Nama : Muhammad Hafidlul Qolbi
NIM : 220605110063
Kelas : A
Mata Kuliah : Linear Algebra
Dosen Pengampuh : Prof. Dr. Suhartono, M.Kom
Jurusan : Teknik Informatika
Lembaga : Universitas Islam Negeri Maulana Malik Ibrahim Malang
===========================================================================================
Tea <- matrix(c(3, 1, 1, 3), 2, 2, byrow = TRUE)
fisher.test(Tea, alternative = "greater")##
## Fisher's Exact Test for Count Data
##
## data: Tea
## p-value = 0.2429
## alternative hypothesis: true odds ratio is greater than 1
## 95 percent confidence interval:
## 0.3135693 Inf
## sample estimates:
## odds ratio
## 6.408309B <- matrix(c(1, 0, 0, 1, 1, 0, 1, 1, 1), 3, 3, byrow = TRUE)
v <- c(2, 4, 0)
B <- matrix(c(1, 0, 0, 1, 1, 0, 1, 1, 1), 3, 3, byrow = TRUE)Library “mvtnorm” di RStudio adalah sebuah paket yang menyediakan fungsi-fungsi untuk analisis multivariat berdasarkan distribusi multivariat normal. “mvtnorm” adalah singkatan dari “Multivariate Normal Distribution”, yang mengacu pada distribusi normal multivariat.
Paket “mvtnorm” memungkinkan Anda untuk menghasilkan sampel dari distribusi multivariat normal, menghitung fungsi kepadatan probabilitas (PDF), menghitung fungsi distribusi kumulatif (CDF), menghitung invers dari CDF, dan melakukan berbagai operasi lainnya terkait distribusi normal multivariat.
Fungsi-fungsi populer dalam paket ini meliputi rmvnorm() untuk menghasilkan sampel acak dari distribusi multivariat normal, dmvnorm() untuk menghitung PDF dari distribusi multivariat normal, dan pnorm() untuk menghitung CDF dan invers CDF dari distribusi normal univariat.
Paket “mvtnorm” sangat berguna dalam analisis multivariat, seperti analisis faktor, analisis komponen utama, analisis kluster, dan banyak lagi. Dengan menggunakan paket ini, Anda dapat mengambil sampel acak dari distribusi multivariat normal, menghitung probabilitas, dan melakukan berbagai analisis statistik yang melibatkan variabel multivariat.
Untuk menggunakan paket “mvtnorm” di RStudio, Anda perlu menginstalnya terlebih dahulu menggunakan perintah install.packages(“mvtnorm”), kemudian memuatnya ke dalam lingkungan R dengan perintah library(mvtnorm). Setelah itu, Anda dapat menggunakan fungsi-fungsi yang disediakan oleh paket “mvtnorm” dalam skrip R Anda.
library(mvtnorm)
set.seed(123)
sigma <- matrix(c(4,2,2,3), ncol=2)
sigma## [,1] [,2]
## [1,] 4 2
## [2,] 2 3x <- rmvnorm(n=500, mean=c(0,0), sigma=sigma)
x## [,1] [,2]
## [1,] -1.205156592 -6.921777e-01
## [2,] 3.031369338 9.917705e-01
## [3,] 1.212307319 2.882441e+00
## [4,] 0.173488321 -1.813413e+00
## [5,] -1.568859453 -1.116247e+00
## [6,] 2.551737218 1.277617e+00
## [7,] 0.831449504 4.066308e-01
## [8,] -0.062314892 2.614990e+00
## [9,] -0.150014479 -2.941996e+00
## [10,] 1.080369843 -3.802846e-01
## [11,] -2.172083277 -9.574019e-01
## [12,] -2.379038272 -1.770917e+00
## [13,] -2.147886254 -3.114656e+00
## [14,] 1.694241593 7.222465e-01
## [15,] -1.479645074 1.414276e+00
## [16,] 