How to create a covariance matrix in R?

To create a covariance matrix, we first need to find the correlation matrix and a vector of standard deviations is also required. The correlation matrix can be found by using cor function with matrix object. For example, if we have matrix M then the correlation matrix can be found as cor(M). Now we can use this matrix to find the covariance matrix but we should make sure that we have the vector of standard deviations.

Example1

> M1<-matrix(rnorm(25,5,1),ncol=5)
> M1

Output

       [,1]       [,2]    [,3]     [,4]    [,5]
[1,] 5.446881 3.918951 4.306415 4.446757 5.438095
[2,] 5.174487 4.401736 4.755313 5.341615 5.470727
[3,] 4.042656 6.303782 4.939945 4.847339 4.698141
[4,] 3.931823 6.870019 5.196559 6.692013 3.689279
[5,] 4.800770 4.841470 4.356387 3.508081 3.913045

Example

> cor(M1)

Output

      [,1]         [,2]      [,3]       [,4]     [,5]
[1,] 1.0000000 -0.9908635 -0.8197813 -0.5066590 0.7190219
[2,] -0.9908635 1.0000000 0.8695808 0.6121477  -0.7017947
[3,] -0.8197813 0.8695808 1.0000000 0.8684189  -0.3766508
[4,] -0.5066590 0.6121477 0.8684189 1.0000000  -0.1766397
[5,] 0.7190219 -0.7017947 -0.3766508 -0.1766397 1.0000000

Example

> SD_M1<-rnorm(5)
> M1_Covariance<-(SD_M1%*%t(SD_M1))*cor(M1)
> M1_Covariance

Output

       [,1]        [,2]     [,3]      [,4]     [,5]
[1,] 0.4916487 0.5972772 0.3299963 0.4854532 0.4018740
[2,] 0.5972772 0.7390424 0.4291690 0.7191096 0.4809114
[3,] 0.3299963 0.4291690 0.3295850 0.6812666 0.1723625
[4,] 0.4854532 0.7191096 0.6812666 1.8672751 0.1924034
[5,] 0.4018740 0.4809114 0.1723625 0.1924034 0.6353903

Example2

> M2<-matrix(rnorm(36,5,3),ncol=6)
> M2

Output

    [,1]            [,2]    [,3]     [,4]     [,5]      [,6]
[1,] 3.97345156 2.215491 3.112134 4.6181951 3.6277630 12.322117
[2,] 8.87011312 4.857979 9.067974 6.7924669 5.4123406 3.062662
[3,] 8.70716339 4.905574 5.092897 7.1700455 8.1998048 2.790839
[4,] 2.79704783 8.857838 3.804275 8.0486804 1.8110960 3.789724
[5,] 4.37050111 4.220881 7.835320 -0.9182616 0.5487265 5.676240
[6,] 0.01411185 4.138786 1.736414 6.8982956 4.4729650 6.719265

Example

> cor(M2)

Output

        [,1]        [,2]       [,3]       [,4]      [,5]       [,6]
[1,] 1.00000000 -0.05099798 0.72101949 0.0606742 0.5573581 -0.4634089
[2,] -0.05099798 1.00000000 0.02406821 0.4332765 -0.1929059 -0.6648619
[3,] 0.72101949 0.02406821 1.00000000 -0.3981214 -0.0489995 -0.4858796
[4,] 0.06067420 0.43327648 -0.39812145 1.0000000 0.5885335 -0.2935423
[5,] 0.55735812 -0.19290585 -0.04899950 0.5885335 1.0000000 -0.2820521
[6,] -0.46340892 -0.66486188 -0.48587961 -0.2935423 -0.2820521 1.0000000

Example

> SD_M2<-rnorm(6)
> M2_Covariance<-round((SD_M2%*%t(SD_M2))*cor(M2),2)
> M2_Covariance

Output

     [,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.02 0.00 0.01 0.00 -0.17 -0.10
[2,] 0.00 0.00 0.00 0.00 0.00 -0.01
[3,] 0.01 0.00 0.00 0.00 0.01 -0.04
[4,] 0.00 0.00 0.00 0.01 -0.09 -0.03
[5,] -0.17 0.00 0.01 -0.09 4.10 0.80
[6,] -0.10 -0.01 -0.04 -0.03 0.80 1.95

