MVTNORM
Haniyah
2023-04-06
Haii!!! MAsuk lagi ke pembahasan selanjutnya dengan library baru dengan pembahasan baru.
perkenalkan saya Haniyah NIM 220605110048 mahasiswa teknik informatika 2022, uin maulana malik ibrahim malang seperti pembahasan sebelumnya ini merupakan mata kulia linear algebra dari dosen pengampu: Prof. Dr. Suhartono, M.Kom
sebelum itu sedikit saya akan membahas tentang 3 library yang digunakan:
Library matlib merupakan sebuah paket (package) dalam bahasa pemrograman R yang berisi berbagai fungsi untuk melakukan operasi matriks dan aljabar linear. Fungsi-fungsi yang terdapat dalam library matlib ini termasuk di antaranya: perhitungan invers matriks, determinan matriks, eigenvalue dan eigenvector, serta transformasi matriks.
Library mvtnorm adalah sebuah paket dalam bahasa pemrograman R yang berisi fungsi-fungsi untuk menghitung distribusi multivariat normal. Fungsi-fungsi dalam library ini dapat digunakan untuk menghitung probabilitas, menghasilkan sampel dari distribusi multivariat normal, dan melakukan operasi statistik pada data yang mengikuti distribusi tersebut.
Library ggplot2 adalah sebuah paket dalam bahasa pemrograman R yang digunakan untuk membuat visualisasi data yang menarik dan informatif dengan menggunakan grammar of graphics. Fungsi-fungsi yang terdapat dalam library ini dapat digunakan untuk membuat berbagai jenis plot, termasuk scatterplot, histogram, boxplot, dan masih banyak lagi. Library ini sangat populer dan digunakan oleh banyak peneliti dan profesional di berbagai bidang, termasuk data science dan statistik.
library(matlib)
library(mvtnorm)
library(ggplot2)## Standard deviation
sigma <- matrix(c(4,2,2,3), ncol = 2, nrow = 2)
## Mean
mu <- c(1, 2)n <- 1000set.seed(123)x <- rmvnorm(n = n, mean = mu, sigma = sigma)Perintah “x <- rmvnorm(n = n, mean = mu, sigma = sigma)” merupakan sintaks dari bahasa pemrograman R yang digunakan untuk menghasilkan sampel acak dari distribusi multivariat normal.
Argumen “n” menentukan jumlah sampel yang akan dihasilkan, sedangkan “mean” dan “sigma” mewakili vektor rata-rata dan matriks kovarians, masing-masing, dari distribusi multivariat normal yang ingin dibuat sampelnya.
Dalam konteks ini, “x” akan menjadi nama variabel yang menyimpan hasil sampel acak dari distribusi multivariat normal yang dibentuk dengan menggunakan rata-rata “mu” dan matriks kovarians “sigma”, dan sebanyak “n” sampel. Oleh karena itu, sintaks tersebut akan menghasilkan “n” sampel acak dari distribusi multivariat normal yang memiliki rata-rata “mu” dan matriks kovarians “sigma”, kemudian disimpan dalam variabel “x” untuk digunakan pada analisis atau pemrosesan data selanjutnya.
d <- data.frame(x)p2 <- ggplot(d, aes(x = X1, y = X2)) +
geom_point(alpha = .5) +
geom_density_2d()
p2
Perintah “p2 <- ggplot(d, aes(x = X1, y = X2)) + geom_point(alpha = .5) + geom_density_2d()” merupakan sintaks dari bahasa pemrograman R yang digunakan untuk membuat plot dua dimensi dengan menggunakan package ggplot2.
Pertama, sintaks ini akan menghasilkan objek plot yang diberi nama “p2” dengan menggunakan data frame “d” sebagai sumber data.
Kemudian, dengan menggunakan fungsi “aes()”, variabel “X1” akan diatur sebagai sumbu x dan variabel “X2” akan diatur sebagai sumbu y pada plot dua dimensi yang akan dibuat.
