library(readxl)
AD <- read_excel("D:/DATA/SEMESTER 4/STATISTIKA MULTIVARIAT/test_scores.xlsx")
head(AD)
X1<-AD$pretest
X2<-AD$posttest
Y<-AD$lunch

diskriminan<-data.frame(X1,X2,Y)
diskriminan.s=scale(diskriminan)

Diskriminan<-as.matrix(diskriminan.s)
Diskriminan
##                   X1           X2          Y
##    [1,]  0.519355359  0.350173051  0.8690232
##    [2,]  0.814273157  0.850645323  0.8690232
##    [3,]  0.666814258  0.636157207  0.8690232
##    [4,]  0.445625909  0.707653246  0.8690232
##    [5,]  0.666814258  0.636157207  0.8690232
##    [6,]  0.814273157  0.493165129  0.8690232
##    [7,]  0.593084808  0.564661168  0.8690232
##    [8,]  0.593084808  0.350173051  0.8690232
##    [9,]  0.666814258  0.707653246  0.8690232
##   [10,]  0.445625909  0.350173051  0.8690232
##   [11,]  0.445625909  0.421669090  0.8690232
##   [12,]  0.666814258  0.493165129  0.8690232
##   [13,]  0.814273157  0.779149285  0.8690232
##   [14,]  0.371896459  0.278677012  0.8690232
##   [15,]  0.666814258  0.707653246  0.8690232
##   [16,]  0.666814258  0.421669090  0.8690232
##   [17,]  0.593084808  0.207180973  0.8690232
##   [18,]  0.888002607  0.421669090  0.8690232
##   [19,]  0.593084808  0.278677012  0.8690232
##   [20,]  0.666814258  0.421669090  0.8690232
##   [21,]  0.371896459  0.064188896  0.8690232
##   [22,]  0.371896459  0.207180973  0.8690232
##   [23,]  0.150708111 -0.078803182  0.8690232
##   [24,]  0.150708111  0.207180973  0.8690232
##   [25,]  0.076978661 -0.150299221 -1.1501778
##   [26,]  0.224437560 -0.007307143  0.8690232
##   [27,]  0.371896459  0.207180973  0.8690232
##   [28,]  0.371896459 -0.007307143  0.8690232
##   [29,] -0.070480238 -0.293291299  0.8690232
##   [30,]  0.371896459  0.564661168  0.8690232
##   [31,]  0.224437560 -0.078803182  0.8690232
##   [32,]  0.814273157  0.278677012  0.8690232
##   [33,]  0.371896459  0.636157207  0.8690232
##   [34,]  0.298167010  0.135684935  0.8690232
##   [35,]  0.150708111  0.135684935  0.8690232
##   [36,]  0.371896459  0.064188896  0.8690232
##   [37,]  0.445625909  0.278677012  0.8690232
##   [38,]  0.445625909 -0.078803182  0.8690232
##   [39,]  0.298167010  0.135684935  0.8690232
##   [40,]  0.519355359  0.350173051  0.8690232
##   [41,]  0.371896459 -0.078803182  0.8690232
##   [42,]  0.445625909  0.564661168  0.8690232
##   [43,]  0.224437560  0.779149285 -1.1501778
##   [44,]  0.666814258  1.065133440 -1.1501778
##   [45,]  0.224437560  0.707653246 -1.1501778
##   [46,]  0.740543707  1.422613635  0.8690232
##   [47,]  0.740543707  0.922141362  0.8690232
##   [48,]  0.519355359  0.564661168 -1.1501778
##   [49,]  0.224437560  0.421669090 -1.1501778
##   [50,]  0.298167010  0.493165129 -1.1501778
##   [51,]  0.298167010  0.493165129 -1.1501778
##   [52,]  0.593084808  0.636157207 -1.1501778
##   [53,]  0.593084808  0.779149285  0.8690232
##   [54,]  0.298167010  0.707653246  0.8690232
##   [55,]  0.445625909  0.707653246 -1.1501778
##   [56,]  0.003249212  0.350173051 -1.1501778
##   [57,]  0.814273157  1.136629479  0.8690232
##   [58,]  0.888002607  0.993637401  0.8690232
##   [59,]  0.961732056  0.850645323  0.8690232
##   [60,]  0.593084808  0.922141362  0.8690232
##   [61,]  0.593084808  1.136629479 -1.1501778
##   [62,]  0.814273157  1.065133440  0.8690232
##   [63,]  0.888002607  1.208125518  0.8690232
##   [64,]  0.888002607  1.136629479 -1.1501778
##   [65,]  1.330379304  1.279621557  0.8690232
##   [66,]  0.961732056  1.422613635  0.8690232
##   [67,]  1.109190955  1.708597790 -1.1501778
##   [68,]  1.404108754  1.279621557 -1.1501778
##   [69,]  0.666814258  1.136629479  0.8690232
##   [70,]  0.519355359  0.779149285 -1.1501778
##   [71,]  1.551567653  1.208125518  0.8690232
##   [72,]  1.330379304  1.351117596  0.8690232
##   [73,]  0.740543707  1.422613635  0.8690232
##   [74,]  0.814273157  0.850645323  0.8690232
##   [75,]  0.814273157  1.208125518  0.8690232
##   [76,]  0.814273157  1.065133440  0.8690232
##   [77,]  0.740543707  1.136629479 -1.1501778
##   [78,]  0.593084808  0.779149285 -1.1501778
##   [79,]  0.961732056  1.208125518 -1.1501778
##   [80,]  0.740543707  0.850645323  0.8690232
##   [81,]  1.109190955  1.136629479  0.8690232
##   [82,]  0.740543707  0.993637401 -1.1501778
##   [83,]  0.445625909  0.493165129 -1.1501778
##   [84,]  0.593084808  0.707653246 -1.1501778
##   [85,]  0.519355359  1.065133440  0.8690232
##   [86,]  1.035461506  0.993637401  0.8690232
##   [87,]  0.593084808  0.564661168 -1.1501778
##   [88,]  0.519355359  0.993637401 -1.1501778
##   [89,]  0.593084808  0.707653246 -1.1501778
##   [90,]  0.298167010  0.493165129 -1.1501778
##   [91,]  0.593084808  0.922141362  0.8690232
##   [92,]  0.814273157  0.636157207  0.8690232
##   [93,]  0.298167010  0.707653246  0.8690232
##   [94,]  0.371896459  0.493165129 -1.1501778
##   [95,]  0.961732056  0.636157207 -1.1501778
##   [96,]  1.404108754  1.065133440 -1.1501778
##   [97,]  0.593084808  0.421669090 -1.1501778
##   [98,]  1.330379304  0.779149285 -1.1501778
##   [99,]  1.477838203  1.136629479  0.8690232
##  [100,]  1.699026552  1.208125518  0.8690232
##  [101,]  1.035461506  0.779149285 -1.1501778
##  [102,]  1.330379304  0.993637401 -1.1501778
##  [103,]  1.404108754  0.922141362 -1.1501778
##  [104,]  1.330379304  0.922141362  0.8690232
##  [105,]  0.961732056  1.065133440 -1.1501778
##  [106,]  1.256649854  1.208125518  0.8690232
##  [107,]  1.330379304  0.922141362  0.8690232
##  [108,]  1.182920405  1.708597790  0.8690232
##  [109,]  1.330379304  0.922141362  0.8690232
##  [110,]  1.551567653  0.922141362  0.8690232
##  [111,]  1.109190955  1.208125518  0.8690232
##  [112,]  1.182920405  0.779149285  0.8690232
##  [113,]  1.551567653  1.279621557  0.8690232
##  [114,]  1.256649854  1.136629479  0.8690232
##  [115,]  1.182920405  1.136629479  0.8690232
##  [116,] -0.439127486  0.064188896 -1.1501778
##  [117,]  0.003249212  0.207180973  0.8690232
##  [118,]  0.371896459  0.421669090 -1.1501778
##  [119,]  0.298167010  0.421669090 -1.1501778
##  [120,]  0.298167010  0.207180973  0.8690232
##  [121,]  0.003249212  0.135684935 -1.1501778
##  [122,]  0.003249212  0.278677012  0.8690232
##  [123,]  0.076978661  0.493165129  0.8690232
##  [124,] -0.144209688  0.135684935 -1.1501778
##  [125,] -0.512856936  0.207180973 -1.1501778
##  [126,]  0.519355359  0.636157207  0.8690232
##  [127,]  0.224437560  0.564661168  0.8690232
##  [128,] -0.217939137  0.135684935 -1.1501778
##  [129,]  0.298167010 -0.007307143  0.8690232
##  [130,] -0.144209688  0.135684935 -1.1501778
##  [131,]  0.150708111  0.350173051  0.8690232
##  [132,]  0.961732056  0.636157207  0.8690232
##  [133,]  0.888002607  0.922141362  0.8690232
##  [134,]  0.888002607  0.636157207 -1.1501778
##  [135,]  0.814273157  1.065133440  0.8690232
##  [136,]  0.224437560  0.350173051  0.8690232
##  [137,]  0.445625909  0.207180973  0.8690232
##  [138,]  0.593084808  0.564661168  0.8690232
##  [139,]  0.961732056  0.707653246  0.8690232
##  [140,]  0.445625909  0.636157207 -1.1501778
##  [141,]  1.477838203  1.136629479  0.8690232
##  [142,]  0.961732056  0.564661168 -1.1501778
##  [143,]  0.740543707  0.350173051 -1.1501778
##  [144,]  0.740543707  0.707653246 -1.1501778
##  [145,]  0.445625909  0.707653246 -1.1501778
##  [146,]  0.519355359  0.135684935 -1.1501778
##  [147,]  0.740543707  0.493165129 -1.1501778
##  [148,]  1.109190955  0.850645323 -1.1501778
##  [149,]  0.740543707  0.493165129 -1.1501778
##  [150,]  0.371896459  0.421669090 -1.1501778
##  [151,]  0.371896459 -0.007307143  0.8690232
##  [152,]  0.519355359  0.207180973  0.8690232
##  [153,]  0.298167010  0.421669090  0.8690232
##  [154,]  0.519355359  0.350173051  0.8690232
##  [155,] -0.070480238  0.064188896  0.8690232
##  [156,]  0.224437560 -0.078803182  0.8690232
##  [157,]  0.224437560 -0.078803182  0.8690232
##  [158,]  0.371896459  0.135684935  0.8690232
##  [159,]  0.961732056  0.779149285  0.8690232
##  [160,]  0.003249212  0.135684935  0.8690232
##  [161,]  0.445625909  0.278677012  0.8690232
##  [162,]  0.445625909  0.278677012  0.8690232
##  [163,]  0.445625909  0.207180973  0.8690232
##  [164,]  0.666814258  0.993637401  0.8690232
##  [165,]  0.445625909  0.350173051  0.8690232
##  [166,] -0.070480238  0.135684935 -1.1501778
##  [167,]  0.076978661 -0.150299221  0.8690232
##  [168,]  0.003249212 -0.221795260  0.8690232
##  [169,]  0.740543707  0.278677012  0.8690232
##  [170,]  0.666814258  0.636157207  0.8690232
##  [171,]  1.256649854  0.850645323  0.8690232
##  [172,]  1.256649854  0.779149285  0.8690232
##  [173,]  0.888002607  0.350173051  0.8690232
##  [174,]  0.666814258  0.493165129  0.8690232
##  [175,]  1.035461506  0.850645323  0.8690232
##  [176,]  0.888002607  0.779149285  0.8690232
##  [177,]  1.109190955  0.636157207  0.8690232
##  [178,]  0.666814258  0.707653246  0.8690232
##  [179,]  0.666814258  0.564661168  0.8690232
##  [180,]  1.035461506  0.779149285  0.8690232
##  [181,]  1.109190955  1.065133440  0.8690232
##  [182,]  1.182920405  0.779149285  0.8690232
##  [183,]  0.888002607  0.922141362  0.8690232
##  [184,]  1.035461506  0.850645323  0.8690232
##  [185,]  1.035461506  0.922141362  0.8690232
##  [186,]  0.814273157  0.993637401  0.8690232
##  [187,]  0.666814258  0.779149285  0.8690232
##  [188,]  1.035461506  1.065133440  0.8690232
##  [189,]  0.888002607  1.065133440  0.8690232
##  [190,]  0.740543707  0.636157207  0.8690232
##  [191,]  0.666814258  1.494109674  0.8690232
##  [192,]  0.666814258  0.922141362  0.8690232
##  [193,]  1.330379304  0.993637401  0.8690232
##  [194,]  0.814273157  1.136629479  0.8690232
##  [195,]  0.076978661  0.779149285  0.8690232
##  [196,]  0.888002607  1.422613635  0.8690232
##  [197,]  0.519355359  1.065133440  0.8690232
##  [198,]  0.961732056  1.065133440  0.8690232
##  [199,]  1.035461506  1.208125518  0.8690232
##  [200,]  0.961732056  1.279621557  0.8690232
##  [201,]  0.593084808  1.065133440  0.8690232
##  [202,]  1.256649854  1.136629479  0.8690232
##  [203,]  1.109190955  1.065133440  0.8690232
##  [204,]  0.961732056  1.422613635  0.8690232
##  [205,]  0.666814258  1.279621557  0.8690232
##  [206,]  0.666814258  0.779149285  0.8690232
##  [207,]  0.445625909  0.707653246  0.8690232
##  [208,]  1.109190955  0.779149285  0.8690232
##  [209,]  0.740543707  0.850645323  0.8690232
##  [210,]  0.593084808  0.350173051  0.8690232
##  [211,]  0.961732056  0.922141362  0.8690232
##  [212,]  0.814273157  0.564661168  0.8690232
##  [213,]  0.666814258  0.564661168  0.8690232
##  [214,]  0.961732056  0.707653246  0.8690232
##  [215,]  0.888002607  0.850645323  0.8690232
##  [216,]  0.814273157  0.564661168  0.8690232
##  [217,]  0.961732056  0.922141362  0.8690232
##  [218,]  1.256649854  1.351117596  0.8690232
##  [219,]  1.035461506  0.636157207  0.8690232
##  [220,]  0.961732056  0.779149285  0.8690232
##  [221,]  0.519355359  0.564661168  0.8690232
##  [222,]  1.182920405  0.922141362  0.8690232
##  [223,]  1.256649854  0.850645323  0.8690232
##  [224,]  0.666814258  0.493165129  0.8690232
##  [225,]  0.003249212  0.207180973  0.8690232
##  [226,]  0.003249212 -0.007307143 -1.1501778
##  [227,]  0.224437560  0.207180973  0.8690232
##  [228,]  0.371896459 -0.007307143  0.8690232
##  [229,]  0.224437560  0.135684935  0.8690232
##  [230,] -0.217939137 -0.293291299  0.8690232
##  [231,] -0.144209688 -0.007307143  0.8690232
##  [232,] -0.144209688  0.064188896  0.8690232
##  [233,] -0.070480238  0.064188896  0.8690232
##  [234,]  0.298167010  0.207180973  0.8690232
##  [235,]  0.003249212 -0.150299221  0.8690232
##  [236,]  0.076978661 -0.007307143  0.8690232
##  [237,]  0.224437560 -0.007307143  0.8690232
##  [238,]  0.224437560 -0.150299221  0.8690232
##  [239,]  0.224437560 -0.150299221 -1.1501778
##  [240,]  0.371896459  0.493165129  0.8690232
##  [241,]  0.371896459  0.135684935  0.8690232
##  [242,]  0.076978661 -0.436283377  0.8690232
##  [243,]  