library (MASS)
iris
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosa
## 7 4.6 3.4 1.4 0.3 setosa
## 8 5.0 3.4 1.5 0.2 setosa
## 9 4.4 2.9 1.4 0.2 setosa
## 10 4.9 3.1 1.5 0.1 setosa
## 11 5.4 3.7 1.5 0.2 setosa
## 12 4.8 3.4 1.6 0.2 setosa
## 13 4.8 3.0 1.4 0.1 setosa
## 14 4.3 3.0 1.1 0.1 setosa
## 15 5.8 4.0 1.2 0.2 setosa
## 16 5.7 4.4 1.5 0.4 setosa
## 17 5.4 3.9 1.3 0.4 setosa
## 18 5.1 3.5 1.4 0.3 setosa
## 19 5.7 3.8 1.7 0.3 setosa
## 20 5.1 3.8 1.5 0.3 setosa
## 21 5.4 3.4 1.7 0.2 setosa
## 22 5.1 3.7 1.5 0.4 setosa
## 23 4.6 3.6 1.0 0.2 setosa
## 24 5.1 3.3 1.7 0.5 setosa
## 25 4.8 3.4 1.9 0.2 setosa
## 26 5.0 3.0 1.6 0.2 setosa
## 27 5.0 3.4 1.6 0.4 setosa
## 28 5.2 3.5 1.5 0.2 setosa
## 29 5.2 3.4 1.4 0.2 setosa
## 30 4.7 3.2 1.6 0.2 setosa
## 31 4.8 3.1 1.6 0.2 setosa
## 32 5.4 3.4 1.5 0.4 setosa
## 33 5.2 4.1 1.5 0.1 setosa
## 34 5.5 4.2 1.4 0.2 setosa
## 35 4.9 3.1 1.5 0.2 setosa
## 36 5.0 3.2 1.2 0.2 setosa
## 37 5.5 3.5 1.3 0.2 setosa
## 38 4.9 3.6 1.4 0.1 setosa
## 39 4.4 3.0 1.3 0.2 setosa
## 40 5.1 3.4 1.5 0.2 setosa
## 41 5.0 3.5 1.3 0.3 setosa
## 42 4.5 2.3 1.3 0.3 setosa
## 43 4.4 3.2 1.3 0.2 setosa
## 44 5.0 3.5 1.6 0.6 setosa
## 45 5.1 3.8 1.9 0.4 setosa
## 46 4.8 3.0 1.4 0.3 setosa
## 47 5.1 3.8 1.6 0.2 setosa
## 48 4.6 3.2 1.4 0.2 setosa
## 49 5.3 3.7 1.5 0.2 setosa
## 50 5.0 3.3 1.4 0.2 setosa
## 51 7.0 3.2 4.7 1.4 versicolor
## 52 6.4 3.2 4.5 1.5 versicolor
## 53 6.9 3.1 4.9 1.5 versicolor
## 54 5.5 2.3 4.0 1.3 versicolor
## 55 6.5 2.8 4.6 1.5 versicolor
## 56 5.7 2.8 4.5 1.3 versicolor
## 57 6.3 3.3 4.7 1.6 versicolor
## 58 4.9 2.4 3.3 1.0 versicolor
## 59 6.6 2.9 4.6 1.3 versicolor
## 60 5.2 2.7 3.9 1.4 versicolor
## 61 5.0 2.0 3.5 1.0 versicolor
## 62 5.9 3.0 4.2 1.5 versicolor
## 63 6.0 2.2 4.0 1.0 versicolor
## 64 6.1 2.9 4.7 1.4 versicolor
## 65 5.6 2.9 3.6 1.3 versicolor
## 66 6.7 3.1 4.4 1.4 versicolor
## 67 5.6 3.0 4.5 1.5 versicolor
## 68 5.8 2.7 4.1 1.0 versicolor
## 69 6.2 2.2 4.5 1.5 versicolor
## 70 5.6 2.5 3.9 1.1 versicolor
## 71 5.9 3.2 4.8 1.8 versicolor
## 72 6.1 2.8 4.0 1.3 versicolor
## 73 6.3 2.5 4.9 1.5 versicolor
## 74 6.1 2.8 4.7 1.2 versicolor
## 75 6.4 2.9 4.3 1.3 versicolor
## 76 6.6 3.0 4.4 1.4 versicolor
## 77 6.8 2.8 4.8 1.4 versicolor
## 78 6.7 3.0 5.0 1.7 versicolor
## 79 6.0 2.9 4.5 1.5 versicolor
## 80 5.7 2.6 3.5 1.0 versicolor
## 81 5.5 2.4 3.8 1.1 versicolor
## 82 5.5 2.4 3.7 1.0 versicolor
## 83 5.8 2.7 3.9 1.2 versicolor
## 84 6.0 2.7 5.1 1.6 versicolor
## 85 5.4 3.0 4.5 1.5 versicolor
## 86 6.0 3.4 4.5 1.6 versicolor
## 87 6.7 3.1 4.7 1.5 versicolor
## 88 6.3 2.3 4.4 1.3 versicolor
## 89 5.6 3.0 4.1 1.3 versicolor
## 90 5.5 2.5 4.0 1.3 versicolor
## 91 5.5 2.6 4.4 1.2 versicolor
## 92 6.1 3.0 4.6 1.4 versicolor
## 93 5.8 2.6 4.0 1.2 versicolor
## 94 5.0 2.3 3.3 1.0 versicolor
## 95 5.6 2.7 4.2 1.3 versicolor
## 96 5.7 3.0 4.2 1.2 versicolor
## 97 5.7 2.9 4.2 1.3 versicolor
## 98 6.2 2.9 4.3 1.3 versicolor
## 99 5.1 2.5 3.0 1.1 versicolor
## 100 5.7 2.8 4.1 1.3 versicolor
## 101 6.3 3.3 6.0 2.5 virginica
## 102 5.8 2.7 5.1 1.9 virginica
## 103 7.1 3.0 5.9 2.1 virginica
## 104 6.3 2.9 5.6 1.8 virginica
## 105 6.5 3.0 5.8 2.2 virginica
## 106 7.6 3.0 6.6 2.1 virginica
## 107 4.9 2.5 4.5 1.7 virginica
## 108 7.3 2.9 6.3 1.8 virginica
## 109 6.7 2.5 5.8 1.8 virginica
## 110 7.2 3.6 6.1 2.5 virginica
## 111 6.5 3.2 5.1 2.0 virginica
## 112 6.4 2.7 5.3 1.9 virginica
## 113 6.8 3.0 5.5 2.1 virginica
## 114 5.7 2.5 5.0 2.0 virginica
## 115 5.8 2.8 5.1 2.4 virginica
## 116 6.4 3.2 5.3 2.3 virginica
## 117 6.5 3.0 5.5 1.8 virginica
## 118 7.7 3.8 6.7 2.2 virginica
## 119 7.7 2.6 6.9 2.3 virginica
## 120 6.0 2.2 5.0 1.5 virginica
## 121 6.9 3.2 5.7 2.3 virginica
## 122 5.6 2.8 4.9 2.0 virginica
## 123 7.7 2.8 6.7 2.0 virginica
## 