Centering often reduces the correlation between the individual variables (x1, x2) and the product term (x1 (\times) x2). In the example below, r(x1, x1x2) = .80. With the centered variables, r(x1c, x1x2c) = -.15.
NOTE: For examples of when centering may not reduce multicollinearity but may make it worse, see EPM article.
set.seed(123) x1 <- rnorm(100, 10, 1) x2 <- rnorm(100, 15, 1) x1x2 <- x1*x2 x1c <- x1 - mean(x1) x2c <- x2 - mean(x2) x1x2c <- x1c * x2c dat <- data.