How to replace missing values with linear interpolation method in an R vector?

The linear interpolation is a method of fitting a curve using linear polynomials and it helps us to create a new data points but these points lie within the range of the original values for which the linear interpolation is done. Sometimes these values may go a little far from the original values but not too far. In R, if we have some missing values then na.approx function of zoo package can be used to replace the NA with linear interpolation method.

Example1

Loading zoo package:

> library(zoo)
> x1<-sample(c(NA,2,5),10,replace=TRUE)
> x1

Output

[1] 2 2 2 5 2 2 5 NA 2 5

Replacing NA with linear interpolation:

Example

> na.approx(x1)

Output

[1] 2.0 2.0 2.0 5.0 2.0 2.0 5.0 3.5 2.0 5.0

Example2

> x2<-sample(c(NA,1:4),150,replace=TRUE)
> x2

Output

[1] 2 NA NA 2 1 1 NA 2 4 NA 1 2 1 4 3 3 1 3 1 4 4 2 3 1 3
[26] 1 4 2 4 2 1 2 1 3 NA 2 NA 3 1 2 3 3 3 2 4 4 3 3 4 3
[51] 1 4 3 1 4 NA NA NA 2 NA 3 4 NA 2 3 3 1 4 2 4 NA NA 4 3 2
[76] 3 NA 3 NA 4 3 2 3 NA 3 1 1 3 2 NA 1 3 3 NA 3 NA 2 NA 4 1
[101] NA 2 2 4 3 NA 4 NA 2 2 NA 3 2 NA NA 3 NA 3 1 NA 1 NA 1 NA 1
[126] 2 1 3 4 1 4 2 3 NA 3 NA NA 4 NA 2 NA 4 2 3 NA 1 2 1 3 4

Example

> na.approx(x2)

Output

 [1] 2.000000 2.000000 2.000000 2.000000 1.000000 1.000000 1.500000 2.000000
 [9] 4.000000 2.500000 1.000000 2.000000 1.000000 4.000000 3.000000 3.000000
[17] 1.000000 3.000000 1.000000 4.000000 4.000000 2.000000 3.000000 1.000000
[25] 3.000000 1.000000 4.000000 2.000000 4.000000 2.000000 1.000000 2.000000
[33] 1.000000 3.000000 2.500000 2.000000 2.500000 3.000000 1.000000 2.000000
[41] 3.000000 3.000000 3.000000 2.000000 4.000000 4.000000 3.000000 3.000000
[49] 4.000000 3.000000 1.000000 4.000000 3.000000 1.000000 4.000000 3.500000
[57] 3.000000 2.500000 2.000000 2.500000 3.000000 4.000000 3.000000 2.000000
[65] 3.000000 3.000000 1.000000 4.000000 2.000000 4.000000 4.000000 4.000000
[73] 4.000000 3.000000 2.000000 3.000000 3.000000 3.000000 3.500000 4.000000
[81] 3.000000 2.000000 3.000000 3.000000 3.000000 1.000000 1.000000 3.000000
[89] 2.000000 1.500000 1.000000 3.000000 3.000000 3.000000 3.000000 2.500000
[97] 2.000000 3.000000 4.000000 1.000000 1.500000 2.000000 2.000000 4.000000
[105] 3.000000 3.500000 4.000000 3.000000 2.000000 2.000000 2.500000 3.000000
[113] 2.000000 2.333333 2.666667 3.000000 3.000000 3.000000 1.000000 1.000000
[121] 1.000000 1.000000 1.000000 1.000000 1.000000 2.000000 1.000000 3.000000
[129] 4.000000 1.000000 4.000000 2.000000 3.000000 3.000000 3.000000 3.333333
[137] 3.666667 4.000000 3.000000 2.000000 3.000000 4.000000 2.000000 3.000000
[145] 2.000000 1.000000 2.000000 1.000000 3.000000 4.000000

Example3

> x3<-sample(c(NA,rnorm(5)),80,replace=TRUE)
> x3

Output

[1] -0.7419539 -0.7419539 -0.7419539 -0.7419539 NA -0.2225833
[7] -0.7240064 0.8134500 -0.2225833 -0.2225833 0.8134500 -0.7419539
[13] -0.7240064 -0.7419539 -0.7240064 -0.7419539 -0.7240064 0.7383318
[19] NA -0.7240064 0.7383318 0.7383318 NA 0.8134500
[25] -0.2225833 -0.7419539 -0.2225833 0.8134500 0.8134500 NA
[31] -0.2225833 -0.2225833 -0.7240064 -0.2225833 0.7383318 NA
[37] NA -0.7419539 -0.7240064 -0.7240064 -0.7419539 0.7383318
[43] 0.8134500 -0.7240064 0.7383318 0.8134500 0.7383318 0.8134500
[49] 0.7383318 -0.7240064 -0.2225833 -0.7240064 -0.7240064 -0.7240064
[55] 0.7383318 0.7383318 NA -0.2225833 -0.7419539 -0.7419539
[61] 0.8134500 -0.2225833 -0.2225833 0.7383318 -0.2225833 0.8134500
[67] -0.2225833 0.7383318 -0.7240064 0.7383318 NA -0.2225833
[73] 0.7383318 -0.7419539 0.8134500 -0.2225833 NA -0.7240064
[79] -0.2225833 -0.2225833

Example

> na.approx(x3)

