Indeks Massa Tubuh Titik Knot Orde 1 Orde 2 Orde 1 Orde 2 ke- MSE GCV MSE GCV MSE GCV MSE GCV Balita Laki-Laki

  IR

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  Ami Andayani, 2017. Rancangan Grafik Acuan Pertumbuhan Tinggi Badan

  

dan Indeks Massa Tubuh Balita di Kabupaten Lamongan dengan Pendekatan

Estimator Spline Truncated Birespon, Skripsi dibawah bimbingan Dr. Nur

Chamidah, M.Si dan Ir. Elly Ana, M.Si, Prodi S1-Statistika, Departemen

Matematika, Fakultas Sains dan Teknologi, Universitas Airlangga, Surabaya

  ABSTRAK Pemantauan status gizi terhadap balita sangat penting dilakukan karena masa

balita merupakan masa penting bagi tumbuh kembang anak. Pemantauan status gizi

balita dapat dilakukan dengan menggunakan Kartu Menuju Sehat (KMS)

diantaranya pada indeks antropometri tinggi badan menurut usia dan indeks massa

tubuh menurut usia. Kabupaten Lamongan merupakan daerah dengan kasus balita

stunting dan obesitas yang tinggi di Jawa Timur. Hal tersebut dapat disebabkan oleh

perbedaan karakteristik sampel yang digunakan dalam perancangan KMS standar

WHO 2005 dengan balita di Kabupaten Lamongan. Penelitian ini bertujuan untuk

merancang grafik acuan pertumbuhan tinggi badan dan indeks massa tubuh balita

di Kabupaten Lamongan dengan pendekatan estimator Spline Truncated birespon

yang dapat mengakomodasi pola data yang berubah pada titik tertentu seperti pola

pertumbuhan balita. Penelitian ini menggunakan data balita yang diperoleh dari

puskesmas dan klinik kandungan di Kabupaten Lamongan sebanyak 2135 data

masing-masing jenis kelamin. Kesimpulan dari penelitian ini adalah rancangan

grafik acuan pertumbuhan tinggi badan dan indeks massa tubuh balita dengan

pendekatan estimator Spline Truncated birespon baik dalam menggambarkan pola

pertumbuhan balita di Kabupaten Lamongan yang ditunjukkan oleh rata-rata nilai

R-Square untuk balita laki-laki dan perempuan masing-masing sebesar 99,82% dan

99,81%. Grafik acuan pertumbuhan berdasarkan estimator Spline Truncated pada

indeks TB/U lebih rendah dibandingkan KMS standar WHO 2005, sedangkan

grafik IMT/U lebih tinggi. Hal ini menunjukkan bahwa terdapat perbedaan

karakteristik balita di Kabupaten Lamongan dan sampel balita yang digunakan

WHO.

  Kata Kunci: Grafik Acuan Pertumbuhan, Spline Truncated, Birespon vii

  

SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  IR

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  Ami Andayani, 2017. Design Chart of Child Standard Growth for Heigh and

  

Body Mass Index in Lamongan Regency based on Spline Truncated Birespon

Estimator Approach, This thesis is under the guidance of Dr. Nur Chamidah, M.Si

and Ir. Elly Ana, M. Si, S1-Statistics Courses, Mathematics Department, Faculty of

Science and Technology, Airlangga University, Surabaya

  

ABSTRACT

Monitoring the nutritional status of child is very important because the

childhood is an important period for child growth. Monitoring the nutritional status

of under-five child can be done by using child growth chart standard called Kartu

Menuju Sehat (KMS), such as the anthropometry index of height for age and body

mass index for age. Lamongan regency is an area with high stunting and obesity

children in East Java. It can be caused by the characteristics of samples for

designing the child growth chart standard by WHO 2005 with children in

Lamongan regency. This study aims to design the growth chart standard of heigh

and body mass index in Lamongan regency based on Spline Truncated birespon

estimator approach that can accommodate the patterns of data that change at certain

points such as the child growth. This study uses data of children under five obtained

from health centers and clinics in Lamongan regency consist of 2135 data for each

gender. The conclusion of this research is the design of growth chart standard for

height and body mass index of child under five with Spline Truncated birespon

estimator approach good in depicting the growth of children in Lamongan Regency,

it is shown by the average of R-Square value for men and women child each obtain

by 99,82% and 99,81%. The growth chart standard based on Spline Truncated

estimator on H/A index is lower than The growth chart standard from WHO 2005,

ndicates that the chart is below the KMS based on WHO 2005, but it is higher on

BMI/A index. It indicates that there are differences characteristics between children

in Lamongan regency and the samples used by WHO.