0.076978661  0.135684935  0.8690232
##  [244,]  0.076978661  0.493165129  0.8690232
##  [245,] -0.217939137  0.064188896  0.8690232
##  [246,] -0.217939137  0.064188896 -1.1501778
##  [247,]  0.076978661 -0.293291299  0.8690232
##  [248,]  0.224437560  0.207180973  0.8690232
##  [249,]  0.445625909  0.278677012  0.8690232
##  [250,]  0.371896459 -0.364787338  0.8690232
##  [251,]  0.150708111 -0.364787338 -1.1501778
##  [252,] -0.365398036 -0.650771493  0.8690232
##  [253,] -0.144209688 -0.722267532  0.8690232
##  [254,]  0.003249212 -0.293291299  0.8690232
##  [255,] -0.660315835 -0.722267532  0.8690232
##  [256,] -0.365398036 -0.579275454  0.8690232
##  [257,] -0.365398036 -0.722267532  0.8690232
##  [258,]  0.076978661 -0.221795260  0.8690232
##  [259,] -0.807774734 -0.650771493 -1.1501778
##  [260,] -0.144209688 -0.221795260  0.8690232
##  [261,] -0.291668587 -0.793763571  0.8690232
##  [262,] -0.365398036 -0.436283377  0.8690232
##  [263,] -0.144209688 -0.436283377  0.8690232
##  [264,] -0.144209688 -0.221795260  0.8690232
##  [265,] -0.217939137 -0.507779415  0.8690232
##  [266,] -0.439127486 -0.436283377  0.8690232
##  [267,]  0.003249212 -0.293291299  0.8690232
##  [268,]  0.076978661 -0.078803182  0.8690232
##  [269,] -0.144209688 -0.364787338  0.8690232
##  [270,] -0.365398036 -0.579275454  0.8690232
##  [271,] -0.365398036 -0.579275454 -1.1501778
##  [272,] -0.217939137 -0.364787338  0.8690232
##  [273,] -0.217939137 -0.650771493  0.8690232
##  [274,] -0.586586385 -0.364787338 -1.1501778
##  [275,] -0.660315835 -0.507779415 -1.1501778
##  [276,] -0.144209688 -0.579275454  0.8690232
##  [277,] -0.291668587 -0.436283377  0.8690232
##  [278,] -0.217939137 -0.150299221  0.8690232
##  [279,] -0.365398036 -0.221795260  0.8690232
##  [280,] -0.217939137 -0.007307143  0.8690232
##  [281,]  0.371896459  0.350173051  0.8690232
##  [282,]  0.003249212  0.135684935  0.8690232
##  [283,] -0.144209688  0.064188896  0.8690232
##  [284,]  0.150708111 -0.007307143  0.8690232
##  [285,]  0.445625909 -0.364787338  0.8690232
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##  [892,]  1.330379304  1.065133440  0.8690232
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##  [894,]  1.699026552  0.993637401  0.8690232
##  [895,]  1.625297102  1.136629479  0.8690232
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##  [898,]  1.182920405  0.850645323  0.8690232
##  [899,]  1.035461506  0.850645323  0.8690232
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##  [901,]  2.067673800  2.066077985  0.8690232
##  [902,]  2.141403249  2.280566101  0.8690232
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##  [904,]  2.067673800  2.352062140  0.8690232
##  [905,]  2.510050497  2.209070062  0.8690232
##  [906,]  2.215132699  2.352062140  0.8690232
##  [907,]  1.846485451  1.994581946  0.8690232
##  [908,]  2.067673800  2.352062140  0.8690232
##  [909,]  2.804968296  2.352062140  0.8690232
##  [910,]  2.067673800  2.352062140  0.8690232
##  [911,]  2.288862149  2.209070062  0.8690232
##  [912,]  2.436321048  2.352062140  0.8690232
##  [913,]  2.141403249  2.066077985  0.8690232
##  [914,]  1.920214901  1.994581946  0.8690232
##  [915,]  2.362591598  2.209070062  0.8690232
##  [916,]  1.920214901  2.352062140  0.8690232
##  [917,]  0.666814258  0.564661168  0.8690232
##  [918,]  1.182920405  0.993637401  0.8690232
##  [919,]  0.666814258  0.993637401  0.8690232
##  [920,]  0.814273157  1.065133440  0.8690232
##  [921,]  1.256649854  0.850645323  0.8690232
##  [922,]  1.182920405  0.564661168  0.8690232
##  [923,]  0.888002607  0.993637401  0.8690232
##  [924,]  0.814273157  0.636157207  0.8690232
##  [925,]  0.961732056  0.850645323  0.8690232
##  [926,]  1.330379304  0.993637401  0.8690232
##  [927,]  0.961732056  0.922141362  0.8690232
##  [928,]  1.182920405  0.993637401  0.8690232
##  [929,]  0.961732056  0.636157207  0.8690232
##  [930,]  0.593084808  0.707653246  0.8690232
##  [931,]  1.109190955  1.351117596  0.8690232
##  [932,]  0.961732056  0.707653246  0.8690232
##  [933,]  1.182920405  0.493165129  0.8690232
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##  [936,] -1.176421982 -0.579275454 -1.1501778
##  [937,] -0.955233633 -0.865259610 -1.1501778
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##  [939,] -0.881504183 -0.722267532 -1.1501778
##  [940,] -1.323880881 -1.079747727 -1.1501778
##  [941,] -0.734045284 -0.007307143  0.8690232
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##  [943,] -1.250151431 -0.722267532 -1.1501778
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##  [945,] -1.102692532 -0.650771493 -1.1501778
##  [946,] -1.028963083 -0.865259610 -1.1501778
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##  [948,] -0.439127486 -0.364787338 -1.1501778
##  [949,] -0.807774734 -0.722267532 -1.1501778
##  [950,] -0.955233633 -0.793763571 -1.1501778
##  [951,] -0.955233633 -1.222739804 -1.1501778
##  [952,] -0.881504183 -0.793763571 -1.1501778
##  [953,] -0.881504183 -0.865259610 -1.1501778
##  [954,] -0.881504183 -0.793763571 -1.1501778
##  [955,] -1.323880881 -0.722267532 -1.1501778
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##  [957,] -0.734045284 -0.650771493 -1.1501778
##  [958,] -0.881504183 -0.364787338 -1.1501778
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##  [960,] -1.176421982 -0.865259610 -1.1501778
##  [961,] -0.807774734 -0.793763571  0.8690232
##  [962,] -1.102692532 -0.793763571 -1.1501778
##  [963,] -1.250151431 -1.294235843 -1.1501778
##  [964,] -1.028963083 -1.437227921 -1.1501778
##  [965,] -0.955233633 -1.151243765 -1.1501778
##  [966,] -0.881504183 -0.793763571 -1.1501778
##  [967,] -1.176421982 -0.865259610 -1.1501778
##  [968,] -1.028963083 -0.936755649  0.8690232
##  [969,] -1.176421982 -0.936755649 -1.1501778
##  [970,] -0.955233633 -0.793763571 -1.1501778
##  [971,] -0.586586385 -0.936755649  0.8690232
##  [972,] -0.512856936 -1.079747727  0.8690232
##  [973,] -1.028963083 -1.437227921 -1.1501778
##  [974,] -1.323880881 -1.294235843 -1.1501778
##  [975,] -0.955233633 -1.294235843 -1.1501778
##  [976,] -0.955233633 -1.151243765  0.8690232
##  [977,] -1.250151431 -1.365731882 -1.1501778
##  [978,] -0.734045284 -1.222739804 -1.1501778
##  [979,] -0.955233633 -0.936755649 -1.1501778
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##  [981,] -1.176421982 -1.365731882 -1.1501778
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##  [984,] -1.176421982 -1.151243765 -1.1501778
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##  [986,] -0.512856936 -0.650771493 -1.1501778
##  [987,] -0.512856936 -0.507779415 -1.1501778
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##  [989,] -0.512856936 -0.865259610 -1.1501778
##  [990,] -0.734045284 -0.579275454 -1.1501778
##  [991,] -0.881504183 -0.364787338 -1.1501778
##  [992,] -0.291668587 -0.364787338 -1.1501778
##  [993,] -0.439127486 -0.364787338 -1.1501778
##  [994,] -0.734045284 -0.793763571 -1.1501778
##  [995,] -0.291668587 -0.436283377 -1.1501778
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##  [997,] -0.512856936 -0.936755649 -1.1501778
##  [998,] -0.734045284 -0.936755649 -1.1501778
##  [999,] -0.512856936 -1.008251688 -1.1501778
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## [1003,] -0.512856936 -0.936755649 -1.1501778
## [1004,] -0.144209688 -0.364787338 -1.1501778
## [1005,] -0.586586385 -0.793763571 -1.1501778
## [1006,] -1.692528129 -1.937700193 -1.1501778
## [1007,] -1.839987028 -1.723212077 -1.1501778
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## [1009,] -1.839987028 -1.794708115 -1.1501778
## [1010,] -1.913716478 -1.794708115 -1.1501778
## [1011,] -1.839987028 -2.223684349 -1.1501778
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## [1018,] -1.692528129 -2.009196232 -1.1501778
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## [1095,] -1.692528129 -1.866204154 -1.1501778
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## [1457,]  1.109190955  0.707653246  0.8690232
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## [1460,]  0.666814258  0.707653246  0.8690232
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## [1468,]  1.182920405  0.993637401  0.8690232
## [1469,]  0.961732056  0.707653246  0.8690232
## [1470,]  0.961732056  0.779149285  0.8690232
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## [1475,]  1.846485451  1.923085907  0.8690232
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## [1478,]  1.993944350  1.923085907  0.8690232
## [1479,]  2.067673800  1.708597790  0.8690232
## [1480,]  1.993944350  1.923085907  0.8690232
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## [1482,]  1.993944350  1.994581946  0.8690232
## [1483,]  2.141403249  1.923085907  0.8690232
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## [1486,]  1.920214901  1.708597790  0.8690232
## [1487,]  2.362591598  1.708597790  0.8690232
## [1488,]  2.067673800  2.209070062  0.8690232
## [1489,]  2.510050497  1.923085907  0.8690232
## [1490,]  1.772756002  1.565605712  0.8690232
## [1491,]  2.362591598  1.851589868  0.8690232
## [1492,]  1.920214901  1.923085907  0.8690232
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## [1494,]  1.993944350  1.851589868  0.8690232
## [1495,]  2.141403249  1.851589868  0.8690232
## [1496,]  1.993944350  1.851589868  0.8690232
## [1497,]  1.920214901  1.851589868  0.8690232
## [1498,]  2.288862149  1.923085907  0.8690232
## [1499,]  2.067673800  1.637101751  0.8690232
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## [1503,]  2.067673800  1.923085907  0.8690232
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## [1505,]  1.920214901  1.923085907  0.8690232
## [1506,]  1.846485451  1.780093829  0.8690232
## [1507,]  2.141403249  1.780093829  0.8690232
## [1508,]  2.067673800  1.851589868  0.8690232
## [1509,]  1.993944350  1.708597790  0.8690232
## [1510,]  2.362591598  1.780093829  0.8690232
## [1511,]  2.288862149  1.851589868  0.8690232
## [1512,]  1.920214901  1.780093829  0.8690232
## [1513,]  2.141403249  1.923085907  0.8690232
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## [1516,]  2.215132699  1.708597790  0.8690232
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## [1518,]  1.551567653  2.066077985  0.8690232
## [1519,]  1.625297102  1.637101751  0.8690232
## [1520,]  1.404108754  1.994581946  0.8690232
## [1521,]  1.477838203  1.851589868  0.8690232
## [1522,]  1.920214901  1.565605712  0.8690232
## [1523,]  1.477838203  1.780093829  0.8690232
## [1524,]  1.551567653  1.851589868  0.8690232
## [1525,]  1.330379304  1.851589868  0.8690232
## [1526,]  1.772756002  1.708597790  0.8690232
## [1527,]  1.772756002  1.780093829  0.8690232
## [1528,]  0.961732056  1.494109674  0.8690232
## [1529,]  1.551567653  1.851589868  0.8690232
## [1530,]  1.772756002  1.851589868  0.8690232
## [1531,]  1.477838203  1.494109674  0.8690232
## [1532,]  1.256649854  1.708597790  0.8690232
## [1533,]  1.551567653  1.637101751  0.8690232
## [1534,]  1.772756002  1.851589868  0.8690232
## [1535,]  1.477838203  1.637101751  0.8690232
## [1536,]  1.404108754  1.351117596  0.8690232
## [1537,]  1.551567653  1.994581946  0.8690232
## [1538,]  1.256649854  1.494109674  0.8690232
## [1539,]  1.699026552  2.066077985  0.8690232
## [1540,]  1.404108754  1.994581946  0.8690232
## [1541,]  1.477838203  1.637101751  0.8690232
## [1542,]  1.551567653  1.780093829  0.8690232
## [1543,]  1.477838203  1.637101751  0.8690232
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## [1545,]  1.699026552  1.565605712  0.8690232
## [1546,]  1.477838203  1.637101751  0.8690232
## [1547,]  1.477838203  1.279621557  0.8690232
## [1548,]  1.551567653  1.637101751  0.8690232
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## [1552,]  1.330379304  1.708597790  0.8690232
## [1553,]  1.477838203  1.851589868  0.8690232
## [1554,]  1.477838203  1.708597790  0.8690232
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## [1559,]  1.109190955  1.351117596  0.8690232