0.652660790 -2.436650e-01
## [17,] 2.211733394 1.941842e+00
## [18,] 1.964047158 1.590054e+00
## [19,] 1.028365830 2.099667e-01
## [20,] -0.801143430 -7.953213e-01
## [21,] -1.450281636 -7.311699e-01
## [22,] -1.209438285 2.841993e+00
## [23,] 1.687144008 -1.160889e+00
## [24,] -1.035622743 -9.910022e-01
## [25,] 1.450170974 3.018904e-01
## [26,] 0.470162825 9.564027e-02
## [27,] 0.687102058 2.218055e+00
## [28,] 0.419176035 2.357484e+00
## [29,] -2.643971532 8.710055e-02
## [30,] 0.359117335 4.234001e-01
## [31,] 0.446276290 -6.095255e-01
## [32,] -1.212158696 -1.856032e+00
## [33,] -1.886525125 -1.052628e-01
## [34,] 0.890075942 3.388056e-01
## [35,] 2.922663410 3.877086e+00
## [36,] -2.240612301 -4.059111e+00
## [37,] 1.531689414 -5.964751e-01
## [38,] -0.743995608 1.293397e+00
## [39,] -1.232833609 -2.159970e+00
## [40,] 0.269907272 -1.256199e-01
## [41,] 0.227656386 6.344381e-01
## [42,] -0.349183552 8.472964e-01
## [43,] -0.236676776 4.196014e-01
## [44,] 2.349881134 1.329559e+00
## [45,] 0.020242354 1.698841e+00
## [46,] 2.215189408 1.456946e+00
## [47,] 0.105224063 -8.944792e-01
## [48,] 2.274142502 -2.184771e-01
## [49,] 5.059879105 3.740499e+00
## [50,] -1.029417541 -1.814070e+00
## [51,] -1.219118051 2.147904e-02
## [52,] -0.668869767 -7.080551e-01
## [53,] -1.851817493 -6.087388e-01
## [54,] -2.444184634 -3.173807e+00
## [55,] -0.213162184 1.291823e+00
## [56,] -0.762522515 6.725742e-01
## [57,] -3.136544235 -1.000550e+00
## [58,] 1.166231676 7.853687e-01
## [59,] -0.157353942 -9.902488e-01
## [60,] -2.206627342 -2.155489e+00
## [61,] -0.306834243 -1.486093e+00
## [62,] -1.085526423 -6.953274e-01
## [63,] 3.172539772 -3.151478e-02
## [64,] 0.495620170 2.600489e-01
## [65,] -1.886242101 -6.575490e-01
## [66,] 3.026443458 1.551773e+00
## [67,] -0.158373671 -6.689888e-01
## [68,] -3.304929812 6.991761e-01
## [69,] -2.387527083 3.911152e-01
## [70,] 2.852556041 -1.292264e+00
## [71,] 1.199581595 -3.503166e-02
## [72,] -3.869019608 -3.365263e+00
## [73,] -3.372393357 -1.770109e+00
## [74,] -2.418918244 3.052471e-01
## [75,] 3.307348632 -9.279013e-01
## [76,] 1.944291052 1.702750e+00
## [77,] 0.070739976 -1.465250e+00
## [78,] -0.386902910 -5.265190e-01
## [79,] 0.871209323 -2.936640e-01
## [80,] 1.664591617 -6.444440e-02
## [81,] 1.430723480 -1.127045e+00
## [82,] -0.596686015 4.601315e+00
## [83,] -0.632447878 2.542362e-01
## [84,] 0.949843563 -4.347089e-01
## [85,] 1.199467937 8.950317e-01
## [86,] -0.376688278 -1.411195e-02
## [87,] 1.131162735 3.467851e+00
## [88,] -2.039030699 -2.212307e+00
## [89,] 0.247072505 5.298983e-01
## [90,] 0.580169401 -5.055313e-01
## [91,] -1.330788096 1.471683e+00
## [92,] -1.157671793 -1.614516e+00
## [93,] -0.564353192 -4.558587e-01
## [94,] 2.177979930 7.627866e-01
## [95,] 1.166618539 -3.940749e-01
## [96,] 0.229070585 -4.113723e-01
## [97,] -0.321805365 -1.413685e+00
## [98,] -1.393135848 2.535105e+00
## [99,] 0.449553756 -1.712234e+00
## [100,] -1.839491539 -2.285729e+00
## [101,] 