UPDATE: Solution
Thanks to Greg Snow for pointing out the empirical = TRUE command in mvrnorm (multivariate random normal stuff)! Here's the explicit code:
samples = 200
r = 0.83
library('MASS')
data = mvrnorm(n=samples, mu=c(0, 0), Sigma=matrix(c(1, r, r, 1), nrow=2), empirical=TRUE)
X = data[, 1] # standard normal (mu=0, sd=1)
Y = data[, 2] # standard normal (mu=0, sd=1)
# Assess that it works
cor(X, Y) # yay, r = 0.83!
cor(X*0.01 + 42, Y*3 - 1) # Linear transformations of X and Y won't change r.
Original question
I want to generate two variables with (pseudo-) random numbers with an exact pearson's r. How do I do that? Python and/or R solutions would be nice!
samples = 200
r = 0.83
# Generate pearson correlated data with approximately cor(X, Y) = r
import numpy as np
data = np.random.multivariate_normal([0, 0], [[1, r], [r, 1]], size=samples)
X, Y = data[:,0], data[:,1]
# That's it! Now let's take a look at the actual correlation:
import scipy.stats as stats
print 'r=', stats.pearsonr(X, Y)[0]
samples = 200
r = 0.83
# Generate pearson correlated data with approximately cor(X, Y) = r
import numpy as np
data = np.random.multivariate_normal([0, 0], [[1, r], [r, 1]], size=samples)
X, Y = data[:,0], data[:,1]
# That's it! Now let's take a look at the actual correlation:
import scipy.stats as stats
print 'r=', stats.pearsonr(X, Y)[0]
The motivation for knowing r is that I'm testing out (bayesian) statistical models that can infer r from data and they are a lot easier to evaluate when r is well specified.
SOLUTION: thanks to Greg Snow for pointing out the empirical=TRUE command in mvrnorm (multivariate random normal stuff)! Here's the explicit code:
samples = 200
r = 0.83
library('MASS')
data = mvrnorm(n=samples, mu=c(0, 0), Sigma=matrix(c(1, r, r, 1), nrow=2), empirical=TRUE)
X = data[, 1] # standard normal (mu=0, sd=1)
Y = data[, 2] # standard normal (mu=0, sd=1)
cor(X, Y) # yay!
cor(X*0.01 + 42, Y*3 - 1) # Linear transformations of X and Y won't change r.