Selanjutnya, dengan menggunakan fungsi “geom_point()”, sintaks tersebut akan menambahkan layer titik pada plot dengan alpha (transparansi) sebesar 0.5, yang akan merepresentasikan setiap data point pada sumbu x dan y.
Terakhir, dengan menggunakan fungsi “geom_density_2d()”, sintaks tersebut akan menambahkan layer densitas pada plot, yang akan merepresentasikan sebaran kepadatan data pada sumbu x dan y. Plot densitas yang dihasilkan oleh fungsi ini akan berupa kontur yang merepresentasikan nilai kepadatan data pada setiap titik di plot dua dimensi.
Secara keseluruhan, sintaks ini akan menghasilkan plot dua dimensi yang menampilkan titik-titik data dengan sebaran kepadatan yang diwakili oleh kontur pada setiap titik. Plot tersebut dapat digunakan untuk memvisualisasikan hubungan antara variabel X1 dan X2 dalam data frame “d”.
y <- x - muE <- eigen(sigma)
E$vectors## [,1] [,2]
## [1,] -0.7882054 0.6154122
## [2,] -0.6154122 -0.7882054y <- y %*% t(inv(E$vectors))Ekspresi y <- y %*% t(inv(E$vectors)) melibatkan beberapa operasi dengan matriks. Mari kita bahas langkah demi langkah:
E\(vectors: E di sini kemungkinan mengacu pada dekomposisi nilai eigen dari sebuah matriks persegi, dan E\)vectors merupakan matriks dari vektor eigen dari matriks tersebut. Jadi E$vectors adalah matriks persegi.
inv(E\(vectors): inv kemungkinan mengacu pada invers dari sebuah matriks, sehingga operasi ini menghitung invers dari E\)vectors. Perlu diingat bahwa tidak semua matriks memiliki invers, tetapi kita mengasumsikan di sini bahwa E$vectors dapat diinvers.
t(inv(E\(vectors)): t adalah operasi transpose, sehingga ini menghitung transpose dari invers dari E\)vectors. Matriks hasilnya juga persegi.
y %*% t(inv(E\(vectors)): %*% adalah operator perkalian matriks, sehingga operasi ini mengalikan y (sebuah vektor kolom) dengan transpose dari invers dari E\)vectors (sebuah matriks persegi). Hasilnya adalah sebuah vektor kolom dengan ukuran yang sama seperti y.
y <- y %*% t(inv(E$vectors)): Akhirnya, hasil perkalian matriks tersebut ditugaskan ke y, sehingga menimpa nilai sebelumnya.
Secara keseluruhan, ekspresi y <- y %*% t(inv(E\(vectors)) menghitung hasil perkalian antara matriks y dan transpose dari invers dari sebuah matriks E\)vectors, dengan mengasumsikan E$vectors dapat diinvers. Hasilnya adalah sebuah vektor kolom yang ditugaskan kembali ke y. Operasi ini mungkin merupakan bagian dari algoritma atau komputasi yang lebih besar yang melibatkan matriks dan aljabar linear.
dd <- data.frame(y)Perintah dd <- data.frame(y) di R membuat bingkai data baru bernama dd dengan satu kolom bernama y.
Fungsi data.frame() digunakan untuk membuat bingkai data di R, yang merupakan struktur data yang umum digunakan untuk bekerja dengan data tabular. Argumen y yang diteruskan ke fungsi dapat berupa vektor, matriks, atau bingkai data lainnya.