Output

[1] -0.741953856 -0.741953856 -0.741953856 -0.741953856 -0.482268589
[6] -0.222583323 -0.724006386 0.813450002 -0.222583323 -0.222583323
[11] 0.813450002 -0.741953856 -0.724006386 -0.741953856 -0.724006386
[16] -0.741953856 -0.724006386 0.738331799 0.007162706 -0.724006386
[21] 0.738331799 0.738331799 0.775890900 0.813450002 -0.222583323
[26] -0.741953856 -0.222583323 0.813450002 0.813450002 0.295433340
[31] -0.222583323 -0.222583323 -0.724006386 -0.222583323 0.738331799
[36] 0.244903247 -0.248525304 -0.741953856 -0.724006386 -0.724006386
[41] -0.741953856 0.738331799 0.813450002 -0.724006386 0.738331799
[46] 0.813450002 0.738331799 0.813450002 0.738331799 -0.724006386
[51] -0.222583323 -0.724006386 -0.724006386 -0.724006386 0.738331799
[56] 0.738331799 0.257874238 -0.222583323 -0.741953856 -0.741953856
[61] 0.813450002 -0.222583323 -0.222583323 0.738331799 -0.222583323
[66] 0.813450002 -0.222583323 0.738331799 -0.724006386 0.738331799
[71] 0.257874238 -0.222583323 0.738331799 -0.741953856 0.813450002
[76] -0.222583323 -0.473294855 -0.724006386 -0.222583323 -0.222583323

Example4

> x4<-sample(c(NA,rpois(20,2)),100,replace=TRUE)
> x4

Output

[1] 3 3 0 2 NA 2 2 2 1 NA 0 1 3 3 3 3 1 1 3 3 1 2 1 1 2
[26] 3 5 5 0 2 1 1 3 2 1 3 2 NA 3 3 0 0 3 3 6 2 3 3 2 3
[51] 3 2 0 NA 2 NA 3 5 NA 0 3 1 5 2 1 NA 3 3 3 2 2 6 5 2 1
[76] 2 1 5 2 3 NA 0 0 2 2 2 0 5 2 3 6 0 3 3 3 3 2 2 3 1

Example

> na.approx(x4)

Output

[1] 3.0 3.0 0.0 2.0 2.0 2.0 2.0 2.0 1.0 0.5 0.0 1.0 3.0 3.0 3.0 3.0 1.0 1.0
[19] 3.0 3.0 1.0 2.0 1.0 1.0 2.0 3.0 5.0 5.0 0.0 2.0 1.0 1.0 3.0 2.0 1.0 3.0
[37] 2.0 2.5 3.0 3.0 0.0 0.0 3.0 3.0 6.0 2.0 3.0 3.0 2.0 3.0 3.0 2.0 0.0 1.0
[55] 2.0 2.5 3.0 5.0 2.5 0.0 3.0 1.0 5.0 2.0 1.0 2.0 3.0 3.0 3.0 2.0 2.0 6.0
[73] 5.0 2.0 1.0 2.0 1.0 5.0 2.0 3.0 1.5 0.0 0.0 2.0 2.0 2.0 0.0 5.0 2.0 3.0
[91] 6.0 0.0 3.0 3.0 3.0 3.0 2.0 2.0 3.0 1.0

Example5

> x5<-sample(c(NA,rpois(5,3)),100,replace=TRUE)
> x5

Output

[1] 3 1 3 6 5 3 5 NA 5 5 3 1 3 1 3 NA 3 5 6 NA 3 3 5 5 3
[26] 5 NA 3 3 3 5 5 NA 5 6 3 1 3 1 3 3 5 NA 5 6 1 3 6 5 5
[51] 1 5 NA 5 NA 1 5 3 1 6 NA 5 1 5 NA NA 6 6 5 1 5 5 NA 3 5
[76] 5 5 5 1 5 NA NA 1 6 5 5 5 5 5 1 5 NA 1 NA 3 NA 3 6 5 1

Example

> na.approx(x5)

Output

 [1] 3.000000 1.000000 3.000000 6.000000 5.000000 3.000000 5.000000 5.000000
 [9] 5.000000 5.000000 3.000000 1.000000 3.000000 1.000000 3.000000 3.000000
[17] 3.000000 5.000000 6.000000 4.500000 3.000000 3.000000 5.000000 5.000000
[25] 3.000000 5.000000 4.000000 3.000000 3.000000 3.000000 5.000000 5.000000
[33] 5.000000 5.000000 6.000000 3.000000 1.000000 3.000000 1.000000 3.000000
[41] 3.000000 5.000000 5.000000 5.000000 6.000000 1.000000 3.000000 6.000000
[49] 5.000000 5.000000 1.000000 5.000000 5.000000 5.000000 3.000000 1.000000
[57] 5.000000 3.000000 1.000000 6.000000 5.500000 5.000000 1.000000 5.000000
[65] 5.333333 5.666667 6.000000 6.000000 5.000000 1.000000 5.000000 5.000000
[73] 4.000000 3.000000 5.000000 5.000000 5.000000 5.000000 1.000000 5.000000
[81] 3.666667 2.333333 1.000000 6.000000 5.000000 5.000000 5.000000 5.000000
[89] 5.000000 1.000000 5.000000 3.000000 1.000000 2.000000 3.000000 3.000000
[97] 3.000000 6.000000 5.000000 1.000000