  Keywords: Growth Chart Standard, Spline Truncated, Birespon viii

  

SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  IR

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI Lampiran 6. Kombinasi Titik Knot, Orde, MSE, dan GSE Tinggi Badan dan Indeks

  Massa Tubuh Balita Persentil Tinggi Badan Indeks Massa Tubuh Titik Knot Orde 1 Orde 2 Orde 1 Orde 2 ke- MSE GCV MSE GCV MSE GCV MSE GCV

  

Balita Laki-Laki

  6 7.782 8.608 5.997 6.868 0.497 0.550 0.440 0.504 12 5.303 5.865 5.237 5.997 0.567 0.628 0.523 0.600 24 7.591 8.396 5.618 6.434 0.576 0.637 0.568 0.650 36 9.716 10.75 6.489 7.431 0.574 0.635 0.569 0.652 48 10.33 11.43 6.971 7.983 0.570 0.630 0.559 0.640

  6,12 5.296 6.065 5.047 5.988 0.421 0.482 0.381 0.452 6,24 6.064 6.945 5.520 6.550 0.474 0.543 0.382 0.454 6,36 6.462 7.401 5.920 7.025 0.494 0.566 0.396 0.470 6,48 6.046 6.924 5.929 7.035 0.497 0.569 0.392 0.466

  12,24 5.241 6.003 5.230 6.205 0.563 0.645 0.458 0.543 12,36 5.125 5.869 5.203 6.173 0.567 0.650 0.480 0.570 12,48 4.545 5.205 4.919 5.836 0.564 0.646 0.478 0.567 24,36 7.558 8.656 5.064 6.009 0.574 0.657 0.547 0.649 24,48 7.307 8.368 4.785 5.677 0.570 0.652 0.537 0.637 36,48 9.549 10.94 5.377 6.380 0.569 0.652 0.543 0.645 3 6,12,24 5.241 6.219 5.022 6.177 0.416 0.493 0.375 0.462

  6,12,36 5.125 6.081 4.923 6.056 0.412 0.489 0.374 0.460 6,12,48 4.544 5.391 4.598 5.656 0.408 0.485 0.362 0.445 6,24,36 6.053 7.183 5.060 6.225 0.458 0.544 0.382 0.470 6,24,48 5.564 6.602 4.768 5.865 0.458 0.544 0.374 0.460 6,36,48 6.020 7.143 5.077 6.245 0.483 0.573 0.390 0.480

  12,24,36 5.103 6.054 4.980 6.126 0.554 0.657 0.457 0.562 12,24,48 4.489 5.326 4.654 5.725 0.552 0.655 0.452 0.556 12,36,48 4.368 5.183 4.650 5.719 0.560 0.665 0.475 0.584 24,36,48 6.603 7.834 4.784 5.885 0.569 0.676 0.537 0.660

  6,12,24,36 5.102 6.275 4.854 6.194 0.412 0.507 0.374 0.477 6,12,24,48 4.487 5.519 4.523 5.772 0.408 0.502 0.362 0.462 6,12,36,48 4.366 5.370 4.466 5.699 0.408 0.502 0.359 0.459 6,24,36,48 5.205 6.403 4.767 6.083 0.456 0.561 0.360 0.459

  12,24,36,48 4.356 5.358 4.626 5.903 0.551 0.678 0.432 0.551 6,12,24,36,48 4.356 5.558 4.465 5.914 0.408 0.521 0.355 0.470 6 5.676 6.278 4.136 4.737 0.450 0.498 0.407 0.466

  12 3.843 4.250 3.475 3.980 0.528 0.584 0.485 0.556 24 6.383 7.060 4.276 4.897 0.537 0.594 0.526 0.603 36 7.821 8.651 5.033 5.764 0.535 0.592 0.529 0.606 48 9.160 10.13 5.453 6.245 0.541 0.598 0.531 0.608

  6,12 3.819 4.373 3.414 4.050 0.378 0.433 0.354 0.419 6,24 4.365 5.000 3.925 4.657 0.435 0.499 0.364 0.432 15 6,36 4.264 4.884 4.110 4.877 0.449 0.514 0.389 0.462 6,48 4.277 4.898 4.103 4.869 0.450 0.515 0.396 0.470

