forecasting 4
simplymathematics
March 3, 2019
Dependencies
library(fpp2)## Loading required package: ggplot2## Loading required package: forecast## Loading required package: fma## Loading required package: expsmoothlibrary(mlbench)
library(plyr)##
## Attaching package: 'plyr'## The following object is masked from 'package:fma':
##
## ozoneProblem 3.1
a
We can use a correlation plot to examine the relationship between the variables and the predicted value.
data(Glass)
pairs(Glass)
We can see that there is a strong linear relationship between Ri and Ca. We also see that the K content is independent of the the other minerals. Likewise, iron is found at all levels with many other minerals in many types of glass. Otherwise, the mineral content with respect to the listed minerals does not appear to be colinear.
b
data(Glass)
sapply(Glass, function(x){
boxplot(as.numeric(x))
})
## RI Na Mg Al Si K
## stats Numeric,5 Numeric,5 Numeric,5 Numeric,5 Numeric,5 Numeric,5
## n 214 214 214 214 214 214
## conf Numeric,2 Numeric,2 Numeric,2 Numeric,2 Numeric,2 Numeric,2
## out Numeric,17 Numeric,7 Numeric,0 Numeric,18 Numeric,12 Numeric,7
## group Numeric,17 Numeric,7 Numeric,0 Numeric,18 Numeric,12 Numeric,7
## names "1" "1" "1" "1" "1" "1"
## Ca Ba Fe Type
## stats Numeric,5 Numeric,5 Numeric,5 Numeric,5
## n 214 214 214 214
## conf Numeric,2 Numeric,2 Numeric,2 Numeric,2
## out Numeric,26 Numeric,38 Numeric,12 Numeric,0
## group Numeric,26 Numeric,38 Numeric,12 Numeric,0
## names "1" "1" "1" "1"We can see from the boxplots, that every variable except Mg has outliers. We can look at density plots to see the distributions. In these plots, we can see that most of the data is skewed right with most data points fairly low, but with some more extreme mineral contents listed.
sapply(Glass, function(x){
plot(density(as.numeric(x)))
})
## $RI
## NULL
##
## $Na
## NULL
##
## $Mg
## NULL
##
## $Al
## NULL
##
## $Si
## NULL
##
## $K
## NULL
##
## $Ca
## NULL
##
## $Ba
## NULL
##
## $Fe
## NULL
##
## $Type
## NULLc
Most of these data vectors are not normal distributions and our model would benefit if there data was transformed using a Box-Cox transformation. The data that has 2 peaks could benefit from a logistic function that bifurcated the data set into one peak or the other. As we can see below, taking the square- or cube-root of the iron vector gives us nicer, bi-modal data. The Box Cox transformation does something even more dramatic..
sq <- Glass$Fe^(1/2)
cub <- Glass$Fe^(1/3)
lambda <- BoxCox.lambda(Glass$Fe)
boxcox <- BoxCox(Glass$Fe, lambda)
plot(density(Glass$Fe))
plot(density(sq))
plot(density(cub))
plot(density(boxcox))
Problem 3.2
a
data("Soybean")
sapply(Soybean, function(x){
barplot(table(x))
})
## $Class
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
## [4,] 4.3
## [5,] 5.5
## [6,] 6.7
## [7,] 7.9
## [8,] 9.1
## [9,] 10.3
## [10,] 11.5
## [11,] 12.7
## [12,] 13.9
## [13,] 15.1
## [14,] 16.3
## [15,] 17.5
## [16,] 18.7
## [17,] 19.9
## [18,] 21.1
## [19,] 22.3
##
## $date
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
## [4,] 4.3
## [5,] 5.5
## [6,] 6.7
## [7,] 7.9
##
## $plant.stand
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $precip
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $temp
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $hail
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $crop.hist
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
## [4,] 4.3
##
## $area.dam
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
## [4,] 4.3
##
## $sever
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $seed.tmt
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $germ
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $plant.growth
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $leaves
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $leaf.halo
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $leaf.marg
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $leaf.size
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $leaf.shread
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $leaf.malf
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $leaf.mild
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $stem
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $lodging
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $stem.cankers
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
## [4,] 4.3
##
## $canker.lesion
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
## [4,] 4.3
##
## $fruiting.bodies
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $ext.decay
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $mycelium
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $int.discolor
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
##
## $sclerotia
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $fruit.pods
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
## [4,] 4.3
##
## $fruit.spots
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1
## [4,] 4.3
##
## $seed
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $mold.growth
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $seed.discolor
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $seed.size
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $shriveling
## [,1]
## [1,] 0.7
## [2,] 1.9
##
## $roots
## [,1]
## [1,] 0.7
## [2,] 1.9
## [3,] 3.1Yes, features 19, 26, 27, 28, 31, 32, 33, 34, and 35 are degenrate, meaning, there is only 1 useful category label for each of these. ### b We can see from the figures below that several of the data vectors have hundreds of missing data points while a couple have very few. In particular, we see that seed.tmt, loding, germ, hail, and sever have the most missing data because they appear to be the hardest to collect.
