library(readxl)
Data_AD <- read_excel("C:/Users/HP/OneDrive/文件/Data_AD.xlsx")
print(Data_AD)
## # A tibble: 306 × 4
## `Surv status` `Usia pasien saat operasi` `Tahun operasi (1958-1969)`
## <dbl> <dbl> <dbl>
## 1 1 30 64
## 2 1 30 62
## 3 1 30 65
## 4 1 31 59
## 5 1 31 65
## 6 1 33 58
## 7 1 33 60
## 8 1 34 58
## 9 1 34 60
## 10 1 34 61
## # ℹ 296 more rows
## # ℹ 1 more variable:
## # `Jumlah kelenjar getah bening yang terdeteksi positif` <dbl>
View(Data_AD)
Y <- Data_AD$`Surv status`
X1 <- Data_AD$`Usia pasien saat operasi`
X2 <- Data_AD$`Tahun operasi (1958-1969)`
X3 <- Data_AD$`Jumlah kelenjar getah bening yang terdeteksi positif`
Data <- data.frame(Y,X1,X2,X3)
Data
## Y X1 X2 X3
## 1 1 30 64 1
## 2 1 30 62 3
## 3 1 30 65 0
## 4 1 31 59 2
## 5 1 31 65 4
## 6 1 33 58 10
## 7 1 33 60 0
## 8 1 34 58 30
## 9 1 34 60 1
## 10 1 34 61 10
## 11 1 34 67 7
## 12 1 34 60 0
## 13 1 35 64 13
## 14 1 35 63 0
## 15 1 36 60 1
## 16 1 36 69 0
## 17 1 37 60 0
## 18 1 37 63 0
## 19 1 37 58 0
## 20 1 37 59 6
## 21 1 37 60 15
## 22 1 37 63 0
## 23 1 38 59 2
## 24 1 38 60 0
## 25 1 38 60 0
## 26 1 38 62 3
## 27 1 38 64 1
## 28 1 38 66 0
## 29 1 38 66 11
## 30 1 38 60 1
## 31 1 38 67 5
## 32 1 39 63 0
## 33 1 39 67 0
## 34 1 39 58 0
## 35 1 39 59 2
## 36 1 39 63 4
## 37 1 40 58 2
## 38 1 40 58 0
## 39 1 40 65 0
## 40 1 41 58 0
## 41 1 41 59 8
## 42 1 41 59 0
## 43 1 41 64 0
## 44 1 41 69 8
## 45 1 41 65 0
## 46 1 41 65 0
## 47 1 42 58 0
## 48 1 42 60 1
## 49 1 42 59 2
## 50 1 42 61 4
## 51 1 42 62 20
## 52 1 42 65 0
## 53 1 42 63 1
## 54 1 43 63 14
## 55 1 43 64 2
## 56 1 43 64 3
## 57 1 43 60 0
## 58 1 43 63 2
## 59 1 43 65 0
## 60 1 43 66 4
## 61 1 44 61 0
## 62 1 44 63 1
## 63 1 44 61 0
## 64 1 44 67 16
## 65 1 45 60 0
## 66 1 45 67 0
## 67 1 45 59 14
## 68 1 45 64 0
## 69 1 45 68 0
## 70 1 45 67 1
## 71 1 46 62 0
## 72 1 46 58 3
## 73 1 46 63 0
## 74 1 47 61 0
## 75 1 47 63 6
## 76 1 47 66 0
## 77 1 47 67 0
## 78 1 47 58 3
## 79 1 47 60 4
## 80 1 47 68 4
## 81 1 47 66 12
## 82 1 48 61 8
## 83 1 48 62 2
## 84 1 48 64 0
## 85 1 48 66 0
## 86 1 49 61 1
## 87 1 49 62 0
## 88 1 49 66 0
## 89 1 49 60 1
## 90 1 49 62 1
## 91 1 49 63 3
## 92 1 49 61 0
## 93 1 49 67 1
## 94 1 50 59 0
## 95 1 50 61 6
## 96 1 50 61 0
## 97 1 50 63 1
## 98 1 50 58 1
## 99 1 50 59 2
## 100 1 50 61 0
## 101 1 50 64 0
## 102 1 50 65 4
## 103 1 50 66 1
## 104 1 51 64 7
## 105 1 51 59 1
## 106 1 51 65 0
## 107 1 51 66 1
## 108 1 52 61 0
## 109 1 52 63 4
## 110 1 52 69 0
## 111 1 52 60 4
## 112 1 52 60 5
## 113 1 52 62 0
## 114 1 52 62 1
## 115 1 52 64 0
## 116 1 52 65 0
## 117 1 52 68 0
## 118 1 53 58 1
## 119 1 53 60 1
## 120 1 53 60 2
## 121 1 53 61 1
## 122 1 53 63 0
## 123 1 54 59 7
## 124 1 54 60 3
## 125 1 54 66 0
## 126 1 54 67 46
## 127 1 54 62 0
## 128 1 54 69 7
## 129 1 54 63 19
## 130 1 54 58 1
## 131 1 54 62 0
## 132 1 55 58 1
## 133 1 55 58 0
## 134 1 55 58 1
## 135 1 55 66 18
## 136 1 55 66 0
## 137 1 55 69 3
## 138 1 55 69 22
## 139 1 55 67 1
## 140 1 56 60 0
## 141 1 56 66 2
## 142 1 56 66 1
## 143 1 56 67 0
## 144 1 56 60 0
## 145 1 57 64 9
## 146 1 57 69 0
## 147 1 57 61 0
## 148 1 57 62 0
## 149 1 57 63 0
## 150 1 57 64 0
## 151 1 57 64 0
## 152 1 57 67 0
## 153 1 58 59 0
## 154 1 58 60 3
## 155 1 58 61 1
## 156 1 58 67 0
## 157 1 58 58 0
## 158 1 58 58 3
## 159 1 58 61 2
## 160 1 59 60 0
## 161 1 59 63 0
## 162 1 59 64 1
## 163 1 59 64 4
## 164 1 59 64 0
## 165 1 59 64 7
## 166 1 59 67 3
## 167 1 60 61 1
## 168 1 60 67 2
## 169 1 60 61 25
## 170 1 60 64 0
## 171 1 61 59 0
## 172 1 61 59 0
## 173 1 61 64 0
## 174 1 61 65 8
## 175 1 61 68 0
## 176 1 61 59 0
## 177 1 62 62 6
## 178 1 62 66 0
## 179 1 62 66 0
## 180 1 62 58 0
## 181 1 63 61 0
## 182 1 63 62 0
## 183 1 63 63 0
## 184 1 63 63 0
## 185 1 63 66 0
## 186 1 63 61 9
## 187 1 63 61 28
## 188 1 64 58 0
## 189 1 64 65 22
## 190 1 64 66 0
## 191 1 64 61 0
## 192 1 64 68 0
## 193 1 65 58 0
## 194 1 65 64 