124 6.3 2.7 4.9 1.8 virginica
## 125 6.7 3.3 5.7 2.1 virginica
## 126 7.2 3.2 6.0 1.8 virginica
## 127 6.2 2.8 4.8 1.8 virginica
## 128 6.1 3.0 4.9 1.8 virginica
## 129 6.4 2.8 5.6 2.1 virginica
## 130 7.2 3.0 5.8 1.6 virginica
## 131 7.4 2.8 6.1 1.9 virginica
## 132 7.9 3.8 6.4 2.0 virginica
## 133 6.4 2.8 5.6 2.2 virginica
## 134 6.3 2.8 5.1 1.5 virginica
## 135 6.1 2.6 5.6 1.4 virginica
## 136 7.7 3.0 6.1 2.3 virginica
## 137 6.3 3.4 5.6 2.4 virginica
## 138 6.4 3.1 5.5 1.8 virginica
## 139 6.0 3.0 4.8 1.8 virginica
## 140 6.9 3.1 5.4 2.1 virginica
## 141 6.7 3.1 5.6 2.4 virginica
## 142 6.9 3.1 5.1 2.3 virginica
## 143 5.8 2.7 5.1 1.9 virginica
## 144 6.8 3.2 5.9 2.3 virginica
## 145 6.7 3.3 5.7 2.5 virginica
## 146 6.7 3.0 5.2 2.3 virginica
## 147 6.3 2.5 5.0 1.9 virginica
## 148 6.5 3.0 5.2 2.0 virginica
## 149 6.2 3.4 5.4 2.3 virginica
## 150 5.9 3.0 5.1 1.8 virginica
data.iris <- iris
iris.lda <- lda(Species~Sepal.Length+Sepal.Width+Petal.Length+Petal.Width,data=iris)
iris.lda
## Call:
## lda(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width,
## data = iris)
##
## Prior probabilities of groups:
## setosa versicolor virginica
## 0.3333333 0.3333333 0.3333333
##
## Group means:
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa 5.006 3.428 1.462 0.246
## versicolor 5.936 2.770 4.260 1.326
## virginica 6.588 2.974 5.552 2.026
##
## Coefficients of linear discriminants:
## LD1 LD2
## Sepal.Length 0.8293776 0.02410215
## Sepal.Width 1.5344731 2.16452123
## Petal.Length -2.2012117 -0.93192121
## Petal.Width -2.8104603 2.83918785
##
## Proportion of trace:
## LD1 LD2
## 0.9912 0.0088
plot(iris.lda)
x<- as.matrix(iris[-5])
x
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## [1,] 5.1 3.5 1.4 0.2
## [2,] 4.9 3.0 1.4 0.2
## [3,] 4.7 3.2 1.3 0.2
## [4,] 4.6 3.1 1.5 0.2
## [5,] 5.0 3.6 1.4 0.2
## [6,] 5.4 3.9 1.7 0.4
## [7,] 4.6 3.4 1.4 0.3
## [8,] 5.0 3.4 1.5 0.2
## [9,] 4.4 2.9 1.4 0.2
## [10,] 4.9 3.1 1.5 0.1
## [11,] 5.4 3.7 1.5 0.2
## [12,] 4.8 3.4 1.6 0.2
## [13,] 4.8 3.0 1.4 0.1
## [14,] 4.3 3.0 1.1 0.1
## [15,] 5.8 4.0 1.2 0.2
## [16,] 5.7 4.4 1.5 0.4
## [17,] 5.4 3.9 1.3 0.4
## [18,] 5.1 3.5 1.4 0.3
## [19,] 5.7 3.8 1.7 0.3
## [20,] 5.1 3.8 1.5 0.3
## [21,] 5.4 3.4 1.7 0.2
## [22,] 5.1 3.7 1.5 0.4
## [23,] 4.6 3.6 1.0 0.2
## [24,] 5.1 3.3 1.7 0.5
## [25,] 4.8 3.4 1.9 0.2
## [26,] 5.0 3.0 1.6 0.2
## [27,] 5.0 3.4 1.6 0.4
## [28,] 5.2 3.5 1.5 0.2
## [29,] 5.2 3.4 1.4 0.2
## [30,] 4.7 3.2 1.6 0.2
## [31,] 4.8 3.1 1.6 0.2
## [32,] 5.4 3.4 1.5 0.4
## [33,] 5.2 4.1 1.5 0.1
## [34,] 5.5 4.2 1.4 0.2
## [35,] 4.9 3.1 1.5 0.2
## [36,] 5.0 3.2 1.2 0.2
## [37,] 5.5 3.5 1.3 0.2
## [38,] 4.9 3.6 1.4 0.1
## [39,] 4.4 3.0 1.3 0.2
## [40,] 5.1 3.4 1.5 0.2
## [41,] 5.0 3.5 1.3 0.3
## [42,] 4.5 2.3 1.3 0.3
## [43,] 4.4 3.2 1.3 0.2
## [44,] 5.0 3.5 1.6 0.6
## [45,] 5.1 3.8 1.9 0.4
## [46,] 4.8 3.0 1.4 0.3
## [47,] 5.1 3.8 1.6 0.2
## [48,] 4.6 3.2 1.4 0.2
## [49,] 5.3 3.7 1.5 0.2
## [50,] 5.0 3.3 1.4 0.2
## [51,] 7.0 3.2 4.7 1.4
## [52,] 6.4 3.2 4.5 1.5
## [53,] 6.9 3.1 4.9 1.5
## [54,] 5.5 2.3 4.0 1.3
## [55,] 6.5 2.8 4.6 1.5
## [56,] 5.7 2.8 4.5 1.3
## [57,] 6.3 3.3 4.7 1.6
## [58,] 4.9 2.4 3.3 1.0
## [59,] 6.6 2.9 4.6 1.3
## [60,] 5.2 2.7 3.9 1.4
## [61,] 5.0 2.0 3.5 1.0
## [62,] 5.9 3.0 4.2 1.5
## [63,] 6.0 2.2 4.0 1.0
## [64,] 6.1 2.9 4.7 1.4
## [65,] 5.6 2.9 3.6 1.3
## [66,] 6.7 3.1 4.4 1.4
## [67,] 5.6 3.0 4.5 1.5
## [68,] 5.8 2.7 4.1 1.0
## [69,] 6.2 2.2 4.5 1.5
## [70,] 5.6 2.5 3.9 1.1
## [71,] 5.9 3.2 4.8 1.8
## [72,] 6.1 2.8 4.0 1.3
## [73,] 6.3 2.5 4.9 1.5
## [74,] 6.1 2.8 4.7 1.2
## [75,] 6.4 2.9 4.3 1.3
## [76,] 6.6 3.0 4.4 1.4
## [77,] 6.8 2.8 4.8 1.4
## [78,] 6.7 3.0 5.0 1.7
## [79,] 6.0 2.9 4.5 1.5
## [80,] 5.7 2.6 3.5 1.0
## [81,] 5.5 2.4 3.8 1.1
## [82,] 5.5 2.4 3.7 1.0
