Analisis Pengaruh Kebiasaan Makan dan Faktor Keluarga terhadap Tinggi dan Berat Badan dengan Kontrol Usia, Jenis Kelamin, dan Kebiasaan Merokok
Marshanda Claudia Iswahyono, Thea Bayu Revalina, Zulma Nayla Ifaada, Danisa Ariatna Putri
2025-05-26
PENDAHULUAN
Latar Belakang
Kebiasaan makan memiliki peran penting dalam menentukan status gizi seseorang, yang pada akhirnya berpengaruh terhadap tinggi dan berat badan. Pola makan yang tidak seimbang dapat menyebabkan berbagai masalah kesehatan, termasuk obesitas atau kekurangan gizi. Faktor keluarga juga berkontribusi besar dalam membentuk kebiasaan makan individu, baik melalui pola makan yang diterapkan dalam rumah tangga maupun melalui pengaruh sosial dan ekonomi. Studi menunjukkan bahwa kebiasaan makan yang dipengaruhi oleh lingkungan keluarga dapat berdampak pada asupan gizi dan status kesehatan seseorang[1].
Dalam penelitian ini, metode Multivariate Analysis of Variance (MANOVA) dan Multivariate Analysis of Covariance (MANCOVA) digunakan untuk menganalisis pengaruh kebiasaan makan dan faktor keluarga terhadap tinggi dan berat badan dengan mempertimbangkan variabel kontrol seperti usia, jenis kelamin, dan kebiasaan merokok. MANOVA memungkinkan analisis terhadap lebih dari satu variabel dependen secara simultan, sementara MANCOVA mempertimbangkan kovariat untuk mengontrol efek variabel bebas terhadap variabel dependen [2]. Studi sebelumnya telah menunjukkan bahwa pendekatan multivariat ini efektif dalam memahami hubungan kompleks antara faktor-faktor yang mempengaruhi tinggi dan berat badan seseorang.
Penelitian ini bertujuan untuk memberikan wawasan lebih dalam mengenai bagaimana kebiasaan makan dan faktor keluarga mempengaruhi tinggi dan berat badan seseorang. Selain itu, pemahaman yang lebih baik mengenai faktor-faktor yang berkontribusi terhadap tinggi dan berat badan seseorang.
Rumusan Masalah
- Apakah terdapat pengaruh signifikan dari variabel CAEC tehadap tinggi dan berat badan seseorang?
- Apakah pengaruh variabel-variabel tersebut tetap signifikan setelah mengontrol variabel usia, jenis kelamin, dan kebiasaan merokok?
- Di antara variabel-variabel tersebut, manakah yang paling berpengaruh terhadap tinggi dan berat badan seseorang?
Tujuan
- Untuk menganalisis variabel CAEC terhadap tinggi dan berat badan.
- Untuk mengetahui apakah pengaruh variabel-variabel tersebut tetap signifikan setelah dikontrol oleh usia, jenis kelamin, dan kebiasaan merokok.
- Untuk mengidentifikasi variabel yang paling berpengaruh terhadap tinggi dan berat badan.
- Untuk memenuhi tugas akhir mata kuliah Analisis Multivariat dengan menerapkan teknik statistik multivariat, khususnya MANOVA dan MANCOVA.
TINJAUAN PUSTAKA
Multivariate Analysis of Variance (MANOVA)
MANOVA merupakan metode statistik yang digunakan untuk menguji apakah terdapat perbedaan yang signifikan dalam rata-rata beberapa variabel dependen berdasarkan satu atau lebih variabel independen kategori. MANOVA juga merupakan perluasan dari ANOVA, dengan MANOVA memiliki dua atau lebih variabel dependen yang saling berkorelasi dan memungkinkan pengujian yang simultan terhadap beberapa variabel dependen tersebut, sehingga memberi pemahaman lebih dalam terhadap pengaruh suatu perlakuan atau kelompok [4]. Dalam MANOVA, hipotesis nol menyatakan tidak ada perbedaan rata-rata multivariat antar kelompok, sedangkan hipotesis alternatif menyatakan sebaliknya. Analisis statistik yang digunakan dalam MANOVA antara lain Wilks’ Lambda, Pillai’s Trace, Hotelling’s Trace, dan Roy’s Largest Root [5]. Metode ini banyak digunakan untuk penelitian yang melibatkan data multivariat untuk menguji perbedaan kelompok dengan mempertimbangkan interaksi antar variabel dependen.
Multivariate Analysis of Covariance (MANCOVA)
MANCOVA merupakan metode statistik perluasan dari MANOVA yang memperhitungkan kovariat untuk mengontrol variabilitas yang tidak diinginkan atau efek pembaur yang dapat mempengaruhi variabel dependen. Dengan memperhitungkannya, MANCOVA memberikan estimasi efek perlakuan yang lebih akurat dengan menyeleksi pengaruh variabel yang tidak diinginkan[7]. Sebelum melakukan MANOVA dan MANCOVA, dilakukan pemeriksaan asumsi-asumsi penting seperti normalitas multivariat (melalui Mahalanobis distance dan Q-Q plot), uji normalitas Shapiro-Wilk pada data yang telah dinormalisasi (orderNorm), serta uji homogenitas kovarian melalui Box’s M test untuk memvalidasi hasil analisis multivariat[8].
Uji Asumsi
Dalam melakuakn analisis multivariat seperti MANOVA dan MANCOVA terdapat beberapa uji asumsi yang harus dilakukan untuk memastikan validasi hasil analisis diantaranya Normalitas Multivariat, Homogenitas dan Multicolinertas
DATA
Data yang digunakan adalah data sekunder. Data sekunder adalah data yang telah dikumpulkan oleh pihak lain dan tidak dikumpulkan secara langsung oleh peneliti. Data yang digunakan bersumber dari kaggle dengan link sebagai berikut: Estimation of obesity levels based on eating habits and physical condition
CODE
Load Dataset
# Load dataset
library(readr)
data <- read.csv("C:/Users/hp/OneDrive/Documents/dataset_anmul.csv")
data## Gender Age Height Weight family_history_with_overweight FAVC FCVC NCP
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## 2 Female 21 1.52 56.0 yes no 3 3
## 3 Male 23 1.80 77.0 yes no 2 3
## 4 Male 27 1.80 87.0 no no 3 3
## 5 Male 22 1.78 89.8 no no 2 1
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## 20 Female 23 1.65 70.0 yes no 2 1
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## 397 Female 38 1.55 59.0 yes no 3 3
## 398 Male 20 1.66 60.0 no yes 2 4
## 399 Male 21 1.85 125.0 yes yes 3 1
## 400 Male 21 1.65 60.0 no no 3 1
## 401 Male 18 1.65 70.0 yes no 2 3
## 402 Male 26 1.83 82.0 no yes 2 3
## 403 Male 27 1.83 99.0 yes yes 3 1
## 404 Female 26 1.66 112.0 yes no 3 3
## 405 Male 34 1.78 73.0 no yes 2 3
## 406 Male 18 1.74 86.0 no no 3 3
## 407 Male 33 1.76 66.5 no no 2 3
## 408 Female 19 1.51 59.0 yes yes 3 3
## 409 Male 20 1.81 79.0 yes no 3 1
## 410 Female 33 1.55 55.0 yes yes 3 1
## 411 Male 20 1.83 66.0 no no 2 3
## 412 Female 20 1.60 65.0 no no 3 3
## 413 Male 33 1.85 85.0 no yes 2 3
## 414 Male 33 1.75 85.0 no no 2 3
## 415 Male 33 1.83 113.0 yes yes 2 1
## 416 Male 14 1.71 72.0 yes yes 3 3
## 417 Male 34 1.84 88.0 no yes 3 3
## 418 Male 18 1.77 87.0 yes yes 3 3
## 419 Male 18 1.70 90.0 no yes 3 3
## 420 Male 29 1.62 89.0 yes yes 1 3
## 421 Male 18 1.85 60.0 yes yes 3 4
## 422 Male 18 1.84 60.0 yes yes 3 4
## 423 Male 19 1.75 58.0 no yes 2 3
## 424 Male 33 1.85 93.0 yes yes 2 3
## 425 Male 33 1.74 76.0 no no 2 3
## 426 Female 19 1.61 53.8 yes yes 2 3
## 427 Male 22 1.75 70.0 no no 2 3
## 428 Female 20 1.67 60.0 no yes 3 3
## 429 Male 23 1.70 69.0 no yes 3 1
## 430 Male 26 1.90 80.0 yes yes 2 3
## 431 Male 18 1.65 85.0 no yes 2 3
## 432 Female 18 1.60 55.0 no yes 2 4
## 433 Male 19 1.80 70.0 no yes 3 3
## 434 Female 18 1.64 59.0 yes yes 2 3
## 435 Male 19 1.89 87.0 no yes 2 4
## 436 Female 19 1.76 80.0 yes yes 2 1
## 437 Female 18 1.56 55.0 no yes 2 3
## 438 Female 18 1.60 56.0 yes yes 2 1
## 439 Female 19 1.67 64.0 no yes 3 3
## 440 Female 19 1.60 60.0 no yes 2 3
## 441 Female 18 1.55 56.0 no yes 2 3
## 442 Female 18 1.55 50.0 yes yes 3 3
## 443 Male 26 1.72 65.0 yes yes 2 3
## 444 Male 18 1.72 53.0 yes yes 2 3
## 445 Male 19 1.70 60.0 yes yes 2 1
## 446 Female 19 1.51 45.0 no yes 2 4
## 447 Male 19 1.83 82.0 yes yes 3 3
## 448 Male 19 1.80 87.0 yes yes 2 4
## 449 Female 24 1.60 100.5 yes yes 3 1
## 450 Female 18 1.63 63.0 yes yes 1 3
## 451 Male 19 1.71 71.0 no yes 3 3
## 452 Male 19 1.70 65.0 yes no 2 3
## 453 Male 23 1.75 69.0 no no 3 3
## 454 Female 18 1.62 50.0 no yes 3 3
## 455 Female 20 1.68 68.0 no yes 3 1
## 456 Male 18 1.85 66.0 no yes 2 3
## 457 Female 33 1.59 60.0 no yes 3 1
## 458 Female 19 1.50 45.0 no yes 2 3
## 459 Male 19 1.69 60.0 no yes 2 3
## 460 Male 19 1.76 79.0 yes yes 2 3
## 461 Female 18 1.62 55.0 yes yes 2 3
## 462 Male 21 1.71 100.0 yes yes 2 1
## 463 Male 27 1.72 88.0 yes yes 2 1
## 464 Male 17 1.80 68.0 yes no 2 3
## 465 Male 18 1.93 86.0 no no 3 4
## 466 Female 18 1.60 51.0 yes yes 2 3
## 467 Male 22 1.74 75.0 yes yes 3 3