0
## 195 1 65 67 0
## 196 1 65 59 2
## 197 1 65 64 0
## 198 1 65 67 1
## 199 1 66 58 0
## 200 1 66 58 1
## 201 1 66 68 0
## 202 1 67 66 0
## 203 1 67 66 0
## 204 1 67 61 0
## 205 1 67 65 0
## 206 1 68 67 0
## 207 1 68 68 0
## 208 1 69 60 0
## 209 1 69 65 0
## 210 1 69 66 0
## 211 1 70 66 14
## 212 1 70 67 0
## 213 1 70 68 0
## 214 1 70 59 8
## 215 1 70 63 0
## 216 1 71 68 2
## 217 1 72 58 0
## 218 1 72 64 0
## 219 1 72 67 3
## 220 1 73 62 0
## 221 1 73 68 0
## 222 1 74 63 0
## 223 1 75 62 1
## 224 1 76 67 0
## 225 1 77 65 3
## 226 2 34 59 0
## 227 2 34 66 9
## 228 2 38 69 21
## 229 2 39 66 0
## 230 2 41 60 23
## 231 2 41 64 0
## 232 2 41 67 0
## 233 2 42 69 1
## 234 2 42 59 0
## 235 2 43 58 52
## 236 2 43 59 2
## 237 2 43 64 0
## 238 2 43 64 0
## 239 2 44 64 6
## 240 2 44 58 9
## 241 2 44 63 19
## 242 2 45 65 6
## 243 2 45 66 0
## 244 2 45 67 1
## 245 2 46 58 2
## 246 2 46 69 3
## 247 2 46 62 5
## 248 2 46 65 20
## 249 2 47 63 23
## 250 2 47 62 0
## 251 2 47 65 0
## 252 2 48 58 11
## 253 2 48 58 11
## 254 2 48 67 7
## 255 2 49 63 0
## 256 2 49 64 10
## 257 2 50 63 13
## 258 2 50 64 0
## 259 2 51 59 13
## 260 2 51 59 3
## 261 2 52 69 3
## 262 2 52 59 2
## 263 2 52 62 3
## 264 2 52 66 4
## 265 2 53 58 4
## 266 2 53 65 1
## 267 2 53 59 3
## 268 2 53 60 9
## 269 2 53 63 24
## 270 2 53 65 12
## 271 2 54 60 11
## 272 2 54 65 23
## 273 2 54 65 5
## 274 2 54 68 7
## 275 2 55 63 6
## 276 2 55 68 15
## 277 2 56 65 9
## 278 2 56 66 3
## 279 2 57 61 5
## 280 2 57 62 14
## 281 2 57 64 1
## 282 2 59 62 35
## 283 2 60 59 17
## 284 2 60 65 0
## 285 2 61 62 5
## 286 2 61 65 0
## 287 2 61 68 1
## 288 2 62 59 13
## 289 2 62 58 0
## 290 2 62 65 19
## 291 2 63 60 1
## 292 2 65 58 0
## 293 2 65 61 2
## 294 2 65 62 22
## 295 2 65 66 15
## 296 2 66 58 0
## 297 2 66 61 13
## 298 2 67 64 8
## 299 2 67 63 1
## 300 2 69 67 8
## 301 2 70 58 0
## 302 2 70 58 4
## 303 2 72 63 0
## 304 2 74 65 3
## 305 2 78 65 1
## 306 2 83 58 2
X <- Data[,-1]
#Mengubah data menjadi matriks
data <- data.matrix(X)
#Mean
mean <- matrix(colMeans(data),3,1)
#Covarians
cov.data <- cov(data)
cov.invers <- solve(cov.data)
#Menghitung nilai diˆ2
di <- mahalanobis(data, mean, cov.data)
#Peringkat untuk nilai diˆ2
rank <- rank(di)
#Peluang nilai k
p <- (rank-0.5)/306
#Nilai Chi Square
chi.square <- qchisq(p, df=3)
#Membuat Kategori dalam tabel
Data$di.kuadrat <- di
Data$k <- rank
Data$p.k <- p
Data$Chi.Square <- chi.square
m <- data.matrix(Data)
m
## Y X1 X2 X3 di.kuadrat k p.k Chi.Square
## [1,] 1 30 64 1 4.921453163 269.0 0.877450980 5.78505723
## [2,] 1 30 62 3 4.402346783 255.0 0.831699346 5.04821229
## [3,] 1 30 65 0 5.526192521 280.0 0.913398693 6.57892554
## [4,] 1 31 59 2 5.133968881 275.0 0.897058824 6.18516023
## [5,] 1 31 65 4 4.670925411 263.0 0.857843137 5.44187341
## [6,] 1 33 58 10 5.552949605 283.0 0.923202614 6.85112500
## [7,] 1 33 60 0 4.215583155 250.0 0.815359477 4.83046679
## [8,] 1 34 58 30 17.080885240 303.0 0.988562092 11.05390973
## [9,] 1 34 60 1 3.728154734 228.0 0.743464052 4.04603452
## [10,] 1 34 61 10 3.620369505 224.0 0.730392157 3.92562725
## [11,] 1 34 67 7 5.070223703 273.0 0.890522876 6.04424952
## [12,] 1 34 60 0 3.894892720 234.0 0.763071895 4.23756115
## [13,] 1 35 64 13 4.177455917 246.0 0.802287582 4.66887780
## [14,] 1 35 63 0 3.088150912 202.0 0.658496732 3.34445384
## [15,] 1 36 60 1 3.142079139 204.0 0.665032680 3.39255304
## [16,] 1 36 69 0 6.904661569 291.0 0.949346405 7.78574501
## [17,] 1 37 60 0 3.036881339 197.0 0.642156863 3.22762816
## [18,] 1 37 63 0 2.502593713 169.5 0.552287582 2.65625581
## [19,] 1 37 58 0 4.347821837 252.0 0.821895425 4.91531092
## [20,] 1 37 59 6 3.209608324 208.0 0.678104575 3.49127549
## [21,] 1 37 60 15 4.688394071 264.0 0.861111111 5.49581921
## [22,] 1 37 63 0 2.502593713 169.5 0.552287582 2.65625581
## [23,] 1 38 59 2 3.069508023 199.0 0.648692810 3.27379064
## [24,] 1 38 60 0 2.785564186 186.5 0.607843137 