## [83,] 5.8 2.7 3.9 1.2
## [84,] 6.0 2.7 5.1 1.6
## [85,] 5.4 3.0 4.5 1.5
## [86,] 6.0 3.4 4.5 1.6
## [87,] 6.7 3.1 4.7 1.5
## [88,] 6.3 2.3 4.4 1.3
## [89,] 5.6 3.0 4.1 1.3
## [90,] 5.5 2.5 4.0 1.3
## [91,] 5.5 2.6 4.4 1.2
## [92,] 6.1 3.0 4.6 1.4
## [93,] 5.8 2.6 4.0 1.2
## [94,] 5.0 2.3 3.3 1.0
## [95,] 5.6 2.7 4.2 1.3
## [96,] 5.7 3.0 4.2 1.2
## [97,] 5.7 2.9 4.2 1.3
## [98,] 6.2 2.9 4.3 1.3
## [99,] 5.1 2.5 3.0 1.1
## [100,] 5.7 2.8 4.1 1.3
## [101,] 6.3 3.3 6.0 2.5
## [102,] 5.8 2.7 5.1 1.9
## [103,] 7.1 3.0 5.9 2.1
## [104,] 6.3 2.9 5.6 1.8
## [105,] 6.5 3.0 5.8 2.2
## [106,] 7.6 3.0 6.6 2.1
## [107,] 4.9 2.5 4.5 1.7
## [108,] 7.3 2.9 6.3 1.8
## [109,] 6.7 2.5 5.8 1.8
## [110,] 7.2 3.6 6.1 2.5
## [111,] 6.5 3.2 5.1 2.0
## [112,] 6.4 2.7 5.3 1.9
## [113,] 6.8 3.0 5.5 2.1
## [114,] 5.7 2.5 5.0 2.0
## [115,] 5.8 2.8 5.1 2.4
## [116,] 6.4 3.2 5.3 2.3
## [117,] 6.5 3.0 5.5 1.8
## [118,] 7.7 3.8 6.7 2.2
## [119,] 7.7 2.6 6.9 2.3
## [120,] 6.0 2.2 5.0 1.5
## [121,] 6.9 3.2 5.7 2.3
## [122,] 5.6 2.8 4.9 2.0
## [123,] 7.7 2.8 6.7 2.0
## [124,] 6.3 2.7 4.9 1.8
## [125,] 6.7 3.3 5.7 2.1
## [126,] 7.2 3.2 6.0 1.8
## [127,] 6.2 2.8 4.8 1.8
## [128,] 6.1 3.0 4.9 1.8
## [129,] 6.4 2.8 5.6 2.1
## [130,] 7.2 3.0 5.8 1.6
## [131,] 7.4 2.8 6.1 1.9
## [132,] 7.9 3.8 6.4 2.0
## [133,] 6.4 2.8 5.6 2.2
## [134,] 6.3 2.8 5.1 1.5
## [135,] 6.1 2.6 5.6 1.4
## [136,] 7.7 3.0 6.1 2.3
## [137,] 6.3 3.4 5.6 2.4
## [138,] 6.4 3.1 5.5 1.8
## [139,] 6.0 3.0 4.8 1.8
## [140,] 6.9 3.1 5.4 2.1
## [141,] 6.7 3.1 5.6 2.4
## [142,] 6.9 3.1 5.1 2.3
## [143,] 5.8 2.7 5.1 1.9
## [144,] 6.8 3.2 5.9 2.3
## [145,] 6.7 3.3 5.7 2.5
## [146,] 6.7 3.0 5.2 2.3
## [147,] 6.3 2.5 5.0 1.9
## [148,] 6.5 3.0 5.2 2.0
## [149,] 6.2 3.4 5.4 2.3
## [150,] 5.9 3.0 5.1 1.8
iris.manova <- manova(x~iris$Species)
iris.manova
## Call:
## manova(x ~ iris$Species)
##
## Terms:
## iris$Species Residuals
## Sepal.Length 63.2121 38.9562
## Sepal.Width 11.3449 16.9620
## Petal.Length 437.1028 27.2226
## Petal.Width 80.4133 6.1566
## Deg. of Freedom 2 147
##
## Residual standard errors: 0.5147894 0.3396877 0.4303345 0.20465
## Estimated effects may be unbalanced
iris.Wilks <- summary(iris.manova , test = "Wilks")
iris.Wilks
## Df Wilks approx F num Df den Df Pr(>F)
## iris$Species 2 0.023439 199.15 8 288 < 2.2e-16 ***
## Residuals 147
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
LD1 <- predict(iris.lda)$x[,1]
LD1
## 1 2 3 4 5 6 7
## 8.0617998 7.1286877 7.4898280 6.8132006 8.1323093 7.7019467 7.2126176
## 8 9 10 11 12 13 14
## 7.6052935 6.5605516 7.3430599 8.3973865 7.2192969 7.3267960 7.5724707
## 15 16 17 18 19 20 21
## 9.8498430 9.1582389 8.5824314 7.7807538 8.0783588 8.0209745 7.4968023
## 22 23 24 25 26 27 28
## 7.5864812 8.6810429 6.2514036 6.5589334 6.7713832 6.8230803 7.9246164
## 29 30 31 32 33 34 35
## 7.9912902 6.8294645 6.7589549 7.3749525 9.1263463 9.4676820 7.0620139
## 36 37 38 39 40 41 42
## 7.9587624 8.6136720 8.3304176 6.9341201 7.6882313 7.9179372 5.6618807
## 43 44 45 46 47 48 49
## 7.2410147 6.4144356 6.8594438 6.7647039 8.0818994 7.1867690 8.3144488
## 50 51 52 53 54 55 56
## 7.6719674 -1.4592755 -1.7977057 -2.4169489 -2.2624735 -2.5486784 -2.4299673
## 57 58 59 60 61 62 63
## -2.4484846 -0.2226665 -1.7502012 -1.9584224 -1.1937603 -1.8589257 -1.1580939
## 64 65 66 67 68 69 70
## -2.6660572 -0.3783672 -1.2011726 -2.7681025 -0.7768540 -3.4980543 -1.0904279
## 71 72 73 74 75 76 77
## -3.7158961 -0.9976104 -3.8352593 -2.2574125 -1.2557133 -1.4375576 -2.4590614
## 78 79 80 81 82 83 84
## -3.5184849 -2.5897987 0.3074879 -1.1066918 -0.6055246 -0.8987038 -4.4984664
## 85 86 87 88 89 90 91
## -2.9339780 -2.1036082 -2.1425821 -2.4794560 -1.3255257 -1.9555789 -2.4015702
## 92 93 94 95 96 97 98
## -2.2924888 -1.2722722 -0.2931761 -2.0059888 -1.1816631 -1.6161564 -1.4215888
## 99 100 101 102 103 104 105
## 0.4759738 -1.5494826 -7.8394740 -5.5074800 -6.2920085 -5.6054563 -6.8505600
## 106 107 108 109 110 111 112
## -7.4181678 -4.6779954 -6.3169269 -6.3277368 -6.8528134 -4.4407251 -5.4500957
## 113 114 115 116 117 118 119
## -5.6603371 -5.9582372 -6.7592628 -5.8070433 -5.0660123 -6.6088188 -9.1714749
## 120 121 122 123 124 125 126
## -4.7645357 -6.2728391 -5.3607119 -7.5811998 -4.3715028 -5.7231753 -5.2791592
## 127 128 129 130 131 132 133
## -4.0808721 -4.0770364 -6.5191040 -4.5837194 -6.2282401 -5.2204877 -6.8001500
## 134 135 136 137 138 139 140
## -3.8151597 -5.1074897 -6.7967163 -6.5244960 -4.9955028 -3.9398530 -5.2038309
## 141 142 143 144 145 146 147
## -6.6530868 -5.1055595 -5.5074800 -6.7960192 -6.8473594 -5.6450035 -5.1795646
## 148 149 150
## -4.9677409 -5.8861454 -4.6831543
LD2 <- predict(iris.lda)$x[,2]
LD2
## 1 2 3 4 5 6
## 0.300420621 -0.786660426 -0.265384488 -0.670631068 0.514462530 1.461720967
## 7 8 9 10 11 12
## 0.355836209 -0.011633838 -1.015163624 -0.947319209 0.647363392 -0.109646389
## 13 14 15 16 17 18
## -1.072989426 -0.805464137 1.585936985 2.737596471 1.834489452 0.584339407
## 19 20 21 22 23 24
## 0.968580703 1.140503656 -0.188377220 1.207970318 0.877590154 0.439696367
## 25 26 27 28 29 30
## -0.389222752 -0.970634453 0.463011612 0.209638715 0.086378713 -0.544960851
## 31 32 33 34 35 36
## -0.759002759 0.565844592 1.224432671 1.825226345 -0.663400423 -0.164961722
## 37 38 39 40 41 42
## 0.403253602 0.228133530 -0.705519379 -0.009223623 0.675121313 -1.934355243
## 43 44 45 46 47 48
## -0.272615132 1.247301306 1.051653957 -0.505151855 0.763392750 -0.360986823
## 49 50 51 52 53 54
## 0.644953177 -0.134893840 0.028543764 0.484385502 -0.092784031 -1.587252508
## 55 56 57 58 59 60
## -0.472204898 -0.966132066 0.795961954 -1.584673183 -0.821180130 -0.351563753
## 61 62 63 64 65 66
## -2.634455704 0.319006544 -2.643409913 -0.642504540 0.086638931 0.084437359
## 67 68 69 70 71 72
## 0.032199536 -1.659161847 -1.684956162 -1.626583496 1.044514421 -0.490530602
## 73 74 75 76 77 78
## -1.405958061 -1.426794234 -0.546424197 -0.134424979 -0.935277280 0.160588866
## 79 80 81 82 83 84
## -0.174611728 -1.318871459 -1.752253714 -1.942980378 -0.904940034 -0.882749915
## 85 86 87 88 89 90
## 0.027379106 1.191567675 0.088779781 -1.940739273 -0.162869550 -1.154348262
## 91 92 93 94 95 96
## -1.594583407 -0.332860296 -1.214584279 -1.798715092 -0.905418042 -0.537570242
## 97 98 99 100 101 102
## -0.470103580 -0.551244626 -0.799905482 -0.593363582 2.139733449 -0.035813989
## 103 104 105 106 107 108
## 0.467175777 -0.340738058 0.829825394 -0.173117995 -0.499095015 -0.968980756
## 109 110 111 112 113 114
## -1.383289934 2.717589632 1.347236918 -0.207736942 0.832713617 -0.094017545
## 115 116 117 118 119 120
## 1.600232061 2.010198817 -0.026273384 1.751635872 -0.748255067 -2.155737197
## 121 122 123 124 125 126
## 1.649481407 0.646120732 -0.980722934 -0.121297458 1.293275530 -0.042458238
## 127 128 129 130 131 132
## 0.185936572 0.523238483 0.296976389 -0.856815813 -0.712719638 1.468195094
## 133 134 135 136 137 138
## 0.580895175 -0.942985932 -2.130589999 0.863090395 2.445035271 0.187768525
## 139 140 141 142 143 144
## 0.614020389 1.144768076 1.805319760 1.992182010 -0.035813989 1.460686950
## 145 146 147 148 149 150
## 2.428950671 1.677717335 -0.363475041 0.821140550 2.345090513 0.332033811
plot(LD1, LD2, xlab = "Linear Diskriminan Pertama", ylab = "Linear Diskriminan Kedua",type = "n")
text(cbind(LD1, LD2),labels = unclass(iris$Species))
sum(LD1 * (iris$Species == "setosa"))/sum(iris$Species=="setosa")
## [1] 7.6076
sum(LD2 * (iris$Species == "setosa"))/sum(iris$Species=="setosa")
## [1] 0.215133
sum(LD1 * (iris$Species == "versicolor"))/sum(iris$Species=="versicolor")