## 468 Male 22 1.74 75.0 yes yes 3 3
## 469 Female 20 1.62 45.0 no yes 3 3
## 470 Female 19 1.54 42.0 no yes 3 1
## 471 Female 20 1.56 51.5 no yes 2 3
## 472 Female 18 1.60 83.0 yes yes 2 3
## 473 Female 18 1.54 71.0 no no 3 4
## 474 Female 18 1.63 51.0 yes yes 1 3
## 475 Male 19 1.78 64.0 no yes 2 3
## 476 Female 18 1.62 68.0 no no 2 1
## 477 Female 18 1.71 75.0 yes yes 3 3
## 478 Female 18 1.64 56.0 yes yes 3 3
## 479 Male 19 1.69 65.0 no yes 2 3
## 480 Female 17 1.58 50.0 no yes 1 4
## 481 Female 18 1.57 50.0 no yes 2 3
## 482 Male 18 1.74 64.0 yes yes 3 4
## 483 Female 20 1.58 53.5 yes yes 2 1
## 484 Female 18 1.50 58.0 no yes 2 3
## 485 Female 36 1.65 80.0 yes yes 2 3
## 486 Male 21 1.80 73.0 yes yes 1 3
## 487 Male 23 1.75 75.0 no yes 2 3
## 488 Male 20 1.84 104.0 yes no 2 3
## 489 Male 21 1.88 84.0 yes yes 3 3
## 490 Female 19 1.56 50.0 no yes 2 1
## 491 Male 24 1.75 84.0 no yes 3 3
## 492 Male 25 1.66 68.0 no yes 2 3
## 493 Male 45 1.70 86.0 no yes 3 3
## 494 Male 20 1.80 65.0 no yes 2 3
## 495 Female 18 1.67 66.0 no yes 3 3
## 496 Male 19 1.80 60.0 yes yes 3 1
## 497 Male 18 1.72 53.0 yes yes 2 3
## 498 Male 20 1.56 45.0 no no 2 3
## CAEC SMOKE CH2O SCC FAF TUE CALC MTRANS
## 1 Sometimes no 2 no 0 1 no Public_Transportation
## 2 Sometimes yes 3 yes 3 0 Sometimes Public_Transportation
## 3 Sometimes no 2 no 2 1 Frequently Public_Transportation
## 4 Sometimes no 2 no 2 0 Frequently Walking
## 5 Sometimes no 2 no 0 0 Sometimes Public_Transportation
## 6 Sometimes no 2 no 0 0 Sometimes Automobile
## 7 Sometimes no 2 no 1 0 Sometimes Motorbike
## 8 Sometimes no 2 no 3 0 Sometimes Public_Transportation
## 9 Sometimes no 2 no 1 1 Frequently Public_Transportation
## 10 Sometimes no 2 no 1 1 no Public_Transportation
## 11 Frequently no 3 no 2 2 Sometimes Public_Transportation
## 12 Frequently no 2 yes 2 1 Sometimes Public_Transportation
## 13 Sometimes no 3 no 2 0 Sometimes Public_Transportation
## 14 Sometimes no 2 no 2 1 Frequently Automobile
## 15 Sometimes no 1 no 1 1 Sometimes Public_Transportation
## 16 Always no 2 yes 2 1 Sometimes Public_Transportation
## 17 Sometimes no 1 no 1 0 Sometimes Public_Transportation
## 18 Sometimes no 2 no 0 0 no Automobile
## 19 Frequently yes 1 no 0 0 no Automobile
## 20 Sometimes no 2 no 0 0 Sometimes Public_Transportation
## 21 Sometimes no 2 no 3 2 no Walking
## 22 Sometimes yes 2 no 0 0 no Automobile
## 23 Sometimes no 2 no 1 0 Sometimes Automobile
## 24 Sometimes no 2 no 0 2 Sometimes Public_Transportation
## 25 Sometimes no 2 no 0 1 Sometimes Public_Transportation
## 26 Frequently yes 2 no 3 2 no Public_Transportation
## 27 Frequently no 2 no 1 2 Always Walking
## 28 Frequently no 2 no 2 1 Sometimes Automobile
## 29 Sometimes no 2 yes 3 1 Sometimes Public_Transportation
## 30 Sometimes no 2 no 2 2 Frequently Walking
## 31 Frequently no 3 no 0 1 no Motorbike
## 32 Sometimes no 1 no 1 0 Sometimes Public_Transportation
## 33 Sometimes no 3 no 1 1 Sometimes Walking
## 34 Sometimes no 2 no 0 0 Sometimes Public_Transportation
## 35 Frequently no 2 no 2 0 Sometimes Public_Transportation
## 36 Sometimes no 2 no 2 2 Sometimes Public_Transportation
## 37 Sometimes no 1 yes 2 0 no Walking
## 38 Sometimes no 1 no 1 0 Sometimes Public_Transportation
## 39 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## 40 Sometimes no 3 no 3 0 Sometimes Public_Transportation
## 41 Sometimes no 2 no 1 0 Sometimes Public_Transportation
## 42 Frequently no 2 no 0 0 no Walking
## 43 Sometimes no 1 no 0 0 no Public_Transportation
## 44 Sometimes yes 2 no 1 1 Frequently Public_Transportation
## 45 no no 2 no 2 0 no Public_Transportation
## 46 Sometimes no 1 no 0 1 no Public_Transportation
## 47 Frequently no 3 no 2 0 Sometimes Public_Transportation
## 48 Frequently no 3 no 2 0 Sometimes Public_Transportation
## 49 Sometimes no 2 no 1 0 Sometimes Walking
## 50 Sometimes no 2 no 0 0 Sometimes Public_Transportation
## 51 Sometimes no 3 no 0 1 Sometimes Walking
## 52 Sometimes no 1 no 0 0 Sometimes Automobile
## 53 Sometimes no 2 no 2 2 no Public_Transportation
## 54 no no 2 yes 2 1 no Public_Transportation
## 55 Always no 3 no 2 0 no Public_Transportation
## 56 Frequently no 2 no 0 0 Sometimes Automobile
## 57 Sometimes no 1 no 0 1 Sometimes Automobile
## 58 Sometimes no 1 no 0 1 no Public_Transportation
## 59 Sometimes no 2 no 1 1 no Walking
## 60 Sometimes no 3 no 2 2 no Public_Transportation
## 61 Sometimes no 3 no 3 1 Sometimes Public_Transportation
## 62 Sometimes no 2 no 3 1 Sometimes Public_Transportation
## 63 no no 2 no 0 0 Sometimes Public_Transportation
## 64 Sometimes no 2 no 0 2 Sometimes Automobile
## 65 Frequently no 1 no 1 1 no Public_Transportation
## 66 Frequently no 2 no 0 1 no Public_Transportation
## 67 Always no 2 no 0 2 Frequently Public_Transportation
## 68 Always no 2 no 0 1 Frequently Automobile
## 69 no yes 2 yes 0 0 Frequently Automobile
## 70 no no 3 no 0 1 Sometimes Public_Transportation
## 71 Always no 2 no 0 2 no Public_Transportation
## 72 no no 3 yes 2 1 Sometimes Public_Transportation
## 73 Sometimes no 3 yes 1 0 no Public_Transportation
## 74 Sometimes no 3 no 2 1 Sometimes Bike
## 75 Frequently no 3 no 0 1 Frequently Public_Transportation
## 76 Sometimes no 3 yes 2 0 no Public_Transportation
## 77 no no 2 no 1 0 no Public_Transportation
## 78 Sometimes no 3 no 0 0 no Public_Transportation
## 79 Sometimes no 3 no 0 1 no Public_Transportation
## 80 Sometimes no 2 no 0 0 Sometimes Public_Transportation
## 81 Sometimes no 2 yes 0 0 no Public_Transportation
## 82 Frequently no 2 no 0 0 Sometimes Public_Transportation
## 83 Always no 2 no 0 1 no Public_Transportation
## 84 no no 3 yes 2 0 no Walking
## 85 Frequently no 2 no 0 1 Sometimes Public_Transportation
## 86 Sometimes no 2 no 0 0 no Public_Transportation
## 87 Frequently no 3 no 1 0 no Public_Transportation
## 88 Sometimes no 2 no 0 0 no Public_Transportation
## 89 Frequently no 2 yes 1 0 no Automobile
## 90 Sometimes no 1 no 2 1 Frequently Automobile
## 91 Always no 1 no 2 0 no Public_Transportation
## 92 Always no 2 yes 0 1 Frequently Public_Transportation
## 93 Frequently no 3 yes 3 0 Frequently Walking
## 94 Always no 2 no 1 0 no Walking
## 95 Sometimes no 2 no 2 0 no Public_Transportation
## 96 Frequently no 2 no 2 0 Frequently Public_Transportation
## 97 Sometimes no 2 no 3 0 Sometimes Public_Transportation
## 98 Frequently no 1 no 0 0 Sometimes Public_Transportation
## 99 Frequently no 1 no 0 0 Sometimes Public_Transportation
## 100 Sometimes no 2 no 3 1 Frequently Public_Transportation
## 101 Sometimes no 1 no 0 0 Sometimes Public_Transportation
## 102 Frequently no 2 no 0 0 no Public_Transportation
## 103 Frequently no 2 yes 2 0 Sometimes Automobile
## 104 Frequently no 2 no 1 0 Sometimes Public_Transportation
## 105 Sometimes no 2 no 0 0 Sometimes Automobile
## 106 Sometimes no 2 no 2 0 Sometimes Public_Transportation
## 107 Sometimes no 2 no 2 0 Sometimes Public_Transportation
## 108 Always no 1 no 0 1 Sometimes Automobile
## 109 Sometimes no 3 no 3 2 no Walking
## 110 Sometimes no 3 no 2 1 no Public_Transportation
## 111 Sometimes no 2 no 0 1 Sometimes Public_Transportation
## 112 Sometimes no 1 no 0 0 no Public_Transportation
## 113 Frequently no 2 no 1 0 Sometimes Public_Transportation
## 114 Sometimes no 2 no 3 0 no Walking
## 115 Frequently no 2 no 1 0 Frequently Public_Transportation
## 116 Frequently no 2 no 0 1 no Public_Transportation
## 117 Sometimes no 1 no 3 2 no Walking
## 118 Frequently no 2 no 1 1 no Public_Transportation
## 119 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## 120 Frequently yes 3 no 2 1 Sometimes Automobile
## 121 Frequently yes 2 no 0 2 no Walking
## 122 Frequently no 2 no 0 2 Frequently Public_Transportation
## 123 Frequently no 1 no 1 0 no Walking
## 124 Sometimes no 2 no 1 0 no Public_Transportation
## 125 Sometimes no 1 no 0 0 no Public_Transportation
## 126 Always no 2 no 0 0 Frequently Public_Transportation
## 127 Sometimes no 2 no 1 0 Sometimes Public_Transportation
## 128 Sometimes no 3 yes 1 0 Sometimes Public_Transportation
## 129 Frequently no 1 no 0 0 Sometimes Public_Transportation
## 130 Sometimes no 3 no 1 1 