missing <- sapply(Soybean, function(x){
sum(is.na(x))
})
missing## Class date plant.stand precip
## 0 1 36 38
## temp hail crop.hist area.dam
## 30 121 16 1
## sever seed.tmt germ plant.growth
## 121 121 112 16
## leaves leaf.halo leaf.marg leaf.size
## 0 84 84 84
## leaf.shread leaf.malf leaf.mild stem
## 100 84 108 16
## lodging stem.cankers canker.lesion fruiting.bodies
## 121 38 38 106
## ext.decay mycelium int.discolor sclerotia
## 38 38 38 38
## fruit.pods fruit.spots seed mold.growth
## 84 106 92 92
## seed.discolor seed.size shriveling roots
## 106 92 106 31missing2 <- as.data.frame(missing)
missing2 <- sort(missing2$missing, decreasing = TRUE)
missing2## [1] 121 121 121 121 112 108 106 106 106 106 100 92 92 92 84 84 84
## [18] 84 84 38 38 38 38 38 38 38 36 31 30 16 16 16 1 1
## [35] 0 0table(Soybean$Class, complete.cases(Soybean))##
## FALSE TRUE
## 2-4-d-injury 16 0
## alternarialeaf-spot 0 91
## anthracnose 0 44
## bacterial-blight 0 20
## bacterial-pustule 0 20
## brown-spot 0 92
## brown-stem-rot 0 44
## charcoal-rot 0 20
## cyst-nematode 14 0
## diaporthe-pod-&-stem-blight 15 0
## diaporthe-stem-canker 0 20
## downy-mildew 0 20
## frog-eye-leaf-spot 0 91
## herbicide-injury 8 0
## phyllosticta-leaf-spot 0 20
## phytophthora-rot 68 20
## powdery-mildew 0 20
## purple-seed-stain 0 20
## rhizoctonia-root-rot 0 20c
We can see below that nearly 10% of our rows are incomplete. To make the data more useful for modelling, we can use imputation.