## [1560,]  1.551567653  1.994581946  0.8690232
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## [1563,]  1.330379304  1.780093829  0.8690232
## [1564,]  1.182920405  1.637101751  0.8690232
## [1565,]  1.404108754  1.851589868  0.8690232
## [1566,]  1.182920405  1.565605712  0.8690232
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## [1568,]  1.330379304  1.780093829  0.8690232
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## [1572,]  1.256649854  1.637101751  0.8690232
## [1573,]  1.477838203  1.708597790  0.8690232
## [1574,]  1.256649854  1.351117596  0.8690232
## [1575,]  1.182920405  1.708597790  0.8690232
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## [1581,]  1.625297102  1.494109674  0.8690232
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## [1583,]  1.477838203  1.351117596  0.8690232
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## [1586,]  1.699026552  1.565605712  0.8690232
## [1587,]  1.625297102  1.637101751  0.8690232
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## [1618,]  1.035461506  0.993637401  0.8690232
## [1619,]  1.256649854  1.494109674  0.8690232
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## [1630,]  0.888002607  1.279621557  0.8690232
## [1631,]  1.109190955  1.279621557  0.8690232
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## [1636,]  1.256649854  1.279621557  0.8690232
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## [1641,]  1.256649854  1.565605712  0.8690232
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## [1649,]  1.256649854  0.850645323  0.8690232
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## [1679,]  0.888002607  0.421669090  0.8690232
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## [1688,] -0.217939137  0.421669090 -1.1501778
## [1689,]  0.298167010  0.278677012 -1.1501778
## [1690,]  0.003249212  0.564661168 -1.1501778
## [1691,]  0.298167010  0.636157207  0.8690232
## [1692,] -0.070480238  0.350173051 -1.1501778
## [1693,]  0.371896459  0.421669090  0.8690232
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## [1695,] -0.439127486  0.207180973 -1.1501778
## [1696,] -0.070480238 -0.007307143 -1.1501778
## [1697,] -0.144209688  0.350173051 -1.1501778
## [1698,]  0.150708111  0.421669090 -1.1501778
## [1699,]  0.076978661  0.493165129 -1.1501778
## [1700,] -0.070480238  0.350173051 -1.1501778
## [1701,]  0.150708111  0.421669090 -1.1501778
## [1702,]  0.003249212  0.350173051 -1.1501778
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## [1712,] -0.660315835 -0.650771493  0.8690232
## [1713,] -0.439127486 -0.364787338 -1.1501778
## [1714,] -0.734045284 -0.936755649 -1.1501778
## [1715,] -0.586586385 -0.793763571 -1.1501778
## [1716,] -0.144209688 -0.650771493 -1.1501778
## [1717,] -0.734045284 -0.722267532 -1.1501778
## [1718,] -0.291668587 -0.293291299  0.8690232
## [1719,]  0.298167010  0.207180973 -1.1501778
## [1720,]  0.076978661  0.207180973 -1.1501778
## [1721,]  0.224437560  0.707653246 -1.1501778
## [1722,] -0.070480238  0.493165129 -1.1501778
## [1723,] -0.291668587 -0.007307143 -1.1501778
## [1724,] -0.144209688 -0.078803182 -1.1501778
## [1725,] -0.365398036  0.135684935 -1.1501778
## [1726,] -0.070480238  0.207180973 -1.1501778
## [1727,]  0.003249212  0.421669090 -1.1501778
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## [1762,]  0.740543707  0.707653246  0.8690232
## [1763,]  0.888002607  0.707653246  0.8690232
## [1764,]  0.814273157  0.779149285  0.8690232
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## [1766,]  0.740543707  0.564661168  0.8690232
## [1767,]  0.888002607  0.493165129  0.8690232
## [1768,]  0.740543707  0.636157207  0.8690232
## [1769,]  0.593084808  0.636157207  0.8690232
## [1770,]  1.035461506  0.707653246  0.8690232
## [1771,]  0.740543707  0.850645323  0.8690232
## [1772,]  0.593084808  0.564661168  0.8690232
## [1773,]  0.961732056  0.850645323  0.8690232
## [1774,]  0.445625909  0.350173051  0.8690232
## [1775,]  0.445625909  0.493165129  0.8690232
## [1776,]  0.371896459  0.850645323  0.8690232
## [1777,]  0.519355359  0.564661168  0.8690232
## [1778,]  0.593084808  0.922141362  0.8690232
## [1779,]  0.371896459  0.493165129 -1.1501778
## [1780,]  0.593084808  0.779149285  0.8690232
## [1781,]  0.888002607  1.065133440  0.8690232
## [1782,]  0.003249212  0.421669090  0.8690232
## [1783,]  0.224437560  0.636157207  0.8690232
## [1784,]  0.445625909  0.922141362  0.8690232
## [1785,] -0.144209688  0.850645323  0.8690232
## [1786,]  0.224437560  0.564661168  0.8690232
## [1787,]  0.814273157  0.922141362  0.8690232
## [1788,]  0.445625909  0.421669090  0.8690232
## [1789,]  0.519355359  0.707653246  0.8690232
## [1790,]  0.666814258  0.707653246  0.8690232
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## [1794,] -0.512856936 -0.364787338  0.8690232
## [1795,] -0.512856936 -0.221795260  0.8690232
## [1796,] -0.512856936 -1.151243765 -1.1501778
## [1797,] -0.439127486 -0.793763571  0.8690232
## [1798,] -0.439127486 -0.650771493  0.8690232
## [1799,] -0.144209688 -0.436283377  0.8690232
## [1800,] -0.365398036 -0.507779415  0.8690232
## [1801,] -0.512856936 -0.507779415  0.8690232
## [1802,] -0.439127486 -0.507779415  0.8690232
## [1803,] -0.586586385 -0.722267532  0.8690232
## [1804,] -0.660315835 -0.579275454  0.8690232
## [1805,] -0.881504183 -0.793763571 -1.1501778
## [1806,] -0.070480238 -0.364787338  0.8690232
## [1807,] -0.365398036 -0.221795260  0.8690232
## [1808,] -0.217939137 -0.650771493  0.8690232
## [1809,] -0.365398036 -0.579275454  0.8690232
## [1810,] -0.291668587 -0.221795260  0.8690232
## [1811,] -0.365398036 -0.865259610  0.8690232
## [1812,] -1.102692532 -0.865259610  0.8690232
## [1813,] -0.881504183 -0.865259610 -1.1501778
## [1814,] -0.955233633 -0.650771493  0.8690232
## [1815,] -0.881504183 -0.650771493  0.8690232
## [1816,] -0.955233633 -0.507779415  0.8690232
## [1817,] -0.881504183 -0.436283377  0.8690232
## [1818,] -0.734045284 -0.507779415  0.8690232
## [1819,] -0.881504183 -0.579275454  0.8690232
## [1820,] -0.881504183 -0.793763571  0.8690232
## [1821,] -1.028963083 -0.793763571 -1.1501778
## [1822,] -0.881504183 -0.579275454  0.8690232
## [1823,] -0.807774734 -0.722267532  0.8690232
## [1824,] -0.881504183 -0.293291299  0.8690232
## [1825,] -0.807774734 -0.579275454  0.8690232
## [1826,] -1.028963083 -0.722267532  0.8690232
## [1827,] -0.291668587 -0.436283377  0.8690232
## [1828,] -1.176421982 -0.650771493  0.8690232
## [1829,] -0.807774734 -0.507779415  0.8690232
## [1830,] -1.250151431 -1.079747727  0.8690232
## [1831,] -0.955233633 -0.436283377  0.8690232
## [1832,] -0.955233633 -0.364787338  0.8690232
## [1833,] -0.660315835 -0.722267532  0.8690232
## [1834,] -1.176421982 -1.294235843 -1.1501778
## [1835,] -0.512856936 -0.936755649 -1.1501778
## [1836,] -1.102692532 -1.437227921 -1.1501778
## [1837,] -0.660315835 -0.865259610 -1.1501778
## [1838,] -1.176421982 -1.651716038 -1.1501778
## [1839,] -1.176421982 -1.151243765 -1.1501778
## [1840,] -1.250151431 -1.151243765 -1.1501778
## [1841,] -0.881504183 -0.936755649 -1.1501778
## [1842,] -1.250151431 -1.079747727 -1.1501778
## [1843,] -1.250151431 -1.294235843 -1.1501778
## [1844,] -0.955233633 -1.365731882 -1.1501778
## [1845,] -0.881504183 -1.008251688 -1.1501778
## [1846,] -0.734045284 -1.365731882 -1.1501778
## [1847,] -1.028963083 -1.365731882 -1.1501778
## [1848,] -1.102692532 -1.222739804 -1.1501778
## [1849,] -0.881504183 -1.008251688 -1.1501778
## [1850,] -0.881504183 -1.151243765 -1.1501778
## [1851,] -0.955233633 -1.294235843 -1.1501778
## [1852,] -1.028963083 -1.151243765 -1.1501778
## [1853,]  0.150708111 -0.364787338 -1.1501778
## [1854,] -1.102692532 -1.294235843 -1.1501778
## [1855,] -1.176421982 -1.222739804 -1.1501778
## [1856,] -1.102692532 -1.008251688 -1.1501778
## [1857,] -0.881504183 -1.508723960 -1.1501778
## [1858,] -1.250151431 -1.222739804 -1.1501778
## [1859,] -0.660315835 -0.936755649 -1.1501778
## [1860,] -1.102692532 -1.437227921 -1.1501778
## [1861,] -1.471339780 -1.508723960 -1.1501778
## [1862,] -1.102692532 -1.008251688 -1.1501778
## [1863,] -1.766257578 -1.294235843 -1.1501778
## [1864,] -1.839987028 -1.294235843 -1.1501778
## [1865,] -1.545069230 -1.294235843 -1.1501778
## [1866,] -1.545069230 -1.151243765 -1.1501778
## [1867,] -1.692528129 -1.365731882 -1.1501778
## [1868,] -1.839987028 -1.723212077 -1.1501778
## [1869,] -1.766257578 -1.580219999 -1.1501778
## [1870,] -1.987445927 -1.508723960 -1.1501778
## [1871,] -1.839987028 -1.508723960 -1.1501778
## [1872,] -1.618798679 -1.580219999 -1.1501778
## [1873,] -1.545069230 -1.222739804 -1.1501778
## [1874,] -2.429822625 -1.437227921 -1.1501778
## [1875,] -1.766257578 -1.437227921 -1.1501778
## [1876,] -1.471339780 -0.936755649 -1.1501778
## [1877,] -1.839987028 -1.723212077 -1.1501778
## [1878,] -1.766257578 -1.294235843 -1.1501778
## [1879,] -1.913716478 -1.365731882 -1.1501778
## [1880,] -1.913716478 -2.009196232 -1.1501778
## [1881,] -1.913716478 -1.437227921 -1.1501778
## [1882,] -1.839987028 -1.437227921 -1.1501778
## [1883,] -1.250151431 -1.079747727 -1.1501778
## [1884,] -1.471339780 -1.294235843 -1.1501778
## [1885,] -1.766257578 -1.365731882 -1.1501778
## [1886,] -1.692528129 -1.580219999 -1.1501778
## [1887,] -1.471339780 -1.008251688 -1.1501778
## [1888,] -1.471339780 -1.079747727 -1.1501778
## [1889,] -1.692528129 -1.365731882 -1.1501778
## [1890,] -1.839987028 -1.294235843 -1.1501778
## [1891,] -1.545069230 -1.508723960 -1.1501778
## [1892,] -1.692528129 -1.437227921 -1.1501778
## [1893,] -1.028963083 -1.151243765 -1.1501778
## [1894,] -1.471339780 -1.008251688 -1.1501778
## [1895,] -1.323880881 -1.294235843 -1.1501778
## [1896,] -1.250151431 -1.079747727 -1.1501778
## [1897,] -1.397610331 -1.580219999 -1.1501778
## [1898,] -1.250151431 -1.365731882 -1.1501778
## [1899,] -1.102692532 -1.365731882 -1.1501778
## [1900,] -0.955233633 -0.936755649 -1.1501778
## [1901,] -1.176421982 -0.936755649 -1.1501778
## [1902,] -1.028963083 -1.580219999 -1.1501778
## [1903,] -1.102692532 -1.294235843 -1.1501778
## [1904,] -1.323880881 -1.437227921 -1.1501778
## [1905,] -1.323880881 -1.151243765 -1.1501778
## [1906,] -1.250151431 -1.151243765 -1.1501778
## [1907,] -0.955233633 -1.365731882 -1.1501778
## [1908,] -1.397610331 -1.222739804 -1.1501778
## [1909,] -1.102692532 -1.294235843 -1.1501778
## [1910,] -1.102692532 -1.222739804 -1.1501778
## [1911,] -1.102692532 -1.222739804 -1.1501778
## [1912,] -1.028963083 -0.936755649 -1.1501778
## [1913,] -1.102692532 -1.294235843 -1.1501778
## [1914,] -1.028963083 -1.294235843 -1.1501778
## [1915,] -1.102692532 -1.437227921 -1.1501778
## [1916,] -1.397610331 -1.222739804 -1.1501778
## [1917,] -1.028963083 -0.364787338  0.8690232
## [1918,] -1.545069230 -1.437227921 -1.1501778
## [1919,] -1.839987028 -1.365731882 -1.1501778
## [1920,] -1.471339780 -1.294235843  0.8690232
## [1921,] -1.323880881 -1.222739804 -1.1501778
## [1922,] -1.839987028 -1.437227921 -1.1501778
## [1923,] -1.913716478 -1.365731882 -1.1501778
## [1924,] -1.397610331 -1.079747727 -1.1501778
## [1925,] -1.692528129 -1.222739804 -1.1501778
## [1926,] -1.987445927 -1.794708115 -1.1501778
## [1927,] -1.839987028 -1.437227921 -1.1501778
## [1928,] -1.618798679 -1.437227921 -1.1501778
## [1929,] -1.618798679 -1.580219999 -1.1501778
## [1930,] -1.471339780 -1.079747727 -1.1501778
## [1931,] -1.545069230 -1.008251688 -1.1501778
## [1932,] -1.618798679 -1.437227921 -1.1501778
## [1933,] -1.692528129 -1.079747727 -1.1501778
## [1934,] -1.471339780 -1.365731882 -1.1501778
## [1935,] -1.545069230 -1.508723960 -1.1501778
## [1936,] -1.618798679 -1.365731882 -1.1501778
## [1937,] -1.839987028 -1.365731882 -1.1501778
## [1938,] -1.692528129 -1.079747727 -1.1501778
## [1939,] -1.987445927 -1.580219999 -1.1501778
## [1940,] -1.692528129 -1.651716038 -1.1501778
## [1941,] -1.766257578 -1.151243765 -1.1501778
## [1942,] -1.545069230 -1.294235843 -1.1501778
## [1943,] -1.913716478 -1.651716038 -1.1501778
## [1944,] -1.545069230 -1.294235843 -1.1501778
## [1945,] -1.618798679 -1.079747727 -1.1501778
## [1946,] -1.618798679 -1.294235843 -1.1501778
## [1947,] -1.323880881 -1.079747727 -1.1501778
## [1948,]  0.814273157  1.351117596  0.8690232
## [1949,]  1.330379304  1.136629479  0.8690232
## [1950,]  0.740543707  0.493165129  0.8690232
## [1951,]  0.519355359  0.993637401  0.8690232
## [1952,]  0.814273157  1.279621557  0.8690232
## [1953,]  0.814273157  0.993637401  0.8690232
## [1954,]  1.109190955  1.065133440  0.8690232
## [1955,]  1.035461506  1.065133440  0.8690232
## [1956,]  0.961732056  0.922141362  0.8690232
## [1957,]  0.519355359  1.065133440  0.8690232
## [1958,]  0.371896459  0.493165129  0.8690232
## [1959,]  0.814273157  1.708597790  0.8690232
## [1960,]  0.740543707  0.779149285  0.8690232
## [1961,]  0.888002607  0.993637401  0.8690232
## [1962,]  0.814273157  0.922141362  0.8690232
## [1963,]  0.445625909  1.065133440 -1.1501778
## [1964,]  0.888002607  0.779149285  0.8690232
## [1965,]  0.814273157  1.136629479  0.8690232
## [1966,]  0.740543707  0.993637401 -1.1501778
## [1967,]  0.445625909  0.922141362  0.8690232
## [1968,]  0.814273157  0.922141362  0.8690232
## [1969,]  0.519355359  0.850645323  0.8690232
## [1970,]  0.666814258  0.707653246  0.8690232
## [1971,]  1.109190955  1.136629479  0.8690232
## [1972,]  0.593084808  0.564661168  0.8690232
## [1973,]  0.740543707  0.636157207  0.8690232
## [1974,]  0.224437560  0.064188896 -1.1501778
## [1975,]  0.593084808  0.779149285  0.8690232
## [1976,]  0.740543707  0.350173051  0.8690232
## [1977,]  1.404108754  0.350173051  0.8690232
## [1978,]  1.109190955  0.993637401  0.8690232
## [1979,]  1.182920405  0.779149285  0.8690232
## [1980,]  0.445625909 -0.078803182 -1.1501778
## [1981,]  0.961732056  0.421669090  0.8690232
## [1982,]  0.519355359  0.064188896  0.8690232
## [1983,]  0.076978661  0.135684935 -1.1501778
## [1984,]  0.814273157  0.493165129  0.8690232
## [1985,]  0.740543707  0.135684935  0.8690232
## [1986,]  0.814273157  0.707653246  0.8690232
## [1987,]  0.593084808  0.707653246  0.8690232
## [1988,]  0.814273157  0.707653246  0.8690232
## [1989,]  1.182920405  0.922141362  0.8690232
## [1990,]  0.666814258  0.135684935 -1.1501778
## [1991,]  0.298167010  0.278677012 -1.1501778
## [1992,]  0.888002607  0.207180973  0.8690232
## [1993,]  0.593084808  0.636157207  0.8690232
## [1994,]  1.772756002  1.923085907  0.8690232
## [1995,]  1.920214901  1.637101751  0.8690232
## [1996,]  1.477838203  1.923085907  0.8690232
## [1997,]  1.625297102  1.565605712  0.8690232
## [1998,]  0.961732056  1.422613635  0.8690232
## [1999,]  1.330379304  1.708597790  0.8690232
## [2000,]  1.035461506  1.565605712  0.8690232
## [2001,]  1.477838203  1.923085907  0.8690232
## [2002,]  1.035461506  1.279621557  0.8690232
## [2003,]  1.256649854  1.279621557  0.8690232
## [2004,]  1.772756002  1.851589868  0.8690232
## [2005,]  1.404108754  1.923085907  0.8690232
## [2006,]  1.551567653  1.637101751  0.8690232
## [2007,]  1.330379304  1.923085907  0.8690232
## [2008,]  1.404108754  1.422613635  0.8690232
## [2009,]  1.772756002  1.923085907  0.8690232
## [2010,]  1.404108754  1.780093829 -1.1501778
## [2011,]  1.256649854  1.494109674  0.8690232
## [2012,]  1.404108754  1.208125518  0.8690232
## [2013,]  1.035461506  1.351117596  0.8690232
## [2014,]  1.404108754  1.637101751  0.8690232
## [2015,]  1.109190955  1.422613635  0.8690232
## [2016,]  1.551567653  1.994581946  0.8690232
## [2017,] -0.734045284 -0.507779415 -1.1501778
## [2018,] -0.439127486 -0.650771493 -1.1501778
## [2019,] -0.144209688 -0.793763571 -1.1501778
## [2020,] -0.586586385 -0.865259610 -1.1501778
## [2021,] -0.439127486 -0.579275454 -1.1501778
## [2022,] -0.439127486 -0.579275454 -1.1501778
## [2023,] -1.028963083 -1.008251688 -1.1501778
## [2024,] -0.070480238 -0.293291299 -1.1501778
## [2025,] -0.217939137 -0.507779415 -1.1501778
## [2026,] -0.439127486 -0.579275454 -1.1501778
## [2027,] -0.660315835 -0.650771493 -1.1501778
## [2028,] -0.512856936 -0.579275454 -1.1501778
## [2029,] -0.660315835 -0.722267532 -1.1501778
## [2030,] -0.881504183 -0.865259610 -1.1501778
## [2031,] -0.734045284 -0.579275454 -1.1501778
## [2032,] -0.217939137 -0.364787338 -1.1501778
## [2033,] -0.512856936 -0.579275454 -1.1501778
## [2034,] -0.144209688 -0.293291299 -1.1501778
## [2035,] -0.660315835 -0.793763571 -1.1501778
## [2036,] -0.070480238 -0.436283377 -1.1501778
## [2037,] -0.586586385 -0.436283377 -1.1501778
## [2038,] -0.439127486 -0.722267532 -1.1501778
## [2039,] -0.365398036 -0.364787338 -1.1501778
## [2040,] -0.660315835 -0.936755649 -1.1501778
## [2041,] -0.070480238 -0.507779415  0.8690232
## [2042,] -0.660315835 -0.865259610 -1.1501778
## [2043,] -0.217939137 -0.364787338  0.8690232
## [2044,] -1.692528129 -0.865259610 -1.1501778
## [2045,] -2.208634276 -1.008251688 -1.1501778
## [2046,] -1.618798679 -0.936755649 -1.1501778
## [2047,] -0.807774734 -0.793763571  0.8690232
## [2048,] -1.545069230 -0.936755649 -1.1501778
## [2049,] -1.250151431 -1.008251688 -1.1501778
## [2050,] -1.545069230 -1.222739804 -1.1501778
## [2051,] -1.176421982 -0.936755649 -1.1501778
## [2052,] -1.028963083 -0.865259610 -1.1501778
## [2053,] -1.397610331 -1.079747727 -1.1501778
## [2054,] -1.250151431 -1.008251688 -1.1501778
## [2055,] -1.250151431 -1.079747727 -1.1501778
## [2056,] -1.323880881 -1.079747727 -1.1501778
## [2057,] -1.471339780 -1.079747727 -1.1501778
## [2058,] -1.839987028 -1.365731882 -1.1501778
## [2059,] -1.250151431 -1.008251688 -1.1501778
## [2060,] -1.250151431 -1.222739804 -1.1501778
## [2061,] -1.397610331 -0.865259610 -1.1501778
## [2062,] -1.323880881 -0.722267532 -1.1501778
## [2063,] -1.471339780 -0.579275454 -1.1501778
## [2064,] -1.028963083 -0.936755649 -1.1501778
## [2065,] -1.323880881 -1.008251688 -1.1501778
## [2066,] -1.323880881 -0.936755649 -1.1501778
## [2067,] -1.176421982 -1.294235843 -1.1501778
## [2068,] -1.323880881 -1.008251688 -1.1501778
## [2069,] -1.102692532 -0.865259610  0.8690232
## [2070,] -1.545069230 -1.222739804 -1.1501778
## [2071,] -1.250151431 -1.008251688 -1.1501778
## [2072,] -1.176421982 -0.793763571 -1.1501778
## [2073,] -1.397610331 -1.294235843 -1.1501778
## [2074,] -0.660315835 -1.294235843 -1.1501778
## [2075,] -0.881504183 -1.079747727  0.8690232
## [2076,] -1.102692532 -1.294235843 -1.1501778
## [2077,] -0.734045284 -1.151243765 -1.1501778
## [2078,] -1.176421982 -1.222739804 -1.1501778
## [2079,] -1.176421982 -1.151243765 -1.1501778
## [2080,] -0.881504183 -1.008251688  0.8690232
## [2081,] -0.734045284 -1.151243765 -1.1501778
## [2082,] -0.807774734 -1.008251688 -1.1501778
## [2083,] -0.660315835 -1.222739804 -1.1501778
## [2084,] -0.807774734 -0.936755649 -1.1501778
## [2085,] -1.323880881 -1.222739804 -1.1501778
## [2086,] -1.028963083 -1.079747727 -1.1501778
## [2087,] -1.250151431 -1.365731882 -1.1501778
## [2088,] -1.102692532 -1.008251688 -1.1501778
## [2089,] -1.323880881 -1.437227921 -1.1501778
## [2090,] -1.250151431 -1.079747727 -1.1501778
## [2091,] -0.734045284 -0.722267532  0.8690232
## [2092,] -0.586586385 -0.865259610 -1.1501778
## [2093,] -0.807774734 -1.079747727 -1.1501778
## [2094,] -0.881504183 -1.580219999 -1.1501778
## [2095,] -1.323880881 -1.508723960 -1.1501778
## [2096,] -1.250151431 -1.222739804 -1.1501778
## [2097,] -1.028963083 -1.151243765 -1.1501778
## [2098,] -1.028963083 -0.865259610 -1.1501778
## [2099,] -0.734045284 -1.008251688 -1.1501778
## [2100,] -1.397610331 -1.437227921 -1.1501778
## [2101,] -0.955233633 -1.222739804 -1.1501778
## [2102,] -1.028963083 -1.365731882 -1.1501778
## [2103,] -1.397610331 -1.365731882 -1.1501778
## [2104,] -1.028963083 -1.508723960 -1.1501778
## [2105,] -0.881504183 -1.079747727 -1.1501778
## [2106,] -1.176421982 -0.936755649 -1.1501778
## [2107,] -1.250151431 -1.294235843 -1.1501778
## [2108,] -0.955233633 -1.151243765 -1.1501778
## [2109,] -1.397610331 -1.723212077 -1.1501778
## [2110,] -1.397610331 -1.008251688 -1.1501778
## [2111,] -1.102692532 -1.365731882 -1.1501778
## [2112,] -0.955233633 -1.365731882 -1.1501778
## [2113,] -1.176421982 -1.294235843 -1.1501778
## [2114,] -1.102692532 -1.437227921 -1.1501778
## [2115,] -1.176421982 -0.865259610  0.8690232
## [2116,] -1.028963083 -1.365731882 -1.1501778
## [2117,] -1.250151431 -1.365731882 -1.1501778
## [2118,] -0.955233633 -0.865259610 -1.1501778
## [2119,] -0.660315835 -1.008251688  0.8690232
## [2120,] -1.028963083 -1.294235843 -1.1501778
## [2121,] -0.955233633 -1.222739804 -1.1501778
## [2122,] -1.176421982 -1.079747727  0.8690232
## [2123,] -1.250151431 -1.508723960 -1.1501778
## [2124,] -1.102692532 -1.508723960 -1.1501778
## [2125,] -1.028963083 -1.222739804 -1.1501778
## [2126,] -0.734045284 -1.437227921 -1.1501778
## [2127,] -1.250151431 -1.151243765 -1.1501778
## [2128,] -1.176421982 -1.222739804 -1.1501778
## [2129,] -1.176421982 -0.865259610  0.8690232
## [2130,] -1.250151431 -1.508723960 -1.1501778
## [2131,] -0.734045284 -1.151243765 -1.1501778
## [2132,] -0.660315835 -1.008251688 -1.1501778
## [2133,] -1.028963083 -1.365731882 -1.1501778
## attr(,"scaled:center")
##       X1       X2        Y 
## 54.95593 67.10220  1.56962 
## attr(,"scaled:scale")
##         X1         X2          Y 
## 13.5631014 13.9867889  0.4952454
nrow(Diskriminan)
## [1] 2133
data_numerik <- Diskriminan

data_numerik
##                   X1           X2          Y
##    [1,]  0.519355359  0.350173051  0.8690232
##    [2,]  0.814273157  0.850645323  0.8690232
##    [3,]  0.666814258  0.636157207  0.8690232
##    [4,]  0.445625909  0.707653246  0.8690232
##    [5,]  0.666814258  0.636157207  0.8690232
##    [6,]  0.814273157  0.493165129  0.8690232
##    [7,]  0.593084808  0.564661168  0.8690232
##    [8,]  0.593084808  0.350173051  0.8690232
##    [9,]  0.666814258  0.707653246  0.8690232
##   [10,]  0.445625909  0.350173051  0.8690232
##   [11,]  0.445625909  0.421669090  0.8690232
##   [12,]  0.666814258  0.493165129  0.8690232
##   [13,]  0.814273157  0.779149285  0.8690232
##   [14,]  0.371896459  0.278677012  0.8690232
##   [15,]  0.666814258  0.707653246  0.8690232
##   [16,]  0.666814258  0.421669090  0.8690232
##   [17,]  0.593084808  0.207180973  0.8690232
##   [18,]  0.888002607  0.421669090  0.8690232
##   [19,]  0.593084808  0.278677012  0.8690232
##   [20,]  0.666814258  0.421669090  0.8690232
##   [21,]  0.371896459  0.064188896  0.8690232
##   [22,]  0.371896459  0.207180973  0.8690232
##   [23,]  0.150708111 -0.078803182  0.8690232
##   [24,]  0.150708111  0.207180973  0.8690232
##   [25,]  0.076978661 -0.150299221 -1.1501778
##   [26,]  0.224437560 -0.007307143  0.8690232
##   [27,]  0.371896459  0.207180973  0.8690232
##   [28,]  0.371896459 -0.007307143  0.8690232
##   [29,] -0.070480238 -0.293291299  0.8690232
##   [30,]  0.371896459  0.564661168  0.8690232
##   [31,]  0.224437560 -0.078803182  0.8690232
##   [32,]  0.814273157  0.278677012  0.8690232
##   [33,]  0.371896459  0.636157207  0.8690232
##   [34,]  0.298167010  0.135684935  0.8690232
##   [35,]  0.150708111  0.135684935  0.8690232
##   [36,]  0.371896459  0.064188896  0.8690232
##   [37,]  0.445625909  0.278677012  0.8690232
##   [38,]  0.445625909 -0.078803182  0.8690232
##   [39,]  0.298167010  0.135684935  0.8690232
##   [40,]  0.519355359  0.350173051  0.8690232
##   [41,]  0.371896459 -0.078803182  0.8690232
##   [42,]  0.445625909  0.564661168  0.8690232
##   [43,]  0.224437560  0.779149285 -1.1501778
##   [44,]  0.666814258  1.065133440 -1.1501778
##   [45,]  0.224437560  0.707653246 -1.1501778
##   [46,]  0.740543707  1.422613635  0.8690232
##   [47,]  0.740543707  0.922141362  0.8690232
##   [48,]  0.519355359  0.564661168 -1.1501778
##   [49,]  0.224437560  0.421669090 -1.1501778
##   [50,]  0.298167010  0.493165129 -1.1501778