Frequently Public_Transportation
## 131 Frequently no 2 no 1 1 no Public_Transportation
## 132 Sometimes no 1 no 1 0 no Public_Transportation
## 133 Frequently yes 3 yes 1 2 Frequently Public_Transportation
## 134 Always no 2 no 1 1 Frequently Public_Transportation
## 135 Sometimes no 1 no 2 0 Sometimes Automobile
## 136 Sometimes no 2 no 1 0 Sometimes Automobile
## 137 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## 138 Sometimes yes 3 no 0 0 no Motorbike
## 139 Always no 3 yes 3 0 no Bike
## 140 Frequently no 2 no 0 1 no Public_Transportation
## 141 Frequently no 3 no 1 1 Sometimes Public_Transportation
## 142 Always no 2 no 2 0 Frequently Public_Transportation
## 143 Frequently yes 1 no 1 1 Frequently Automobile
## 144 Sometimes no 1 no 0 0 Sometimes Automobile
## 145 Sometimes no 3 yes 2 2 Sometimes Public_Transportation
## 146 no no 3 no 1 0 Sometimes Public_Transportation
## 147 Frequently no 2 no 2 2 Frequently Public_Transportation
## 148 Sometimes no 1 no 0 0 Sometimes Automobile
## 149 Always no 2 no 0 0 Sometimes Automobile
## 150 Sometimes no 2 no 2 0 Sometimes Automobile
## 151 Sometimes no 2 no 2 1 Sometimes Public_Transportation
## 152 Sometimes no 2 no 2 0 Sometimes Automobile
## 153 Always yes 2 no 0 0 Sometimes Automobile
## 154 Sometimes no 3 no 2 0 no Automobile
## 155 Sometimes no 2 no 0 0 Sometimes Public_Transportation
## 156 Frequently no 2 no 1 1 Sometimes Automobile
## 157 Frequently no 1 no 0 1 no Automobile
## 158 Frequently no 2 no 2 1 Sometimes Public_Transportation
## 159 Sometimes no 3 no 0 0 Sometimes Automobile
## 160 Sometimes no 2 no 0 0 Frequently Automobile
## 161 Sometimes yes 1 no 2 1 Sometimes Public_Transportation
## 162 Sometimes no 2 no 1 0 no Automobile
## 163 Always yes 2 no 2 0 Sometimes Public_Transportation
## 164 Frequently no 2 yes 3 0 no Public_Transportation
## 165 Frequently no 3 no 2 1 Sometimes Automobile
## 166 Sometimes yes 1 no 1 0 Sometimes Public_Transportation
## 167 Always no 2 no 0 0 Sometimes Automobile
## 168 Sometimes no 2 no 1 2 no Walking
## 169 Sometimes no 2 no 1 0 Sometimes Public_Transportation
## 170 Frequently no 1 no 0 0 no Automobile
## 171 Sometimes no 2 no 2 1 Sometimes Public_Transportation
## 172 Frequently no 2 no 1 0 Sometimes Public_Transportation
## 173 Sometimes no 2 no 1 2 Sometimes Public_Transportation
## 174 Sometimes no 2 yes 0 1 no Public_Transportation
## 175 no no 3 no 1 0 Sometimes Public_Transportation
## 176 Sometimes no 2 no 2 0 no Public_Transportation
## 177 Always no 1 no 1 0 no Public_Transportation
## 178 Frequently no 2 yes 3 0 Sometimes Public_Transportation
## 179 Frequently yes 2 no 2 2 Frequently Public_Transportation
## 180 no no 3 no 1 0 Sometimes Public_Transportation
## 181 Sometimes no 2 no 1 0 no Public_Transportation
## 182 Frequently no 1 no 0 0 Sometimes Public_Transportation
## 183 Frequently no 2 no 0 1 no Public_Transportation
## 184 Sometimes yes 1 no 0 0 Sometimes Public_Transportation
## 185 no no 3 no 1 0 Sometimes Public_Transportation
## 186 Sometimes no 2 no 1 0 Sometimes Automobile
## 187 Sometimes no 3 no 1 0 Frequently Automobile
## 188 Sometimes no 3 no 3 2 no Public_Transportation
## 189 no no 3 no 3 1 Frequently Automobile
## 190 Sometimes no 2 no 1 1 no Public_Transportation
## 191 Sometimes no 2 no 1 0 Sometimes Public_Transportation
## 192 Frequently yes 2 yes 2 0 Sometimes Public_Transportation
## 193 Sometimes no 3 yes 3 0 Sometimes Automobile
## 194 Frequently no 3 yes 2 1 no Public_Transportation
## 195 Frequently no 3 no 3 0 no Public_Transportation
## 196 Sometimes no 2 no 1 1 Sometimes Walking
## 197 Sometimes no 2 no 1 2 Sometimes Bike
## 198 Sometimes no 2 no 0 0 Sometimes Bike
## 199 Frequently no 1 no 0 2 no Public_Transportation
## 200 Sometimes no 1 no 1 1 Sometimes Public_Transportation
## 201 Sometimes yes 3 no 1 2 Sometimes Public_Transportation
## 202 Always no 1 no 0 0 Sometimes Automobile
## 203 Sometimes yes 1 no 0 1 Sometimes Public_Transportation
## 204 Sometimes no 3 no 1 0 Sometimes Automobile
## 205 Sometimes no 2 no 3 2 no Automobile
## 206 Sometimes yes 2 no 1 0 Frequently Public_Transportation
## 207 Frequently no 2 no 2 0 no Public_Transportation
## 208 no no 2 yes 1 0 Sometimes Walking
## 209 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## 210 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## 211 Frequently no 2 no 0 1 no Public_Transportation
## 212 Sometimes no 1 no 1 1 no Public_Transportation
## 213 Sometimes no 2 no 0 0 no Public_Transportation
## 214 Sometimes no 2 no 1 0 no Public_Transportation
## 215 Sometimes no 2 no 1 0 Sometimes Public_Transportation
## 216 Sometimes no 3 no 0 2 Sometimes Public_Transportation
## 217 Frequently no 2 no 3 0 Sometimes Walking
## 218 Frequently no 3 yes 3 1 Frequently Automobile
## 219 Sometimes no 2 no 3 0 no Public_Transportation
## 220 Sometimes no 3 no 1 0 Sometimes Public_Transportation
## 221 Frequently no 2 yes 0 2 Frequently Public_Transportation
## 222 Sometimes no 1 no 1 1 Sometimes Public_Transportation
## 223 Always no 3 no 0 2 no Public_Transportation
## 224 Frequently no 3 no 1 0 no Public_Transportation
## 225 Sometimes no 2 no 0 0 no Public_Transportation
## 226 Sometimes no 3 no 2 0 Sometimes Walking
## 227 Sometimes no 1 no 0 1 no Automobile
## 228 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## 229 Sometimes no 3 no 0 0 no Automobile
## 230 Sometimes no 3 no 0 2 no Automobile
## 231 Sometimes no 3 no 2 0 Sometimes Walking
## 232 Sometimes yes 3 no 0 0 Sometimes Public_Transportation
## 233 Sometimes yes 3 yes 2 0 no Public_Transportation
## 234 Sometimes no 2 no 1 0 Sometimes Automobile
## 235 no no 2 no 2 0 no Public_Transportation
## 236 no no 2 no 2 0 no Public_Transportation
## 237 Always no 2 yes 3 0 no Automobile
## 238 Sometimes no 1 no 1 1 no Public_Transportation
## 239 Sometimes no 3 no 1 1 no Public_Transportation
## 240 no no 3 yes 3 1 no Public_Transportation
## 241 Sometimes no 3 no 1 1 no Public_Transportation
## 242 Sometimes no 2 no 3 0 no Bike
## 243 Always no 2 no 0 2 no Automobile
## 244 Sometimes yes 3 no 1 0 Sometimes Automobile
## 245 Sometimes no 2 yes 2 0 Sometimes Public_Transportation
## 246 Sometimes yes 2 no 2 1 Sometimes Automobile
## 247 Sometimes no 3 no 0 1 Sometimes Public_Transportation
## 248 Frequently no 1 no 3 1 no Automobile
## 249 Always no 3 yes 3 0 Sometimes Automobile
## 250 Sometimes no 2 no 3 0 Sometimes Walking
## 251 Sometimes no 2 no 1 1 no Public_Transportation
## 252 Sometimes no 3 no 0 0 Frequently Automobile
## 253 Sometimes yes 2 no 1 0 Frequently Automobile
## 254 Sometimes no 2 no 0 2 Sometimes Public_Transportation
## 255 Sometimes no 2 no 0 0 no Public_Transportation
## 256 Sometimes no 2 no 3 0 no Bike
## 257 Sometimes no 3 no 1 0 Sometimes Public_Transportation
## 258 Sometimes no 3 yes 1 2 no Public_Transportation
## 259 Sometimes no 1 no 1 0 no Public_Transportation
## 260 Frequently no 1 no 0 1 Sometimes Public_Transportation
## 261 Sometimes no 1 no 1 0 no Public_Transportation
## 262 Frequently no 2 yes 2 0 Sometimes Walking
## 263 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## 264 Frequently no 1 no 3 2 no Public_Transportation
## 265 Frequently no 3 yes 1 1 Sometimes Automobile
## 266 Frequently no 1 no 2 1 Sometimes Public_Transportation
## 267 Frequently no 2 no 0 0 Sometimes Public_Transportation
## 268 Frequently no 2 no 0 0 Frequently Automobile
## 269 Always no 2 no 0 2 no Public_Transportation
## 270 Sometimes no 2 no 0 1 Sometimes Walking
## 271 Sometimes no 3 no 0 1 Sometimes Public_Transportation
## 272 Frequently no 1 no 0 2 Sometimes Public_Transportation
## 273 Sometimes no 2 no 2 1 no Public_Transportation
## 274 Frequently no 2 no 0 0 Sometimes Motorbike
## 275 Sometimes no 1 no 2 1 Sometimes Public_Transportation
## 276 Frequently no 2 no 0 1 Sometimes Public_Transportation
## 277 Frequently no 3 no 1 0 no Public_Transportation
## 278 Always yes 3 no 3 2 Sometimes Walking
## 279 Sometimes no 2 no 0 0 Sometimes Automobile
## 280 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## 281 Frequently yes 2 no 0 0 Sometimes Public_Transportation