## [1] -1.825049
sum(LD2 * (iris$Species == "versicolor"))/sum(iris$Species=="versicolor")
## [1] -0.7278996
sum(LD1 * (iris$Species == "virginica"))/sum(iris$Species=="virginica")
## [1] -5.78255
sum(LD2 * (iris$Species == "virginica"))/sum(iris$Species=="virginica")
## [1] 0.5127666
## $class
## [1] setosa setosa setosa setosa setosa setosa
## [7] setosa setosa setosa setosa setosa setosa
## [13] setosa setosa setosa setosa setosa setosa
## [19] setosa setosa setosa setosa setosa setosa
## [25] setosa setosa setosa setosa setosa setosa
## [31] setosa setosa setosa setosa setosa setosa
## [37] setosa setosa setosa setosa setosa setosa
## [43] setosa setosa setosa setosa setosa setosa
## [49] setosa setosa versicolor versicolor versicolor versicolor
## [55] versicolor versicolor versicolor versicolor versicolor versicolor
## [61] versicolor versicolor versicolor versicolor versicolor versicolor
## [67] versicolor versicolor versicolor versicolor virginica versicolor
## [73] versicolor versicolor versicolor versicolor versicolor versicolor
## [79] versicolor versicolor versicolor versicolor versicolor virginica
## [85] versicolor versicolor versicolor versicolor versicolor versicolor
## [91] versicolor versicolor versicolor versicolor versicolor versicolor
## [97] versicolor versicolor versicolor versicolor virginica virginica
## [103] virginica virginica virginica virginica virginica virginica
## [109] virginica virginica virginica virginica virginica virginica
## [115] virginica virginica virginica virginica virginica virginica
## [121] virginica virginica virginica virginica virginica virginica
## [127] virginica virginica virginica virginica virginica virginica
## [133] virginica versicolor virginica virginica virginica virginica
## [139] virginica virginica virginica virginica virginica virginica
## [145] virginica virginica virginica virginica virginica virginica
## Levels: setosa versicolor virginica
##
## $posterior
## setosa versicolor virginica
## 1 1.000000e+00 3.896358e-22 2.611168e-42
## 2 1.000000e+00 7.217970e-18 5.042143e-37
## 3 1.000000e+00 1.463849e-19 4.675932e-39
## 4 1.000000e+00 1.268536e-16 3.566610e-35
## 5 1.000000e+00 1.637387e-22 1.082605e-42
## 6 1.000000e+00 3.883282e-21 4.566540e-40
## 7 1.000000e+00 1.113469e-18 2.302608e-37
## 8 1.000000e+00 3.877586e-20 1.074496e-39
## 9 1.000000e+00 1.902813e-15 9.482936e-34
## 10 1.000000e+00 1.111803e-18 2.724060e-38
## 11 1.000000e+00 1.185277e-23 3.237084e-44
## 12 1.000000e+00 1.621649e-18 1.833201e-37
## 13 1.000000e+00 1.459225e-18 3.262506e-38
## 14 1.000000e+00 1.117219e-19 1.316642e-39
## 15 1.000000e+00 5.487399e-30 1.531265e-52
## 16 1.000000e+00 1.261505e-27 2.268705e-48
## 17 1.000000e+00 6.754338e-25 3.868271e-45
## 18 1.000000e+00 4.223741e-21 1.224313e-40
## 19 1.000000e+00 1.774911e-22 2.552153e-42
## 20 1.000000e+00 2.593237e-22 5.792079e-42
## 21 1.000000e+00 1.274639e-19 4.357774e-39
## 22 1.000000e+00 1.465999e-20 1.987241e-39
## 23 1.000000e+00 6.569280e-25 7.769177e-46
## 24 1.000000e+00 8.912348e-15 9.178624e-32
## 25 1.000000e+00 1.070702e-15 1.167516e-33
## 26 1.000000e+00 2.497339e-16 5.710269e-35
## 27 1.000000e+00 3.967732e-17 4.378624e-35
## 28 1.000000e+00 1.548165e-21 1.595360e-41
## 29 1.000000e+00 9.271847e-22 6.297955e-42
## 30 1.000000e+00 9.665144e-17 2.977974e-35
## 31 1.000000e+00 2.299936e-16 7.182666e-35
## 32 1.000000e+00 1.975404e-19 2.788334e-38
## 33 1.000000e+00 7.100041e-27 2.216408e-48
## 34 1.000000e+00 1.610295e-28 2.743783e-50
## 35 1.000000e+00 1.205219e-17 1.277245e-36
## 36 1.000000e+00 1.597186e-21 9.033772e-42
## 37 1.000000e+00 1.939869e-24 1.662808e-45
## 38 1.000000e+00 3.310234e-23 7.004971e-44
## 39 1.000000e+00 4.190242e-17 