4.958119998 3.386205e+00
## [102,] -0.203543387 7.408483e-01
## [103,] -1.063001365 -1.013156e+00
## [104,] -1.847893005 -1.417479e+00
## [105,] 3.138322651 8.395762e-01
## [106,] 0.365868834 4.662646e-01
## [107,] 2.075457023 -1.525977e-01
## [108,] -0.962959114 2.187306e+00
## [109,] -1.253239136 -1.432594e+00
## [110,] -3.095088254 -2.799721e+00
## [111,] -0.754252522 6.897644e-01
## [112,] 2.527989176 1.783151e+00
## [113,] -0.664401860 -1.065498e-01
## [114,] -1.755576485 -1.571108e+00
## [115,] 1.127033114 -1.166503e+00
## [116,] 3.702149787 9.512373e-01
## [117,] -0.003399063 -1.089309e+00
## [118,] -1.842848106 -2.480547e+00
## [119,] -0.115561729 5.835760e-01
## [120,] 0.183102920 -1.098063e+00
## [121,] -1.795974859 -1.266082e+00
## [122,] 2.232130778 -1.022184e+00
## [123,] 0.725783831 3.015947e+00
## [124,] -0.958268421 -2.284567e+00
## [125,] -1.003025144 4.216071e-01
## [126,] -1.036788996 -1.131664e+00
## [127,] -0.609228599 -4.508074e-02
## [128,] 3.018334744 7.535379e-01
## [129,] 2.429040352 1.640945e+00
## [130,] -1.079866956 -2.575210e+00
## [131,] -1.275604961 -1.095502e+00
## [132,] 0.821438362 2.156600e+00
## [133,] 5.271260259 3.824472e+00
## [134,] -1.243031162 -2.952539e+00
## [135,] -0.696061279 -7.241357e-02
## [136,] 2.162992850 2.051932e+00
## [137,] 0.529059858 -1.901154e+00
## [138,] 1.379735197 -2.539431e-01
## [139,] 0.377420734 2.204045e-01
## [140,] 0.835680233 2.811268e-01
## [141,] -2.786459546 2.691843e-01
## [142,] 0.591585075 -2.181998e-01
## [143,] 0.302114962 2.860102e-01
## [144,] 1.346650546 2.812418e+00
## [145,] -0.325956647 1.521950e-01
## [146,] 2.835184422 2.383875e+00
## [147,] 1.873544267 -3.022233e-01
## [148,] 3.880994377 1.235009e+00
## [149,] 2.823735907 -1.163672e+00
## [150,] 0.742938750 2.059508e+00
## [151,] -1.795950122 -1.635203e+00
## [152,] -2.393089872 -2.251930e+00
## [153,] -0.652890373 2.968070e-01
## [154,] -3.746838188 -7.850437e-01
## [155,] 3.519093503 4.033340e+00
## [156,] 2.922868434 1.971291e+00
## [157,] -3.652376148 -1.956152e+00
## [158,] -0.280206464 9.546604e-01
## [159,] -0.910395549 -2.121426e+00
## [160,] 3.745404750 2.440053e+00
## [161,] 1.140498819 2.129081e+00
## [162,] -2.198104933 3.299918e-01
## [163,] -0.619279493 8.262022e-01
## [164,] 0.239091476 1.002775e+00
## [165,] 2.567445320 7.627302e-01
## [166,] 1.284966314 -1.374949e+00
## [167,] -0.530965483 2.083242e+00
## [168,] -0.429350985 -3.149962e+00
## [169,] -2.730959978 -1.095756e+00
## [170,] 1.604471885 3.198011e-01
## [171,] 1.737167548 1.922020e+00
## [172,] 3.238856650 1.031187e+00
## [173,] -1.085388477 -2.901519e+00
## [174,] -0.130830529 -8.810123e-01
## [175,] -1.970618598 -8.422953e-01
## [176,] 0.827785408 -2.694113e+00
## [177,] -0.754535424 -4.911860e-02
## [178,] -1.526682234 4.489310e-02
## [179,] 0.771112673 1.771707e-01
## [180,] -3.287366302 2.826520e+00
## [181,] -0.027963552 9.514249e-01
## [182,] 1.101497895 1.832606e+00
## [183,] 1.451448437 1.159628e-01
## [184,] 