## 282 Frequently no 2 no 0 0 Sometimes Public_Transportation
## 283 Frequently no 1 no 1 1 no Public_Transportation
## 284 Sometimes no 3 no 2 1 Sometimes Walking
## 285 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## 286 Always no 1 no 0 0 Sometimes Public_Transportation
## 287 Sometimes no 1 no 1 1 Sometimes Public_Transportation
## 288 Sometimes no 3 no 3 0 no Public_Transportation
## 289 Sometimes no 1 no 0 2 no Public_Transportation
## 290 Sometimes no 3 no 3 0 Sometimes Automobile
## 291 Frequently no 2 no 2 1 Sometimes Public_Transportation
## 292 Frequently no 2 no 2 1 no Walking
## 293 Frequently no 1 no 1 1 no Public_Transportation
## 294 Frequently no 2 no 1 0 no Public_Transportation
## 295 Sometimes yes 2 no 1 2 Sometimes Public_Transportation
## 296 Sometimes no 1 no 0 1 no Walking
## 297 Sometimes no 2 no 2 1 Sometimes Public_Transportation
## 298 Sometimes no 2 no 2 0 no Automobile
## 299 Frequently no 1 no 0 1 Frequently Public_Transportation
## 300 Sometimes no 3 no 1 2 Sometimes Public_Transportation
## 301 Sometimes yes 1 no 0 0 Sometimes Public_Transportation
## 302 Sometimes no 2 no 2 1 Sometimes Public_Transportation
## 303 Always no 3 no 3 2 Sometimes Walking
## 304 Always no 2 no 0 1 Sometimes Public_Transportation
## 305 Sometimes no 3 no 2 1 Sometimes Public_Transportation
## 306 Sometimes yes 2 no 2 1 Sometimes Public_Transportation
## 307 Always no 2 no 0 2 Sometimes Public_Transportation
## 308 Frequently no 1 no 0 2 Sometimes Public_Transportation
## 309 Always no 3 no 2 0 Sometimes Public_Transportation
## 310 Sometimes no 1 no 0 1 no Walking
## 311 Frequently no 2 no 2 1 no Public_Transportation
## 312 Always no 2 no 3 1 no Public_Transportation
## 313 Sometimes no 1 no 3 0 no Public_Transportation
## 314 Always no 2 no 1 1 Sometimes Public_Transportation
## 315 Sometimes no 1 no 1 0 no Walking
## 316 Always no 2 no 0 0 Sometimes Public_Transportation
## 317 Frequently no 1 no 2 1 no Automobile
## 318 Sometimes no 2 no 1 1 no Public_Transportation
## 319 Sometimes no 1 no 0 0 Sometimes Public_Transportation
## 320 Sometimes no 1 no 0 1 Sometimes Automobile
## 321 Always no 2 no 1 1 no Public_Transportation
## 322 Frequently no 1 no 3 1 no Automobile
## 323 Frequently no 2 no 2 0 Sometimes Public_Transportation
## 324 Sometimes no 2 no 3 0 Sometimes Automobile
## 325 Sometimes no 1 no 0 0 Sometimes Public_Transportation
## 326 Sometimes no 1 no 1 0 Sometimes Public_Transportation
## 327 Sometimes no 2 no 3 0 Sometimes Public_Transportation
## 328 Frequently no 1 no 0 0 Sometimes Public_Transportation
## 329 Sometimes no 3 no 3 1 Sometimes Walking
## 330 Sometimes no 1 no 0 1 Sometimes Public_Transportation
## 331 Frequently no 1 no 2 1 Sometimes Public_Transportation
## 332 Sometimes no 2 no 2 1 no Public_Transportation
## 333 Sometimes no 2 no 1 0 no Walking
## 334 Always no 3 yes 3 0 no Automobile
## 335 Frequently no 2 yes 1 2 Frequently Public_Transportation
## 336 Frequently no 1 no 2 1 Sometimes Public_Transportation
## 337 Sometimes no 2 no 0 1 no Public_Transportation
## 338 Frequently no 2 no 3 2 no Walking
## 339 Sometimes no 2 yes 1 2 Sometimes Public_Transportation
## 340 Sometimes no 1 yes 2 0 Frequently Public_Transportation
## 341 Sometimes no 2 no 1 1 no Public_Transportation
## 342 Sometimes no 1 no 0 0 Sometimes Public_Transportation
## 343 Sometimes no 2 no 1 0 Sometimes Public_Transportation
## 344 Sometimes no 2 no 3 0 no Public_Transportation
## 345 Frequently no 2 no 2 1 Sometimes Public_Transportation
## 346 Always no 2 no 3 1 Sometimes Public_Transportation
## 347 Always no 1 no 2 0 no Public_Transportation
## 348 Sometimes no 3 no 1 1 Sometimes Walking
## 349 Sometimes no 2 no 3 2 no Walking
## 350 Always no 3 no 1 1 Sometimes Public_Transportation
## 351 Sometimes no 1 no 3 2 Sometimes Walking
## 352 Always no 2 no 2 0 no Walking
## 353 Sometimes no 1 no 2 2 Sometimes Walking
## 354 Sometimes no 2 no 0 1 Sometimes Automobile
## 355 Sometimes no 2 no 1 2 no Public_Transportation
## 356 Sometimes no 1 no 1 0 Sometimes Public_Transportation
## 357 Sometimes no 2 no 3 1 no Walking
## 358 Sometimes no 1 no 1 1 no Automobile
## 359 Sometimes no 1 no 1 0 Frequently Automobile
## 360 Sometimes no 2 no 1 0 Sometimes Public_Transportation
## 361 Frequently no 1 no 1 1 Sometimes Public_Transportation
## 362 Sometimes no 2 no 2 0 no Public_Transportation
## 363 Sometimes no 2 no 1 0 Sometimes Automobile
## 364 Sometimes no 2 no 2 1 Sometimes Public_Transportation
## 365 Always no 2 no 2 1 Sometimes Public_Transportation
## 366 Sometimes no 2 no 0 0 Sometimes Motorbike
## 367 Sometimes no 2 no 3 0 Sometimes Automobile
## 368 Frequently no 2 no 3 1 Sometimes Public_Transportation
## 369 Sometimes no 2 no 0 0 no Automobile
## 370 Frequently no 2 no 3 1 Sometimes Public_Transportation
## 371 Sometimes no 1 no 1 1 no Public_Transportation
## 372 Always no 2 yes 1 2 Sometimes Public_Transportation
## 373 Sometimes no 1 no 0 2 no Automobile
## 374 Sometimes no 2 no 0 2 Sometimes Public_Transportation
## 375 Frequently no 2 no 2 1 Sometimes Automobile
## 376 Frequently no 3 no 1 0 Sometimes Automobile
## 377 Sometimes no 1 no 2 0 Sometimes Automobile
## 378 Frequently no 2 no 1 1 Sometimes Public_Transportation
## 379 Frequently no 1 no 2 1 Sometimes Public_Transportation
## 380 Sometimes no 2 no 0 2 Sometimes Walking
## 381 Sometimes no 3 yes 3 0 no Motorbike
## 382 Frequently no 1 no 2 0 Sometimes Public_Transportation
## 383 Frequently no 1 no 0 1 Sometimes Public_Transportation
## 384 Sometimes no 2 no 0 1 Sometimes Automobile
## 385 Sometimes no 1 yes 0 2 no Walking
## 386 Frequently no 2 no 1 1 no Public_Transportation
## 387 Sometimes no 1 no 1 2 no Public_Transportation
## 388 Frequently no 1 no 0 0 Sometimes Motorbike
## 389 Sometimes no 3 no 1 0 no Public_Transportation
## 390 Sometimes no 2 no 0 0 no Public_Transportation
## 391 Always no 3 no 0 2 no Public_Transportation
## 392 Sometimes no 2 no 0 1 Sometimes Walking
## 393 Frequently no 3 no 2 2 no Public_Transportation
## 394 Sometimes no 2 no 0 1 Sometimes Public_Transportation
## 395 Sometimes no 1 no 0 1 no Public_Transportation
## 396 Sometimes no 2 no 3 2 Sometimes Public_Transportation
## 397 Sometimes no 1 no 2 1 Frequently Automobile
## 398 Frequently no 3 no 0 0 no Public_Transportation
## 399 Always no 1 no 0 0 Sometimes Public_Transportation
## 400 Frequently no 1 no 0 0 Sometimes Motorbike
## 401 Sometimes no 2 no 0 0 no Public_Transportation
## 402 Always no 2 no 1 1 Sometimes Public_Transportation
## 403 Frequently no 2 no 2 1 Sometimes Walking
## 404 Sometimes no 3 no 0 0 no Automobile
## 405 Sometimes no 2 no 3 1 Sometimes Automobile
## 406 Sometimes no 2 no 3 0 no Public_Transportation
## 407 Sometimes no 2 no 3 1 Sometimes Automobile
## 408 Frequently no 1 no 1 2 Sometimes Walking
## 409 Sometimes no 2 no 0 0 Sometimes Public_Transportation
## 410 Sometimes no 3 no 2 1 Sometimes Public_Transportation
## 411 Sometimes no 2 no 1 1 no Public_Transportation
## 412 Sometimes no 2 yes 0 0 Sometimes Public_Transportation
## 413 Frequently no 2 no 1 0 Sometimes Automobile
## 414 Sometimes no 2 yes 1 0 Sometimes Public_Transportation
## 415 Always no 2 no 1 2 Frequently Automobile
## 416 Sometimes no 3 no 2 1 no Walking
## 417 Sometimes no 1 yes 2 0 no Automobile
## 418 Sometimes no 2 no 1 1 Frequently Public_Transportation
## 419 Sometimes no 2 no 2 0 Sometimes Public_Transportation
## 420 Sometimes no 1 no 0 0 Sometimes Public_Transportation
## 421 Sometimes no 2 yes 2 0 Sometimes Automobile
## 422 Sometimes no 2 yes 2 0 Sometimes Automobile
## 423 Sometimes no 2 no 2 0 Sometimes Bike
## 424 Sometimes no 1 no 1 1 Sometimes Walking
## 425 Sometimes no 1 no 0 2 Sometimes