2.99655351
## [25,] 1 38 60 0 2.785564186 186.5 0.607843137 2.99655351
## [26,] 1 38 62 3 1.863119187 129.0 0.419934641 1.96326850
## [27,] 1 38 64 1 2.273641916 152.0 0.495098039 2.33999655
## [28,] 1 38 66 0 3.404643749 212.0 0.691176471 3.59360275
## [29,] 1 38 66 11 3.768325432 231.0 0.753267974 4.14005927
## [30,] 1 38 60 1 2.625376825 178.0 0.580065359 2.82173375
## [31,] 1 38 67 5 3.757939847 230.0 0.750000000 4.10834494
## [32,] 1 39 63 0 1.986409796 138.0 0.449346405 2.10622914
## [33,] 1 39 67 0 3.906132213 235.0 0.766339869 4.27088450
## [34,] 1 39 58 0 3.883126139 233.0 0.759803922 4.20465666
## [35,] 1 39 59 2 2.843958325 189.0 0.616013072 3.04995576
## [36,] 1 39 63 4 1.583323433 108.0 0.351307190 1.64739005
## [37,] 1 40 58 2 3.402471346 211.0 0.687908497 3.56766619
## [38,] 1 40 58 0 3.676793271 227.0 0.740196078 4.01541938
## [39,] 1 40 65 0 2.321996884 155.0 0.504901961 2.39214749
## [40,] 1 41 58 0 3.487803723 215.0 0.700980392 3.67290440
## [41,] 1 41 59 8 2.563082880 177.0 0.576797386 2.80180654
## [42,] 1 41 59 0 2.716263312 183.0 0.596405229 2.92334957
## [43,] 1 41 64 0 1.722807498 118.5 0.385620915 1.80255506
## [44,] 1 41 69 8 5.336802597 276.0 0.900326797 6.25886230
## [45,] 1 41 65 0 2.096965583 146.5 0.477124183 2.24635432
## [46,] 1 41 65 0 2.096965583 146.5 0.477124183 2.24635432
## [47,] 1 42 58 0 3.316157496 210.0 0.684640523 3.54196947
## [48,] 1 42 60 1 1.800092043 123.0 0.400326797 1.87069423
## [49,] 1 42 59 2 2.271369154 151.0 0.491830065 2.32278516
## [50,] 1 42 61 4 1.176815796 83.0 0.269607843 1.29469933
## [51,] 1 42 62 20 5.656653085 285.0 0.929738562 7.05191201
## [52,] 1 42 65 0 1.889277603 132.0 0.429738562 2.01034936
## [53,] 1 42 63 1 1.188080374 84.0 0.272875817 1.30846409
## [54,] 1 43 63 14 2.562326950 176.0 0.573529412 2.78200621
## [55,] 1 43 64 2 1.068609655 77.0 0.250000000 1.21253290
## [56,] 1 43 64 3 0.993648061 68.0 0.220588235 1.09031838
## [57,] 1 43 60 0 1.789128228 122.0 0.397058824 1.85546018
## [58,] 1 43 63 2 0.896026773 62.0 0.200980392 1.00922576
## [59,] 1 43 65 0 1.698932943 117.0 0.380718954 1.78007208
## [60,] 1 43 66 4 1.874892413 130.0 0.423202614 1.97890112
## [61,] 1 44 61 0 1.236783620 90.5 0.294117647 1.39851716
## [62,] 1 44 63 1 0.848604975 59.0 0.191176471 0.96870613
## [63,] 1 44 61 0 1.236783620 90.5 0.294117647 1.39851716
## [64,] 1 44 67 16 5.053650248 272.0 0.887254902 5.97678635
## [65,] 1 45 60 0 1.511957089 105.0 0.341503268 1.60394022
## [66,] 1 45 67 0 2.650248428 179.0 0.583333333 2.84178997
## [67,] 1 45 59 14 3.568341230 219.0 0.714052288 3.78233373
## [68,] 1 45 64 0 1.016710786 71.0 0.230392157 1.13095218
## [69,] 1 45 68 0 3.576660475 220.0 0.717320261 3.81039148
## [70,] 1 45 67 1 2.500377327 167.5 0.545751634 2.61854084
## [71,] 1 46 62 0 0.759566205 47.0 0.151960784 0.80596727
## [72,] 1 46 58 3 2.479270547 166.0 0.540849673 2.59054054
## [73,] 1 46 63 0 0.726080682 43.0 0.138888889 0.75115367
## [74,] 1 47 61 0 0.883625387 61.0 0.197712418 0.99572003
## [75,] 1 47 63 6 0.322464219 10.0 0.031045752 0.25105667
## [76,] 1 47 66 0 1.645202410 112.0 0.364379085 1.70590889
## [77,] 1 47 67 0 2.370367063 157.0 0.511437908 2.42735890
## [78,] 1 47 58 3 2.399253891 158.0 0.514705882 2.44510203
## [79,] 1 47 60 4 0.955444728 65.0 0.210784314 1.04975269
## [80,] 1 47 68 4 2.932522007 194.0 0.632352941 3.15973325
## [81,] 1 47 66 12 2.451892259 161.0 0.524509804 2.49889842
## [82,] 1 48 61 8 0.736498459 46.0 0.148692810 0.79230285
## [83,] 1 48 62 2 0.316429038 8.0 0.024509804 0.21284088
## [84,] 1 48 64 0 0.669243116 39.0 0.125816993 0.69583565
## [85,] 1 48 66 0 1.536425530 107.0 0.348039216 1.63286628
## [86,] 1 49 61 1 0.592566121 32.0 0.102941176 0.59726229
## [87,] 1 49 62 0 0.495021429 23.0 0.073529412 0.46518583
## [88,] 1 49 66 0 1.444991971 101.0 0.328431373 1.54655175
## [89,] 1 49 60 1 1.023561513 73.0 0.236928105 1.15809290