Dengan menugaskan hasil data.frame(y) ke dd, kita membuat objek baru di lingkungan R yang disebut dd, yang merupakan bingkai data yang berisi satu kolom data. Ini dapat berguna untuk melakukan berbagai tugas manipulasi dan analisis data, seperti subset, menggabungkan, dan memplot data.
p3 <- ggplot(dd, aes(x = X1, y = X2)) +
geom_point(alpha = .5) +
geom_density_2d()
p3
x <- rmvnorm(n = n, mean = mu, sigma = sigma)
d <- data.frame(x)
d## X1 X2
## 1 0.151244424 2.100563009
## 2 0.645904500 3.692973095
## 3 0.988345528 1.089911245
## 4 -2.829946598 -0.070310445
## 5 4.611815544 2.231522332
## 6 -0.237521589 2.599738577
## 7 2.269545766 3.479461284
## 8 1.097585790 3.682954387
## 9 -1.278142553 1.260721430
## 10 0.031198593 2.719428102
## 11 1.873374341 3.891099835
## 12 5.030088724 3.387659273
## 13 -0.489080808 0.350302869
## 14 0.456013513 1.738102988
## 15 4.188246110 1.269930759
## 16 -1.327630678 0.717062535
## 17 2.589345496 3.675520105
## 18 -0.671241758 1.697711985
## 19 1.589581034 3.933971328
## 20 2.915003896 2.100706780
## 21 1.455219469 3.095199552
## 22 -2.348082293 0.562146114
## 23 1.809246406 1.465974405
## 24 0.873185253 1.931899575
## 25 -0.948021359 -0.036053349
## 26 0.421293252 1.319111579
## 27 3.460986455 4.975280080
## 28 1.201237736 2.646434485
## 29 1.202913271 2.945611277
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## 848 1.992287027 5.787310043
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## 903 1.137856984 3.019290155
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## 905 1.200450491 2.328261572
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## 913 0.149655517 2.194081446
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## 915 1.902052064 1.034430601
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## 917 -0.191369548 1.824089883
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## 920 1.089928739 0.491079693
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## 922 1.793350922 4.208965294
## 923 0.513177350 1.700622712
## 924 4.839898450 6.125419269
## 925 5.544703376 2.751056383
## 926 -0.659134295 2.473608627
## 927 2.558571652 4.350411027
## 928 1.378722128 2.347912694
## 929 3.996523035 3.116375048
## 930 2.581839760 3.177307673
## 931 0.613987705 1.098828111
## 932 -0.743279836 -1.381994373
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## 934 -0.341959139 1.061219900
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## 937 4.481742925 3.737431422
## 938 2.543778851 3.745314618
## 939 -1.850862414 1.149493275
## 940 0.980526979 0.864424514
## 941 0.617844311 0.825083498
## 942 0.418400148 -0.800515496
## 943 1.188192676 1.117491349
## 944 1.693714929 -0.704442055
## 945 0.957409985 1.661987534
## 946 1.916975312 -0.059769218
## 947 0.346971039 2.857749714
## 948 2.376648859 2.928314235
## 949 0.615869140 -0.571315373
## 950 2.754802488 2.831942914
## 951 -2.580596024 0.695665357
## 952 3.226277135 3.689180989
## 953 0.298553359 3.132001643
## 954 0.452807698 2.402595656
## 955 3.001763940 3.161866069
## 956 0.208193836 2.976432481
## 957 3.313363336 1.308280634
## 958 1.214528354 3.541850876
## 959 -1.601864481 -1.295784934
## 960 0.650039294 3.469105689
## 961 -1.753472780 0.827619574
## 962 2.872677025 2.617647907
## 963 3.001076887 4.979240845
## 964 3.061258825 3.474922504
## 965 1.291156378 0.378205183
## 966 2.915481642 3.359893865
## 967 1.806852176 2.320613431
## 968 -1.353260358 1.537085708
## 969 3.064833785 1.703339839
## 970 -1.423205957 3.998824621
## 971 0.558017578 3.551005206
## 972 3.129715294 5.066661785
## 973 0.750312082 1.484125306
## 974 5.537171815 6.506824753
## 975 1.706837089 2.457318771
## 976 2.046760897 1.315521778
## 977 1.399181111 0.658599703
## 978 0.875886853 3.135008951
## 979 0.013940892 2.965040106
## 980 2.769871398 4.631183262
## 981 4.833241260 2.274841834
## 982 2.626011768 4.773134917
## 983 1.014487438 1.040767593
## 984 -0.127416692 3.733518094
## 985 5.400615864 1.745581871
## 986 0.330641244 -0.506797724
## 987 0.961037460 1.535919975
## 988 2.604263528 6.735809905
## 989 -1.441658828 1.921628126
## 990 4.174042746 2.029237038
## 991 -0.545460423 1.618535188
## 992 3.303339792 2.168995003
## 993 -0.929208629 1.538910023
## 994 -3.702389162 -1.551566569
## 995 3.343251735 3.362444992
## 996 -2.825489871 1.789675184
## 997 -3.675017832 -0.027945628
## 998 0.771787689 -0.171878784
## 999 4.115549371 4.702250299
## 1000 0.334908570 3.457165992Kode x <- rmvnorm(n = n, mean = mu, sigma = sigma) menghasilkan sampel acak berukuran n dari distribusi normal multivariat dengan mean mu dan matriks kovarians sigma. Objek yang dihasilkan x adalah matriks di mana setiap baris mewakili observasi multivariat.
