I am trying to generate random data (using R programming) for variables e1,e2,e3 which should have zero correlation with random variable R. Variables e should have zero correlation with each other. The code written for generating variable e with zero correlation with R as follows:

R <- rnorm(120,mean=8,sd=16)

n <- 120 # length of vectors e

rho <- 0 # desired correlation = cos(angle)

nrSamples = 3 # since we have three vectors to estimate (e1,e2,e3)

Id <- diag(n)

theta<- acos(rho) # corresponding angle

e <- list(mode="vector",length=nrSamples)

x <- list(mode="vector",length=nrSamples)

X <- list(mode="vector",length=nrSamples)

Xctr <- list(mode="vector",length=nrSamples)

Q <- list(mode="vector",length=nrSamples)

P <- list(mode="vector",length=nrSamples)

x2o <- list(mode="vector",length=nrSamples)

Xc2 <- list(mode="vector",length=nrSamples)

Y <- list(mode="vector",length=nrSamples)

for (i in 1:nrSamples) {

x[[i]] <- rnorm(n, 0, 2)

X[[i]] <- cbind(R, x[[i]]) # matrix

Xctr[[i]] <- scale(X[[i]], center=TRUE, scale=FALSE) # centered columns(mean 0)

Q[[i]] <- qr.Q(qr(Xctr[[i]][ , 1, drop=FALSE]))

P[[i]] <- tcrossprod(Q[[i]]) # = Q Q' # projection onto space defined by x1

x2o[[i]] <- (Id-P[[i]]) %*% Xctr[[i]][ , 2] # x2ctr made orthogonal to x1ctr

Xc2[[i]] <- cbind(Xctr[[i]][ , 1], x2o[[i]]) # bind to matrix

Y [[i]] <- Xc2[[i]] %*% diag(1/sqrt(colSums(Xc2[[i]]^2)))

e[[i]] <- Y[[i]][ , 2] + (1 / tan(theta)) * Y[[i]][ , 1]

} vector_1 <- e[[1]]

vector_2 <- e[[2]]

vector_3 <- e[[3]]

This code successfully provided three vectors of e with zero correlation with R. I also need to have zero correlation between e vectors but I do not know how. Any help is appreciated