0.194362553 -1.336251e+00
## [185,] 1.385567272 -2.735747e-01
## [186,] 3.710503558 -1.346247e+00
## [187,] -0.426558123 1.091365e+00
## [188,] 0.647742920 -6.789549e-01
## [189,] -1.831967228 -3.236677e-01
## [190,] -1.033902268 -2.941028e+00
## [191,] 0.173257781 3.310743e-01
## [192,] -0.257734267 -1.630189e+00
## [193,] 1.688863784 2.526153e+00
## [194,] 0.237291676 -1.603931e+00
## [195,] -0.641594266 3.221086e-01
## [196,] -2.454879839 -3.898581e+00
## [197,] 1.230894100 -8.618190e-01
## [198,] -0.255425347 2.141374e+00
## [199,] -1.010423142 9.503457e-01
## [200,] -2.619024656 -1.289557e+00
## [201,] -0.798160844 -1.955931e+00
## [202,] -1.234528051 -4.040865e-01
## [203,] 0.359424461 -2.327015e+00
## [204,] -0.246077923 1.042585e+00
## [205,] -0.906395428 6.946616e-02
## [206,] 1.095335381 7.155049e-01
## [207,] 1.184857517 1.662101e-01
## [208,] -2.279893752 -4.562778e+00
## [209,] 0.063505008 6.526788e-01
## [210,] 0.715465884 -6.087174e-01
## [211,] 3.576536327 1.469626e+00
## [212,] 0.957675653 2.155342e+00
## [213,] -1.632166150 -1.141681e+00
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## [215,] 2.326731390 -1.438337e+00
## [216,] -0.152933174 5.128621e-01
## [217,] 0.010545964 -1.478843e+00
## [218,] -0.568727192 -1.754291e+00
## [219,] 1.977765732 2.177827e+00
## [220,] -3.575896758 7.735938e-01
## [221,] -2.126361257 4.736292e-02
## [222,] 1.154222744 4.350122e-02
## [223,] -1.145271373 -9.182090e-02
## [224,] 1.338819385 1.693789e+00
## [225,] -4.859107902 -3.834610e+00
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## [227,] 1.237530120 1.416370e+00
## [228,] 0.264505279 -3.843733e+00
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## [231,] 1.477719351 -8.070400e-02
## [232,] 0.775567389 -3.485650e-01
## [233,] -1.417227844 1.368006e+00
## [234,] 2.391385518 3.241338e+00
## [235,] 0.757496219 1.879699e+00
## [236,] 3.633311501 6.493730e-01
## [237,] -2.673783436 -1.135848e+00
## [238,] -0.325553352 1.281679e-01
## [239,] 3.103191819 4.282898e-01
## [240,] 0.587935455 -1.633188e-01
## [241,] 0.215805963 5.260116e-01
## [242,] 2.617531546 9.454351e-01
## [243,] 1.806056466 1.676730e+00
## [244,] 1.432877712 -4.267624e-01
## [245,] 2.908418257 2.904683e-01
## [246,] 0.586275391 2.240761e+00
## [247,] 1.871060664 -1.058219e+00
## [248,] -2.439213084 -2.715729e+00
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## [250,] 1.009275440 1.109284e+00
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## [252,] 2.392999878 1.807677e+00
## [253,] -2.950131860 -1.004285e+00
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## [336,] -1.159529204 -7.730047e-01
