Create a data.frame with a fixed correlation between x and y

create_correlation.r

create_correlation <- function(n=1000, r=0.5) {
  # Based on caracal:s answer at
  # https://stats.stackexchange.com/questions/15011/generate-a-random-variable-with-a-defined-correlation-to-an-existing-variables/15040#15040
  theta <- acos(r)               # corresponding angle
  x1    <- rnorm(n, 1, 1)        # fixed given data
  x2    <- rnorm(n, 2, 0.5)      # new random data
  X     <- cbind(x1, x2)         # matrix
  Xctr  <- scale(X, center=TRUE, scale=FALSE)   # centered columns (mean 0)
  Id   <- diag(n)                               # identity matrix
  Q    <- qr.Q(qr(Xctr[ , 1, drop=FALSE]))      # QR-decomposition, just matrix Q
  P    <- tcrossprod(Q)          # = Q Q'       # projection onto space defined by x1
  x2o  <- (Id-P) %*% Xctr[ , 2]                 # x2ctr made orthogonal to x1ctr
  Xc2  <- cbind(Xctr[ , 1], x2o)                # bind to matrix
  Y    <- Xc2 %*% diag(1/sqrt(colSums(Xc2^2)))  # scale columns to length 1
  y <- Y[ , 2] + (1 / tan(theta)) * Y[ , 1]     # final new vector
  return(data.frame(x=x1, y=y))
}

df <- create_correlation()

cor.test(df$x, df$y)
plot(df)