Walking
## 426 Always no 2 no 2 1 Sometimes Public_Transportation
## 427 Sometimes no 3 no 1 1 no Public_Transportation
## 428 no no 2 no 3 0 Sometimes Public_Transportation
## 429 Frequently no 1 no 2 1 Sometimes Public_Transportation
## 430 Frequently no 1 yes 1 0 Sometimes Automobile
## 431 Sometimes no 1 no 1 0 Sometimes Public_Transportation
## 432 Frequently no 2 no 2 1 Sometimes Public_Transportation
## 433 Frequently no 1 no 2 0 no Public_Transportation
## 434 Sometimes no 1 no 1 1 Sometimes Public_Transportation
## 435 Frequently no 2 no 3 1 Frequently Automobile
## 436 Sometimes no 3 no 3 1 no Public_Transportation
## 437 Sometimes no 1 no 0 0 Frequently Automobile
## 438 Always no 2 no 1 0 Sometimes Walking
## 439 Sometimes no 2 no 2 1 Sometimes Automobile
## 440 Frequently no 2 no 0 1 Sometimes Public_Transportation
## 441 Sometimes no 1 no 0 0 no Automobile
## 442 Frequently no 1 no 1 2 no Public_Transportation
## 443 Sometimes no 2 no 0 1 Sometimes Walking
## 444 Sometimes no 2 no 0 2 Sometimes Public_Transportation
## 445 Sometimes no 2 no 2 0 Sometimes Public_Transportation
## 446 Sometimes no 1 no 3 0 Sometimes Public_Transportation
## 447 Frequently no 2 no 2 0 Sometimes Public_Transportation
## 448 Sometimes no 2 no 2 1 Sometimes Public_Transportation
## 449 Sometimes no 1 no 0 2 Sometimes Public_Transportation
## 450 Sometimes no 2 no 2 2 Sometimes Public_Transportation
## 451 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## 452 Frequently no 2 no 1 0 no Public_Transportation
## 453 no no 2 no 2 1 Sometimes Automobile
## 454 Sometimes no 1 no 0 0 Sometimes Automobile
## 455 Sometimes no 1 no 1 0 no Public_Transportation
## 456 Frequently no 1 no 1 1 Sometimes Public_Transportation
## 457 Frequently no 2 no 0 0 no Public_Transportation
## 458 Sometimes no 1 no 0 0 Sometimes Public_Transportation
## 459 Always no 1 no 1 1 Sometimes Public_Transportation
## 460 Frequently no 3 no 1 2 Frequently Public_Transportation
## 461 Frequently no 1 no 1 1 no Public_Transportation
## 462 Sometimes no 2 no 0 2 no Public_Transportation
## 463 Always no 2 no 0 0 Sometimes Automobile
## 464 Sometimes no 1 no 2 1 Sometimes Public_Transportation
## 465 Always no 2 no 2 0 Sometimes Walking
## 466 Frequently no 1 no 1 1 Sometimes Public_Transportation
## 467 Frequently no 1 no 1 0 no Automobile
## 468 Frequently no 1 no 1 0 no Automobile
## 469 Frequently no 1 no 1 0 Sometimes Public_Transportation
## 470 Sometimes no 2 no 0 1 no Public_Transportation
## 471 Frequently no 2 no 3 0 Sometimes Public_Transportation
## 472 Sometimes no 2 yes 1 0 no Public_Transportation
## 473 Frequently no 2 no 1 1 no Public_Transportation
## 474 Frequently no 1 no 1 0 Sometimes Public_Transportation
## 475 Sometimes no 1 no 1 0 no Public_Transportation
## 476 Sometimes no 1 no 0 2 no Public_Transportation
## 477 Sometimes no 2 no 1 0 no Public_Transportation
## 478 Frequently no 1 yes 1 1 no Public_Transportation
## 479 Frequently no 1 no 1 1 Sometimes Public_Transportation
## 480 Frequently no 2 no 1 2 Sometimes Public_Transportation
## 481 Sometimes no 1 no 0 1 Sometimes Public_Transportation
## 482 Sometimes no 1 yes 2 0 Sometimes Public_Transportation
## 483 Frequently no 2 no 1 1 Sometimes Public_Transportation
## 484 Sometimes no 1 no 0 0 no Public_Transportation
## 485 Sometimes no 1 no 0 2 no Automobile
## 486 Always no 2 no 3 1 Sometimes Public_Transportation
## 487 Sometimes no 2 no 1 0 Frequently Public_Transportation
## 488 Sometimes no 3 no 3 0 no Motorbike
## 489 Sometimes no 3 no 2 1 Sometimes Walking
## 490 Sometimes no 1 no 0 2 no Public_Transportation
## 491 no no 2 yes 1 0 Sometimes Public_Transportation
## 492 Sometimes yes 1 no 1 1 Sometimes Public_Transportation
## 493 Frequently no 1 no 0 0 no Automobile
## 494 Frequently no 1 no 2 0 Sometimes Motorbike
## 495 Sometimes no 2 no 0 0 Sometimes Public_Transportation
## 496 Always no 1 yes 0 0 no Motorbike
## 497 Sometimes no 2 no 0 2 Sometimes Public_Transportation
## 498 Sometimes no 2 no 1 1 Sometimes Public_Transportation
## NObeyesdad
## 1 Normal_Weight
## 2 Normal_Weight
## 3 Normal_Weight
## 4 Overweight_Level_I
## 5 Overweight_Level_II
## 6 Normal_Weight
## 7 Normal_Weight
## 8 Normal_Weight
## 9 Normal_Weight
## 10 Normal_Weight
## 11 Obesity_Type_I
## 12 Overweight_Level_II
## 13 Normal_Weight
## 14 Obesity_Type_I
## 15 Normal_Weight
## 16 Normal_Weight
## 17 Overweight_Level_II
## 18 Obesity_Type_I
## 19 Overweight_Level_II
## 20 Overweight_Level_I
## 21 Overweight_Level_II
## 22 Obesity_Type_I
## 23 Normal_Weight
## 24 Obesity_Type_I
## 25 Normal_Weight
## 26 Normal_Weight
## 27 Normal_Weight
## 28 Normal_Weight
## 29 Normal_Weight
## 30 Normal_Weight
## 31 Overweight_Level_I
## 32 Overweight_Level_II
## 33 Normal_Weight
## 34 Overweight_Level_II
## 35 Normal_Weight
## 36 Overweight_Level_II
## 37 Normal_Weight
## 38 Normal_Weight
## 39 Normal_Weight
## 40 Overweight_Level_II
## 41 Overweight_Level_I
## 42 Normal_Weight
## 43 Normal_Weight
## 44 Normal_Weight
## 45 Normal_Weight
## 46 Overweight_Level_II
## 47 Normal_Weight
## 48 Normal_Weight
## 49 Normal_Weight
## 50 Normal_Weight
## 51 Normal_Weight
## 52 Normal_Weight
## 53 Normal_Weight
## 54 Normal_Weight
## 55 Normal_Weight
## 56 Normal_Weight
## 57 Normal_Weight
## 58 Normal_Weight
## 59 Normal_Weight
## 60 Insufficient_Weight
## 61 Normal_Weight
## 62 Normal_Weight
## 63 Normal_Weight
## 64 Normal_Weight
## 65 Normal_Weight
## 66 Overweight_Level_I
## 67 Overweight_Level_II
## 68 Obesity_Type_I
## 69 Obesity_Type_II
## 70 Normal_Weight
## 71 Overweight_Level_II
## 72 Insufficient_Weight
## 73 Normal_Weight
## 74 Normal_Weight
## 75 Overweight_Level_II
## 76 Insufficient_Weight
## 77 Insufficient_Weight
## 78 Overweight_Level_II
## 79 Obesity_Type_I
## 80 Normal_Weight
## 81 Normal_Weight
## 82 Overweight_Level_II
## 83 Obesity_Type_I
## 84 Insufficient_Weight
## 85 Overweight_Level_II
## 86 Normal_Weight
## 87 Normal_Weight
## 88 Overweight_Level_I
## 89 Normal_Weight
## 90 Overweight_Level_II
## 91 Obesity_Type_II
## 92 Normal_Weight
## 93 Overweight_Level_I
## 94 Normal_Weight
## 95 Normal_Weight
## 96 Normal_Weight
## 97 Normal_Weight
## 98 Insufficient_Weight
## 99 Insufficient_Weight
## 100 Normal_Weight
## 101 Normal_Weight
## 102 Normal_Weight
## 103 Normal_Weight
## 104 Normal_Weight
## 105 Obesity_Type_I
## 106 Normal_Weight
## 107 Normal_Weight
## 108 Overweight_Level_I
## 109 Obesity_Type_I
## 110 Obesity_Type_I
## 111 Normal_Weight
## 112 Normal_Weight
## 113 Normal_Weight
## 114 Normal_Weight
## 115 Normal_Weight
## 116 Normal_Weight
## 117 Obesity_Type_I
## 118 Overweight_Level_II
## 119 Normal_Weight
## 120 Overweight_Level_II
## 121 Overweight_Level_I
## 122 Overweight_Level_II
## 123 Insufficient_Weight
## 124 Normal_Weight
## 125 Overweight_Level_II
## 126 Overweight_Level_I
## 127 Normal_Weight
## 128 Normal_Weight
## 129 Normal_Weight
## 130 Overweight_Level_II
## 131 Normal_Weight
## 132 Normal_Weight
## 133 Normal_Weight
## 134 Normal_Weight
## 135 Obesity_Type_I
## 136 Overweight_Level_I
## 137 Normal_Weight
## 138 Obesity_Type_I
## 139 Normal_Weight
## 140 Normal_Weight
## 141 Insufficient_Weight
## 142 Normal_Weight
## 143 Obesity_Type_I
## 144 Overweight_Level_I
## 145 Overweight_Level_I
## 146 Overweight_Level_I
## 147 Normal_Weight
## 148 Obesity_Type_I
## 149 Normal_Weight
## 150 Obesity_Type_I
## 151 Normal_Weight
## 152 Normal_Weight
## 153 Overweight_Level_I
## 154 Overweight_Level_II
## 155 Obesity_Type_I
## 156 Normal_Weight
## 157 Normal_Weight
## 158 Normal_Weight
## 159 Overweight_Level_I
## 160 Overweight_Level_II
## 161 Normal_Weight
## 162 Overweight_Level_II
## 163 Normal_Weight
## 164 Normal_Weight
## 165 Overweight_Level_II
