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How to create normal random variables with specific correlation between them in R?
To create normal random variables with specific correlation between them, we can use mvrnorm function of MASS package. For example, if we want to create two variables of size 10 with means equal to 2 and 4 and standard deviation of 0.5 then it can be done by using the command −
mvrnorm(10,mu=c(2,4),Sigma=matrix(c(1,0.5,0.5,1),ncol=2),empirical=TRUE)
Example1
library(MASS) X<-mvrnorm(20,mu=c(5,6),Sigma=matrix(c(1,0.97,0.97,1),ncol=2),empirical=TRUE) X
Output
[,1] [,2] [1,] 4.734045 5.860623 [2,] 3.844051 4.920516 [3,] 4.387584 5.769242 [4,] 5.720935 6.694407 [5,] 5.749076 6.905320 [6,] 4.814826 5.649758 [7,] 5.320584 6.716148 [8,] 5.791732 6.629848 [9,] 6.234083 7.088140 [10,] 4.209064 5.523264 [11,] 4.658825 5.334275 [12,] 6.499547 7.302753 [13,] 6.296104 6.828497 [14,] 4.203930 5.353094 [15,] 3.679087 4.464786 [16,] 3.547234 4.457977 [17,] 6.116487 7.273061 [18,] 4.872711 5.646771 [19,] 3.395766 4.340987 [20,] 5.924329 7.240531
cor(X)
[,1] [,2] [1,] 1.00 0.97 [2,] 0.97 1.00
Example2
Y<-mvrnorm(20,mu=c(100,120),Sigma=matrix(c(1,-0.78,-0.78,1),ncol=2),empirical=TRUE) Y
Output
[,1] [,2] [1,] 100.35035 119.5481 [2,] 98.80491 121.2622 [3,] 100.70750 118.3223 [4,] 100.87404 119.8765 [5,] 101.06911 119.1632 [6,] 99.80321 119.5711 [7,] 98.89158 120.5820 [8,] 98.63285 121.2333 [9,] 100.98014 120.7017 [10,] 98.20288 120.8348 [11,] 98.96695 121.0503 [12,] 99.97610 120.4775 [13,] 99.96563 119.2600 [14,] 100.59370 119.1507 [15,] 100.66358 119.3445 [16,] 101.25303 119.4787 [17,] 100.59732 119.3951 [18,] 99.67970 119.8449 [19,] 101.37637 118.6709 [20,] 98.61106 122.2320
cor(Y)
[,1] [,2] [1,] 1.00 -0.78 [2,] -0.78 1.00
Example3
Z<-mvrnorm(20,mu=c(1,1),Sigma=matrix(c(1,-0.40,-0.40,1),ncol=2),empirical=TRUE) Z
Output
[,1] [,2] [1,] 0.344030694 1.10411548 [2,] 0.922039529 0.24012450 [3,] 0.631725557 2.00128990 [4,] 2.229289991 -0.50200549 [5,] 1.180211078 1.99181844 [6,] 1.012940481 1.49396082 [7,] 2.506394541 1.11997765 [8,] 1.019857403 -0.04125523 [9,] -0.004349292 -0.04837025 [10,] -0.770750258 2.35083803 [11,] -0.368335882 1.29590311 [12,] 1.338721298 2.92684775 [13,] 0.378076422 1.72233721 [14,] 2.650859368 -0.81180597 [15,] 1.355467066 0.37518755 [16,] 2.500790061 0.72880980 [17,] -0.619248618 1.58565187 [18,] 0.924785938 -0.10665410 [19,] 1.196351320 1.06036152 [20,] 1.571143303 1.51286741
cor(Z)
[,1] [,2] [1,] 1.0 -0.4 [2,] -0.4 1.0
Updated on: 06-Mar-2021
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