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I have developed this exercise with Excel in another post for the same calculations , I am going to develop it this time with “R”.Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
edad long. peso mg.kg
1 28 31 130.0 68.12
2 24 28 143.0 127.89
3 28 20 136.0 89.03
4 32 34 130.5 78.28
5 22 15 125.0 134.08
6 26 37 147.5 135.31
7 24 19 135.0 130.48
8 28 22 125.0 86.48
9 24 26 127.0 129.47
10 30 21 139.0 82.43
11 22 20 121.5 127.41
12 30 38 150.5 71.21
13 24 17 120.0 132.06
14 26 20 125.0 90.85
We import the data into R.
x<-read.table("C:\\lead_fish.txt",header=TRUE)
We are going to apply the Mahalanobis Distance formula:
D^2 = (x – μ)’ Σ^-1 (x – μ)
We calculate μ (mean) with:
mean<-colMeans(x)
edad long. peso mg.kg
26.28571 24.85714 132.50000 105.93571
26.28571 24.85714 132.50000 105.93571
We calculate Σ (covariance matrix (Sx)) with:
Sx<-cov(x)
> Sx
edad long. peso mg.kg
edad 9.758242 12.81319 12.07692 -72.15407
long. 12.813187 56.90110 49.11538 -70.62066
peso 12.076923 49.11538 92.80769 -46.06962
mg.kg -72.154066 -70.62066 -46.06962 714.00118
edad long. peso mg.kg
edad 9.758242 12.81319 12.07692 -72.15407
long. 12.813187 56.90110 49.11538 -70.62066
peso 12.076923 49.11538 92.80769 -46.06962
mg.kg -72.154066 -70.62066 -46.06962 714.00118
The default value for the Mahalanobis function is inverted=FALSE, so the function will calculate the inverse of Sx. If we calculated appart remember to change to TRUE.
See R help:
O.K. Let´s go:
>D2<-mahalanobis(x,mean,Sx)
> D2
[1] 5.571677 2.863499 2.686127 7.766153 2.379621 6.366793 2.135347 1.538248
[9] 2.018812 5.143830 3.082734 5.470313 3.158651 1.818195
These are the values in the Diagonal Matrix we saw with the calculations in Excel.
[1] 5.571677 2.863499 2.686127 7.766153 2.379621 6.366793 2.135347 1.538248
[9] 2.018812 5.143830 3.082734 5.470313 3.158651 1.818195
These are the values in the Diagonal Matrix we saw with the calculations in Excel.
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