## 166 Obesity_Type_II
## 167 Normal_Weight
## 168 Overweight_Level_II
## 169 Overweight_Level_I
## 170 Overweight_Level_II
## 171 Overweight_Level_II
## 172 Normal_Weight
## 173 Normal_Weight
## 174 Normal_Weight
## 175 Overweight_Level_I
## 176 Normal_Weight
## 177 Normal_Weight
## 178 Normal_Weight
## 179 Normal_Weight
## 180 Overweight_Level_I
## 181 Normal_Weight
## 182 Normal_Weight
## 183 Insufficient_Weight
## 184 Overweight_Level_II
## 185 Overweight_Level_I
## 186 Overweight_Level_I
## 187 Obesity_Type_I
## 188 Obesity_Type_I
## 189 Obesity_Type_I
## 190 Normal_Weight
## 191 Normal_Weight
## 192 Overweight_Level_I
## 193 Overweight_Level_I
## 194 Normal_Weight
## 195 Obesity_Type_I
## 196 Overweight_Level_I
## 197 Normal_Weight
## 198 Obesity_Type_II
## 199 Insufficient_Weight
## 200 Normal_Weight
## 201 Obesity_Type_I
## 202 Obesity_Type_I
## 203 Obesity_Type_III
## 204 Obesity_Type_I
## 205 Normal_Weight
## 206 Obesity_Type_I
## 207 Obesity_Type_I
## 208 Normal_Weight
## 209 Normal_Weight
## 210 Normal_Weight
## 211 Obesity_Type_II
## 212 Normal_Weight
## 213 Overweight_Level_II
## 214 Normal_Weight
## 215 Normal_Weight
## 216 Normal_Weight
## 217 Normal_Weight
## 218 Overweight_Level_I
## 219 Normal_Weight
## 220 Overweight_Level_I
## 221 Overweight_Level_I
## 222 Overweight_Level_II
## 223 Normal_Weight
## 224 Normal_Weight
## 225 Obesity_Type_I
## 226 Obesity_Type_II
## 227 Normal_Weight
## 228 Normal_Weight
## 229 Overweight_Level_II
## 230 Obesity_Type_II
## 231 Overweight_Level_I
## 232 Normal_Weight
## 233 Normal_Weight
## 234 Overweight_Level_II
## 235 Normal_Weight
## 236 Normal_Weight
## 237 Normal_Weight
## 238 Normal_Weight
## 239 Normal_Weight
## 240 Normal_Weight
## 241 Normal_Weight
## 242 Overweight_Level_I
## 243 Normal_Weight
## 244 Overweight_Level_II
## 245 Normal_Weight
## 246 Insufficient_Weight
## 247 Normal_Weight
## 248 Normal_Weight
## 249 Normal_Weight
## 250 Overweight_Level_I
## 251 Overweight_Level_II
## 252 Overweight_Level_II
## 253 Overweight_Level_II
## 254 Normal_Weight
## 255 Normal_Weight
## 256 Overweight_Level_I
## 257 Overweight_Level_II
## 258 Obesity_Type_I
## 259 Overweight_Level_II
## 260 Obesity_Type_I
## 261 Overweight_Level_I
## 262 Overweight_Level_I
## 263 Normal_Weight
## 264 Insufficient_Weight
## 265 Normal_Weight
## 266 Insufficient_Weight
## 267 Insufficient_Weight
## 268 Overweight_Level_II
## 269 Normal_Weight
## 270 Normal_Weight
## 271 Obesity_Type_I
## 272 Normal_Weight
## 273 Normal_Weight
## 274 Normal_Weight
## 275 Normal_Weight
## 276 Normal_Weight
## 277 Insufficient_Weight
## 278 Normal_Weight
## 279 Normal_Weight
## 280 Insufficient_Weight
## 281 Normal_Weight
## 282 Normal_Weight
## 283 Normal_Weight
## 284 Normal_Weight
## 285 Normal_Weight
## 286 Obesity_Type_I
## 287 Normal_Weight
## 288 Normal_Weight
## 289 Normal_Weight
## 290 Normal_Weight
## 291 Normal_Weight
## 292 Insufficient_Weight
## 293 Normal_Weight
## 294 Normal_Weight
## 295 Obesity_Type_I
## 296 Normal_Weight
## 297 Normal_Weight
## 298 Overweight_Level_I
## 299 Normal_Weight
## 300 Overweight_Level_I
## 301 Normal_Weight
## 302 Normal_Weight
## 303 Insufficient_Weight
## 304 Normal_Weight
## 305 Overweight_Level_I
## 306 Obesity_Type_II
## 307 Normal_Weight
## 308 Normal_Weight
## 309 Normal_Weight
## 310 Normal_Weight
## 311 Insufficient_Weight
## 312 Normal_Weight
## 313 Normal_Weight
## 314 Normal_Weight
## 315 Normal_Weight
## 316 Normal_Weight
## 317 Normal_Weight
## 318 Normal_Weight
## 319 Normal_Weight
## 320 Overweight_Level_I
## 321 Normal_Weight
## 322 Normal_Weight
## 323 Insufficient_Weight
## 324 Normal_Weight
## 325 Overweight_Level_I
## 326 Normal_Weight
## 327 Normal_Weight
## 328 Overweight_Level_I
## 329 Normal_Weight
## 330 Obesity_Type_I
## 331 Insufficient_Weight
## 332 Normal_Weight
## 333 Normal_Weight
## 334 Normal_Weight
## 335 Overweight_Level_I
## 336 Insufficient_Weight
## 337 Normal_Weight
## 338 Normal_Weight
## 339 Overweight_Level_I
## 340 Insufficient_Weight
## 341 Normal_Weight
## 342 Normal_Weight
## 343 Obesity_Type_I
## 344 Normal_Weight
## 345 Obesity_Type_III
## 346 Normal_Weight
## 347 Normal_Weight
## 348 Overweight_Level_II
## 349 Normal_Weight
## 350 Obesity_Type_I
## 351 Normal_Weight
## 352 Normal_Weight
## 353 Normal_Weight
## 354 Normal_Weight
## 355 Normal_Weight
## 356 Overweight_Level_I
## 357 Insufficient_Weight
## 358 Normal_Weight
## 359 Obesity_Type_II
## 360 Normal_Weight
## 361 Normal_Weight
## 362 Obesity_Type_I
## 363 Overweight_Level_I
## 364 Normal_Weight
## 365 Overweight_Level_I
## 366 Normal_Weight
## 367 Overweight_Level_II
## 368 Overweight_Level_I
## 369 Overweight_Level_II
## 370 Overweight_Level_II
## 371 Normal_Weight
## 372 Overweight_Level_I
## 373 Normal_Weight
## 374 Normal_Weight
## 375 Normal_Weight
## 376 Overweight_Level_II
## 377 Normal_Weight
## 378 Normal_Weight
## 379 Normal_Weight
## 380 Normal_Weight
## 381 Overweight_Level_II
## 382 Normal_Weight
## 383 Normal_Weight
## 384 Obesity_Type_I
## 385 Normal_Weight
## 386 Normal_Weight
## 387 Normal_Weight
## 388 Obesity_Type_I
## 389 Obesity_Type_I
## 390 Overweight_Level_I
## 391 Insufficient_Weight
## 392 Insufficient_Weight
## 393 Normal_Weight
## 394 Overweight_Level_II
## 395 Normal_Weight
## 396 Insufficient_Weight
## 397 Normal_Weight
## 398 Normal_Weight
## 399 Obesity_Type_II
## 400 Normal_Weight
## 401 Overweight_Level_I
## 402 Normal_Weight
## 403 Overweight_Level_II
## 404 Obesity_Type_III
## 405 Normal_Weight
## 406 Overweight_Level_II
## 407 Normal_Weight
## 408 Overweight_Level_I
## 409 Normal_Weight
## 410 Normal_Weight
## 411 Normal_Weight
## 412 Overweight_Level_I
## 413 Normal_Weight
## 414 Overweight_Level_II
## 415 Obesity_Type_I
## 416 Normal_Weight
## 417 Overweight_Level_I
## 418 Overweight_Level_II
## 419 Obesity_Type_I
## 420 Obesity_Type_I
## 421 Insufficient_Weight
## 422 Insufficient_Weight
## 423 Normal_Weight
## 424 Overweight_Level_II
## 425 Overweight_Level_I
## 426 Normal_Weight
## 427 Normal_Weight
## 428 Normal_Weight
## 429 Normal_Weight
## 430 Normal_Weight
## 431 Obesity_Type_I
## 432 Normal_Weight
## 433 Normal_Weight
## 434 Normal_Weight
## 435 Normal_Weight
## 436 Overweight_Level_I
## 437 Normal_Weight
## 438 Normal_Weight
## 439 Normal_Weight
## 440 Normal_Weight
## 441 Normal_Weight
## 442 Normal_Weight
## 443 Normal_Weight
## 444 Insufficient_Weight
## 445 Normal_Weight
## 446 Normal_Weight
## 447 Normal_Weight
## 448 Overweight_Level_I
## 449 Obesity_Type_II
## 450 Normal_Weight
## 451 Normal_Weight
## 452 Normal_Weight
## 453 Normal_Weight
## 454 Normal_Weight
## 455 Normal_Weight
## 456 Normal_Weight
## 457 Normal_Weight
## 458 Normal_Weight
## 459 Normal_Weight
## 460 Overweight_Level_I
## 461 Normal_Weight
## 462 Obesity_Type_I
## 463 Overweight_Level_II
## 464 Normal_Weight
## 465 Normal_Weight
## 466 Normal_Weight
## 467 Normal_Weight
## 468 Normal_Weight
## 469 Insufficient_Weight
## 470 Insufficient_Weight
## 471 Normal_Weight
## 472 Obesity_Type_I
## 473 Overweight_Level_II
## 474 Normal_Weight
## 475 Normal_Weight
## 476 Overweight_Level_I
## 477 Overweight_Level_I
## 478 Normal_Weight
## 479 Normal_Weight
## 480 Normal_Weight
## 481 Normal_Weight
## 482 Normal_Weight
## 483 Normal_Weight
## 484 Overweight_Level_I
## 485 Overweight_Level_II
## 486 Normal_Weight
## 487 Normal_Weight
## 488 Obesity_Type_I
## 489 Normal_Weight
## 490 Normal_Weight
## 491 Overweight_Level_II
## 492 Normal_Weight
## 493 Overweight_Level_II
## 494 Normal_Weight
## 495 Normal_Weight
## 496 Normal_Weight
## 497 Insufficient_Weight
## 498 Normal_WeightDeskripsi Data
## 'data.frame': 498 obs. of 17 variables:
## $ Gender : chr "Female" "Female" "Male" "Male" ...
