Create a Random Vector With Fixed Correlation With Another Vector

rand_with_cor() creates a vector of random number that has correlation rho with a given vector y. Also mean and standard deviation of the random vector can be fixed by the user. By default, they will be equal to the mean and standard deviation of y, respectively.

Usage

rand_with_cor(y, rho, mu = mean(y), sigma = sd(y))

Source

This solution is based on an answer by whuber on Cross Validated.

Arguments

y

a numeric vector

rho

numeric value between -1 and 1 giving the desired correlation.

mu

numeric value giving the desired mean

sigma

numeric value giving the desired standard deviation

Value

a vector of the same length as y that has correlation rho with y.

Examples

x <- runif(1000, 5, 8)

# create a random vector with positive correlation
y1 <- rand_with_cor(x, 0.8)
all.equal(cor(x, y1), 0.8)
#> [1] TRUE

# create a random vector with negative correlation
# and fixed mean and standard deviation
y2 <- rand_with_cor(x, -0.3, 2, 3)
all.equal(cor(x, y2), -0.3)
#> [1] TRUE
all.equal(mean(y2), 2)
#> [1] TRUE
all.equal(sd(y2), 3)
#> [1] TRUE