How can centering predictor variables reduce correlation between them? In Statistical Rethinking by Richard McElreath on pg. 320 he states “centering predictors can aid in inference, by reducing correlations among parameters”.  For a linear equation with an interaction term.
What is this supposed to mean? Surely centering a variable will not change its correlation with another variable?
 A: Centering or scaling variables will not change their correlations, however it might change the linear model variance-covariance matrix, for ex.
> library(nlme)
> mod.lm0<-lm(distance~age*Sex,data=Orthodont)
> round(vcov(mod.lm0),2)

              (Intercept)   age SexFemale age:SexFemale
(Intercept)          2.01 -0.18     -2.01          0.18
age                 -0.18  0.02      0.18         -0.02
SexFemale           -2.01  0.18      4.92         -0.43
age:SexFemale        0.18 -0.02     -0.43          0.04

> mod.lm<-lm(distance~scale(age,scale=F)*Sex,data=Orthodont)
> round(vcov(mod.lm),2)

                                (Intercept) scale(age, scale = F) SexFemale scale(age, scale = F):SexFemale
(Intercept)                            0.08                  0.00     -0.08                            0.00
scale(age, scale = F)                  0.00                  0.02      0.00                           -0.02
SexFemale                             -0.08                  0.00      0.20                            0.00
scale(age, scale = F):SexFemale        0.00                 -0.02      0.00                            0.04