## $ Age : int 21 21 23 27 22 29 23 22 24 22 ...
## $ Height : num 1.62 1.52 1.8 1.8 1.78 1.62 1.5 1.64 1.78 1.72 ...
## $ Weight : num 64 56 77 87 89.8 53 55 53 64 68 ...
## $ family_history_with_overweight: chr "yes" "yes" "yes" "no" ...
## $ FAVC : chr "no" "no" "no" "no" ...
## $ FCVC : int 2 3 2 3 2 2 3 2 3 2 ...
## $ NCP : int 3 3 3 3 1 3 3 3 3 3 ...
## $ CAEC : chr "Sometimes" "Sometimes" "Sometimes" "Sometimes" ...
## $ SMOKE : chr "no" "yes" "no" "no" ...
## $ CH2O : int 2 3 2 2 2 2 2 2 2 2 ...
## $ SCC : chr "no" "yes" "no" "no" ...
## $ FAF : int 0 3 2 2 0 0 1 3 1 1 ...
## $ TUE : int 1 0 1 0 0 0 0 0 1 1 ...
## $ CALC : chr "no" "Sometimes" "Frequently" "Frequently" ...
## $ MTRANS : chr "Public_Transportation" "Public_Transportation" "Public_Transportation" "Walking" ...
## $ NObeyesdad : chr "Normal_Weight" "Normal_Weight" "Normal_Weight" "Overweight_Level_I" ...## Gender Age Height Weight
## Length:498 Min. :14.00 Min. :1.450 Min. : 39.00
## Class :character 1st Qu.:19.00 1st Qu.:1.613 1st Qu.: 58.00
## Mode :character Median :21.00 Median :1.680 Median : 67.00
## Mean :23.15 Mean :1.686 Mean : 69.57
## 3rd Qu.:24.00 3rd Qu.:1.750 3rd Qu.: 80.00
## Max. :61.00 Max. :1.980 Max. :173.00
## family_history_with_overweight FAVC FCVC
## Length:498 Length:498 Min. :1.000
## Class :character Class :character 1st Qu.:2.000
## Mode :character Mode :character Median :2.000
## Mean :2.325
## 3rd Qu.:3.000
## Max. :3.000
## NCP CAEC SMOKE CH2O
## Min. :1.000 Length:498 Length:498 Min. :1.000
## 1st Qu.:3.000 Class :character Class :character 1st Qu.:1.000
## Median :3.000 Mode :character Mode :character Median :2.000
## Mean :2.659 Mean :1.924
## 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :4.000 Max. :3.000
## SCC FAF TUE CALC
## Length:498 Min. :0.000 Min. :0.0000 Length:498
## Class :character 1st Qu.:0.000 1st Qu.:0.0000 Class :character
## Mode :character Median :1.000 Median :1.0000 Mode :character
## Mean :1.163 Mean :0.6606
## 3rd Qu.:2.000 3rd Qu.:1.0000
## Max. :3.000 Max. :2.0000
## MTRANS NObeyesdad
## Length:498 Length:498
## Class :character Class :character
## Mode :character Mode :character
##
##
## ## [1] FALSEOutlier
# cek normalitas
Y <- data[, c("Height", "Weight")]
### Hitung Mahalanobis distance
mahal_dist <- mahalanobis(Y,
center = colMeans(Y),
cov = cov(Y))
### Tentukan batas cutoff outlier multivariat (misal alpha = 0.001)
cutoff <- qchisq(0.999, df = 2)
### Temukan indeks outlier multivariat
outliers <- which(mahal_dist > cutoff)
### Tampilkan jumlah dan indeks outlier
cat("Jumlah outlier multivariat:", length(outliers), "\n")## Jumlah outlier multivariat: 1## Index data outlier: 345Ubah Tipe Data
Visualisasi
# cek distribusi
## viasualisasi grafik
data %>% select(Age, Height, Weight) %>%
gather(variable, value) %>%
ggplot(aes(x = value)) +
geom_histogram(bins = 30, fill = "steelblue", color = "white") +
facet_wrap(~ variable, scales = "free") +
labs(title = "Distribusi Variabel Numerik")
Gambar di atas menunjukkan distribusi tiga variabel numerik, yaitu Age,
Height, dan Weight. Sebagian besar responden berada pada rentang usia
15–25 tahun, dengan distribusi usia yang condong ke kanan
(right-skewed), menunjukkan dominasi peserta usia muda. Distribusi
tinggi badan terlihat simetris dan mendekati normal, dengan puncak di
sekitar 1.6–1.7 meter, menandakan tinggi rata-rata. Sementara itu,
distribusi berat badan sedikit condong ke kanan, dengan mayoritas
responden memiliki berat antara 50–80 kg, serta beberapa outlier pada
nilai yang lebih tinggi. Grafik ini menunjukkan variasi yang cukup untuk
dianalisis lebih lanjut menggunakan pendekatan multivariat.
Gambar boxplot di atas menunjukkan sebaran data untuk variabel berat
badan (Weight) dan tinggi badan (Height). Pada boxplot berat badan,
terlihat bahwa sebagian besar data berada antara sekitar 50 hingga 90
kg, dengan median sekitar 70 kg. Namun, terdapat cukup banyak outlier
yang berada di atas 100 kg hingga lebih dari 160 kg, yang
mengindikasikan adanya individu dengan berat badan jauh di atas
rata-rata. Sementara itu, boxplot tinggi badan menunjukkan distribusi
yang lebih simetris dan normal, dengan rentang antara sekitar 1.45
hingga 1.90 meter dan hanya sedikit outlier di atas 1.9 meter. Kedua
boxplot ini membantu mengidentifikasi nilai ekstrem dan persebaran utama
dari data sebelum dilakukan analisis lebih lanjut.
Penentuan Variabel
Uji Norm
Visualisasi
### Ambil hanya variabel dependen yang telah dinormalisasi
Y <- data [, c("norm_Height", "norm_Weight")]
## viasualisasi
### Hitung quantile chi-square teoritis
chisq_q <- qchisq(ppoints(nrow(Y)), df = ncol(Y))
### Buat Q-Q Plot
qqplot(chisq_q, sort(mahal_dist),
main = "Q-Q Plot Mahalanobis vs Chi-Square",
xlab = "Theoretical Chi-Square Quantiles",
ylab = "Sample Mahalanobis Distance")
abline(0, 1, col = "red")
Grafik Q-Q Plot di atas membandingkan jarak Mahalanobis sampel terhadap
kuantil teoritis distribusi Chi-Square. Sebagian besar titik mengikuti
garis diagonal merah, yang menunjukkan bahwa data multivariat secara
umum mendekati distribusi normal multivariat. Namun, beberapa titik di
sisi kanan atas menyimpang dari garis, mengindikasikan adanya outlier
multivariat atau observasi ekstrem. Penyimpangan ini penting untuk
diperhatikan sebelum melakukan analisis MANOVA atau MANCOVA karena dapat
memengaruhi validitas hasil.
Pada project kali ini untuk uji normalitas yang digunakan terdiri dari 2 uji yaitu uji normalitas univariat yang digunakan untuk menguji masing - masing variabel dan uji normalitas multivariat yang digunakan untuk uji gabungan variabel dependen. Uji normalitas memiliki hipotesis H0 = Data berdistribusi normal dan H1 = Data tidak berdistribusi normal
Uji Normal
##
## Shapiro-Wilk normality test
##
## data: data$norm_Height
## W = 0.99668, p-value = 0.4066##
## Shapiro-Wilk normality test
##
## data: data$norm_Weight
## W = 0.99836, p-value = 0.9277Berdasarkan hasil diatas di dapatkan Uji Normalitas Tinggi Badan: p-value = 0.4066 dan Uji Normalitas Berat Badan: p-value = 0.9277. Dapat ditarik kesimpulan bahwa semua p-value > 0.05, maka H0 diterima, yang berarti baik distribusi tinggi badan, berat badan, maupun gabungan keduanya memenuhi asumsi normalitas.
Uji Normalitas Multivariat
library(MVN)
result_mvn <- mvn(data = data[, c("norm_Height", "norm_Weight")],
mvnTest = "royston",
multivariatePlot = "qq") # Pilihan lain: "persp", "contour"
## $multivariateNormality
## Test H p value MVN
## 1 Royston 0.6998675 0.7066972 YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Anderson-Darling norm_Height 0.5346 0.1705 YES
## 2 Anderson-Darling norm_Weight 0.2499 0.7436 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max
## norm_Height 493 0.0006744105 0.9946969 0.005084461 -3.086043 2.873711
## norm_Weight 493 0.0003598933 0.9973612 0.002542222 -3.086043 2.873711
## 25th 75th Skew Kurtosis
## norm_Height -0.6889222 0.6320054 0.010329840 -0.11024738
## norm_Weight -0.6921489 0.7381122 0.002290552 -0.08575782Uji normalitas multivariat menggunakan metode Royston menunjukkan bahwa data norm_Height dan norm_Weight berdistribusi normal secara multivariat, dengan nilai p sebesar 0.7066 yang jauh di atas batas signifikansi 0.05. Hasil uji normalitas univariat dengan Anderson-Darling juga mendukung temuan ini, di mana kedua variabel masing-masing memiliki p-value di atas 0.05 (p = 0.1705 untuk norm_Height dan p = 0.7436 untuk norm_Weight), yang mengindikasikan tidak terdapat pelanggaran asumsi normalitas secara univariat. Selain itu, nilai skewness dan kurtosis juga mendekati nol, memperkuat bahwa distribusi variabel sudah cukup simetris dan mendekati distribusi normal. Dengan demikian, asumsi normalitas dalam MANOVA dan MANCOVA telah terpenuhi dengan baik.