##   [51,]  0.298167010  0.493165129 -1.1501778
##   [52,]  0.593084808  0.636157207 -1.1501778
##   [53,]  0.593084808  0.779149285  0.8690232
##   [54,]  0.298167010  0.707653246  0.8690232
##   [55,]  0.445625909  0.707653246 -1.1501778
##   [56,]  0.003249212  0.350173051 -1.1501778
##   [57,]  0.814273157  1.136629479  0.8690232
##   [58,]  0.888002607  0.993637401  0.8690232
##   [59,]  0.961732056  0.850645323  0.8690232
##   [60,]  0.593084808  0.922141362  0.8690232
##   [61,]  0.593084808  1.136629479 -1.1501778
##   [62,]  0.814273157  1.065133440  0.8690232
##   [63,]  0.888002607  1.208125518  0.8690232
##   [64,]  0.888002607  1.136629479 -1.1501778
##   [65,]  1.330379304  1.279621557  0.8690232
##   [66,]  0.961732056  1.422613635  0.8690232
##   [67,]  1.109190955  1.708597790 -1.1501778
##   [68,]  1.404108754  1.279621557 -1.1501778
##   [69,]  0.666814258  1.136629479  0.8690232
##   [70,]  0.519355359  0.779149285 -1.1501778
##   [71,]  1.551567653  1.208125518  0.8690232
##   [72,]  1.330379304  1.351117596  0.8690232
##   [73,]  0.740543707  1.422613635  0.8690232
##   [74,]  0.814273157  0.850645323  0.8690232
##   [75,]  0.814273157  1.208125518  0.8690232
##   [76,]  0.814273157  1.065133440  0.8690232
##   [77,]  0.740543707  1.136629479 -1.1501778
##   [78,]  0.593084808  0.779149285 -1.1501778
##   [79,]  0.961732056  1.208125518 -1.1501778
##   [80,]  0.740543707  0.850645323  0.8690232
##   [81,]  1.109190955  1.136629479  0.8690232
##   [82,]  0.740543707  0.993637401 -1.1501778
##   [83,]  0.445625909  0.493165129 -1.1501778
##   [84,]  0.593084808  0.707653246 -1.1501778
##   [85,]  0.519355359  1.065133440  0.8690232
##   [86,]  1.035461506  0.993637401  0.8690232
##   [87,]  0.593084808  0.564661168 -1.1501778
##   [88,]  0.519355359  0.993637401 -1.1501778
##   [89,]  0.593084808  0.707653246 -1.1501778
##   [90,]  0.298167010  0.493165129 -1.1501778
##   [91,]  0.593084808  0.922141362  0.8690232
##   [92,]  0.814273157  0.636157207  0.8690232
##   [93,]  0.298167010  0.707653246  0.8690232
##   [94,]  0.371896459  0.493165129 -1.1501778
##   [95,]  0.961732056  0.636157207 -1.1501778
##   [96,]  1.404108754  1.065133440 -1.1501778
##   [97,]  0.593084808  0.421669090 -1.1501778
##   [98,]  1.330379304  0.779149285 -1.1501778
##   [99,]  1.477838203  1.136629479  0.8690232
##  [100,]  1.699026552  1.208125518  0.8690232
##  [101,]  1.035461506  0.779149285 -1.1501778
##  [102,]  1.330379304  0.993637401 -1.1501778
##  [103,]  1.404108754  0.922141362 -1.1501778
##  [104,]  1.330379304  0.922141362  0.8690232
##  [105,]  0.961732056  1.065133440 -1.1501778
##  [106,]  1.256649854  1.208125518  0.8690232
##  [107,]  1.330379304  0.922141362  0.8690232
##  [108,]  1.182920405  1.708597790  0.8690232
##  [109,]  1.330379304  0.922141362  0.8690232
##  [110,]  1.551567653  0.922141362  0.8690232
##  [111,]  1.109190955  1.208125518  0.8690232
##  [112,]  1.182920405  0.779149285  0.8690232
##  [113,]  1.551567653  1.279621557  0.8690232
##  [114,]  1.256649854  1.136629479  0.8690232
##  [115,]  1.182920405  1.136629479  0.8690232
##  [116,] -0.439127486  0.064188896 -1.1501778
##  [117,]  0.003249212  0.207180973  0.8690232
##  [118,]  0.371896459  0.421669090 -1.1501778
##  [119,]  0.298167010  0.421669090 -1.1501778
##  [120,]  0.298167010  0.207180973  0.8690232
##  [121,]  0.003249212  0.135684935 -1.1501778
##  [122,]  0.003249212  0.278677012  0.8690232
##  [123,]  0.076978661  0.493165129  0.8690232
##  [124,] -0.144209688  0.135684935 -1.1501778
##  [125,] -0.512856936  0.207180973 -1.1501778
##  [126,]  0.519355359  0.636157207  0.8690232
##  [127,]  0.224437560  0.564661168  0.8690232
##  [128,] -0.217939137  0.135684935 -1.1501778
##  [129,]  0.298167010 -0.007307143  0.8690232
##  [130,] -0.144209688  0.135684935 -1.1501778
##  [131,]  0.150708111  0.350173051  0.8690232
##  [132,]  0.961732056  0.636157207  0.8690232
##  [133,]  0.888002607  0.922141362  0.8690232
##  [134,]  0.888002607  0.636157207 -1.1501778
##  [135,]  0.814273157  1.065133440  0.8690232
##  [136,]  0.224437560  0.350173051  0.8690232
##  [137,]  0.445625909  0.207180973  0.8690232
##  [138,]  0.593084808  0.564661168  0.8690232
##  [139,]  0.961732056  0.707653246  0.8690232
##  [140,]  0.445625909  0.636157207 -1.1501778
##  [141,]  1.477838203  1.136629479  0.8690232
##  [142,]  0.961732056  0.564661168 -1.1501778
##  [143,]  0.740543707  0.350173051 -1.1501778
##  [144,]  0.740543707  0.707653246 -1.1501778
##  [145,]  0.445625909  0.707653246 -1.1501778
##  [146,]  0.519355359  0.135684935 -1.1501778
##  [147,]  0.740543707  0.493165129 -1.1501778
##  [148,]  1.109190955  0.850645323 -1.1501778
##  [149,]  0.740543707  0.493165129 -1.1501778
##  [150,]  0.371896459  0.421669090 -1.1501778
##  [151,]  0.371896459 -0.007307143  0.8690232
##  [152,]  0.519355359  0.207180973  0.8690232
##  [153,]  0.298167010  0.421669090  0.8690232
##  [154,]  0.519355359  0.350173051  0.8690232
##  [155,] -0.070480238  0.064188896  0.8690232
##  [156,]  0.224437560 -0.078803182  0.8690232
##  [157,]  0.224437560 -0.078803182  0.8690232
##  [158,]  0.371896459  0.135684935  0.8690232
##  [159,]  0.961732056  0.779149285  0.8690232
##  [160,]  0.003249212  0.135684935  0.8690232
##  [161,]  0.445625909  0.278677012  0.8690232
##  [162,]  0.445625909  0.278677012  0.8690232
##  [163,]  0.445625909  0.207180973  0.8690232
##  [164,]  0.666814258  0.993637401  0.8690232
##  [165,]  0.445625909  0.350173051  0.8690232
##  [166,] -0.070480238  0.135684935 -1.1501778
##  [167,]  0.076978661 -0.150299221  0.8690232
##  [168,]  0.003249212 -0.221795260  0.8690232
##  [169,]  0.740543707  0.278677012  0.8690232
##  [170,]  0.666814258  0.636157207  0.8690232
##  [171,]  1.256649854  0.850645323  0.8690232
##  [172,]  1.256649854  0.779149285  0.8690232
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## [1425,]  0.519355359  0.064188896  0.8690232
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## [1454,]  0.961732056  0.707653246  0.8690232
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## [1457,]  1.109190955  0.707653246  0.8690232
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## [1462,]  0.740543707  0.421669090  0.8690232
## [1463,]  0.888002607  0.564661168  0.8690232
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## [1468,]  1.182920405  0.993637401  0.8690232
## [1469,]  0.961732056  0.707653246  0.8690232
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## [1606,]  0.888002607  0.636157207  0.8690232
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## [1609,]  0.371896459  0.350173051  0.8690232
## [1610,]  0.445625909  0.779149285  0.8690232
## [1611,]  0.003249212  0.278677012  0.8690232
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## [1901,] -1.176421982 -0.936755649 -1.1501778
## [1902,] -1.028963083 -1.580219999 -1.1501778
## [1903,] -1.102692532 -1.294235843 -1.1501778
## [1904,] -1.323880881 -1.437227921 -1.1501778
## [1905,] -1.323880881 -1.151243765 -1.1501778
## [1906,] -1.250151431 -1.151243765 -1.1501778
## [1907,] -0.955233633 -1.365731882 -1.1501778
## [1908,] -1.397610331 -1.222739804 -1.1501778
## [1909,] -1.102692532 -1.294235843 -1.1501778
## [1910,] -1.102692532 -1.222739804 -1.1501778
## [1911,] -1.102692532 -1.222739804 -1.1501778
## [1912,] -1.028963083 -0.936755649 -1.1501778
## [1913,] -1.102692532 -1.294235843 -1.1501778
## [1914,] -1.028963083 -1.294235843 -1.1501778
## [1915,] -1.102692532 -1.437227921 -1.1501778
## [1916,] -1.397610331 -1.222739804 -1.1501778
## [1917,] -1.028963083 -0.364787338  0.8690232
## [1918,] -1.545069230 -1.437227921 -1.1501778
## [1919,] -1.839987028 -1.365731882 -1.1501778
## [1920,] -1.471339780 -1.294235843  0.8690232
## [1921,] -1.323880881 -1.222739804 -1.1501778
## [1922,] -1.839987028 -1.437227921 -1.1501778
## [1923,] -1.913716478 -1.365731882 -1.1501778
## [1924,] -1.397610331 -1.079747727 -1.1501778
## [1925,] -1.692528129 -1.222739804 -1.1501778
## [1926,] -1.987445927 -1.794708115 -1.1501778
## [1927,] -1.839987028 -1.437227921 -1.1501778
## [1928,] -1.618798679 -1.437227921 -1.1501778
## [1929,] -1.618798679 -1.580219999 -1.1501778
## [1930,] -1.471339780 -1.079747727 -1.1501778
## [1931,] -1.545069230 -1.008251688 -1.1501778
## [1932,] -1.618798679 -1.437227921 -1.1501778
## [1933,] -1.692528129 -1.079747727 -1.1501778
## [1934,] -1.471339780 -1.365731882 -1.1501778
## [1935,] -1.545069230 -1.508723960 -1.1501778
## [1936,] -1.618798679 -1.365731882 -1.1501778
## [1937,] -1.839987028 -1.365731882 -1.1501778
## [1938,] -1.692528129 -1.079747727 -1.1501778
## [1939,] -1.987445927 -1.580219999 -1.1501778
## [1940,] -1.692528129 -1.651716038 -1.1501778
## [1941,] -1.766257578 -1.151243765 -1.1501778
## [1942,] -1.545069230 -1.294235843 -1.1501778
## [1943,] -1.913716478 -1.651716038 -1.1501778
## [1944,] -1.545069230 -1.294235843 -1.1501778
## [1945,] -1.618798679 -1.079747727 -1.1501778
## [1946,] -1.618798679 -1.294235843 -1.1501778
## [1947,] -1.323880881 -1.079747727 -1.1501778
## [1948,]  0.814273157  1.351117596  0.8690232
## [1949,]  1.330379304  1.136629479  0.8690232
## [1950,]  0.740543707  0.493165129  0.8690232
## [1951,]  0.519355359  0.993637401  0.8690232
## [1952,]  0.814273157  1.279621557  0.8690232
## [1953,]  0.814273157  0.993637401  0.8690232
## [1954,]  1.109190955  1.065133440  0.8690232
## [1955,]  1.035461506  1.065133440  0.8690232
## [1956,]  0.961732056  0.922141362  0.8690232
## [1957,]  0.519355359  1.065133440  0.8690232
## [1958,]  0.371896459  0.493165129  0.8690232
## [1959,]  0.814273157  1.708597790  0.8690232
## [1960,]  0.740543707  0.779149285  0.8690232
## [1961,]  0.888002607  0.993637401  0.8690232
## [1962,]  0.814273157  0.922141362  0.8690232
## [1963,]  0.445625909  1.065133440 -1.1501778
## [1964,]  0.888002607  0.779149285  0.8690232
## [1965,]  0.814273157  1.136629479  0.8690232
## [1966,]  0.740543707  0.993637401 -1.1501778
## [1967,]  0.445625909  0.922141362  0.8690232
## [1968,]  0.814273157  0.922141362  0.8690232
## [1969,]  0.519355359  0.850645323  0.8690232
## [1970,]  0.666814258  0.707653246  0.8690232
## [1971,]  1.109190955  1.136629479  0.8690232
## [1972,]  0.593084808  0.564661168  0.8690232
## [1973,]  0.740543707  0.636157207  0.8690232
## [1974,]  0.224437560  0.064188896 -1.1501778
## [1975,]  0.593084808  0.779149285  0.8690232
## [1976,]  0.740543707  0.350173051  0.8690232
## [1977,]  1.404108754  0.350173051  0.8690232
## [1978,]  1.109190955  0.993637401  0.8690232
## [1979,]  1.182920405  0.779149285  0.8690232
## [1980,]  0.445625909 -0.078803182 -1.1501778
## [1981,]  0.961732056  0.421669090  0.8690232
## [1982,]  0.519355359  0.064188896  0.8690232
## [1983,]  0.076978661  0.135684935 -1.1501778
## [1984,]  0.814273157  0.493165129  0.8690232
## [1985,]  0.740543707  0.135684935  0.8690232
## [1986,]  0.814273157  0.707653246  0.8690232
## [1987,]  0.593084808  0.707653246  0.8690232
## [1988,]  0.814273157  0.707653246  0.8690232
## [1989,]  1.182920405  0.922141362  0.8690232
## [1990,]  0.666814258  0.135684935 -1.1501778
## [1991,]  0.298167010  0.278677012 -1.1501778
## [1992,]  0.888002607  0.207180973  0.8690232
## [1993,]  0.593084808  0.636157207  0.8690232
## [1994,]  1.772756002  1.923085907  0.8690232
## [1995,]  1.920214901  1.637101751  0.8690232
## [1996,]  1.477838203  1.923085907  0.8690232
## [1997,]  1.625297102  1.565605712  0.8690232
## [1998,]  0.961732056  1.422613635  0.8690232
## [1999,]  1.330379304  1.708597790  0.8690232
## [2000,]  1.035461506  1.565605712  0.8690232
## [2001,]  1.477838203  1.923085907  0.8690232
## [2002,]  1.035461506  1.279621557  0.8690232
## [2003,]  1.256649854  1.279621557  0.8690232
## [2004,]  1.772756002  1.851589868  0.8690232
## [2005,]  1.404108754  1.923085907  0.8690232
## [2006,]  1.551567653  1.637101751  0.8690232
## [2007,]  1.330379304  1.923085907  0.8690232