ordered <- unlist(lapply(Soybean, is.ordered))
ordered <- names(ordered)[ordered]
list <- as.character(unique(Soybean$Class[complete.cases(Soybean)]))
complete <- subset(Soybean, Class %in% list)
complete## Class date plant.stand precip temp hail crop.hist
## 1 diaporthe-stem-canker 6 0 2 1 0 1
## 2 diaporthe-stem-canker 4 0 2 1 0 2
## 3 diaporthe-stem-canker 3 0 2 1 0 1
## 4 diaporthe-stem-canker 3 0 2 1 0 1
## 5 diaporthe-stem-canker 6 0 2 1 0 2
## 6 diaporthe-stem-canker 5 0 2 1 0 3
## 7 diaporthe-stem-canker 5 0 2 1 0 2
## 8 diaporthe-stem-canker 4 0 2 1 1 1
## 9 diaporthe-stem-canker 6 0 2 1 0 3
## 10 diaporthe-stem-canker 4 0 2 1 0 2
## 11 charcoal-rot 6 0 0 2 0 1
## 12 charcoal-rot 4 0 0 1 1 1
## 13 charcoal-rot 3 0 0 1 0 1
## 14 charcoal-rot 6 0 0 1 1 3
## 15 charcoal-rot 6 0 0 2 0 1
## 16 charcoal-rot 5 0 0 2 1 3
## 17 charcoal-rot 6 0 0 2 1 0
## 18 charcoal-rot 4 0 0 1 0 2
## 19 charcoal-rot 3 0 0 2 0 2
## 20 charcoal-rot 5 0 0 2 1 2
## 21 rhizoctonia-root-rot 1 1 2 0 0 2
## 22 rhizoctonia-root-rot 1 1 2 0 0 1
## 23 rhizoctonia-root-rot 3 0 2 0 1 3
## 24 rhizoctonia-root-rot 0 1 2 0 0 0
## 25 rhizoctonia-root-rot 0 1 2 0 0 1
## 26 rhizoctonia-root-rot 1 1 2 0 0 3
## 27 rhizoctonia-root-rot 1 1 2 0 0 0
## 28 rhizoctonia-root-rot 2 1 2 0 0 2
## 29 rhizoctonia-root-rot 1 1 2 0 0 1
## 30 rhizoctonia-root-rot 2 1 2 0 0 1
## 31 phytophthora-rot 0 1 2 1 1 1
## 32 phytophthora-rot 1 1 2 1 <NA> 3
## 33 phytophthora-rot 2 1 2 2 <NA> 2
## 34 phytophthora-rot 1 1 2 0 0 2
## 35 phytophthora-rot 2 1 2 2 <NA> 2
## 36 phytophthora-rot 3 1 2 1 <NA> 2
## 37 phytophthora-rot 0 1 1 1 0 1
## 38 phytophthora-rot 3 1 2 0 0 2
## 39 phytophthora-rot 2 1 1 1 <NA> 0
## 40 phytophthora-rot 2 1 2 0 0 1
## 41 phytophthora-rot 2 1 2 1 <NA> 1
## 42 phytophthora-rot 1 1 2 1 <NA> 1
## 43 phytophthora-rot 0 1 2 1 0 3
## 44 phytophthora-rot 0 1 1 1 1 2
## 45 phytophthora-rot 3 1 2 0 0 1
## 46 phytophthora-rot 2 1 2 2 <NA> 3
## 47 phytophthora-rot 0 1 2 1 0 2
## 48 phytophthora-rot 2 1 1 2 <NA> 2
## 49 phytophthora-rot 2 1 2 1 1 1
## 50 phytophthora-rot 0 1 2 1 0 3
## 51 phytophthora-rot 1 1 2 1 0 0
## 52 phytophthora-rot 1 1 2 1 <NA> 0
## 53 phytophthora-rot 3 1 2 1 <NA> 1
## 54 phytophthora-rot 2 1 2 1 <NA> 1
## 55 phytophthora-rot 3 1 2 2 <NA> 2
## 56 phytophthora-rot 1 1 2 1 1 3
## 57 phytophthora-rot 3 1 1 1 <NA> 3
## 58 phytophthora-rot 2 1 2 2 <NA> 1
## 59 phytophthora-rot 3 1 1 2 <NA> 2
## 60 phytophthora-rot 1 1 2 2 <NA> 1
## 61 