated (p<0.05) with the majority of
components.
13.2.2 Simple Linear Regression Analysis
The simple linear regression accepts that the variablesX,Yare related by themath-
ematical model Y=β 0 +β 1 X+ε,whereβ 0 is the intercept,β 1 the slope,εthe error
term, which means summarising the dependence ofX(independent variable) onY
(dependent variable) by a straight line (Yˆ =β 0 +β 1 X). The following hypothe-
ses are accepted (Draper and Smith 1981): theXvalues are fixed and measured
without error, and the errors are independent and have a normal distribution with
a common standard deviation for eachXvalue (ε∼N(0,σ)), which means that
the responseYcan be assumed to be normally distributed with a common standard
deviation for eachXvalue (Y∼ N(β 0 +β 1 X,σ)). From the experimental data,
{(xi,yi)}i= 1 ,..,n, the parametersβ 0 and β 1 can beestimatedasb 0 and b 1 ,by
applying thetechnique of least-squares(min
∑n
i= 1(yi−β 0 −β 1 xi)^2 ), according to
b 1 =
∑n
i= 1(xi− ̄x)(yi−y ̄)/
∑n
i= 1(xi−x ̄)^2 andb 0 =y ̄−b 1 x ̄. With these regression
coefficientsb 0 and b 1 it is possible to obtain the fitted value ˆyifor a fixedxivalue
ofX(ˆyi=b 0 +b 1 xi), and the residual ˆyi−yi.