Example3

> M3<-matrix(runif(36,2,5),ncol=6)
> M3

Output

      [,1]       [,2]     [,3]     [,4]    [,5]     [,6]
[1,] 3.532356 3.325595 2.533484 3.858067 4.209765 4.520970
[2,] 2.836041 4.624075 2.739955 4.294261 2.815741 3.037129
[3,] 2.171741 2.277840 3.939984 3.464941 4.209270 3.565684
[4,] 3.363305 2.623304 2.398647 2.180268 3.740313 3.967784
[5,] 4.637331 2.672298 4.518063 4.851971 2.905769 2.946685
[6,] 3.855836 4.070287 3.698472 4.741746 3.726380 2.603361

Example

> cor(M3)

Output

        [,1]      [,2]       [,3]       [,4]      [,5]     [,6]
[1,] 1.00000000 0.02856209 0.3130817 0.4599297 -0.3979636 -0.2620906
[2,] 0.02856209 1.00000000 -0.3159665 0.4775255 -0.4282192 -0.4020013
[3,] 0.31308166 -0.31596655 1.0000000 0.5990245 -0.2107199 -0.6214000
[4,] 0.45992975 0.47752549 0.5990245 1.0000000 -0.4594787 -0.6584400
[5,] -0.39796357 -0.42821922 -0.2107199 -0.4594787 1.0000000 0.6207340
[6,] -0.26209064 -0.40200135 -0.6214000 -0.6584400 0.6207340 1.0000000

Example

> SD_M3<-runif(6,2,3)
> M3_Covariance<-round((SD_M3%*%t(SD_M3))*cor(M3),4)
> M3_Covariance

Output

[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 8.2937 0.1818 2.7005 3.6199 -3.2048 -1.9410
[2,] 0.1818 4.8857 -2.0918 2.8846 -2.6467 -2.2850
[3,] 2.7005 -2.0918 8.9705 4.9032 -1.7648 -4.7860
[4,] 3.6199 2.8846 4.9032 7.4690 -3.5114 -4.6274
[5,] -3.2048 -2.6467 -1.7648 -3.5114 7.8193 4.4635
[6,] -1.9410 -2.2850 -4.7860 -4.6274 4.4635 6.6127

Example4

> M4<-matrix(rpois(64,10),ncol=8)
> M4

Output

[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 2 12 6 6 20 6 5 13
[2,] 11 14 11 10 13 8 14 9
[3,] 7 10 10 10 13 6 9 13
[4,] 6 15 12 11 9 7 14 11
[5,] 9 14 18 14 13 7 15 15
[6,] 12 12 6 14 9 11 6 5
[7,] 11 9 12 9 10 8 12 3
[8,] 12 15 9 15 8 10 4 9

Example

> round(cor(M4),2)

Output

[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1.00 0.06 0.15 0.69 -0.75 0.80 0.06 -0.63
[2,] 0.06 1.00 0.20 0.48 -0.20 0.20 0.12 0.37
[3,] 0.15 0.20 1.00 0.27 -0.16 -0.32 0.82 0.33
[4,] 0.69 0.48 0.27 1.00 -0.73 0.68 -0.03 -0.08
[5,] -0.75 -0.20 -0.16 -0.73 1.00 -0.68 -0.10 0.54
[6,] 0.80 0.20 -0.32 0.68 -0.68 1.00 -0.37 -0.67
[7,] 0.06 0.12 0.82 -0.03 -0.10 -0.37 1.00 0.15
[8,] -0.63 0.37 0.33 -0.08 0.54 -0.67 0.15 1.00

Example

> SD_M4<-rpois(8,2)
> M4_Covariance<-round((SD_M4%*%t(SD_M4))*cor(M4),2)
> M4_Covariance

Output

[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 4.00 0.12 1.17 1.39 -1.51 3.20 0.24 -2.52
[2,] 0.12 1.00 0.82 0.48 -0.20 0.39 0.24 0.74
[3,] 1.17 0.82 16.00 1.10 -0.63 -2.54 6.56 2.66
[4,] 1.39 0.48 1.10 1.00 -0.73 1.36 -0.06 -0.15
[5,] -1.51 -0.20 -0.63 -0.73 1.00 -1.35 -0.20 1.09
[6,] 3.20 0.39 -2.54 1.36 -1.35 4.00 -1.50 -2.70
[7,] 0.24 0.24 6.56 -0.06 -0.20 -1.50 4.00 0.58
[8,] -2.52 0.74 2.66 -0.15 1.09 -2.70 0.58 4.00