6.991441e-36
## 40 1.000000e+00 1.769359e-20 3.541694e-40
## 41 1.000000e+00 1.063014e-21 2.003866e-41
## 42 1.000000e+00 2.174217e-11 1.213781e-28
## 43 1.000000e+00 1.540753e-18 1.305719e-37
## 44 1.000000e+00 8.940589e-16 1.315511e-32
## 45 1.000000e+00 1.616206e-17 3.205992e-35
## 46 1.000000e+00 1.714743e-16 7.172435e-35
## 47 1.000000e+00 2.083089e-22 2.289783e-42
## 48 1.000000e+00 2.793482e-18 2.629539e-37
## 49 1.000000e+00 2.597560e-23 9.820820e-44
## 50 1.000000e+00 2.322258e-20 4.241757e-40
## 51 1.969732e-18 9.998894e-01 1.105878e-04
## 52 1.242878e-19 9.992575e-01 7.425297e-04
## 53 2.088263e-22 9.958069e-01 4.193053e-03
## 54 2.198898e-22 9.996423e-01 3.576502e-04
## 55 4.213678e-23 9.955903e-01 4.409655e-03
## 56 8.127287e-23 9.985020e-01 1.497982e-03
## 57 3.549900e-22 9.858346e-01 1.416542e-02
## 58 5.007065e-14 9.999999e-01 1.119811e-07
## 59 5.683334e-20 9.998781e-01 1.218649e-04
## 60 1.241039e-20 9.995027e-01 4.973085e-04
## 61 1.956628e-18 9.999986e-01 1.420841e-06
## 62 5.968900e-20 9.992294e-01 7.705716e-04
## 63 2.716128e-18 9.999988e-01 1.220169e-06
## 64 1.184445e-23 9.943267e-01 5.673286e-03
## 65 5.574931e-14 9.999984e-01 1.649215e-06
## 66 2.369511e-17 9.999573e-01 4.268212e-05
## 67 8.429328e-24 9.806471e-01 1.935289e-02
## 68 2.505072e-16 9.999991e-01 9.151716e-07
## 69 1.670352e-27 9.595735e-01 4.042653e-02
## 70 1.341503e-17 9.999967e-01 3.296105e-06
## 71 7.408118e-28 2.532282e-01 7.467718e-01
## 72 9.399292e-17 9.999907e-01 9.345291e-06
## 73 7.674672e-29 8.155328e-01 1.844672e-01
## 74 2.683018e-22 9.995723e-01 4.277469e-04
## 75 7.813875e-18 9.999758e-01 2.421458e-05
## 76 2.073207e-18 9.999171e-01 8.290530e-05
## 77 6.357538e-23 9.982541e-01 1.745936e-03
## 78 5.639473e-27 6.892131e-01 3.107869e-01
## 79 3.773528e-23 9.925169e-01 7.483138e-03
## 80 9.555338e-12 1.000000e+00 1.910624e-08
## 81 1.022109e-17 9.999970e-01 3.007748e-06
## 82 9.648075e-16 9.999997e-01 3.266704e-07
## 83 1.616405e-16 9.999962e-01 3.778441e-06
## 84 4.241952e-32 1.433919e-01 8.566081e-01
## 85 1.724514e-24 9.635576e-01 3.644242e-02
## 86 1.344746e-20 9.940401e-01 5.959931e-03
## 87 3.304868e-21 9.982223e-01 1.777672e-03
## 88 2.034571e-23 9.994557e-01 5.443096e-04
## 89 5.806986e-18 9.999486e-01 5.137101e-05
## 90 5.981190e-21 9.998183e-01 1.816870e-04
## 91 5.878614e-23 9.993856e-01 6.144200e-04
## 92 5.399006e-22 9.980934e-01 1.906591e-03
## 93 3.559507e-18 9.999887e-01 1.128570e-05
## 94 2.104146e-14 9.999999e-01 1.135016e-07
## 95 4.700877e-21 9.996980e-01 3.020226e-04
## 96 1.584328e-17 9.999817e-01 1.826327e-05
## 97 2.802293e-19 9.998892e-01 1.108315e-04
## 98 1.626918e-18 9.999536e-01 4.640488e-05
## 99 7.638378e-11 1.000000e+00 1.867332e-08
## 100 4.679301e-19 9.999269e-01 7.305863e-05
## 101 7.503075e-52 7.127303e-09 1.000000e+00
## 102 5.213802e-38 1.078251e-03 9.989217e-01
## 103 1.231264e-42 2.592826e-05 9.999741e-01
## 104 1.537499e-38 1.068139e-03 9.989319e-01
## 105 6.242501e-46 1.812963e-06 9.999982e-01
## 106 4.209281e-49 6.656263e-07 9.999993e-01
## 107 3.797837e-33 4.862025e-02 9.513797e-01
## 108 1.352176e-42 1.395463e-04 9.998605e-01
## 109 1.323390e-42 2.235313e-04 9.997765e-01
## 110 3.453358e-46 1.727277e-07 9.999998e-01
## 111 5.452660e-32 1.305353e-02 9.869465e-01
## 112 1.182560e-37 1.673875e-03 9.983261e-01
## 113 5.204321e-39 2.006352e-04 9.997994e-01
## 114 1.269953e-40 1.948672e-04 9.998051e-01
## 115 1.685361e-45 1.000455e-06 9.999990e-01
## 116 5.141640e-40 2.605493e-05 9.999739e-01
## 117 1.909820e-35 6.083553e-03 9.939164e-01
## 118 1.207799e-44 1.503799e-06 9.999985e-01
## 119 3.181265e-59 1.317279e-09 1.000000e+00
## 120 1.598511e-33 2.207990e-01 7.792010e-01
## 121 1.119461e-42 6.451865e-06 9.999935e-01
## 122 3.038170e-37 8.272676e-04 