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Generating a random data set with certain correlations

n.d <- 6
r12 <- .3
r13 <- .4
r23 <- .5
n.var <- length(mu)
mu <- c(0, 0, 2)
stddev <- c(1, 1, 1.2)

corMat <- matrix(c(1, r12, r13,
                   r12, 1, r23,
                   r13, r23, 1),
                 ncol = n.var)
corMat
covMat <- stddev %*% t(stddev) * corMat
covMat
set.seed(1)
library(MASS)
d1 <- mvrnorm(n = n.d, mu = mu, Sigma = covMat, empirical = TRUE)
colMeans(d1)
cor(d1)
plot(d1)

mu <- c(4, 3, 2)
stddev <- c(1.5, 1, .5)

corMat <- matrix(c(1, 0.78, 0.23,
                   0.78, 1, 0.27,
                   0.23, 0.27, 1),
                 ncol = 3)
corMat

covMat <- stddev %*% t(stddev) * corMat
covMat

set.seed(1024)
library(MASS)
d1 <- mvrnorm(n = 100, mu = mu, Sigma = covMat, empirical = TRUE)
colMeans(d1)
cor(d1)