Kode d <- data.frame(x) mengubah matriks x menjadi bingkai data, di mana setiap kolom sesuai dengan variabel dalam distribusi normal multivariat.
Bingkai data yang dihasilkan d dapat digunakan untuk analisis atau visualisasi lebih lanjut. Ini berisi n baris dan jumlah kolom sama dengan jumlah variabel dalam distribusi normal multivariat. Setiap kolom mewakili variabel acak, dan setiap baris mewakili pengamatan.
p2 <- ggplot(d, aes(x = X1, y = X2)) +
geom_point(alpha = .5) +
geom_density_2d()
p2
mu## [1] 1 2y <- x - mu
head (y)## [,1] [,2]
## [1,] -0.84875558 1.10056301
## [2,] -1.35409550 1.69297310
## [3,] -0.01165447 0.08991125
## [4,] -4.82994660 -2.07031044
## [5,] 3.61181554 1.23152233
## [6,] -2.23752159 0.59973858y <- data.frame(x)
y## X1 X2
## 1 0.151244424 2.100563009
## 2 0.645904500 3.692973095
## 3 0.988345528 1.089911245
## 4 -2.829946598 -0.070310445
## 5 4.611815544 2.231522332
## 6 -0.237521589 2.599738577
## 7 2.269545766 3.479461284
## 8 1.097585790 3.682954387
## 9 -1.278142553 1.260721430
## 10 0.031198593 2.719428102
## 11 1.873374341 3.891099835
## 12 5.030088724 3.387659273
## 13 -0.489080808 0.350302869
## 14 0.456013513 1.738102988
## 15 4.188246110 1.269930759
## 16 -1.327630678 0.717062535
## 17 2.589345496 3.675520105
## 18 -0.671241758 1.697711985
## 19 1.589581034 3.933971328
## 20 2.915003896 2.100706780
## 21 1.455219469 3.095199552
## 22 -2.348082293 0.562146114
## 23 1.809246406 1.465974405
## 24 0.873185253 1.931899575
## 25 -0.948021359 -0.036053349
## 26 0.421293252 1.319111579
## 27 3.460986455 4.975280080
## 28 1.201237736 2.646434485
## 29 1.202913271 2.945611277
## 30 1.552379476 2.510441428
## 31 2.580993585 1.007973060
## 32 3.975241180 3.385889009
## 33 1.032112857 1.183818816
## 34 0.895533044 2.520073890
## 35 -3.299180064 -0.145618925
## 36 1.959183744 1.846982468
## 37 -0.893873258 0.508521530
## 38 0.533436132 -0.545784506
## 39 1.452899317 -1.063546865
## 40 -0.408622552 0.427411629
## 41 -2.002487134 -0.467840142
## 42 1.412656681 1.944362246
## 43 -0.882108393 -1.971194064
## 44 -1.615672924 1.040389595
## 45 -1.133189801 0.201063954
## 46 3.113163098 2.877682655
## 47 -1.267006338 0.645326696
## 48 0.070724905 0.725321124
## 49 -0.879494351 1.373169020
## 50 2.550153144 2.788324300
## 51 0.833865262 2.522842164
## 52 2.444827262 2.216115119
## 53 1.230851094 0.379468976
## 54 0.284550189 1.171087237
## 55 1.576425841 2.695386459
## 56 0.331989764 0.675231317
## 57 -0.627886095 1.933638348
## 58 3.161763027 1.473222443
## 59 0.447328976 2.325425796
## 60 0.003824605 1.887379077
## 61 0.472260839 0.701524440
## 62 3.071608303 3.853901052
## 63 3.678527234 4.653074894
## 64 -0.233011033 0.954386943
## 65 1.855585106 3.179098632
## 66 0.110141671 1.115514715
## 67 0.646559036 4.080690423
## 68 -3.908296351 0.315445976
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## 70 0.633937086 -1.005968425