9.991727e-01
## 123 6.032879e-50 9.509838e-07 9.999990e-01
## 124 1.951261e-31 9.711942e-02 9.028806e-01
## 125 1.956408e-39 8.836845e-05 9.999116e-01
## 126 1.109337e-36 2.679310e-03 9.973207e-01
## 127 7.841997e-30 1.883675e-01 8.116325e-01
## 128 7.964690e-30 1.342431e-01 8.657569e-01
## 129 6.190641e-44 1.303681e-05 9.999870e-01
## 130 1.406448e-32 1.036823e-01 8.963177e-01
## 131 4.108129e-42 1.442338e-04 9.998558e-01
## 132 1.555697e-36 5.198047e-04 9.994802e-01
## 133 1.320330e-45 3.014091e-06 9.999970e-01
## 134 1.283891e-28 7.293881e-01 2.706119e-01
## 135 1.926560e-35 6.602253e-02 9.339775e-01
## 136 1.271083e-45 2.152818e-06 9.999978e-01
## 137 3.038963e-44 8.881859e-07 9.999991e-01
## 138 4.605973e-35 6.165648e-03 9.938344e-01
## 139 4.538634e-29 1.925262e-01 8.074738e-01
## 140 2.140232e-36 8.290895e-04 9.991709e-01
## 141 6.570902e-45 1.180810e-06 9.999988e-01
## 142 6.202588e-36 4.276398e-04 9.995724e-01
## 143 5.213802e-38 1.078251e-03 9.989217e-01
## 144 1.073945e-45 1.028519e-06 9.999990e-01
## 145 4.048249e-46 2.524984e-07 9.999997e-01
## 146 4.970070e-39 7.473361e-05 9.999253e-01
## 147 4.616611e-36 5.898784e-03 9.941012e-01
## 148 5.548962e-35 3.145874e-03 9.968541e-01
## 149 1.613687e-40 1.257468e-05 9.999874e-01
## 150 2.858012e-33 1.754229e-02 9.824577e-01
##
## $x
## LD1 LD2
## 1 8.0617998 0.300420621
## 2 7.1286877 -0.786660426
## 3 7.4898280 -0.265384488
## 4 6.8132006 -0.670631068
## 5 8.1323093 0.514462530
## 6 7.7019467 1.461720967
## 7 7.2126176 0.355836209
## 8 7.6052935 -0.011633838
## 9 6.5605516 -1.015163624
## 10 7.3430599 -0.947319209
## 11 8.3973865 0.647363392
## 12 7.2192969 -0.109646389
## 13 7.3267960 -1.072989426
## 14 7.5724707 -0.805464137
## 15 9.8498430 1.585936985
## 16 9.1582389 2.737596471
## 17 8.5824314 1.834489452
## 18 7.7807538 0.584339407
## 19 8.0783588 0.968580703
## 20 8.0209745 1.140503656
## 21 7.4968023 -0.188377220
## 22 7.5864812 1.207970318
## 23 8.6810429 0.877590154
## 24 6.2514036 0.439696367
## 25 6.5589334 -0.389222752
## 26 6.7713832 -0.970634453
## 27 6.8230803 0.463011612
## 28 7.9246164 0.209638715
## 29 7.9912902 0.086378713
## 30 6.8294645 -0.544960851
## 31 6.7589549 -0.759002759
## 32 7.3749525 0.565844592
## 33 9.1263463 1.224432671
## 34 9.4676820 1.825226345
## 35 7.0620139 -0.663400423
## 36 7.9587624 -0.164961722
## 37 8.6136720 0.403253602
## 38 8.3304176 0.228133530
## 39 6.9341201 -0.705519379
## 40 7.6882313 -0.009223623
## 41 7.9179372 0.675121313
## 42 5.6618807 -1.934355243
## 43 7.2410147 -0.272615132
## 44 6.4144356 1.247301306
## 45 6.8594438 1.051653957
## 46 6.7647039 -0.505151855
## 47 8.0818994 0.763392750
## 48 7.1867690 -0.360986823
## 49 8.3144488 0.644953177
## 50 7.6719674 -0.134893840
## 51 -1.4592755 0.028543764
## 52 -1.7977057 0.484385502
## 53 -2.4169489 -0.092784031
## 54 -2.2624735 -1.587252508
## 55 -2.5486784 -0.472204898
## 56 -2.4299673 -0.966132066
## 57 -2.4484846 0.795961954
## 58 -0.2226665 -1.584673183
## 59 -1.7502012 -0.821180130
## 60 -1.9584224 -0.351563753
## 61 -1.1937603 -2.634455704
## 62 -1.8589257 0.319006544
## 63 -1.1580939 -2.643409913
## 64 -2.6660572 -0.642504540
## 65 -0.3783672 0.086638931
## 66 -1.2011726 0.084437359
## 67 -2.7681025 0.032199536
## 68 -0.7768540 -1.659161847
## 69 -3.4980543 -1.684956162
## 70 -1.0904279 -1.626583496
## 71 -3.7158961 1.044514421
## 72 -0.9976104 -0.490530602
## 73 -3.8352593 -1.405958061
## 74 -2.2574125 -1.426794234
## 75 -1.2557133 -0.546424197
## 76 -1.4375576 -0.134424979
## 77 -2.4590614 -0.935277280
## 78 -3.5184849 0.160588866
## 79 -2.5897987 -0.174611728
## 80 0.3074879 -1.318871459
## 81 -1.1066918 -1.752253714
## 82 -0.6055246 -1.942980378
## 83 -0.8987038 -0.904940034
## 84 -4.4984664 -0.882749915
## 85 -2.9339780 