## [2008,]  1.404108754  1.422613635  0.8690232
## [2009,]  1.772756002  1.923085907  0.8690232
## [2010,]  1.404108754  1.780093829 -1.1501778
## [2011,]  1.256649854  1.494109674  0.8690232
## [2012,]  1.404108754  1.208125518  0.8690232
## [2013,]  1.035461506  1.351117596  0.8690232
## [2014,]  1.404108754  1.637101751  0.8690232
## [2015,]  1.109190955  1.422613635  0.8690232
## [2016,]  1.551567653  1.994581946  0.8690232
## [2017,] -0.734045284 -0.507779415 -1.1501778
## [2018,] -0.439127486 -0.650771493 -1.1501778
## [2019,] -0.144209688 -0.793763571 -1.1501778
## [2020,] -0.586586385 -0.865259610 -1.1501778
## [2021,] -0.439127486 -0.579275454 -1.1501778
## [2022,] -0.439127486 -0.579275454 -1.1501778
## [2023,] -1.028963083 -1.008251688 -1.1501778
## [2024,] -0.070480238 -0.293291299 -1.1501778
## [2025,] -0.217939137 -0.507779415 -1.1501778
## [2026,] -0.439127486 -0.579275454 -1.1501778
## [2027,] -0.660315835 -0.650771493 -1.1501778
## [2028,] -0.512856936 -0.579275454 -1.1501778
## [2029,] -0.660315835 -0.722267532 -1.1501778
## [2030,] -0.881504183 -0.865259610 -1.1501778
## [2031,] -0.734045284 -0.579275454 -1.1501778
## [2032,] -0.217939137 -0.364787338 -1.1501778
## [2033,] -0.512856936 -0.579275454 -1.1501778
## [2034,] -0.144209688 -0.293291299 -1.1501778
## [2035,] -0.660315835 -0.793763571 -1.1501778
## [2036,] -0.070480238 -0.436283377 -1.1501778
## [2037,] -0.586586385 -0.436283377 -1.1501778
## [2038,] -0.439127486 -0.722267532 -1.1501778
## [2039,] -0.365398036 -0.364787338 -1.1501778
## [2040,] -0.660315835 -0.936755649 -1.1501778
## [2041,] -0.070480238 -0.507779415  0.8690232
## [2042,] -0.660315835 -0.865259610 -1.1501778
## [2043,] -0.217939137 -0.364787338  0.8690232
## [2044,] -1.692528129 -0.865259610 -1.1501778
## [2045,] -2.208634276 -1.008251688 -1.1501778
## [2046,] -1.618798679 -0.936755649 -1.1501778
## [2047,] -0.807774734 -0.793763571  0.8690232
## [2048,] -1.545069230 -0.936755649 -1.1501778
## [2049,] -1.250151431 -1.008251688 -1.1501778
## [2050,] -1.545069230 -1.222739804 -1.1501778
## [2051,] -1.176421982 -0.936755649 -1.1501778
## [2052,] -1.028963083 -0.865259610 -1.1501778
## [2053,] -1.397610331 -1.079747727 -1.1501778
## [2054,] -1.250151431 -1.008251688 -1.1501778
## [2055,] -1.250151431 -1.079747727 -1.1501778
## [2056,] -1.323880881 -1.079747727 -1.1501778
## [2057,] -1.471339780 -1.079747727 -1.1501778
## [2058,] -1.839987028 -1.365731882 -1.1501778
## [2059,] -1.250151431 -1.008251688 -1.1501778
## [2060,] -1.250151431 -1.222739804 -1.1501778
## [2061,] -1.397610331 -0.865259610 -1.1501778
## [2062,] -1.323880881 -0.722267532 -1.1501778
## [2063,] -1.471339780 -0.579275454 -1.1501778
## [2064,] -1.028963083 -0.936755649 -1.1501778
## [2065,] -1.323880881 -1.008251688 -1.1501778
## [2066,] -1.323880881 -0.936755649 -1.1501778
## [2067,] -1.176421982 -1.294235843 -1.1501778
## [2068,] -1.323880881 -1.008251688 -1.1501778
## [2069,] -1.102692532 -0.865259610  0.8690232
## [2070,] -1.545069230 -1.222739804 -1.1501778
## [2071,] -1.250151431 -1.008251688 -1.1501778
## [2072,] -1.176421982 -0.793763571 -1.1501778
## [2073,] -1.397610331 -1.294235843 -1.1501778
## [2074,] -0.660315835 -1.294235843 -1.1501778
## [2075,] -0.881504183 -1.079747727  0.8690232
## [2076,] -1.102692532 -1.294235843 -1.1501778
## [2077,] -0.734045284 -1.151243765 -1.1501778
## [2078,] -1.176421982 -1.222739804 -1.1501778
## [2079,] -1.176421982 -1.151243765 -1.1501778
## [2080,] -0.881504183 -1.008251688  0.8690232
## [2081,] -0.734045284 -1.151243765 -1.1501778
## [2082,] -0.807774734 -1.008251688 -1.1501778
## [2083,] -0.660315835 -1.222739804 -1.1501778
## [2084,] -0.807774734 -0.936755649 -1.1501778
## [2085,] -1.323880881 -1.222739804 -1.1501778
## [2086,] -1.028963083 -1.079747727 -1.1501778
## [2087,] -1.250151431 -1.365731882 -1.1501778
## [2088,] -1.102692532 -1.008251688 -1.1501778
## [2089,] -1.323880881 -1.437227921 -1.1501778
## [2090,] -1.250151431 -1.079747727 -1.1501778
## [2091,] -0.734045284 -0.722267532  0.8690232
## [2092,] -0.586586385 -0.865259610 -1.1501778
## [2093,] -0.807774734 -1.079747727 -1.1501778
## [2094,] -0.881504183 -1.580219999 -1.1501778
## [2095,] -1.323880881 -1.508723960 -1.1501778
## [2096,] -1.250151431 -1.222739804 -1.1501778
## [2097,] -1.028963083 -1.151243765 -1.1501778
## [2098,] -1.028963083 -0.865259610 -1.1501778
## [2099,] -0.734045284 -1.008251688 -1.1501778
## [2100,] -1.397610331 -1.437227921 -1.1501778
## [2101,] -0.955233633 -1.222739804 -1.1501778
## [2102,] -1.028963083 -1.365731882 -1.1501778
## [2103,] -1.397610331 -1.365731882 -1.1501778
## [2104,] -1.028963083 -1.508723960 -1.1501778
## [2105,] -0.881504183 -1.079747727 -1.1501778
## [2106,] -1.176421982 -0.936755649 -1.1501778
## [2107,] -1.250151431 -1.294235843 -1.1501778
## [2108,] -0.955233633 -1.151243765 -1.1501778
## [2109,] -1.397610331 -1.723212077 -1.1501778
## [2110,] -1.397610331 -1.008251688 -1.1501778
## [2111,] -1.102692532 -1.365731882 -1.1501778
## [2112,] -0.955233633 -1.365731882 -1.1501778
## [2113,] -1.176421982 -1.294235843 -1.1501778
## [2114,] -1.102692532 -1.437227921 -1.1501778
## [2115,] -1.176421982 -0.865259610  0.8690232
## [2116,] -1.028963083 -1.365731882 -1.1501778
## [2117,] -1.250151431 -1.365731882 -1.1501778
## [2118,] -0.955233633 -0.865259610 -1.1501778
## [2119,] -0.660315835 -1.008251688  0.8690232
## [2120,] -1.028963083 -1.294235843 -1.1501778
## [2121,] -0.955233633 -1.222739804 -1.1501778
## [2122,] -1.176421982 -1.079747727  0.8690232
## [2123,] -1.250151431 -1.508723960 -1.1501778
## [2124,] -1.102692532 -1.508723960 -1.1501778
## [2125,] -1.028963083 -1.222739804 -1.1501778
## [2126,] -0.734045284 -1.437227921 -1.1501778
## [2127,] -1.250151431 -1.151243765 -1.1501778
## [2128,] -1.176421982 -1.222739804 -1.1501778
## [2129,] -1.176421982 -0.865259610  0.8690232
## [2130,] -1.250151431 -1.508723960 -1.1501778
## [2131,] -0.734045284 -1.151243765 -1.1501778
## [2132,] -0.660315835 -1.008251688 -1.1501778
## [2133,] -1.028963083 -1.365731882 -1.1501778
## attr(,"scaled:center")
##       X1       X2        Y 
## 54.95593 67.10220  1.56962 
## attr(,"scaled:scale")
##         X1         X2          Y 
## 13.5631014 13.9867889  0.4952454
x_bar <- colMeans(data_numerik)  # Vektor mean
cov_matrix <- cov(data_numerik)  # Matriks kovarians

Di<-mahalanobis(data_numerik,x_bar,cov_matrix)
Di
##    [1]  0.9893315  0.9321087  0.7811614  1.5749378  0.7811614  1.7253261
##    [7]  0.7598696  1.2610197  0.8304573  0.8366320  0.7707495  1.0028852
##   [13]  0.8772085  0.8716059  0.8304573  1.2739049  2.1289789  2.8479581
##   [19]  1.6416134  1.2739049  1.7182911  1.0470625  1.5579524  1.0360438
##   [25]  2.8129569  1.4639108  1.0470625  2.2140632  1.9470045  1.2374981
##   [31]  1.8585154  3.4825186  1.5959008  1.1026597  1.0063632  1.7182911
##   [37]  1.0092864  3.4741359  1.1026597  0.9893315  2.8166071  0.9593000
##   [43]  6.2731841  6.5375048  5.4611980  6.1459876  1.2968840  3.8918428
##   [49]  3.2809722  3.5249330  3.5249330  4.2014838  1.2196662  2.6662014
##   [55]  4.4596231  3.5157731  2.2194280  1.1741404  1.0908074  2.0600564
##   [61]  7.7412539  1.7374404  2.3081941  6.5282988  1.7747396  3.7102809
##   [67] 11.4974242  8.6716670  3.3684411  4.7598495  3.1627435  1.8492551
##   [73]  6.1459876  0.9321087  2.8081874  1.7374404  6.8967991  4.6789875
##   [79]  6.9354522  1.0312423  1.3492654  5.7674556  3.6000230  4.3868497
##   [85]  4.0955425  1.1549377  4.1228898  6.5888028  4.3868497  3.5249330
##   [91]  2.0600564  1.0877236  2.6662014  3.5029837  6.6216999  9.3043595
##   [97]  4.2860172 10.4147423  2.9388066  4.6615184  6.6925767  8.8126967
##  [103] 10.2600137  3.0037399  6.2163830  1.5930574  3.0037399  4.9700969
##  [109]  3.0037399  5.6071234  1.5221462  2.6862184  2.8185782  1.6281160
##  [115]  1.4291964  3.9666250  1.6236412  3.3260243  3.2440039  0.9244009
##  [121]  2.3862966  1.9680329  2.8726676  2.6993737  6.5618754  0.9505538
##  [127]  2.1508603  3.0343951  1.7794926  2.6993737  1.4157205  1.8702403
##  [133]  1.0096661  5.8996794  1.7374404  1.0924654  1.2887126  0.7598696
##  [139]  1.5036575  4.0663179  2.9388066  7.0629541  5.9706164  4.7900309
##  [145]  4.4596231  5.0386692  5.1780667  7.1157571  5.1780667  3.3260243
##  [151]  2.2140632  1.6493515  1.0302558  0.9893315  1.5195155  1.8585154
##  [157]  1.8585154  1.3292909  1.2438465  1.3860212  1.0092864  1.0092864
##  [163]  1.2887126  2.0953591  0.8366320  2.4833408  1.6698153  1.7994993
##  [169]  2.7498949  0.7811614  2.8360686  3.4049863  3.5376586  1.0028852
##  [175]  1.3486398  1.0010332  3.1287116  0.8304573  0.8386374  1.6056485
##  [181]  1.2831565  2.6862184  1.0096661  1.3486398  1.1984028  1.3622246
##  [187]  0.9865250  1.2182445  1.4453864  0.8749482  8.4196533  1.6189759
##  [193]  2.5443961  2.2194280  6.1833365  4.4031945  4.0955425  1.2723211
##  [199]  1.6651735  2.4147815  3.3275340  1.6281160  1.2831565  3.7102809
##  [205]  5.0686104  0.9865250  1.5749378  2.0864392  1.0312423  1.2610197
##  [211]  1.0445402  1.3531389  0.8386374  1.5036575  0.9519637  1.3531389
##  [217]  1.0445402  1.8432558  2.4399816  1.2438465  0.8000905  1.8630941
##  [223]  2.8360686  1.0028852  1.6236412  2.1671716  0.9207280  2.2140632
##  [229]  0.9950171  1.7929584  1.6708309  1.9028465  1.5195155  0.9244009
##  [235]  1.5032600  1.1897129  1.4639108  2.3598918  4.0455691  0.9858673
##  [241]  1.3292909  3.9112822  1.1366979  2.8726676  2.4051661  2.5595377
##  [247]  2.5770051  0.9207280  1.0092864  6.2945012  5.1063189  3.1322587
##  [253]  5.2231267  2.2025104  3.2324614  2.7152367  3.6560526  2.0700242
##  [259]  1.4978470  1.6154153  4.7939574  2.2015081  2.5209463  1.6154153
##  [265]  2.7068959  2.3330060  2.2025104  1.3763782  2.1123308  2.7152367
##  [271]  2.0381692  1.9908324  3.8500468  1.7736004  1.4989929  3.6584928
##  [277]  2.1889989  1.7175260  2.2317041  2.0691809  0.8029212  1.3860212
##  [283]  1.9028465  1.2673175  7.3679087  3.5955310  2.0269252  2.2469567
##  [289]  3.5955310  1.7868281  2.2533364  1.9553592  2.3528178  1.7175260
##  [295]  1.0834544  1.4556933  6.5820086  1.7182911  1.9072859  2.7676223
##  [301]  2.2251471  1.7929584  1.8872776  3.0704883  1.7929584  1.9470045
##  [307]  2.3598918  2.2533364  3.5401771  1.8579642  3.4884053  1.5271153
##  [313]  3.9781626  3.0994175  4.0537528  2.6871931  2.0959228  3.4563360
##  [319]  2.0691809  0.8116388  5.6866699  2.2164227  1.3860212  3.2395242
##  [325]  2.4191965  2.6871931  3.2124747  4.2266997  1.2703481  3.5732011
##  [331]  3.2866304  1.3914696  1.7151386  2.0269252  2.6871931  2.7068959
##  [337]  3.5894215  3.9112822  1.4250200  1.5162798  2.5528105  3.1090134
##  [343]  5.6726467  1.6479630  2.1784053  2.7122934  1.8104871  1.7868281
##  [349]  9.2703859  1.7755964  6.3272650  3.4143694  2.3453679  3.6834145
##  [355]  3.3376074  1.7367433  1.8913609  2.9518476  4.2193266  2.1148669
##  [361]  2.8904251  4.6771124  1.9750293  6.9363316  4.1002518  1.4978470
##  [367]  5.0019394  8.1893125  3.1758619  2.6947254  1.4217174  3.6690549
##  [373]  1.8012777  8.1893125  6.5955476  3.7657203  1.7367433  1.5743494
##  [379]  2.2224846  3.6658709  2.0425749  3.7013694  3.4369291  3.8160510
##  [385]  3.0325091  2.2233482  4.4133184  3.0548326  7.1919420  2.1508603
##  [391]  2.6330216  2.1671716  6.0015434  0.7707495  2.0643699  3.3260243
##  [397]  2.7172023  2.0643699  3.2558368  0.8304573  0.7563990  4.3047127
##  [403]  4.4071065  1.5749378  4.3047127  4.6187318  6.8673877  0.8201478
##  [409]  1.5162798  7.4309044  2.8090959  3.5029837  3.0044623  2.7669072
##  [415]  2.9580564  1.2659556  2.3284859  2.2177668  0.8029212  1.2659556
##  [421]  2.6392728  4.5064768  2.2780669  3.1770333  3.9257975  3.1880063
##  [427]  1.2610197  8.8369781  2.8465142  3.6859053  2.8166071  1.7182911
##  [433]  0.9893315  2.1289789  0.8116388  2.4082411  4.5064768  2.2177668
##  [439]  