I realize that, in regression analysis, if there is an interaction term included, it is recommended to center the variables (subtracting variable's mean).
My query is, should we
1) centering variable first, then create the interaction term,
2）create the interaction term first, then centering all variables including the interaction term？
these two operations can give different result， I am wondering which one is correct.
For example, we have 2 independent variables v1 & v2, and an interaction term v1 * v2,
let: v1 <- c(3, 5, 4, 2, 9) v2 <- c(1, 0, 1, 1, 0)
when creating the interaction term, I am confusing which one is correct:
v1*v2 - mean(v1*v2)
 1.2 -1.8 2.2 0.2 -1.8
(v1-mean(v1)) * (v2-mean(v2))
 -0.64 -0.24 -0.24 -1.04 -2.64