## [337,] 0.454285913 -6.777666e-01
## [338,] -0.927636230 -3.162521e+00
## [339,] -2.895920743 -2.804810e+00
## [340,] -2.028170774 -1.615709e+00
## [341,] 1.285897234 1.823898e+00
## [342,] -1.956507437 -2.042015e+00
## [343,] -2.232451185 -1.264818e+00
## [344,] -0.186909339 6.579268e-01
## [345,] -1.785202772 -3.585789e+00
## [346,] 0.491904113 1.893544e+00
## [347,] 1.843588037 -6.226621e-01
## [348,] -1.588903533 3.156882e+00
## [349,] -0.366531247 -2.509612e-01
## [350,] -0.100127608 -2.407817e+00
## [351,] -2.263708368 -2.933060e+00
## [352,] -1.263488713 -1.949277e-01
## [353,] -2.287706750 1.993599e-01
## [354,] 0.047035175 -1.318698e+00
## [355,] 0.854948636 1.352800e+00
## [356,] 1.916973352 2.478098e-01
## [357,] -0.228471298 -1.947019e-01
## [358,] 3.399173484 2.653530e+00
## [359,] 1.439987801 -1.670142e-03
## [360,] 0.943104339 8.705279e-01
## [361,] -2.970951964 -3.417046e+00
## [362,] 0.372175317 -2.144624e+00
## [363,] 0.143913251 4.109229e-01
## [364,] 1.188757488 6.273224e-01
## [365,] -0.852110072 1.203957e+00
## [366,] 3.832446130 2.421025e+00
## [367,] -2.943778657 1.200239e+00
## [368,] 0.187498805 8.284443e-01
## [369,] 1.139555482 1.912890e-01
## [370,] 0.428481171 1.627355e+00
## [371,] 1.922519520 2.022369e+00
## [372,] 4.947222579 2.428108e+00
## [373,] -0.844709679 -3.505056e+00
## [374,] 4.895038165 7.224385e-01
## [375,] 4.768598090 1.948774e+00
## [376,] 2.891134791 6.851218e-01
## [377,] 1.101980161 6.380565e-01
## [378,] -0.424915445 -3.018703e-01
## [379,] 1.830746171 2.393392e-01
## [380,] -4.021181343 -1.466444e+00
## [381,] 1.382608180 1.313382e+00
## [382,] 0.232171798 -2.425523e+00
## [383,] 1.251851667 1.792921e+00
## [384,] 2.323755357 3.491035e-01
## [385,] 0.218587042 2.256539e+00
## [386,] -3.446936714 -1.653308e+00
## [387,] -0.031425560 -2.393197e+00
## [388,] 1.592385658 3.233668e+00
## [389,] -0.164332177 -4.584688e-01
## [390,] 0.754643580 -1.902180e-01
## [391,] 2.069658823 1.938988e+00
## [392,] -0.656333895 -1.926240e+00
## [393,] -2.863512897 -1.712560e+00
## [394,] 0.429622209 -2.759828e+00
## [395,] -3.988083238 -2.131509e+00
## [396,] 0.243409284 -1.274962e+00
## [397,] 1.889406275 1.044657e+00
## [398,] 0.132800145 1.245542e+00
## [399,] 0.494723904 -5.122401e-01
## [400,] 0.807606254 1.190735e+00
## [401,] 0.313925004 -8.777143e-01
## [402,] 2.289591328 2.369602e+00
## [403,] 0.611283194 3.913970e-01
## [404,] 1.069929374 3.498493e+00
## [405,] 0.441362588 -1.039940e-01
## [406,] -5.693565387 -3.974246e+00
## [407,] -0.033111124 2.943022e-01
## [408,] 0.993245446 1.501508e+00
## [409,] 0.310154976 1.880692e+00
## [410,] -2.448075897 -2.497817e+00
## [411,] -1.941577660 5.251931e-01
## [412,] 0.284857654 1.247329e+00
## [413,] -0.846570148 -1.120182e+00
## [414,] -1.748487653 -3.242184e+00
## [415,] -3.055587295 -3.019980e+00
## [416,] 1.687829660 -3.858871e-01
## [417,] 2.367786795 2.928248e+00
## [418,] -0.208498042 3.572636e-01
## [419,] -3.821170394 -2.325608e+00
## [420,] 0.276034336 5.215907e-01
## [421,] 0.051782338 3.971644e+00
## [422,] -0.843702678 -1.524438e-01
## [423,] 1.232561517 3.226672e-01
## [424,] -0.647602611 1.350711e+00
## [425,] 3.084129669 8.595629e-01
## [426,] 1.024434492 1.565003e-01
## [427,] 1.300987763 -1.322708e+00
## [428,] 4.115293398 3.159623e-01
## [429,] -2.997341134 -1.395022e+00
## [430,] 1.194337229 2.742423e+00
## [431,] 1.829030594 7.456411e-01
## [432,] -3.153787196 -2.199938e+00
## [433,] 1.121829299 4.090781e+00
## [434,] -2.934613318 8.072229e-01
## [435,] -0.075386592 2.432967e+00
## [436,] -2.105802365 -4.051283e-01
## [437,] -1.602511479 8.620803e-01
## [438,] 3.944551264 4.029965e+00
## [439,] 2.567115210 3.468175e+00
## [440,] 2.318207604 4.846530e-01
## [441,] 0.369183757 -1.324224e+00
## [442,] 0.330917543 1.896167e+00
## [443,] 1.296034602 1.053573e+00
## [444,] -2.332392149 -1.573968e+00
## [445,] -1.245335566 2.177678e-01
## [446,] -1.585184232 3.639490e-01
## [447,] -1.114868021 2.368032e+00
## [448,] 0.489960667 -8.895108e-01
## [449,] 0.264516999 -4.419089e-01
## [450,] 0.849275374 6.076231e-01
## [451,] -2.391308577 -1.866499e+00
## [452,] 1.496454546 2.853651e+00
## [453,] 1.730664327 -4.134789e-01
## [454,] 1.557944671 3.847399e-01
## [455,] 0.724698398 5.959346e-01
## [456,] 4.276897668 -4.939978e-01
## [457,] -0.806946400 -2.859370e+00
## [458,] 1.748590585 2.128141e+00
## [459,] 1.692497390 -2.341223e+00
## [460,] 1.687999355 2.842435e+00
## [461,] -0.913912467 -5.803093e-01
## [462,] 0.135074026 5.774633e-01
## [463,] 2.017523638 2.532894e+00
## [464,] -0.072934145 2.678785e-01
## [465,] 5.017729017 2.104937e+00
## [466,] -0.392281551 -2.092861e+00
## [467,] -0.118940963 -3.609889e-01
## [468,] -0.344683108 -9.489056e-01
## [469,] -1.723447378 -1.566937e+00
## [470,] 0.357409473 2.120798e+00
## [471,] 1.811214214 2.375487e-05
## [472,] -3.710689516 -2.331436e+00
## [473,] -0.820347886 -8.755070e-02
## [474,] -0.143691623 2.915010e+00
## [475,] -1.205023322 -2.141843e+00
## [476,] -0.836325396 -1.726504e+00
## [477,] 0.431061589 4.705435e-01
## [478,] -0.229256123 -2.457160e+00
## [479,] 0.598151237 6.326817e-01
## [480,] -2.190549977 7.662542e-01
## [481,] 2.797886246 4.208260e+00
## [482,] 0.327042534 1.646563e-01
## [483,] 0.224603994 1.685943e-01
## [484,] -4.487352019 -3.776931e+00
## [485,] -0.475483882 -9.955419e-01
## [486,] -1.081797058 -3.427982e+00
## [487,] -3.495770568 -2.647062e+00
## [488,] 1.275069257 -1.245304e+00
## [489,] -1.489657264 -3.186064e-01
## [490,] -0.537157143 5.843444e-02
## [491,] 3.792039883 -5.465822e-01
## [492,] -0.876814315 -1.018323e+00
## [493,] 2.470259526 -4.104105e-01
## [494,] 0.284947524 1.243400e+00
## [495,] -1.101333656 2.116537e+00
## [496,] 0.693149429 -1.379960e+00
## [497,] 0.752586453 -9.390743e-02
## [498,] 0.550619353 2.868291e-02
## [499,] 1.295164921 -1.611671e+00
## [500,] -1.143180044 -7.020435e-01pca<- princomp(x)
pca## Call:
## princomp(x = x)
##
## Standard deviations:
## Comp.1 Comp.2
## 2.241521 1.231119
##
## 2 variables and 500 observations.pca$loadings##
## Loadings:
## Comp.1 Comp.2
## [1,] 0.781 0.625
## [2,] 0.625 -0.781
##
## Comp.1 Comp.2
## SS loadings 1.0 1.0
## Proportion Var 0.5 0.5
## Cumulative Var 0.5 1.0Sumber Referensi: Ruriko Yoshida - Linear Algebra and its Application with R