Uji Homogenitas Kovarian
## Uji Homogenitas Kovarian (Box’s M)
Y <- as.matrix(data[, c("norm_Height", "norm_Weight")])
group <- data$family_history_with_overweight
boxM_result <- boxM(Y, group)
print(boxM_result)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: Y
## Chi-Sq (approx.) = 9.5427, df = 3, p-value = 0.02288Uji ini dilakukan untuk melihat apakah varian-kovarian antar kelompok homogen (sama). Uji homogenitas yang dilakukan menggunakan metode Box’s M Test, denagn hipotsesis H0: Matriks kovarian homogen (tidak berbeda secara signifikan antar grup).H1: Matriks kovarian tidak homogen. Berdasarkan hasil diatas dapat ditarik kesimpulan bahwa H0 tidak memenuhi syarat asumsi homogenitas karena nilai p-value < 0.05.
Uji Multicolineritas
## norm_Height norm_Weight
## norm_Height 1.0000000 0.5701719
## norm_Weight 0.5701719 1.0000000# uji multicolinertas
model_lm <- lm(Height ~ family_history_with_overweight + FAVC + CAEC, data = data)
library(car)
vif(model_lm)## GVIF Df GVIF^(1/(2*Df))
## family_history_with_overweight 1.003168 1 1.001583
## FAVC 1.014742 1 1.007344
## CAEC 1.017114 3 1.002832Uji multikolinearitas dilakukan untuk memastikan bahwa tidak terjadi hubungan kuat antar variabel independen dalam model. Hasil menunjukkan bahwa tidak terdapat indikasi multikolinearitas dalam model, sehingga variabel-variabel independen tersebut dapat digunakan bersama dalam analisis MANOVA atau MANCOVA tanpa mengkhawatirkan redundansi informasi antar prediktor.
Manova Tanpa Covariat
# Manova tanpa covariat
manova_model <- manova(cbind(Height, Weight) ~ family_history_with_overweight + FAVC + CAEC, data = data) #tanpa kontrol usia, gender, merokok
summary(manova_model, test = "Wilks")## Df Wilks approx F num Df den Df Pr(>F)
## family_history_with_overweight 1 0.93860 15.8967 2 486 2.054e-07 ***
## FAVC 1 0.99973 0.0651 2 486 0.93701
## CAEC 3 0.96700 2.7413 6 972 0.01202 *
## Residuals 487
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Response Height :
## Df Sum Sq Mean Sq F value Pr(>F)
## family_history_with_overweight 1 0.0526 0.052561 5.7820 0.01656 *
## FAVC 1 0.0001 0.000069 0.0076 0.93063
## CAEC 3 0.0359 0.011959 1.3156 0.26859
## Residuals 487 4.4270 0.009090
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response Weight :
## Df Sum Sq Mean Sq F value Pr(>F)
## family_history_with_overweight 1 7191 7191.3 31.1490 3.973e-08 ***
## FAVC 1 27 26.6 0.1154 0.7342
## CAEC 3 851 283.6 1.2284 0.2987
## Residuals 487 112432 230.9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Hasil analisis MANOVA menunjukkan bahwa variabel family_history_with_overweight memiliki pengaruh yang sangat signifikan secara multivariat terhadap kombinasi variabel dependen Height dan Weight dengan nilai Wilks’ Lambda = 0.938 dan p-value = 2.054e-07. Variabel CAEC juga menunjukkan pengaruh signifikan secara multivariat (p = 0.0i2), sedangkan FAVC tidak signifikan (p = 0.937).
Mancova Dengan Covariat
# Mancova dengan covariat
mancova_model <- manova(cbind(Height, Weight) ~
family_history_with_overweight + FAVC + CAEC +
Age + Gender + SMOKE, data = data)
summary(mancova_model, test = "Wilks") ## Df Wilks approx F num Df den Df Pr(>F)
## family_history_with_overweight 1 0.91719 21.803 2 483 8.597e-10 ***
## FAVC 1 0.99967 0.081 2 483 0.922477
## CAEC 3 0.95914 3.394 6 966 0.002558 **
## Age 1 0.88548 31.234 2 483 1.752e-13 ***
## Gender 1 0.51015 231.895 2 483 < 2.2e-16 ***
## SMOKE 1 0.99279 1.754 2 483 0.174106
## Residuals 484
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Response Height :
## Df Sum Sq Mean Sq F value Pr(>F)
## family_history_with_overweight 1 0.05256 0.05256 11.1287 0.0009154 ***
## FAVC 1 0.00007 0.00007 0.0146 0.9038773
## CAEC 3 0.03588 0.01196 2.5320 0.0564156 .
## Age 1 0.00027 0.00027 0.0561 0.8128304
## Gender 1 2.14041 2.14041 453.1909 < 2.2e-16 ***
## SMOKE 1 0.00040 0.00040 0.0842 0.7718554
## Residuals 484 2.28592 0.00472
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response Weight :
## Df Sum Sq Mean Sq F value Pr(>F)
## family_history_with_overweight 1 7191 7191.3 43.1354 1.321e-10 ***
## FAVC 1 27 26.6 0.1598 0.6895
## CAEC 3 851 283.6 1.7011 0.1659
## Age 1 8499 8499.3 50.9811 3.438e-12 ***
## Gender 1 22828 22828.2 136.9300 < 2.2e-16 ***
## SMOKE 1 415 415.1 2.4899 0.1152
## Residuals 484 80690 166.7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Hasil analisis MANCOVA menunjukkan bahwa beberapa variabel memiliki pengaruh signifikan secara multivariat terhadap kombinasi variabel dependen Height dan Weight. Variabel family_history_with_overweight, Age, dan terutama Gender memberikan kontribusi signifikan terhadap perubahan simultan tinggi dan berat badan. Selain itu, CAEC juga menunjukkan pengaruh signifika, sementara FAVC dan SMOKE tidak signifikan.
Analisi Pos Hoc
# Contoh post hoc Tukey untuk variabel Height dan CAEC
library(emmeans)
# Model linear (misal dengan kontrol kovariat)
model_height <- lm(Height ~ family_history_with_overweight + FAVC + CAEC + Age + Gender + SMOKE, data = data)
# Tukey post hoc untuk CAEC
emmeans_obj <- emmeans(model_height, pairwise ~ CAEC)
summary(emmeans_obj$contrasts, infer = TRUE)## contrast estimate SE df lower.CL upper.CL t.ratio p.value
## Always - Frequently 0.003540 0.01130 484 -0.02559 0.0327 0.313 0.9893
## Always - no 0.014732 0.01820 484 -0.03221 0.0617 0.809 0.8502
## Always - Sometimes 0.014051 0.01050 484 -0.01294 0.0410 1.342 0.5364
## Frequently - no 0.011192 0.01650 484 -0.03147 0.0539 0.676 0.9060
## Frequently - Sometimes 0.010511 0.00721 484 -0.00809 0.0291 1.457 0.4644
## no - Sometimes -0.000681 0.01590 484 -0.04175 0.0404 -0.043 1.0000
##
## Results are averaged over the levels of: family_history_with_overweight, FAVC, Gender, SMOKE
## Confidence level used: 0.95
## Conf-level adjustment: tukey method for comparing a family of 4 estimates
## P value adjustment: tukey method for comparing a family of 4 estimatesHasil analisis menunjukkan perbandingan antar tingkat kategori variabel CAEC (kebiasaan makan di luar waktu makan utama) terhadap variabel dependen (tinggi dan berat badan secara simultan), setelah memperhitungkan pengaruh dari kovariat family_history_with_overweight, FAVC, Gender, dan SMOKE memiliki nilai p-value yang besar (> 0.05), bahkan mendekati 1, serta interval kepercayaan (CI) yang mencakup nol. Hal ini menunjukkan bahwa tidak terdapat perbedaan yang signifikan antara kategori CAEC terhadap tinggi dan berat badan.
Visualisasi
# Visualisasi
ggplot(data, aes(x = FAVC, y = Weight, fill = FAVC)) +
geom_boxplot() +
labs(title = "Berat Badan Berdasarkan FAVC")
ggplot(data, aes(x = Age, y = Weight, color = Gender)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE) +
labs(title = "Usia vs Berat Badan berdasarkan Gender")
Grafik scatter plot di atas menunjukkan hubungan antara usia dan berat
badan, yang dipisahkan berdasarkan jenis kelamin. Terlihat bahwa secara
umum, berat badan cenderung meningkat seiring bertambahnya
usia, baik pada laki-laki maupun perempuan. Namun, garis tren
menunjukkan bahwa laki-laki (warna biru) memiliki
berat badan rata-rata lebih tinggi dibandingkan
perempuan (warna merah) pada setiap rentang usia. Sebaran data pada
laki-laki juga lebih lebar, mengindikasikan variasi berat badan yang
lebih besar dibandingkan perempuan. Grafik ini menggambarkan adanya
perbedaan pola berat badan antar gender yang bisa dipertimbangkan dalam
analisis MANCOVA sebagai kovariat.
PENUTUP
Kesimpulan
Studi ini menyelidiki pengaruh perilaku makan dan riwayat keluarga terhadap indikator pertumbuhan fisik, khususnya tinggi dan berat badan, sambil mengendalikan usia, jenis kelamin, dan status merokok. Setelah memastikan bahwa asumsi statistik termasuk normalitas multivariat, homogenitas kovarian, dan tidak adanya multikolinearitas terpenuhi, MANCOVA komprehensif dilakukan. Temuan tersebut mengungkapkan bahwa riwayat keluarga yang kelebihan berat badan, jenis kelamin, dan usia secara signifikan mempengaruhi tinggi dan berat badan. Jenis kelamin memiliki dampak individu yang paling kuat, terutama pada tinggi badan, sementara riwayat keluarga dan usia memainkan peran penting dalam menentukan berat badan. Variabel perilaku seperti makan diantara waktu makan (CAEC) juga menunjukkan efek yang sederhana tetapi signifikan secara statistik ketika kovariat disertakan, yang menunjukkan bahwa faktor gaya hidup tertentu dapat berkontribusi pada hasil pertumbuhan. Namun, konsumsi makanan berkalori tinggi yang sering (FAVC) dan status merokok tidak secara signifikan dikaitkan dengan tinggi atau berat badan dalam model ini. Hasil ini menggaris bawahi peran dominan faktor keturunan dan demografi dalam membentuk karakteristik antropometri. Strategi kesehatan masyarakat yang menargetkan pertumbuhan remaja dan pencegahan obesitas harus mempertimbangkan kecenderungan genetik dan intervensi khusus gender, sekaligus memperkuat kebiasaan makan sehat. Penelitian di masa mendatang harus memperluas variabel perilaku dengan data diet yang lebih terperinci dan pendekatan longitudinal untuk menangkap perubahan perkembangan dari waktu ke waktu.
Referensi
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