0.027379106
## 86 -2.1036082 1.191567675
## 87 -2.1425821 0.088779781
## 88 -2.4794560 -1.940739273
## 89 -1.3255257 -0.162869550
## 90 -1.9555789 -1.154348262
## 91 -2.4015702 -1.594583407
## 92 -2.2924888 -0.332860296
## 93 -1.2722722 -1.214584279
## 94 -0.2931761 -1.798715092
## 95 -2.0059888 -0.905418042
## 96 -1.1816631 -0.537570242
## 97 -1.6161564 -0.470103580
## 98 -1.4215888 -0.551244626
## 99 0.4759738 -0.799905482
## 100 -1.5494826 -0.593363582
## 101 -7.8394740 2.139733449
## 102 -5.5074800 -0.035813989
## 103 -6.2920085 0.467175777
## 104 -5.6054563 -0.340738058
## 105 -6.8505600 0.829825394
## 106 -7.4181678 -0.173117995
## 107 -4.6779954 -0.499095015
## 108 -6.3169269 -0.968980756
## 109 -6.3277368 -1.383289934
## 110 -6.8528134 2.717589632
## 111 -4.4407251 1.347236918
## 112 -5.4500957 -0.207736942
## 113 -5.6603371 0.832713617
## 114 -5.9582372 -0.094017545
## 115 -6.7592628 1.600232061
## 116 -5.8070433 2.010198817
## 117 -5.0660123 -0.026273384
## 118 -6.6088188 1.751635872
## 119 -9.1714749 -0.748255067
## 120 -4.7645357 -2.155737197
## 121 -6.2728391 1.649481407
## 122 -5.3607119 0.646120732
## 123 -7.5811998 -0.980722934
## 124 -4.3715028 -0.121297458
## 125 -5.7231753 1.293275530
## 126 -5.2791592 -0.042458238
## 127 -4.0808721 0.185936572
## 128 -4.0770364 0.523238483
## 129 -6.5191040 0.296976389
## 130 -4.5837194 -0.856815813
## 131 -6.2282401 -0.712719638
## 132 -5.2204877 1.468195094
## 133 -6.8001500 0.580895175
## 134 -3.8151597 -0.942985932
## 135 -5.1074897 -2.130589999
## 136 -6.7967163 0.863090395
## 137 -6.5244960 2.445035271
## 138 -4.9955028 0.187768525
## 139 -3.9398530 0.614020389
## 140 -5.2038309 1.144768076
## 141 -6.6530868 1.805319760
## 142 -5.1055595 1.992182010
## 143 -5.5074800 -0.035813989
## 144 -6.7960192 1.460686950
## 145 -6.8473594 2.428950671
## 146 -5.6450035 1.677717335
## 147 -5.1795646 -0.363475041
## 148 -4.9677409 0.821140550
## 149 -5.8861454 2.345090513
## 150 -4.6831543 0.332033811
## [1] setosa setosa setosa setosa setosa setosa
## [7] setosa setosa setosa setosa setosa setosa
## [13] setosa setosa setosa setosa setosa setosa
## [19] setosa setosa setosa setosa setosa setosa
## [25] setosa setosa setosa setosa setosa setosa
## [31] setosa setosa setosa setosa setosa setosa
## [37] setosa setosa setosa setosa setosa setosa
## [43] setosa setosa setosa setosa setosa setosa
## [49] setosa setosa versicolor versicolor versicolor versicolor
## [55] versicolor versicolor versicolor versicolor versicolor versicolor
## [61] versicolor versicolor versicolor versicolor versicolor versicolor
## [67] versicolor versicolor versicolor versicolor virginica versicolor
## [73] versicolor versicolor versicolor versicolor versicolor versicolor
## [79] versicolor versicolor versicolor versicolor versicolor virginica
## [85] versicolor versicolor versicolor versicolor versicolor versicolor
## [91] versicolor versicolor versicolor versicolor versicolor versicolor
## [97] versicolor versicolor versicolor versicolor virginica virginica
## [103] virginica virginica virginica virginica virginica virginica
## [109] virginica virginica virginica virginica virginica virginica
## [115] virginica virginica virginica virginica virginica virginica
## [121] virginica virginica virginica virginica virginica virginica
## [127] virginica virginica virginica virginica virginica virginica
## [133] virginica versicolor virginica virginica virginica virginica
## [139] virginica virginica virginica virginica virginica virginica
## [145] virginica virginica virginica virginica virginica virginica
## Levels: setosa versicolor virginica
## [1] 0.98
## Predicted
## Original setosa versicolor virginica
## setosa 50 0 0
## versicolor 0 48 2
## virginica 0 1 49
## [1] -0.7918878