## [90,] 1 49 62 1 0.352520477 11.0 0.034313725 0.26934810
## [91,] 1 49 63 3 0.134634528 3.0 0.008169935 0.10006131
## [92,] 1 49 61 0 0.734903167 45.0 0.145424837 0.77861392
## [93,] 1 49 67 1 2.016538505 140.0 0.455882353 2.13872799
## [94,] 1 50 59 0 1.749467406 120.0 0.390522876 1.82515112
## [95,] 1 50 61 6 0.425058981 16.0 0.050653595 0.35513461
## [96,] 1 50 61 0 0.686557038 40.5 0.130718954 0.71664933
## [97,] 1 50 63 1 0.246418467 5.0 0.014705882 0.14952489
## [98,] 1 50 58 1 2.427139540 159.0 0.517973856 2.46293867
## [99,] 1 50 59 2 1.507570798 104.0 0.338235294 1.58953634
## [100,] 1 50 61 0 0.686557038 40.5 0.130718954 0.71664933
## [101,] 1 50 64 0 0.524314606 26.5 0.084967320 0.51748906
## [102,] 1 50 65 4 0.519792569 25.0 0.080065359 0.49524580
## [103,] 1 50 66 1 1.229382818 89.0 0.289215686 1.37763997
## [104,] 1 51 64 7 0.316768790 9.0 0.027777778 0.23225116
## [105,] 1 51 59 1 1.590028317 110.0 0.357843137 1.67656310
## [106,] 1 51 65 0 0.800535198 54.0 0.174836601 0.90109564
## [107,] 1 51 66 1 1.174273556 82.0 0.266339869 1.28095610
## [108,] 1 52 61 0 0.641894741 36.0 0.116013072 0.65391205
## [109,] 1 52 63 4 0.004259847 1.0 0.001633987 0.03377150
## [110,] 1 52 69 0 3.945862095 238.0 0.776143791 4.37348888
## [111,] 1 52 60 4 0.772211317 50.0 0.161764706 0.84683371
## [112,] 1 52 60 5 0.790337354 51.0 0.165032680 0.86041996
## [113,] 1 52 62 0 0.386566537 12.0 0.037581699 0.28719600
## [114,] 1 52 62 1 0.248978554 6.0 0.017973856 0.17168022
## [115,] 1 52 64 0 0.448759377 19.0 0.060457516 0.40338435
## [116,] 1 52 65 0 0.766280422 48.0 0.155228758 0.81960924
## [117,] 1 52 68 0 2.864542053 192.0 0.625816993 3.11533063
## [118,] 1 53 58 1 2.437413441 160.0 0.521241830 2.48087030
## [119,] 1 53 60 1 0.961382832 66.0 0.214052288 1.06326879
## [120,] 1 53 60 2 0.864606868 60.0 0.194444444 0.98221391
## [121,] 1 53 61 1 0.509792151 24.0 0.076797386 0.48027696
## [122,] 1 53 63 0 0.315574271 7.0 0.021241830 0.19270569
## [123,] 1 54 59 7 1.649737581 115.0 0.374183007 1.75026574
## [124,] 1 54 60 3 0.837766399 56.0 0.181372549 0.92815971
## [125,] 1 54 66 0 1.247973982 93.0 0.302287582 1.43345222
## [126,] 1 54 67 46 35.927197550 305.0 0.995098039 12.88064344
## [127,] 1 54 62 0 0.400979878 13.5 0.042483660 0.31325636
## [128,] 1 54 69 7 3.755749499 229.0 0.746732026 4.07700659
## [129,] 1 54 63 19 4.414009299 256.0 0.834967320 5.09413209
## [130,] 1 54 58 1 2.475524715 162.0 0.527777778 2.51702455
## [131,] 1 54 62 0 0.400979878 13.5 0.042483660 0.31325636
## [132,] 1 55 58 1 2.530979310 172.5 0.562091503 2.71367426
## [133,] 1 55 58 0 2.662998704 180.0 0.586601307 2.86197740
## [134,] 1 55 58 1 2.530979310 172.5 0.562091503 2.71367426
## [135,] 1 55 66 18 4.804171448 266.0 0.867647059 5.60742159
## [136,] 1 55 66 0 1.260600345 94.0 0.305555556 1.44747748
## [137,] 1 55 69 3 3.600444441 222.0 0.723856209 3.86739405
## [138,] 1 55 69 22 9.914833752 299.0 0.975490196 9.39188273
## [139,] 1 55 67 1 1.811079885 124.0 0.403594771 1.88598249
## [140,] 1 56 60 0 1.227563233 87.5 0.284313725 1.35682235
## [141,] 1 56 66 2 1.066030628 76.0 0.246732026 1.19890073
## [142,] 1 56 66 1 1.158877052 81.0 0.263071895 1.26723355
## [143,] 1 56 67 0 1.969395285 136.0 0.442810458 2.07400530
## [144,] 1 56 60 0 1.227563233 87.5 0.284313725 1.35682235
## [145,] 1 57 64 9 0.794307700 52.0 0.168300654 0.87399124
## [146,] 1 57 69 0 3.931761584 237.0 0.772875817 4.33883575
## [147,] 1 57 61 0 0.833747106 55.0 0.178104575 0.91463195
## [148,] 1 57 62 0 0.552674792 28.0 0.089869281 0.53950384
## [149,] 1 57 63 0 0.462552228 21.0 0.066993464 0.43459629
## [150,] 1 57 64 0 0.563379414 29.5 0.094771242 0.56131353
## [151,] 1 57 64 0 0.563379414 29.5 0.094771242 0.56131353
## [152,] 1 57 67 0 2.011559467 139.0 0.452614379 2.12244365
## [153,] 1 58 59 0 2.069439060 144.0 0.468954248 2.20458542
## [154,] 1 58 60 3 1.135555378 80.0 0.259803922 