How to generate two negatively correlated random series of numbers?

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How to generate correlated random numbers (given means, variances and degree of correlation)?

I have been trying to generate two random variables with correlation of -0.9 but have not been successful. I have tried:

x1 <- rnorm(200, mean=0, sd=1)
x2 <- rnorm(200, mean=0, sd=1) 
z <- -0.9*x1+sqrt((1-(-0.9)))*x2
cor(x1,z)

But it did not work.

I tried also the ?mvrnorm function, but it did not work either. How I can get this done??

I don't know why `mvrnorm` didn't work, note that @user603 [demonstrates](http://stats.stackexchange.com/questions/48534/how-to-generate-two-negatively-correlated-random-series-of-numbers/48535#48535) its use properly. Note also that my answer at the linked thread provides a way of generating correlated numbers exactly along the lines you're going for here (although I agree that you don't need to re-invent the wheel). — gung - Reinstate Monica, Jan 25 '13 at 19:33
Your expression in your line of code for `z` is wrong. (Note that even when you get it right, the sample correlation will still vary somewhat from -0.9) — Glen_b, Jan 26 '13 at 03:08

user603 · Answer 1 · 2013-01-25T19:06:14.213

5

Don't re-invent the wheel!

library(MASS)
M<-matrix(-0.9,2,2)
diag(M)<-1
X<-mvrnorm(200,rep(0,2),M,empirical=TRUE)
cor(X)

edited Jan 25 '13 at 19:06

answered Jan 25 '13 at 19:00

user603

1 Answers1