## 71 1.897844514 -0.188198433
## 72 -3.657106480 -0.489242229
## 73 0.944800551 1.023666298
## 74 0.113841176 2.231469524
## 75 -1.080680365 1.264072728
## 76 2.874294421 4.956857373
## 77 2.884230691 5.078797307
## 78 1.867957883 2.249442770
## 79 -4.019581612 -1.274889802
## 80 0.788210562 2.987588400
## 81 0.686600976 2.709342163
## 82 -1.195950606 0.952856346
## 83 1.214478384 1.533219213
## 84 0.839491383 0.964556546
## 85 1.672938910 2.077654666
## 86 -0.185853139 -1.219111191
## 87 -1.130448682 -0.819171866
## 88 -2.359606493 0.288195181
## 89 0.850800419 2.374221052
## 90 3.344360582 3.341527041
## 91 2.646657893 1.706710534
## 92 1.019190655 3.604753633
## 93 0.057735073 -0.752034900
## 94 -0.058412552 3.174811754
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## 96 0.748261562 1.194822163
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## 98 2.096352089 4.140555813
## 99 0.097473511 0.375192961
## 100 1.714946181 3.248802054
## 101 5.119261363 2.523208488
## 102 0.869718630 3.262306197
## 103 3.088966280 1.641193507
## 104 1.957839722 1.447714089
## 105 -0.496337877 2.480333464
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## 107 0.894882803 4.614337637
## 108 2.066453621 1.760627975
## 109 1.666069709 0.405347621
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## 111 1.149397965 3.385479716
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## 121 -0.566974323 1.614803136
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## 152 1.291595561 2.691585168
## 153 0.150910821 3.430765889
## 154 6.054503809 5.657277713
## 155 -0.896965372 -1.241861928
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## 157 1.802145659 0.422756501
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## 185 3.062319191 2.245803523
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## 189 3.774510358 5.865606927
## 190 1.686418252 0.098019202
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## 201 -0.226019920 0.857900572
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## 220 -1.822285856 -0.357324373
## 221 0.176324924 3.549130459
## 222 0.211601394 0.653256000
## 223 3.276470880 4.649054809
## 224 -0.583187498 0.880631060
## 225 1.660003323 2.186171611
## 226 2.743635718 5.036786180
## 227 0.726293913 1.506183251
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## 229 2.079001193 1.985982475
## 230 0.972195422 -0.312512358
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## 232 -1.517301716 0.653989973
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## 235 2.407707816 1.934132465
## 236 -1.706813509 0.794083846
## 237 3.176706555 2.458531889
## 238 -1.866321319 1.884588897
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## 243 0.732146085 4.880942183
## 244 3.746348842 2.466551284
## 245 -1.097367660 -0.628196058
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## 247 0.466051013 3.432277761
## 248 -0.702055554 2.572163187
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## 250 4.146199752 3.866907287
## 251 0.019980735 2.559281044
## 252 -0.652410634 0.729127469
## 253 2.218947722 1.656133583
## 254 1.525969964 3.655689614
## 255 -0.417124781 3.935799896
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## 270 3.333577702 4.271373389
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## 826 2.850238682 3.909860132