1.25353082
## [155,] 1 58 61 1 0.796549401 53.0 0.171568627 0.88754926
## [156,] 1 58 67 0 2.071066970 145.0 0.472222222 2.22123541
## [157,] 1 58 58 0 2.928509444 193.0 0.629084967 3.13744799
## [158,] 1 58 58 3 2.663729825 181.0 0.589869281 2.88229827
## [159,] 1 58 61 2 0.707797813 42.0 0.135620915 0.73737768
## [160,] 1 59 60 0 1.514211002 106.0 0.344771242 1.61838327
## [161,] 1 59 63 0 0.640101130 35.0 0.112745098 0.63983767
## [162,] 1 59 64 1 0.604178474 33.0 0.106209150 0.61151692
## [163,] 1 59 64 4 0.457901193 20.0 0.063725490 0.41907477
## [164,] 1 59 64 0 0.730630672 44.0 0.142156863 0.76489828
## [165,] 1 59 64 7 0.661242883 38.0 0.122549020 0.68190763
## [166,] 1 59 67 3 1.883625712 131.0 0.426470588 1.99459441
## [167,] 1 60 61 1 1.032655543 74.0 0.240196078 1.17168166
## [168,] 1 60 67 2 2.030345977 142.0 0.462418301 2.17151046
## [169,] 1 60 61 25 9.702873375 298.0 0.972222222 9.11678640
## [170,] 1 60 64 0 0.840271281 57.0 0.184640523 0.94168038
## [171,] 1 61 59 0 2.475593217 164.0 0.534313725 2.55357704
## [172,] 1 61 59 0 2.475593217 164.0 0.534313725 2.55357704
## [173,] 1 61 64 0 0.967255211 67.0 0.217320261 1.07679032
## [174,] 1 61 65 8 1.339414000 99.0 0.321895425 1.51807666
## [175,] 1 61 68 0 3.197680298 205.0 0.668300654 3.41691176
## [176,] 1 61 59 0 2.475593217 164.0 0.534313725 2.55357704
## [177,] 1 62 62 6 1.007795827 69.0 0.223856209 1.10385402
## [178,] 1 62 66 0 1.834597862 126.5 0.411764706 1.92444617
## [179,] 1 62 66 0 1.834597862 126.5 0.411764706 1.92444617
## [180,] 1 62 58 0 3.525330249 217.5 0.709150327 3.74078242
## [181,] 1 63 61 0 1.636299519 111.0 0.361111111 1.69121400
## [182,] 1 63 62 0 1.324334274 96.0 0.312091503 1.47562020
## [183,] 1 63 63 0 1.203318779 85.5 0.277777778 1.32915343
## [184,] 1 63 63 0 1.203318779 85.5 0.277777778 1.32915343
## [185,] 1 63 66 0 1.985970790 137.0 0.446078431 2.09008337
## [186,] 1 63 61 9 1.960086678 135.0 0.439542484 2.05799389
## [187,] 1 63 61 28 12.976820249 302.0 0.985294118 10.50812491
## [188,] 1 64 58 0 3.927800574 236.0 0.769607843 4.30463859
## [189,] 1 64 65 22 8.076143609 295.0 0.962418301 8.44942057
## [190,] 1 64 66 0 2.154687037 149.0 0.485294118 2.28861290
## [191,] 1 64 61 0 1.830759877 125.0 0.406862745 1.90132584
## [192,] 1 64 68 0 3.620906148 225.0 0.733660131 3.95522426
## [193,] 1 65 58 0 4.155050718 244.5 0.797385621 4.61083722
## [194,] 1 65 64 0 1.648624136 113.5 0.369281046 1.72803550
## [195,] 1 65 67 0 2.973232464 196.0 0.638888889 3.20482007
## [196,] 1 65 59 2 3.067171661 198.0 0.645424837 3.25061719
## [197,] 1 65 64 0 1.648624136 113.5 0.369281046 1.72803550
## [198,] 1 65 67 1 2.856114489 190.0 0.619281046 3.07158746
## [199,] 1 66 58 0 4.399644182 253.5 0.826797386 4.98087940
## [200,] 1 66 58 1 4.285639007 251.0 0.818627451 4.87253130
## [201,] 1 66 68 0 3.989773317 239.0 0.779411765 4.40861142
## [202,] 1 67 66 0 2.764895703 184.5 0.601307190 2.95450576
## [203,] 1 67 66 0 2.764895703 184.5 0.601307190 2.95450576
## [204,] 1 67 61 0 2.518200871 171.0 0.557189542 2.68483573
## [205,] 1 67 65 0 2.333657238 156.0 0.508169935 2.40970786
## [206,] 1 68 67 0 3.620024625 223.0 0.727124183 3.89635311
## [207,] 1 68 68 0 4.428013768 257.0 0.838235294 5.14091520
## [208,] 1 69 60 0 3.597019396 221.0 0.720588235 3.83874259
## [209,] 1 69 65 0 2.837477261 188.0 0.612745098 3.02848018
## [210,] 1 69 66 0 3.258418082 209.0 0.681372549 3.51650754
## [211,] 1 70 66 14 5.543509470 281.0 0.916666667 6.66620333
## [212,] 1 70 67 0 4.137936002 243.0 0.792483660 4.55408645
## [213,] 1 70 68 0 4.935627501 270.0 0.880718954 5.84728793
## [214,] 1 70 59 8 4.857350824 267.0 0.870915033 5.66520074
## [215,] 1 70 63 0 2.856667502 191.0 0.622549020 3.09337812
## [216,] 1 71 68 2 5.039384016 271.0 0.883986928 5.91116643
## [217,] 1 72 58 0 6.231414695 290.0 0.946078431 7.64607611
## [218,] 1 72 64 0 3.508737593 216.0 0.704248366 