phytophthora-rot 2 1 2 2 <NA> 3
## 62 phytophthora-rot 3 1 1 1 <NA> 0
## 63 phytophthora-rot 2 1 2 0 0 1
## 64 phytophthora-rot 3 1 1 1 <NA> 1
## 65 phytophthora-rot 2 1 2 2 <NA> 1
## 66 phytophthora-rot 1 1 2 0 0 0
## 67 phytophthora-rot 3 1 2 1 <NA> 2
## 68 phytophthora-rot 3 1 2 1 <NA> 3
## 69 phytophthora-rot 3 1 1 0 0 2
## 70 phytophthora-rot 3 1 2 2 <NA> 2
## 71 brown-stem-rot 4 0 0 1 0 1
## 72 brown-stem-rot 4 0 0 1 0 1
## 73 brown-stem-rot 3 1 0 0 0 3
## 74 brown-stem-rot 5 0 0 2 0 1
## 75 brown-stem-rot 5 0 0 2 0 2
## 76 brown-stem-rot 4 0 0 1 0 3
## 77 brown-stem-rot 5 0 0 1 1 3
## 78 brown-stem-rot 6 0 1 1 1 2
## 79 brown-stem-rot 5 1 0 0 0 3
## 80 brown-stem-rot 5 1 0 1 0 1
## 81 brown-stem-rot 4 0 1 0 1 2
## 82 brown-stem-rot 4 1 0 0 0 3
## 83 brown-stem-rot 4 0 0 1 0 2
## 84 brown-stem-rot 3 1 0 0 0 2
## 85 brown-stem-rot 5 0 0 1 0 3
## 86 brown-stem-rot 4 0 0 1 0 3
## 87 brown-stem-rot 4 0 0 1 0 3
## 88 brown-stem-rot 4 0 0 1 0 1
## 89 brown-stem-rot 4 0 0 1 0 1
## 90 brown-stem-rot 3 0 0 1 0 3
## 91 powdery-mildew 5 0 0 1 1 3
## 92 powdery-mildew 6 0 1 0 1 0
## 93 powdery-mildew 1 1 0 1 0 3
## 94 powdery-mildew 6 1 1 0 0 2
## 95 powdery-mildew 4 1 1 0 0 2
## 96 powdery-mildew 6 0 0 1 1 1
## 97 powdery-mildew 2 1 1 0 0 2
## 98 powdery-mildew 6 1 0 1 0 1
## 99 powdery-mildew 5 1 0 1 0 1
## 100 powdery-mildew 1 1 0 1 0 1
## 101 downy-mildew 6 0 2 0 1 2
## 102 downy-mildew 2 0 2 1 1 1
## 103 downy-mildew 1 0 2 1 1 3
## 104 downy-mildew 4 1 2 2 0 2
## 105 downy-mildew 1 0 2 0 1 0
## 106 downy-mildew 2 1 2 0 0 3
## 107 downy-mildew 2 1 2 1 0 2
## 108 downy-mildew 4 1 2 2 0 2
## 109 downy-mildew 4 1 2 0 0 1
## 110 downy-mildew 5 1 2 1 0 3
## 111 brown-spot 1 1 2 2 1 3
## 112 brown-spot 2 0 2 1 0 2
## 113 brown-spot 2 0 2 1 0 2
## 114 brown-spot 2 0 2 1 0 1
## 115 brown-spot 1 1 2 2 1 3
## 116 brown-spot 1 1 2 1 0 2
## 117 brown-spot 0 1 2 2 1 3
## 118 brown-spot 2 0 2 1 0 2
## 119 brown-spot 1 0 2 1 0 2
## 120 brown-spot 2 1 2 1 0 3
## 121 brown-spot 5 0 2 1 0 2
## 122 brown-spot 1 1 2 1 0 3
## 123 brown-spot 1 0 2 1 0 3
## 124 brown-spot 4 0 2 1 0 1
## 125 brown-spot 1 0 2 1 0 2
## 126 brown-spot 4 1 2 1 0 3
## 127 brown-spot 2 0 2 1 0 3
## 128 brown-spot 0 1 1 1 1 2
## 129 brown-spot 1 1 1 1 1 2
## 130 brown-spot 1 1 2 1 0 1
## 131 brown-spot 1 0 2 1 0 1
## 132 brown-spot 2 0 2 1 0 3
## 133 brown-spot 3 0 2 1 0 2
## 134 brown-spot 2 1 2 2 1 3
## 135 brown-spot 1 0 2 1 0 2
## 136 brown-spot 1 1 2 1 0 2