4.2293064  2.7795080  2.7669072  2.7459277  2.1395192  2.3751339
##  [445]  4.1772179  1.9526017  5.3313038  3.4357773  2.7364587  6.5381230
##  [451]  1.7888726  1.2887126  2.9580564  2.3284859  1.2196662  0.9519637
##  [457]  1.2137330  3.4563360  1.5930574  0.8723724  3.7118747  0.8304573
##  [463]  1.2968840  1.0312423  4.1651399  3.3044482  4.1702018  8.6740227
##  [469]  7.4551445  5.7316505  4.5181883  1.3622246  1.2723211  5.9385681
##  [475]  1.3883231  2.2194280  6.8967991  6.0502887  6.0104965  2.1918242
##  [481]  3.5980892  1.6281160  3.7118747  1.2137330  3.7102809  6.1079020
##  [487]  0.9505538  1.1760780  2.4082411  0.7811614  3.2809722  4.6789875
##  [493]  3.3903161  1.5749378  0.9858673  2.4191965  1.2790844  1.6189759
##  [499]  1.0363938  2.9529677  1.8964984  1.3857666  1.4280902  3.1245462
##  [505]  7.2231823  1.4978470  1.3264279  1.4280902  1.8780671  1.3520074
##  [511]  1.4280902  4.6143032  1.7367433  1.4061219  1.7728273  1.3657225
##  [517]  1.3403699  1.6387217  1.5904338  1.4050449  3.1176267  3.7797845
##  [523]  4.1772179  6.5311557  6.1389667  4.8126043  5.2785395  6.5311557
##  [529]  3.7867149  6.2787414  3.8160510  1.0312423  3.5608154  5.2373338
##  [535]  3.9126338  5.5665491  1.2968840  5.7674556 11.4498513  4.6789875
##  [541]  5.0120540  4.6744928  3.3260243  3.4271693  1.5463694  1.1741404
##  [547]  3.5029837  4.5289460  2.6392728  3.5955310  1.8564536  3.1880063
##  [553]  2.2251471  1.9126532  2.0756246  4.0455691  2.4191965  3.9847827
##  [559]  6.7978783  0.9244009  1.7755964  0.8201478  2.5491742  3.0101835
##  [565]  2.4833408  2.4833408  1.9526017  2.8129569  3.1907577  4.3830474
##  [571]  1.6048045  4.9449757  2.7847891  2.8102997  1.8825945  1.3612641
##  [577]  1.9714119  3.1681702  1.4217891  1.3520074  1.4617393  1.5060689
##  [583]  1.5087409  3.7325140  3.0905536  2.8151843  4.2184868  1.5884934
##  [589]  1.6669774  1.3657225  3.2137888  3.9248641  1.6170202  3.0905536
##  [595]  2.6109552  1.4556933  2.5516202  3.0905536  2.3862966  1.4882350
##  [601]  1.7868281  2.6392728  4.4206970  2.0562764  3.1810655  1.3701956
##  [607]  1.5662010  2.4834097  1.4280902  1.3292909  2.4834097  2.3751339
##  [613]  2.5595377  2.2469567  4.0723205  1.9301383  2.6392728  6.7504254
##  [619]  2.6109552  2.7669072  0.8366320  1.0470625  3.0325091  2.2233482
##  [625]  3.6418393  1.7755964  4.4526681  3.9247263  1.6788242  1.8579642
##  [631]  5.0083511  3.4884053  4.0614040  3.9126338  0.9244009  3.0343951
##  [637]  2.4833408  3.7892148  3.2866304  2.5739917  3.9247263  2.7795080
##  [643]  2.2164227  1.1760780  3.0418479  3.0325091  3.4884053  2.8314904
##  [649]  5.4195091  1.9028465  2.5595377  2.0722394  3.9247263  1.8215285
##  [655]  4.3047127  3.6160244  2.7218830  2.4833408  3.2228467  6.5618754
##  [661]  5.0043226  2.6993737  2.3130018  3.3716718  1.5743494  6.5851732
##  [667]  1.5240058  1.3946835  3.3916610  1.9049430  1.5087409  2.2815270
##  [673]  4.4022197  1.3657225  2.0789156  2.2840031  2.2840031  1.6473477
##  [679]  3.4240352  2.2815270  2.4225886  1.4250200  2.9147843  4.1252109
##  [685]  5.2956618  1.3612641  2.2741975  3.3997077  1.4217891  3.5132497
##  [691]  1.9714119  1.5679858  3.3916610  1.3657225  4.0414177  3.4548989
##  [697]  2.2846891  1.4217174  1.6387217  3.3997077  1.7025363  2.5526038
##  [703]  3.0905536  1.4891228  2.9147843  2.0031036  2.8428783  2.1975383
##  [709]  2.7122934  1.6387217  1.6788242  2.0031036  4.2553623  8.5946770
##  [715]  3.2279616  7.7388326  8.4395822  4.5574831  3.1494451  2.6644569
##  [721]  3.3929014  3.0011864  3.6803692  2.7252930  3.4067793  3.0011864
##  [727]  2.5613870  5.7348436  7.5239032  4.2988625  2.8894506  3.9583140
##  [733]  5.5744550  6.3868880  3.6880386  2.6644569  4.2489880  3.7595320
##  [739]  3.5098470  4.9574264 11.3252101  3.3929014  4.8002973  4.8555142
##  [745]  4.9574264  5.1895739  5.7498390  4.0890440  3.3269733  4.0890440
##  [751]  3.4857954  5.8068085  3.2611887  3.5274290  3.1494451  4.3040208
##  [757]  3.6803692  3.5274290  3.2345866  3.2279616  3.1085920  3.7548506
##  [763]  3.4857954  4.2988625  2.4890569  1.8663771  2.9817252  3.5098470
##  [769]  1.6669774  1.7755462  1.9426936  2.0964027  1.5060689  5.1887977
##  [775]  3.2222662  2.1725487  2.4104427  2.2840031  1.8825945  3.5454364
##  [781]  1.4563544  4.0751564  1.6669774  2.0934675  3.9039615  1.6473477
##  [787]  1.8068057  1.7094091  2.3066778  1.5743494  1.6473477  2.2061097
##  [793]  1.6669774  3.6296549  2.6997487  3.6296549  2.2840031  2.5603752
##  [799]  2.3066778  3.9892375  3.3361834  2.2679329  1.8068057  1.5789486
##  [805]  3.1322654  2.2457970  2.0934675  4.3601117  1.7728273  3.1758619
##  [811]  2.0379907  2.1015026  2.6997487  5.2584757  3.0333616  7.3053111
##  [817]  9.0527464  2.7127875  5.4282118  2.8018244  4.3562226  5.9636707
##  [823]  5.6386249  5.9636707  4.6771124  1.4414656  5.7189085  2.2715562
##  [829]  7.2379948  1.7094091  2.1442004  1.8663771  1.9370967  3.1417847
##  [835]  7.9982061  2.4225886  2.6415718  1.4978470  2.8018244  2.7326908
##  [841]  2.0036972  4.8631374  1.8630941  3.4045016  4.3840120  2.1918242
##  [847]  2.7326908  1.7747396  2.0036972  2.1285128  6.2309435  2.2182195
##  [853]  2.0036972  2.1399232  2.0036972  2.0036972  1.1984028  1.8630941
##  [859]  2.0036972  1.1549377  2.3739227  4.2188682  3.2545204  4.5385566
##  [865]  5.8123613  4.7576752  6.5032974  6.5138882  2.9579002  3.0389943
##  [871]  6.9593171  3.3990323  3.1526779  2.1285128  2.7007276  2.8414704
##  [877]  4.1482151  2.7134326  4.1760194  4.4608183  2.6993290  5.0832039
##  [883]  3.0937308  2.2716873  6.4851480  2.5918390  2.6814196  2.1882233
##  [889]  1.3883231  3.6136807  1.4291964  2.1918242  3.0037399  6.9584635
##  [895]  4.4075435  2.2182195  2.8285471  2.2212703  1.3486398  5.4531179
##  [901]  4.6742625  5.5857741  6.0869930  6.1521301  7.3879122  5.9897167
##  [907]  4.1482151  6.1521301 10.0996089  6.1521301  5.7583335  6.6385115
##  [913]  4.9494402  4.1703965  6.1825378  6.7904980  0.8386374  1.6116897
##  [919]  2.0953591  1.7374404  2.8360686  4.7216938  1.1741404  1.0877236
##  [925]  1.0908074  2.5443961  1.0445402  1.6116897  1.8702403  0.9596288
##  [931]  2.1882233  1.5036575  5.6137293  4.7577427  1.8068525  4.7577427
##  [937]  1.4414656  3.3470253  1.5240058  2.2744839  8.1893125  4.0488840
##  [943]  4.1002518  1.7755462  3.2607906  1.6297869  3.1681702  1.4882350
##  [949]  1.3657225  1.5679858  2.4104427  1.3946835  1.3721330  1.3946835
##  [955]  4.9724669  2.5865195  1.3545827  3.7721950  3.1090134  2.3633952
##  [961]  3.7413454  2.2715562  1.8964984  3.6296549  2.0031036  1.3946835
##  [967]  2.3633952  4.7850486  2.0317380  1.5679858  4.4361620  6.3871301
##  [973]  3.6296549  1.9369563  2.9245536  5.1071166  2.1015026  4.1189558
##  [979]  1.4217174  4.8360548  2.2840031  1.5087409  9.3643420  1.6773972
##  [985]  2.6997487  1.6387217  1.3915289  3.0905536  2.8102997  1.4895094
##  [991]  3.7721950  1.6788242  1.4882350  1.4050449  1.8473999  3.4548989
##  [997]  3.4143694  1.8825945  4.1252109  4.2184868  1.4061219  2.0381692
## [1003]  3.4143694  2.3453679  1.8913609  3.9985366  3.3929014  4.0549265
## [1009]  3.4067793  3.6713586  5.7322553  4.0748769  4.6861969  4.0417143
## [1015]  3.6880386  3.8114906  3.8114906  4.5406693  3.7614504  3.2611887
## [1021]  4.3662238  4.7181771  4.8555142  5.4520040  4.6387436  3.0127694
## [1027]  3.4067793  3.3269733  2.7856073  3.7614504  3.2611887  4.9449649
## [1033]  2.7821714  2.6699282  3.9892375  2.4079126  3.6803692  3.0011864
## [1039]  4.1447407  2.5693945  4.0417143  3.3269733  2.8894506  2.4572843
## [1045]  2.5693945  2.0964027  2.6699282  2.8977241  2.0964027  3.3929014
## [1051]  2.8894506  3.4143694  2.1725487  1.5679858  2.1029659  1.5904338
## [1057]  1.5240058  1.3520074  1.4217891  4.9264374  1.8825945  2.7872314
## [1063]  2.7847891  1.9451127  1.4891228  1.3721330  1.7600194  2.4104427
## [1069]  1.8012777  2.2744839  1.4050449  2.1029659  1.7736004  3.9871192
## [1075]  2.6997487  2.4225886  2.7722615  2.3744387  3.4304295  3.9583140
## [1081]  2.9879489  5.1895739  3.2279616  2.6644569  3.5631757  2.5878494
## [1087]  3.2611887  5.9137723  2.5878494  4.7706021  3.4857954  4.0748769
## [1093]  3.7614504  3.7396694  3.5631757  2.7252930  0.8749482  5.1878395
## [1099]  0.9207280  0.9519637  1.0470625  1.1026597  0.9532108  0.7563990
## [1105]  1.7182911  1.7253261  0.9244009  2.1289789  1.2673175  0.9207280
## [1111]  0.9532108  2.7498949  2.2650294  2.7900159  1.2610197  1.0302558
## [1117]  1.2739049  1.2659556  3.2395242  1.5107702  2.7900159  2.1613618
## [1123]  1.6493515  1.2374981  1.7794926  1.0470625  1.2610197  0.8194793
## [1129]  3.4825186  2.5770051  0.8716059  1.1026597  1.4556933  1.2887126
## [1135]  2.8166071  1.0470625  2.1484830  1.7374404  1.8234044  1.9271895
## [1141]  0.8201478  2.0600564  1.8579642  2.6330216  2.6404093  1.2968840
## [1147]  1.0445402  1.2493645  1.0312423  1.8234044  2.6201256  4.1214306
## [1153]  1.0010332  2.8465142  1.2077890  0.9596288  5.0568593  2.0429145
## [1159]  0.8723724  3.0028454  3.2991834  2.3081941  4.1702018  1.5717960
## [1165]  0.8723724  2.6404093  1.2077890  4.0955425  3.3275340  4.9894917
## [1171]  2.4049865  3.1681702  2.8904251  2.3496496  2.7152367  2.8904251
## [1177]  2.5790316  3.7413454  2.4964469  3.7413454  2.1123308  3.9039615
## [1183]  6.9774796  5.9492767  3.6584928  2.9479913  3.4240352  2.4325147
## [1189]  3.5347526  2.9479913  4.6260568  4.0751564  1.0470625  1.2551732
## [1195]  1.3876902  0.8716059  0.7811614  0.7563990  1.6416134  2.8166071
## [1201]  1.1760780  0.8366320  0.8194793  0.8881990  3.4369291  6.8705383
## [1207]  0.9593000  1.0092864  2.2233482  1.0834544  1.1760780  2.2780669
## [1213]  2.1395192  2.3453679  3.3974521  0.9871978  3.4878661  1.1897129
## [1219]  1.2673175  2.4834097  5.3400824  0.8529140  2.2177668  1.9028465
## [1225]  1.2673175  2.7676223  1.0063632  3.5259229  1.6912902  1.3876902
## [1231]  1.8585154  1.3876902  1.6912902  3.1907577  3.7345976  5.6207548
## [1237]  3.4240352  3.8346217  3.9188907  8.7056383  7.9178452  9.2521722
## [1243] 10.1923601  1.5679858  8.0347576  4.6789081  4.3549854  3.7325140
## [1249]  2.5790316  4.6789081  4.6789081  6.9896889  2.1148669 10.1923601
## [1255]  3.4901445  4.6260568  6.3108548  1.6048045  2.9529677  4.0414177
## [1261]  3.1234028  5.6386249  3.2250854  2.2015081  3.4847599  2.2015081
## [1267]  3.2290312  1.8944184  2.6387952  6.5833437  4.1968381  2.5834925
## [1273]  1.6479630  2.9106667  5.2231267  1.9072859  3.4316584  2.2015081
## [1279]  3.8982679  3.1322587  2.5209463  4.5316358  2.6387952  3.8982679
## [1285]  3.4200896  3.1245462  4.3874238  2.9518476  3.3288482  1.8104871
## [1291]  3.9039615  2.2015081  2.2015081  2.2015081  3.8982679  2.7068959
## [1297]  2.4325147  3.2324614  2.1048016  2.7152367  2.1148669  2.2954782
## [1303]  2.4543042  4.2073750  6.6733943  1.6479630  2.7068959  2.4325147
## [1309]  2.2780669  3.4370402  3.4316584  1.7994993  1.5714234  1.9072859
## [1315]  1.1366979  1.4556933  1.8104871  1.9883227  1.7994993  1.3860212
## [1321]  3.5259229  1.9883227  2.1123308  1.9883227  4.7385785  2.3528178
## [1327]  4.3830474  1.6479630  2.3528178  4.2866183  3.2250854  2.1889989
## [1333]  2.3528178  2.9479913  2.5209463  1.7175260  1.6416134  4.7598495
## [1339]  0.8063633  2.6201256  0.8063633  1.2374981 11.0631411  5.1172749
## [1345]  0.8723724  8.4094719  4.1702018  3.3903161  2.0970572  0.8063633
## [1351]  0.9519637  0.8723724  1.5864754  1.0312423  3.4369291  0.9505538
## [1357]  0.8201478  0.8749482  2.6176630  1.3622246  3.3044482  1.0302558
## [1363]  1.0834544  6.2343077  1.3701956  1.4556933  0.9244009  1.5579524
## [1369]  3.8418469  1.1366979  1.6708309  1.1026597  0.9858673  1.0092864
## [1375]  0.9207280  1.1366979  2.5516202  0.9871978  0.9207280  1.1098195
## [1381]  1.3876902  