3.69985413
## [219,] 1 72 67 3 4.524797175 259.0 0.844771242 5.23721398
## [220,] 1 73 62 0 3.997899048 240.0 0.782679739 4.44421743
## [221,] 1 73 68 0 5.827123003 287.0 0.936274510 7.27164504
## [222,] 1 74 63 0 4.182991252 247.0 0.805555556 4.70831985
## [223,] 1 75 62 1 4.640809961 261.0 0.851307190 5.33741687
## [224,] 1 76 67 0 6.107909823 289.0 0.942810458 7.51440251
## [225,] 1 77 65 3 5.371614961 278.0 0.906862745 6.41349346
## [226,] 2 34 59 0 4.439441629 258.0 0.841503268 5.18859673
## [227,] 2 34 66 9 4.526527153 260.0 0.848039216 5.28680662
## [228,] 2 38 69 21 11.054868525 300.0 0.978758170 9.70559443
## [229,] 2 39 66 0 3.139776985 203.0 0.661764706 3.36840177
## [230,] 2 41 60 23 8.392539362 297.0 0.968954248 8.87173521
## [231,] 2 41 64 0 1.722807498 118.5 0.385620915 1.80255506
## [232,] 2 41 67 0 3.418131003 213.0 0.694444444 3.61978435
## [233,] 2 42 69 1 5.119700273 274.0 0.893790850 6.11366701
## [234,] 2 42 59 0 2.539468263 174.0 0.566993464 2.74277780
## [235,] 2 43 58 52 46.785476891 306.0 0.998366013 15.22517901
## [236,] 2 43 59 2 2.115192738 148.0 0.482026144 2.27164950
## [237,] 2 43 64 0 1.335072501 97.5 0.316993464 1.49681104
## [238,] 2 43 64 0 1.335072501 97.5 0.316993464 1.49681104
## [239,] 2 44 64 6 0.843816012 58.0 0.187908497 0.95519540
## [240,] 2 44 58 9 3.073068366 200.0 0.651960784 3.29715210
## [241,] 2 44 63 19 4.776008936 265.0 0.864379085 5.55098224
## [242,] 2 45 65 6 1.055712121 75.0 0.243464052 1.18528396
## [243,] 2 45 66 0 1.914786131 133.0 0.433006536 2.02616692
## [244,] 2 45 67 1 2.500377327 167.5 0.545751634 2.61854084
## [245,] 2 46 58 2 2.548335743 175.0 0.570261438 2.76233064
## [246,] 2 46 69 3 4.205968178 248.0 0.808823529 4.74838423
## [247,] 2 46 62 5 0.410962127 15.0 0.047385621 0.33859115
## [248,] 2 46 65 20 5.654691120 284.0 0.926470588 6.94936199
## [249,] 2 47 63 23 7.086960791 292.0 0.952614379 7.93446929
## [250,] 2 47 62 0 0.654041292 37.0 0.119281046 0.66793420
## [251,] 2 47 65 0 1.110987507 78.0 0.253267974 1.22618138
## [252,] 2 48 58 11 3.208737369 206.5 0.673202614 3.45384807
## [253,] 2 48 58 11 3.208737369 206.5 0.673202614 3.45384807
## [254,] 2 48 67 7 2.057512035 143.0 0.465686275 2.18801082
## [255,] 2 49 63 0 0.446089440 18.0 0.057189542 0.38750961
## [256,] 2 49 64 10 0.907914443 63.0 0.204248366 1.02273232
## [257,] 2 50 63 13 1.584123146 109.0 0.354575163 1.66195539
## [258,] 2 50 64 0 0.524314606 26.5 0.084967320 0.51748906
## [259,] 2 51 59 13 2.955252307 195.0 0.635620915 3.18218953
## [260,] 2 51 59 3 1.429100126 100.0 0.325163399 1.53229660
## [261,] 2 52 69 3 3.646195802 226.0 0.736928105 3.98515219
## [262,] 2 52 59 2 1.490054414 103.0 0.334967320 1.57517083
## [263,] 2 52 62 3 0.090342246 2.0 0.004901961 0.07076769
## [264,] 2 52 66 4 0.954856122 64.0 0.207516340 1.03624091
## [265,] 2 53 58 4 2.264608635 150.0 0.488562092 2.30565770
## [266,] 2 53 65 1 0.612926926 34.0 0.109477124 0.62570729
## [267,] 2 53 59 3 1.449545695 102.0 0.331699346 1.56084289
## [268,] 2 53 60 9 1.274878583 95.0 0.308823529 1.46153321
## [269,] 2 53 63 24 7.770481155 294.0 0.959150327 8.26452677
## [270,] 2 53 65 12 1.675936927 116.0 0.377450980 1.76514484
## [271,] 2 54 60 11 1.785908238 121.0 0.393790850 1.84027943
## [272,] 2 54 65 23 7.477477714 293.0 0.955882353 8.09353560
## [273,] 2 54 65 5 0.464244432 22.0 0.070261438 0.44996259
## [274,] 2 54 68 7 2.685874434 182.0 0.593137255 2.90275488
## [275,] 2 55 63 6 0.140041382 4.0 0.011437908 0.12586698
## [276,] 2 55 68 15 4.893509596 268.0 0.874183007 5.72438805
## [277,] 2 56 65 9 1.017408758 72.0 0.233660131 1.14451673
## [278,] 2 56 66 3 1.012030756 70.0 0.227124183 1.11739828
## [279,] 2 57 61 5 0.576033649 31.0 0.099673203 0.58293879
## [280,] 2 57 62 14 2.276115237 154.0 0.501633987 2.37467639
## [281,] 2 57 64 1 0.433651903 17.0 0.053921569 0.37143305
## [282,] 2 59 62 35 19.439866351 304.0 0.991830065 