## 137 brown-spot 5 0 2 1 0 1
## 138 brown-spot 4 1 1 1 1 2
## 139 brown-spot 3 1 2 1 0 1
## 140 brown-spot 1 0 2 1 0 3
## 141 brown-spot 4 0 2 1 0 2
## 142 brown-spot 2 1 2 1 0 2
## 143 brown-spot 2 1 1 1 1 0
## 144 brown-spot 3 1 2 1 0 3
## 145 brown-spot 3 0 2 1 0 3
## 146 brown-spot 2 0 2 1 0 2
## 147 brown-spot 3 0 2 1 0 3
## 148 brown-spot 3 1 2 1 0 3
## 149 brown-spot 2 1 2 1 0 3
## 150 brown-spot 5 1 2 1 0 3
## 151 bacterial-blight 5 0 2 1 1 3
## 152 bacterial-blight 4 0 2 2 1 2
## 153 bacterial-blight 2 0 1 1 0 0
## 154 bacterial-blight 3 0 1 1 0 1
## 155 bacterial-blight 3 0 1 1 0 3
## 156 bacterial-blight 3 0 2 1 1 2
## 157 bacterial-blight 3 0 1 1 0 1
## 158 bacterial-blight 4 0 2 1 1 0
## 159 bacterial-blight 2 0 1 1 0 3
## 160 bacterial-blight 4 1 2 2 1 2
## 161 bacterial-pustule 2 1 1 2 0 2
## 162 bacterial-pustule 3 0 2 0 1 2
## 163 bacterial-pustule 2 0 1 0 0 0
## 164 bacterial-pustule 4 1 2 1 0 3
## 165 bacterial-pustule 3 0 2 1 1 1
## 166 bacterial-pustule 3 1 1 0 0 2
## 167 bacterial-pustule 3 0 1 1 1 2
## 168 bacterial-pustule 3 1 2 1 0 0
## 169 bacterial-pustule 4 0 1 1 1 1
## 170 bacterial-pustule 5 1 1 1 0 2
## 171 purple-seed-stain 6 0 2 0 1 2
## 172 purple-seed-stain 6 0 2 0 0 2
## 173 purple-seed-stain 4 0 2 1 1 1
## 174 purple-seed-stain 4 0 2 1 1 0
## 175 purple-seed-stain 4 0 2 0 0 0
## 176 purple-seed-stain 6 0 2 2 0 2
## 177 purple-seed-stain 3 0 2 0 1 0
## 178 purple-seed-stain 3 0 2 1 1 3
## 179 purple-seed-stain 5 0 2 1 0 1
## 180 purple-seed-stain 4 0 2 1 0 0
## 181 anthracnose 5 1 2 1 0 3
## 182 anthracnose 5 1 2 2 1 2
## 183 anthracnose 6 0 2 1 0 1
## 184 anthracnose 2 1 2 2 1 0
## 185 anthracnose 3 0 2 1 0 3
## 186 anthracnose 4 1 2 2 1 2
## 187 anthracnose 6 0 2 1 0 2
## 188 anthracnose 1 0 2 1 0 1
## 189 anthracnose 6 1 2 1 0 2
## 190 anthracnose 5 0 2 1 0 1
## 191 anthracnose 5 1 2 2 1 3
## 192 anthracnose 0 0 2 1 0 3
## 193 anthracnose 6 0 2 1 0 2
## 194 anthracnose 5 1 2 1 0 1
## 195 anthracnose 5 0 2 1 0 2
## 196 anthracnose 6 1 2 2 1 0
## 197 anthracnose 5 0 2 1 0 1
## 198 anthracnose 6 1 2 2 1 3
## 199 anthracnose 5 1 2 1 0 3
## 200 anthracnose 5 1 2 1 0 2
## 201 phyllosticta-leaf-spot 3 1 1 1 0 0
## 202 phyllosticta-leaf-spot 3 0 0 1 1 0
## 203 phyllosticta-leaf-spot 3 1 1 1 0 0
## 204 phyllosticta-leaf-spot 3 0 0 1 1 2
## 205 phyllosticta-leaf-spot 3 1 1 2 0 3
## 206 phyllosticta-leaf-spot 2 0 0 1 1 0
## 207 phyllosticta-leaf-spot 1 0 0 2 1 3
## 208 phyllosticta-leaf-spot 