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## 872 -1.663900579 -1.008337883
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## 875 3.000452320 4.198318227
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## 878 1.236656902 2.789031643
## 879 1.304160280 -0.436771914
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## 883 -2.593341893 -1.697011137
## 884 0.515207941 2.811608641
## 885 1.245147479 1.125036069
## 886 0.914273081 1.829451455
## 887 0.704098872 1.256039045
## 888 1.084132872 0.429143639
## 889 1.533789457 1.656183376
## 890 0.752644861 2.967642450
## 891 -0.374600440 0.145351341
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## 893 -3.712809503 0.005272527
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## 896 -3.000510564 -0.479143759
## 897 4.014416819 1.918230835
## 898 -1.336471847 0.051707074
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## 900 -0.237194442 1.934893335
## 901 2.536295129 2.945376161
## 902 1.988958488 1.109458396
## 903 1.137856984 3.019290155
## 904 1.225054904 2.379349936
## 905 1.200450491 2.328261572
## 906 0.334599780 0.185017895
## 907 1.077975214 1.351798280
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## 911 3.279153979 2.444904596
## 912 1.447041837 2.573460787
## 913 0.149655517 2.194081446
## 914 4.238617249 3.857785381
## 915 1.902052064 1.034430601
## 916 1.508568107 2.581239015
## 917 -0.191369548 1.824089883
## 918 4.240070006 1.512897260
## 919 1.457639655 0.551629075
## 920 1.089928739 0.491079693
## 921 1.420021969 0.253815879
## 922 1.793350922 4.208965294
## 923 0.513177350 1.700622712
## 924 4.839898450 6.125419269
## 925 5.544703376 2.751056383
## 926 -0.659134295 2.473608627
## 927 2.558571652 4.350411027
## 928 1.378722128 2.347912694
## 929 3.996523035 3.116375048
## 930 2.581839760 3.177307673
## 931 0.613987705 1.098828111
## 932 -0.743279836 -1.381994373
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## 934 -0.341959139 1.061219900
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## 936 2.646905778 2.048779902
## 937 4.481742925 3.737431422
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## 939 -1.850862414 1.149493275
## 940 0.980526979 0.864424514
## 941 0.617844311 0.825083498
## 942 0.418400148 -0.800515496
## 943 1.188192676 1.117491349
## 944 1.693714929 -0.704442055
## 945 0.957409985 1.661987534
## 946 1.916975312 -0.059769218
## 947 0.346971039 2.857749714
## 948 2.376648859 2.928314235
## 949 0.615869140 -0.571315373
## 950 2.754802488 2.831942914
## 951 -2.580596024 0.695665357
## 952 3.226277135 3.689180989
## 953 0.298553359 3.132001643
## 954 0.452807698 2.402595656
## 955 3.001763940 3.161866069
## 956 0.208193836 2.976432481
## 957 3.313363336 1.308280634
## 958 1.214528354 3.541850876
## 959 -1.601864481 -1.295784934
## 960 0.650039294 3.469105689
## 961 -1.753472780 0.827619574
## 962 2.872677025 2.617647907
## 963 3.001076887 4.979240845
## 964 3.061258825 3.474922504
## 965 1.291156378 0.378205183
## 966 2.915481642 3.359893865
## 967 1.806852176 2.320613431
## 968 -1.353260358 1.537085708
## 969 3.064833785 1.703339839
## 970 -1.423205957 3.998824621
## 971 0.558017578 3.551005206
## 972 3.129715294 5.066661785
## 973 0.750312082 1.484125306
## 974 5.537171815 6.506824753
## 975 1.706837089 2.457318771
## 976 2.046760897 1.315521778
## 977 1.399181111 0.658599703
## 978 0.875886853 3.135008951
## 979 0.013940892 2.965040106
## 980 2.769871398 4.631183262
## 981 4.833241260 2.274841834
## 982 2.626011768 4.773134917
## 983 1.014487438 1.040767593
## 984 -0.127416692 3.733518094
## 985 5.400615864 1.745581871
## 986 0.330641244 -0.506797724
## 987 0.961037460 1.535919975
## 988 2.604263528 6.735809905
## 989 -1.441658828 1.921628126
## 990 4.174042746 2.029237038
## 991 -0.545460423 1.618535188
## 992 3.303339792 2.168995003
## 993 -0.929208629 1.538910023
## 994 -3.702389162 -1.551566569
## 995 3.343251735 3.362444992
## 996 -2.825489871 1.789675184
## 997 -3.675017832 -0.027945628
## 998 0.771787689 -0.171878784
## 999 4.115549371 4.702250299
## 1000 0.334908570 3.457165992p2 <- ggplot(y, aes(x = X1, y = X2)) +
geom_point(alpha = .5) +
geom_density_2d()
p2
# Load the mvtnorm package
library(mvtnorm)
# Set mean and covariance matrix
mu <- c(1, 2)
sigma <- matrix(c(1, 0.5, 0.5, 2), nrow = 2)
# Generate 1000 random samples from the multivariate normal distribution
set.seed(123) # For reproducibility
samples <- rmvnorm(n = 1000, mean = mu, sigma = sigma)
# Plot the samples
plot(samples, main = "Random Samples from Multivariate Normal Distribution")
library(mvtnorm)
# Menentukan parameter distribusi multivariat normal
mean <- c(0, 0) # rata-rata
sigma <- matrix(c(1, 0.5, 0.5, 2), nrow = 2) # matriks kovariansi
# Menghasilkan sampel dari distribusi multivariat normal
n <- 1000 # jumlah sampel yang diinginkan
sampel <- rmvnorm(n, mean = mean, sigma = sigma)
# Menampilkan scatterplot dari sampel
plot(sampel[,1], sampel[,2], main = "Sampel dari distribusi multivariat normal",
xlab = "Variabel 1", ylab = "Variabel 2", col = "blue")
Program di atas menghasilkan 1000 sampel dari distribusi multivariat normal dengan rata-rata mean = c(0, 0) dan matriks kovariansi sigma = matrix(c(1, 0.5, 0.5, 2), nrow = 2). Kemudian, program menampilkan scatterplot dari sampel dengan variabel pertama pada sumbu x dan variabel kedua pada sumbu y.
library(MASS)
# menghasilkan sampel data multivariat normal dengan mean = c(1,2) dan kovarians = matriks(2,2)
sampel <- rmvnorm(n = 100, mean = c(1, 2), sigma = matrix(c(2, 1, 1, 2), nrow = 2))
# melihat sebagian data sampel
head(sampel)## [,1] [,2]
## [1,] 1.5064499 2.9600133
## [2,] 1.4465744 0.4914124
## [3,] -0.9605118 4.2709238
## [4,] 1.4535791 2.5978315
## [5,] -0.2150833 3.1104351
## [6,] 4.0720113 4.7604046d2 <- data.frame(sampel)
d2## X1 X2