11.78161995
## [283,] 2 60 59 17 5.498080993 279.0 0.910130719 6.49476265
## [284,] 2 60 65 0 1.116601751 79.0 0.256535948 1.23984706
## [285,] 2 61 62 5 0.771961310 49.0 0.158496732 0.83323075
## [286,] 2 61 65 0 1.238436859 92.0 0.299019608 1.41945664
## [287,] 2 61 68 1 3.073847793 201.0 0.655228758 3.32070524
## [288,] 2 62 59 13 4.106339493 242.0 0.789215686 4.51693924
## [289,] 2 62 58 0 3.525330249 217.5 0.709150327 3.74078242
## [290,] 2 62 65 19 5.708016179 286.0 0.933006536 7.15918328
## [291,] 2 63 60 1 2.019968561 141.0 0.459150327 2.15508322
## [292,] 2 65 58 0 4.155050718 244.5 0.797385621 4.61083722
## [293,] 2 65 61 2 1.849141015 128.0 0.416666667 1.94769560
## [294,] 2 65 62 22 8.135288330 296.0 0.965686275 8.65073327
## [295,] 2 65 66 15 4.665323543 262.0 0.854575163 5.38908977
## [296,] 2 66 58 0 4.399644182 253.5 0.826797386 4.98087940
## [297,] 2 66 61 13 3.813282069 232.0 0.756535948 4.17215968
## [298,] 2 67 64 8 2.274264404 153.0 0.498366013 2.35729319
## [299,] 2 67 63 1 1.930842513 134.0 0.436274510 2.04204810
## [300,] 2 69 67 8 4.073473319 241.0 0.785947712 4.48032159
## [301,] 2 70 58 0 5.551451242 282.0 0.919934641 6.75684366
## [302,] 2 70 58 4 5.354712358 277.0 0.903594771 6.33491956
## [303,] 2 72 63 0 3.485142736 214.0 0.697712418 3.64621639
## [304,] 2 74 65 3 4.210921309 249.0 0.812091503 4.78909235
## [305,] 2 78 65 1 5.867661095 288.0 0.939542484 7.38984037
## [306,] 2 83 58 2 11.077777616 301.0 0.982026144 10.07079293
ks.test(di, "pchisq", df = 3)
## Warning in ks.test.default(di, "pchisq", df = 3): ties should not be present
## for the one-sample Kolmogorov-Smirnov test
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: di
## D = 0.061354, p-value = 0.1996
## alternative hypothesis: two-sided
#Plot Normalitas
plot(Data$di.kuadrat, Data$Chi.Square,
main = "QQ Plot",
xlab = "Diˆ2",
ylab = "Xˆ2",
col = "blue")
abline(lm(Data$Chi.Square~Data$di.kuadrat), col = "red")
cor(X)
## X1 X2 X3
## X1 1.00000000 0.089529446 -0.063176102
## X2 0.08952945 1.000000000 -0.003764474
## X3 -0.06317610 -0.003764474 1.000000000
#Uji asumsi Homogenitas matriks varians kovarians
library(biotools)
## Warning: package 'biotools' was built under R version 4.4.3
## Loading required package: MASS
## ---
## biotools version 4.2
X <- as.matrix(Data[,-1])
Y <- Data[[1]]
Y <- as.factor(Y)
#Pisahkan data berdasarkan kelompok Y
grup.data <- split(as.data.frame(X),Y)
#Hitung matriks kovarian tiap klp
Sj_list <- lapply(grup.data, function(grup) {
grup <- as.matrix(grup)
if (nrow(grup) > 1) {cov(grup)} else {stop("Ada grup dengan kurang dari 2 observasi. Tidak bisa menghitung kovarians.")}
})
# Tampilkan hasil
Sj_list
## $`1`
## X1 X2 X3 di.kuadrat k
## X1 121.26753968 6.27478175 -5.5498413 0.3923483 6.005089
## X2 6.27478175 10.38718254 0.7076984 0.9740786 27.783661
## X3 -5.54984127 0.70769841 34.4606349 12.7389145 176.040089
## di.kuadrat 0.39234826 0.97407861 12.7389145 9.2834523 175.477160
## k 6.00508929 27.78366071 176.0400893 175.4771598 7380.121607
## p.k 0.01962447 0.09079628 0.5752944 0.5734548 24.118044
## Chi.Square 0.68670798 0.82934100 7.4242999 5.6507768 171.453116
## p.k Chi.Square
## X1 0.01962447 0.6867080
## X2 0.09079628 0.8293410
## X3 0.57529441 7.4242999
## di.kuadrat 0.57345477 5.6507768
## k 24.11804447 171.4531165
## p.k 0.07881714 0.5603043
## Chi.Square 0.56030430 4.7192213
##
## $`2`
## X1 X2 X3 di.kuadrat k
## X1 103.3706790 -5.54367284 -8.939043 -0.3172266 160.09097
## X2 -5.5436728 11.16975309 -2.195062 -2.9123401 -19.86736
## X3 -8.9390432 -2.19506173 84.376235 39.1566875 423.77847
## di.kuadrat -0.3172266 -2.91234012 39.156687 32.3145921 297.90102
## k 160.0909722 -19.86736111 423.778472 297.9010160 8841.28125
## p.k 0.5231731 -0.06492602 1.384897 0.9735327 28.89308
## Chi.Square 3.9762899 -0.89410677 19.401829 13.9255825 250.36561
## p.k Chi.Square
## X1 0.52317311 3.9762899
## X2 -0.06492602 -0.8941068
## X3 1.38489697 19.4018285
## di.kuadrat 0.97353273 13.9255825
## k 28.89307598 250.3656106
## p.k 0.09442182 0.8181883
## Chi.Square 0.81818827 8.9371835
#Matrriks kovarians Gabungan (W)