2 1 1 1 0 2
## 209 phyllosticta-leaf-spot 2 0 0 2 1 3
## 210 phyllosticta-leaf-spot 2 1 1 2 0 3
## 211 alternarialeaf-spot 4 1 2 1 0 1
## 212 alternarialeaf-spot 4 0 1 1 0 3
## 213 alternarialeaf-spot 3 0 2 1 0 0
## 214 alternarialeaf-spot 6 0 2 2 0 3
## 215 alternarialeaf-spot 6 0 1 1 1 2
## 216 alternarialeaf-spot 5 0 2 2 0 3
## 217 alternarialeaf-spot 6 0 1 1 0 3
## 218 alternarialeaf-spot 5 1 2 2 0 3
## 219 alternarialeaf-spot 6 0 2 2 0 3
## 220 alternarialeaf-spot 6 0 2 2 0 3
## 221 alternarialeaf-spot 5 0 2 2 0 2
## 222 alternarialeaf-spot 4 1 2 1 0 3
## 223 alternarialeaf-spot 6 0 2 1 0 1
## 224 alternarialeaf-spot 5 0 2 2 0 2
## 225 alternarialeaf-spot 5 1 2 1 0 0
## 226 alternarialeaf-spot 4 0 2 1 0 2
## 227 alternarialeaf-spot 4 0 2 1 0 1
## 228 alternarialeaf-spot 5 0 2 1 0 2
## 229 alternarialeaf-spot 6 0 2 2 0 3
## 230 alternarialeaf-spot 6 1 2 2 0 1
## 231 alternarialeaf-spot 5 1 2 2 0 3
## 232 alternarialeaf-spot 5 1 2 2 0 3
## 233 alternarialeaf-spot 4 1 2 1 0 2
## 234 alternarialeaf-spot 6 1 1 2 0 2
## 235 alternarialeaf-spot 4 1 2 1 0 1
## 236 alternarialeaf-spot 6 1 2 2 0 2
## 237 alternarialeaf-spot 4 1 2 1 0 0
## 238 alternarialeaf-spot 4 0 2 2 0 3
## 239 alternarialeaf-spot 5 0 2 2 0 2
## 240 alternarialeaf-spot 3 0 2 1 0 0
## 241 alternarialeaf-spot 5 0 2 1 0 1
## 242 alternarialeaf-spot 5 0 2 2 0 1
## 243 alternarialeaf-spot 4 0 2 2 0 1
## 244 alternarialeaf-spot 5 1 2 1 0 3
## 245 alternarialeaf-spot 6 0 2 1 0 2
## 246 alternarialeaf-spot 5 0 2 1 0 0
## 247 alternarialeaf-spot 6 0 2 1 0 0
## 248 alternarialeaf-spot 5 1 2 2 0 2
## 249 alternarialeaf-spot 5 0 2 1 0 3
## 250 alternarialeaf-spot 6 0 2 1 0 1
## 251 frog-eye-leaf-spot 6 0 1 2 0 3
## 252 frog-eye-leaf-spot 4 0 1 2 0 1
## 253 frog-eye-leaf-spot 5 0 1 1 0 2
## 254 frog-eye-leaf-spot 5 1 2 1 0 3
## 255 frog-eye-leaf-spot 6 1 2 2 0 3
## 256 frog-eye-leaf-spot 4 0 1 1 0 3
## 257 frog-eye-leaf-spot 3 0 2 1 0 2
## 258 frog-eye-leaf-spot 5 0 2 2 0 2
## 259 frog-eye-leaf-spot 5 0 2 1 0 1
## 260 frog-eye-leaf-spot 5 0 2 2 0 2
## 261 frog-eye-leaf-spot 5 0 2 1 0 0
## 262 frog-eye-leaf-spot 4 0 2 1 0 2
## 263 frog-eye-leaf-spot 4 0 2 2 0 1
## 264 frog-eye-leaf-spot 4 0 2 1 0 2
## 265 frog-eye-leaf-spot 3 1 2 1 0 3
## 266 frog-eye-leaf-spot 5 0 2 1 0 3
## 267 frog-eye-leaf-spot 5 0 2 2 0 1
## 268 frog-eye-leaf-spot 4 0 2 2 0 1
## 269 frog-eye-leaf-spot 5 0 2 2 0 2
## 270 frog-eye-leaf-spot 5 0 2 1 0 3
## 271 frog-eye-leaf-spot 3 0 2 