## 1 1.50644993 2.96001334
## 2 1.44657440 0.49141245
## 3 -0.96051180 4.27092385
## 4 1.45357913 2.59783146
## 5 -0.21508329 3.11043507
## 6 4.07201130 4.76040461
## 7 -2.14517828 -0.16205926
## 8 1.38864725 2.98769644
## 9 -0.05721639 0.62812283
## 10 0.96886209 0.79643300
## 11 3.12330110 0.25430140
## 12 0.96431661 -0.54080281
## 13 0.86804749 3.84670769
## 14 2.01997981 0.49835059
## 15 -0.99511920 1.53908467
## 16 -0.15326813 2.20547863
## 17 -0.93343089 -0.55961542
## 18 -0.03571366 0.17024448
## 19 2.36183318 1.94038564
## 20 1.45364014 3.87207217
## 21 3.51844989 2.60767843
## 22 1.93450873 3.91027021
## 23 0.37968656 0.51052294
## 24 1.80004798 0.28121308
## 25 0.51777902 1.36087707
## 26 -0.72197280 -1.95283722
## 27 0.66178206 3.51499523
## 28 0.13292524 0.98275271
## 29 -0.23014026 0.56125993
## 30 1.41644215 2.86320116
## 31 2.40573966 0.39094262
## 32 1.48397517 1.93538788
## 33 1.01207322 0.69506993
## 34 0.63991780 0.44079260
## 35 1.55484192 0.94894883
## 36 0.30818600 -0.88259396
## 37 1.85209976 3.63285580
## 38 2.43226903 3.71977914
## 39 -0.91422092 1.27242049
## 40 1.16839658 2.95829322
## 41 0.69640045 1.66090341
## 42 3.69167579 4.10448267
## 43 -1.54012531 0.83170853
## 44 0.73236232 5.69610554
## 45 0.74493820 3.38731251
## 46 1.17134359 2.18390255
## 47 1.62429511 1.98641466
## 48 2.34272282 3.06960960
## 49 -1.50525209 0.62423154
## 50 0.09983930 1.11708809
## 51 2.99949589 4.42123804
## 52 -0.06102438 2.40221204
## 53 -0.80183827 0.81084928
## 54 1.33856097 1.85117264
## 55 -0.38977037 0.03323129
## 56 0.59333461 1.95759919
## 57 1.44745446 1.00940383
## 58 1.37552870 0.62493317
## 59 0.41884659 2.41533578
## 60 -0.23134571 0.68157365
## 61 0.94831234 2.03107956
## 62 2.19110088 2.02323290
## 63 -1.56337313 0.48157685
## 64 -0.20249426 0.49564862
## 65 2.35543821 5.53529961
## 66 2.02817773 2.07917070
## 67 2.21611200 4.15521305
## 68 0.82074991 2.79449756
## 69 1.72268101 2.03814706
## 70 1.31585195 2.91119695
## 71 0.83988843 1.52661808
## 72 0.29509411 2.18004617
## 73 0.78877290 1.47205662
## 74 0.95826220 1.00860681
## 75 0.40663453 3.58262027
## 76 -0.08836832 2.10877580
## 77 -0.40724966 1.33052728
## 78 1.16372869 0.76382962
## 79 1.89296648 2.51684303
## 80 0.65735475 2.21942759
## 81 0.79517991 0.88048504
## 82 -0.86957788 1.63361781
## 83 -0.38536605 1.58413513
## 84 -1.59136340 0.12768027
## 85 1.75432498 3.52753696
## 86 0.86725033 0.70353680
## 87 0.83293717 3.34191069
## 88 1.99661263 3.26496871
## 89 2.49968169 2.88044872
## 90 2.15922023 1.07662627
## 91 1.28506388 1.64593630
## 92 1.76070978 3.88436886
## 93 1.45773167 1.32430149
## 94 0.17346648 0.57228197
## 95 0.69444629 1.28466365
## 96 1.90095759 1.61665729
## 97 2.23411348 3.24452890
## 98 0.92746008 3.78928204
## 99 0.79783116 1.11808843
## 100 0.73891395 0.67355208library(ggplot2)
# Membuat data frame
df <- data.frame(
x = c(1, 2, 3, 4, 5),
y = c(3, 5, 4, 6, 7)
)
# Membuat scatter plot dengan ggplot
ggplot(data = df, aes(x = x, y = y)) +
geom_point()
ini akan membuat scatter plot berdasarkan data frame df, dengan sumbu x diisi oleh kolom x, dan sumbu y diisi oleh kolom y. Fungsi geom_point() digunakan untuk membuat titik-titik pada scatter plot.
Anda dapat mengubah warna, ukuran, dan bentuk titik-titik tersebut dengan menggunakan argumen tambahan pada geom_point(). Misalnya, untuk mengubah warna titik-titik menjadi merah, ukurannya menjadi 3, dan bentuknya menjadi segitiga, dapat dilakukan seperti berikut:
ggplot(data = df, aes(x = x, y = y)) +
geom_point(color = "red", size = 3, shape = 24)