#Hitung jumlah sampel per kelompok
n <- sapply(grup.data, nrow)
#Hitung Matriks kovarians gabungan (W)
W <-(((14*Sj_list[[1]])+(14*Sj_list[[2]])) / (sum(n)- length(n)))
W
## X1 X2 X3 di.kuadrat k
## X1 10.34518112 0.033669489 -0.66725126 0.00345955 7.6491607
## X2 0.03366949 0.992753614 -0.06849699 -0.08926204 0.3645664
## X3 -0.66725126 -0.068496995 5.47275057 2.38992904 27.6232232
## di.kuadrat 0.00345955 -0.089262043 2.38992904 1.91569941 21.8003107
## k 7.64916073 0.364566429 27.62322323 21.80031073 747.0382895
## p.k 0.02499726 0.001191394 0.09027197 0.07124285 2.4413016
## Chi.Square 0.21474332 -0.002982634 1.23541381 0.90154286 19.4258624
## p.k Chi.Square
## X1 0.024997257 0.214743324
## X2 0.001191394 -0.002982634
## X3 0.090271971 1.235413811
## di.kuadrat 0.071242846 0.901542863
## k 2.441301600 19.425862434
## p.k 0.007978110 0.063483211
## Chi.Square 0.063483211 0.628913379
#Hitung determinan matriks kovarians per kelompok
det.Sj <- sapply(Sj_list, det)
#Hitung determinan matriks W
det.W <- det(W)
#Hitung nilai lambda
lambda <- ((det.Sj[[1]]^((n[1]- 1) / 2)) *
(det.Sj[[2]]^((n[2]- 1) / 2))) /
((det.W/28)^((sum(n)- length(n)) / 2))
ln <--2 * log(lambda)
#Hitung nilai box's M
BoxM <- (sum(n)- length(n)) * log(det.W/28)
(((n[[1]]-1) * log(det.Sj[[1]])) + ((n[[2]]-1) * log(det.Sj[[2]])))
## Warning in log(det.Sj[[2]]): NaNs produced
## [1] NaN
#Rata-rata kelompok 1
klp1 <- Data[1:225, c("X1","X2","X3")]
x1 <- colMeans(klp1)
x1
## X1 X2 X3
## 52.017778 62.862222 2.791111
#Rata-rata kelompok 2
klp2 <- Data[226:306, c("X1","X2","X3")]
x2 <- colMeans(klp2)
x2
## X1 X2 X3
## 53.67901 62.82716 7.45679
#Selisisih rata2 klp 1 dengan klp 2
x1.x2 <- x1-x2
x1.x2
## X1 X2 X3
## -1.66123457 0.03506173 -4.66567901
#Matriks kovarian klp 1 (S1)
s1 <- cov(klp1)
s1
## X1 X2 X3
## X1 121.267540 6.2747817 -5.5498413
## X2 6.274782 10.3871825 0.7076984
## X3 -5.549841 0.7076984 34.4606349
#Matriks kovarian klp 2 (S2)
s2 <- cov(klp2)
s2
## X1 X2 X3
## X1 103.370679 -5.543673 -8.939043
## X2 -5.543673 11.169753 -2.195062
## X3 -8.939043 -2.195062 84.376235
#Matriks kovarians gabungan (Spl)
g <- Data[, c("X1","X2","X3")]
spl <- cov(g)
spl
## X1 X2 X3
## X1 116.714583 3.142912 -4.907082
## X2 3.142912 10.558631 -0.087946
## X3 -4.907082 -0.087946 51.691118
#Inversmatrikskovariangabungan(Splˆ-1)
Spl.inv<-solve(spl)
Spl.inv
## X1 X2 X3
## X1 0.0086716602 -2.574411e-03 8.188281e-04
## X2 -0.0025744110 9.547487e-02 -8.195245e-05
## X3 0.0008188281 -8.195245e-05 1.942328e-02
#Kombinasilinearfisher
a<-Spl.inv %*%x1.x2
a
## [,1]
## X1 -0.018316314
## X2 0.008006578
## X3 -0.091985911
#rataanskordiskriminanklp1
z11<-0.125121317 * klp1$X1
z12<-0.069125866 * klp1$X2
z13<-0.005156851 * klp1$X3
Z1<-z11 +z12 + z13
z1.bar<-sum(Z1)/15
z1.bar
## [1] 163.025
#rataanskordiskriminanklp1
z21<-0.125121317 * klp2$X1
z22<-0.069125866 * klp2$X2
z23<-0.005156851 * klp2$X3
Z2<-z21 +z22 + z23
z2.bar<-sum(Z2)/15
z2.bar
## [1] 59.92825
#CuttingScore
n1<-225
n2<-81
m<-(n1* z1.bar +n2 *z2.bar) / (n1+ n2)
m
## [1] 135.7347
#Cara cepat analisis diskriminan
library(MASS)
fit <- lda(Y~X1+X2+X3, data=Data)
fit
## Call:
## lda(Y ~ X1 + X2 + X3, data = Data)
##
## Prior probabilities of groups:
## 1 2
## 0.7352941 0.2647059
##
## Group means:
## X1 X2 X3
## 1 52.01778 62.86222 2.791111
## 2 53.67901 62.82716 7.456790
##
## Coefficients of linear discriminants:
## LD1
## X1 0.02826395
## X2 -0.01235497
## X3 0.14194367
#Hit Rasio
fit.val <- predict(fit, Data[,-1])
ct <- table(Data$Y, fit.val$class)
ct
##
## 1 2
## 1 215 10
## 2 67 14
#Percent Correct for each category of 3
diag(prop.table(ct,1))
## 1 2
## 0.9555556 0.1728395
#Akurasi
sum(diag(prop.table(ct)))
## [1] 0.748366