1 0 1
## 272 frog-eye-leaf-spot 6 0 1 2 0 3
## 273 frog-eye-leaf-spot 5 0 1 1 0 1
## 274 frog-eye-leaf-spot 5 0 2 1 0 3
## 275 frog-eye-leaf-spot 5 1 2 1 0 3
## 276 frog-eye-leaf-spot 3 1 2 1 0 3
## 277 frog-eye-leaf-spot 6 1 2 2 0 3
## 278 frog-eye-leaf-spot 4 0 2 1 0 1
## 279 frog-eye-leaf-spot 4 0 2 2 0 1
## 280 frog-eye-leaf-spot 6 1 2 2 0 3
## 281 frog-eye-leaf-spot 5 1 2 2 0 3
## 282 frog-eye-leaf-spot 4 0 2 1 0 0
## 283 frog-eye-leaf-spot 4 0 2 1 0 2
## 284 frog-eye-leaf-spot 4 1 1 2 0 1
## 285 frog-eye-leaf-spot 4 0 2 1 0 2
## 286 frog-eye-leaf-spot 5 1 2 1 0 1
## 287 frog-eye-leaf-spot 4 0 2 2 0 1
## 288 frog-eye-leaf-spot 5 0 2 1 0 1
## 289 frog-eye-leaf-spot 5 0 2 2 0 2
## 290 frog-eye-leaf-spot 5 1 2 1 0 2
## 308 diaporthe-stem-canker 6 0 2 1 0 1
## 309 diaporthe-stem-canker 3 0 2 1 0 2
## 310 diaporthe-stem-canker 4 0 2 1 0 3
## 311 diaporthe-stem-canker 5 0 2 1 0 1
## 312 diaporthe-stem-canker 3 0 2 1 0 3
## 313 diaporthe-stem-canker 5 0 2 1 0 2
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## 383 phytophthora-rot 2 1 1 1 <NA> 3
## 384 phytophthora-rot 3 1 1 1 <NA> 2
## 385 phytophthora-rot 3 1 1 1 <NA> 3
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## 647 0 0 0dim(complete)## [1] 630 36dim(Soybean)## [1] 683 36We can use a correlation plot to see which variable are colinear and can be combined or eliminated.
data <- sapply(Soybean, as.numeric)
data <- as.data.frame(data)
results <- round(cor(data, use = 'complete.obs'),2)
corrplot:: corrplot(results)
We see that plant growth, leaves, leaf.mard, and leaf.halo are are all strongly colinear. Additionally, canker.lesions, fruiting bodies, and fruit spots are all similarly colinear with mold, seed discoloration, and shriveling. These data points could likely be combined into a singular ‘health’ dummy variable.
Additionally, we can impute data using the K-nearest neighbor model for missing values, which finds the likely value of a data point by looking at the same data point when compared to other vectors. However, a simpler approach is more appropriate for some data points. We can use a variable with high correlation to the data vector in question, compute a linear regression model, and fill in the missing data. The accuracy of that depends entirely on the correlation between two data points. If a data point has no correlation with any of the other vectors (including the target vector), then it’s likely that it can be discarded altogether.