3.4240255  0.8529140  1.2887126  2.0700242  4.2305809
## [1387]  2.2140632  2.3119300  1.6708309  2.7231163  1.3860212  1.7994993
## [1393]  0.8716059  2.8834130  1.1760780  1.5032600  3.4401701  2.4553131
## [1399]  1.1026597  1.3763782  0.7598696  0.9244009  2.7275950  3.4257021
## [1405]  1.0470625  1.1741404  2.7364587  1.2438465  2.7669072  0.7707495
## [1411]  0.8749482  1.6912902  2.6176630  2.8479581  1.0877236  2.7900159
## [1417]  1.3492654  0.7563990  0.9893315  0.8202744  1.3531389  1.2739049
## [1423]  2.1613618  1.3486398  2.7364587  2.9237214  1.6416134  3.8100055
## [1429]  1.5195155  2.1395192  1.4639108  1.7182911  1.2610197  1.1366979
## [1435]  1.5579524  1.1760780  1.1366979  1.1897129  1.3292909  2.1613618
## [1441]  3.4401701  1.6416134  1.0834544  1.8399675  0.9950171  1.2673175
## [1447]  1.4639108  2.8166071  1.6788242  3.5698555  1.1568745  1.0908074
## [1453]  2.0864392  1.5036575  3.4825186  1.6692976  2.5541894  0.9519637
## [1459]  2.1362598  0.8304573  1.7888726  1.6796007  1.7888726  1.8702403
## [1465]  7.8511528  1.3486398  2.2212703  1.6116897  1.5036575  1.2438465
## [1471]  4.9508726  4.6869662  6.0243206  7.2223596  3.8405407  3.9090416
## [1477]  9.0692412  4.2118315  5.2292946  4.2118315  5.6611824  4.3115666
## [1483]  5.0590768  5.5857741  5.8567614  3.9962086  9.1233303  5.1996526
## [1489]  9.2594913  3.3767355  7.7492447  3.9666918  6.2823355  4.2188682
## [1495]  5.2740529  4.2188682  3.8697589  6.3822767  5.6606165  9.1764345
## [1501]  5.3449763  6.8051921  4.5759598  6.0661331  3.9666918  3.5455074
## [1507]  5.5958008  4.6869662  4.5532573  8.3829016  6.8051921  3.8795978
## [1513]  5.0590768  5.8567614  4.3115666  6.9383352  2.6796800  6.0797009
## [1519]  2.7654042  6.5138882  4.2738641  4.5497457  3.6598851  3.9090416
## [1525]  5.3604750  3.2390771  3.3304057  4.5181883  3.9090416  3.5285061
## [1531]  2.2716873  4.3372592  2.6993290  3.5285061  2.7522425  1.9742430
## [1537]  5.2493759  2.5205416  5.0832039  6.5138882  2.7522425  3.3990323
## [1543]  2.7522425  1.6737904  2.9687134  2.7522425  2.3516433  2.6993290
## [1549]  6.9380819  3.4285497  5.3150716  3.8234101  4.2738641  3.1526779
## [1555]  1.5221462  2.9241446  3.8234101  5.8931827  2.1882233  5.2493759
## [1561]  2.9241446  1.6737904  4.5385566  4.1537828  4.7576752  3.4442407
## [1567]  2.2356501  4.5385566  1.7699463  4.8016395  5.5684849  3.6249148
## [1573]  3.1526779  1.8432558  4.9700969  9.5005586  4.2195912  6.8435760
## [1579]  6.0860433  6.5032974  2.7007276  3.5455074  2.2182195  5.2740529
## [1585]  4.1482151  2.9687134  2.7654042  5.0692222  3.9414813  3.8697589
## [1591]  5.3147337  2.7007276  3.3767355  4.6764314  3.2342926  3.8526367
## [1597]  2.9687134  3.3255199  0.8000905  1.3860212  1.6493515  2.3970553
## [1603]  0.9244009  0.8029212  1.0363938  1.4194876  0.8881990  5.1063189
## [1609]  0.8029212  2.0429145  1.9680329  0.7563990  0.8194793  1.2659556
## [1615]  1.2723211  6.5375048  2.1484830  1.1549377  2.5205416  2.6404093
## [1621]  1.5221462  4.4031945  1.5463694  3.3255199  2.1915675  2.0185486
## [1627]  3.0091452  0.9519637  4.6510034  2.8997557  1.8017988  3.6249148
## [1633]  2.1285128  3.1363559  2.7134326  1.6647707  5.7219232  3.4045016
## [1639]  1.6116897  4.1537828  3.0193423  2.8414704  2.2182195  1.4291964
## [1645]  1.5930574  1.6647707  2.8997557  1.0096661  2.8360686  3.9364302
## [1651]  3.4049863  5.5299625  1.0908074  0.8723724  1.7254607  1.4670571
## [1657]  0.8304573  2.0864392  1.8630941  1.7254607  3.6106197  6.3943216
## [1663]  2.8360686  2.9237214  0.9290801  3.0173059  3.5270333  4.4042899
## [1669]  1.7254607  1.4194876  2.2194280  1.0937807  3.8100055  1.6189759
## [1675]  0.8723724  1.0010332  0.8063633  4.2427429  2.8479581  3.0173059
## [1681]  1.2493645  0.8194793  3.0698468  2.5595377  2.2233482  2.6993737
## [1687]  1.8137279  6.0015434  3.0024614  5.6061961  2.0970572  3.9247263
## [1693]  0.8410083  3.7118747  5.6469297  2.0562764  4.4526681  3.4369291
## [1699]  4.3047127  3.9247263  3.4369291  3.5157731  1.3857666  2.9937584
## [1705]  6.2060362  1.5887086  1.5032600  1.4250200  3.2051699  1.7600194
## [1711]  2.3066778  3.1245462  1.4882350  1.8825945  1.8913609  4.4920594
## [1717]  1.3264279  1.8944184  3.0418479  2.5739917  5.4611980  5.4195091
## [1723]  2.4375229  1.9070258  4.0614040  2.8570308  4.1058089  2.4191965
## [1729]  3.4884053  2.8465142  2.3284859  2.3284859  3.1176267  5.7258040
## [1735]  3.7413454  4.0764767  5.9958900  6.6733943  3.5347526  4.5075359
## [1741]  5.8680653  5.5952137  3.8548650  2.0934675  4.3681425  2.9127300
## [1747]  4.0669268  3.1245462  4.4170771  5.3135260  2.9479913  3.6859053
## [1753]  4.2860172  1.6912902  0.8723724  0.8063633  1.2739049  1.0312423
## [1759]  4.8762320  0.8410083  3.2440039  0.8202744  1.1568745  0.8772085
## [1765]  0.8529140  1.0363938  2.2650294  0.8749482  0.8063633  1.9694292
## [1771]  1.0312423  0.7598696  1.0908074  0.8366320  0.8116388  3.3117398
## [1777]  0.8000905  2.0600564  3.5029837  1.2196662  1.4453864  2.9771320
## [1783]  2.7172023  3.2991834 11.5019593  2.1508603  1.0937807  0.7707495
## [1789]  1.2077890  0.8304573  2.3119300  2.7122934  2.5834925  2.6947254
## [1795]  3.2375065  5.8672095  3.8982679  2.9518476  2.5209463  2.4049865
## [1801]  2.5790316  2.4325147  3.1598762  3.1234028  1.3946835  2.3528178
## [1807]  2.2317041  3.8500468  2.7152367  1.9072859  5.0239559  5.4552438
## [1813]  1.3721330  5.0206518  4.3681425  5.9568942  5.6207548  3.7325140
## [1819]  4.6789081  4.0669268  1.8602767  4.6789081  3.7345976  6.9896889
## [1825]  4.0414177  5.3802168  2.1889989  7.6921118  4.3549854  6.0791010
## [1831]  6.5851732  7.3202240  3.2324614  1.9750293  3.4143694  3.1052075
## [1837]  1.8780671  4.5876167  1.6773972  1.8068057  1.4563544  1.9221171
## [1843]  1.8964984  3.5454364  1.6473477  5.8777675  3.0059700  1.8663771
## [1849]  1.6473477  2.3496496  2.9245536  1.7755462  5.1063189  2.1725487
## [1855]  1.7728273  1.5884934  5.9739118  1.7982662  2.2741975  3.1052075
## [1861]  2.3744387  1.5884934  4.6784646  5.5518428  2.7722615  3.5143261
## [1867]  3.5052611  3.3929014  3.2279616  5.4718034  3.9918988  2.6699282
## [1873]  3.0899079 14.0122111  3.7396694  4.5109398  3.3929014  4.6784646
## [1879]  5.8134869  4.0417143  5.1895359  4.4051083  1.9221171  2.3748378
## [1885]  4.1556810  2.8894506  3.8701757  3.3361834  3.5052611  5.5518428
## [1891]  2.4599535  3.1932190  1.7755462  3.8701757  1.9369563  1.9221171
## [1897]  2.7252930  2.1015026  2.5854922  1.4217174  2.0317380  5.1973404
## [1903]  2.1725487  2.2457970  2.0552029  1.8068057  3.5454364  2.2061097
## [1909]  2.1725487  1.8663771  1.8663771  1.5060689  2.1725487  2.4890569
## [1915]  3.1052075  2.2061097  8.5076006  2.4572843  4.9250897  7.4419262
## [1921]  1.9426936  4.4051083  5.8134869  2.7458394  4.4496606  4.0549265
## [1927]  4.4051083  2.7657574  2.6699282  3.3361834  4.6834781  2.7657574
## [1933]  5.8211475  2.2679329  2.4599535  2.9738297  4.9250897  5.8211475
## [1939]  4.9574264  2.8977241  6.0443471  2.7722615  3.9583140  2.7722615
## [1945]  4.8738375  3.2886739  2.2744839  4.3060218  1.9460242  1.3046113
## [1951]  3.3044482  3.5037187  1.3622246  1.2831565  1.2182445  1.0445402
## [1957]  4.0955425  0.9858673  9.9191150  0.8723724  1.1741404  1.0937807
## [1963]  8.0277269  1.0010332  2.2194280  5.7674556  3.2991834  1.0937807
## [1969]  2.0425749  0.8304573  1.3492654  0.7598696  0.8749482  2.9580564
## [1975]  1.2196662  2.1613618 12.1028393  1.3238194  2.6862184  6.0057170
## [1981]  3.6106197  2.7364587  2.4082411  1.7253261  4.2472764  0.9290801
## [1987]  0.9596288  0.9290801  1.8630941  6.8673877  3.0024614  5.2373751
## [1993]  0.8063633  3.8333783  4.2195912  4.9946150  2.6796800  3.7102809
## [1999]  3.8234101  4.6510034  4.9946150  2.0487958  1.6647707  3.5285061
## [2005]  5.5823958  2.6993290  6.2891652  2.0515606  3.8333783 10.9323991
## [2011]  2.5205416  2.1399232  2.5391899  2.9241446  2.6814196  5.2493759
## [2017]  1.7312079  1.9714119  6.2060362  2.2846891  1.6904599  1.6904599
## [2023]  1.4891228  2.4834097  2.6044644  1.6904599  1.3303071  1.4617393
## [2029]  1.4061219  1.3721330  1.4895094  1.9526017  1.4617393  2.0756246
## [2035]  1.5887086  3.3376074  1.5262976  2.3591358  1.5240353  2.2741975
## [2041]  3.4847599  1.8780671  1.9908324  8.6791667 17.3576883  6.4644725
## [2047]  3.7413454  5.4282118  2.1442004  3.0899079  2.0317380  1.6297869
## [2053]  2.7458394  2.1442004  1.9221171  2.2744839  3.3361834  4.9250897
## [2059]  2.1442004  1.7982662  4.3562226  4.9724669  9.3163378  1.5060689
## [2065]  2.6005368  3.0333616  1.9750293  2.6005368  5.4552438  3.0899079
## [2071]  2.1442004  2.8018244  2.0964027  5.8564270  4.7457575  2.1725487
## [2077]  3.3997077  1.7728273  1.6773972  4.4158921  3.3997077  1.9049430
## [2083]  4.9264374  1.6099801  1.9426936  1.5789486  2.1015026  1.5884934
## [2089]  2.2457970  1.9221171  3.4240352  2.2846891  2.3066778  7.0190798
## [2095]  2.5603752  1.7982662  1.7755462  1.6297869  2.2815270  2.1973042
## [2101]  2.4104427  3.0059700  2.0934675  4.3601117  1.9451127  2.0317380
## [2107]  1.8964984  2.0031036  3.6803692  3.1758619  2.5854922  3.5454364
## [2113]  1.9750293  3.1052075  6.1528101  3.0059700  2.1015026  1.4414656
## [2119]  4.7318407  2.4890569  2.4104427  5.5744550  2.8318264  3.7316946
## [2125]  2.0789156  6.9173311  1.8068057  1.7728273  6.1528101  2.8318264
## [2131]  3.3997077  2.7770997  3.0059700
hasil <- data.frame(Obs = 1:length(Di), Mahalanobis_Distance = Di)

hasil<- hasil[order(hasil$Mahalanobis_Distance), ]
hasil$Rank <- c(1:nrow(data_numerik))

hasil$Probability<-((hasil$Rank-0.5)/nrow(data_numerik))

hasil
hasil$X2<-qchisq(hasil$Probability,3)
hasil
plot(hasil$Mahalanobis_Distance,hasil$X2,
     xlab= "Mahalanobis Distance",ylab="Chi-Square",,col="red",main = "QQ plot Normalitas",
     pch=19,
     cex=0.8)

cor_matrix <- cor(Diskriminan)
cor_matrix
##           X1        X2         Y
## X1 1.0000000 0.9508843 0.6224203
## X2 0.9508843 1.0000000 0.5983709
## Y  0.6224203 0.5983709 1.0000000
AD1 <- diskriminan[diskriminan$Y == 1, ]
AD11<-as.matrix(AD1[, -ncol(Diskriminan)])

AD2 <- diskriminan[diskriminan$Y == 2, ]
AD22<-as.matrix(AD2[, -ncol(Diskriminan)])


x_bar1 <- colMeans(AD11)
x_bar1
##       X1       X2 
## 45.24619 57.47603
x_bar2 <- colMeans(AD22)
x_bar2
##       X1       X2 
## 62.29218 74.37531
selisih<-x_bar1-x_bar2
selisih
##        X1        X2 
## -17.04599 -16.89927
cov_matriks1<-cov(AD11)
cov_matriks1
##          X1       X2
## X1 108.1596 106.2633
## X2 106.2633 122.8757
cov_matriks2<-cov(AD22)
cov_matriks2
##          X1       X2
## X1 116.2070 112.4454
## X2 112.4454 127.7355
Spooled<-((((nrow(AD11)-1)*cov_matriks1**2)+((nrow(AD22)-1)*cov_matriks2**2))/(nrow(AD11)+nrow(AD22)-2))
Spooled
##          X1       X2
## X1 12727.10 12062.15
## X2 12062.15 15792.26
SP<-solve(Spooled)
SP
##               X1            X2
## X1  0.0002845748 -0.0002173586
## X2 -0.0002173586  0.0002293410
a=SP%*%selisih
a
##             [,1]
## X1 -0.0011776569
## X2 -0.0001706025
C = ((-0.5*(selisih%*%a))+log(0.5/0.5))[1,1]
C
## [1] -0.01147869
Z1= C + AD11%*%a
head(Z1)
##           [,1]
## 25 -0.08851664
## 43 -0.09308979
## 44 -0.10083814
## 45 -0.09291918
## 48 -0.09728861
## 49 -0.09223677
Z2= C + AD22%*%a
head(Z2)
##          [,1]
## 1 -0.09677680
## 2 -0.10268164
## 3 -0.09981452
## 4 -0.09645215
## 5 -0.09981452
## 6 -0.10182863
Z1_bar=mean(Z1)
Z1_bar
## [1] -0.07456873
Z2_bar=mean(Z2)
Z2_bar
## [1] -0.09752612
m=(((nrow(AD11)*Z1_bar)+(nrow(AD22)*Z2_bar))/(nrow(AD11)+nrow(AD22)))
m
## [1] -0.08764573
lebih_besar <- length(Z1[Z1 > m])  # Hitung yang lebih besar dari m
lebih_kecil <- length(Z2[Z2 < m])  # Hitung yang lebih kecil dari m

print(lebih_besar)
## [1] 727
print(lebih_kecil)
## [1] 910
akurasi = ((lebih_besar+lebih_kecil)/nrow(AD))
akurasi
## [1] 0.7674637