  12,24 3.820 4.375 3.435 4.075 0.527 0.603 0.440 0.522 12,36 3.559 4.076 3.385 4.017 0.527 0.604 0.471 0.558 12,48 3.255 3.728 3.254 3.862 0.528 0.604 0.477 0.566 24,36 6.375 7.301 3.823 4.536 0.535 0.613 0.525 0.622 24,48 6.174 7.071 3.794 4.502 0.537 0.615 0.524 0.621 36,48 7.805 8.939 4.438 5.266 0.534 0.611 0.526 0.624

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  12,24,36 1.773 2.104 1.483 1.824 0.643 0.763 0.442 0.544 12,24,48 2.013 2.388 1.405 1.728 0.648 0.769 0.461 0.567 12,36,48 1.864 2.211 1.380 1.698 0.663 0.786 0.529 0.651 24,36,48 4.636 5.500 2.087 2.567 0.676 0.802 0.656 0.807

  48

  10.88 12.03 5.258 6.022 1.335 1.477 1.333 1.526

  36

  85 24 7.569 8.372 4.857 5.563 1.335 1.477 1.332 1.526

  12 4.938 5.462 4.225 4.839 1.335 1.477 1.261 1.445

  12,24,36,48 1.770 2.177 1.379 1.760 0.643 0.791 0.432 0.551 6,12,24,36,48 1.471 1.877 1.341 1.777 0.357 0.456 0.253 0.335 6 5.878 6.502 4.690 5.371 1.204 1.331 0.992 1.136

  6,12,24,36 1.473 1.812 1.454 1.856 0.357 0.440 0.258 0.329 6,12,24,48 1.673 2.058 1.379 1.760 0.358 0.440 0.260 0.332 6,12,36,48 1.491 1.834 1.344 1.715 0.358 0.440 0.262 0.335 6,24,36,48 1.823 2.243 1.415 1.806 0.456 0.561 0.266 0.340

  6,12,36 1.491 1.769 1.465 1.802 0.358 0.424 0.263 0.324 6,12,48 1.748 2.074 1.411 1.736 0.361 0.428 0.263 0.323 6,24,36 1.823 2.164 1.564 1.924 0.457 0.542 0.274 0.337 6,24,48 1.924 2.283 1.523 1.873 0.468 0.555 0.286 0.352 6,36,48 1.920 2.278 1.560 1.919 0.516 0.612 0.340 0.418

  IR

  12,24 2.197 2.516 1.508 1.789 0.654 0.748 0.463 0.550 12,36 1.865 2.136 1.524 1.808 0.665 0.761 0.531 0.630 12,48 2.021 2.314 1.491 1.770 0.665 0.762 0.553 0.656 24,36 4.640 5.314 2.328 2.763 0.676 0.775 0.656 0.778 24,48 4.636 5.309 2.450 2.907 0.677 0.775 0.658 0.781 36,48 6.371 7.297 3.159 3.749 0.676 0.775 0.667 0.791 50 6,12,24 1.831 2.173 1.468 1.806 0.360 0.427 0.260 0.320

  10.43 3.471 3.976 0.677 0.748 0.673 0.771 6,12 2.134 2.444 1.468 1.742 0.368 0.421 0.264 0.313 6,24 2.026 2.321 1.565 1.857 0.478 0.547 0.288 0.341 6,36 1.934 2.214 1.614 1.915 0.521 0.597 0.342 0.406 6,48 2.702 3.095 1.560 1.851 0.533 0.610 0.367 0.435

  12 2.328 2.575 1.525 1.746 0.665 0.736 0.577 0.660 24 4.645 5.138 2.450 2.806 0.678 0.750 0.666 0.763 36 6.543 7.237 3.160 3.619 0.677 0.749 0.672 0.770 48 9.432

  12,24,36,48 3.150 3.874 3.221 4.110 0.517 0.637 0.417 0.532 6,12,24,36,48 3.121 3.983 3.068 4.064 0.363 0.463 0.344 0.456 6 3.656 4.044 1.728 1.979 0.535 0.592 0.396 0.453

  6,12,24,36 3.325 4.090 3.244 4.139 0.364 0.448 0.349 0.445 6,12,24,48 3.140 3.862 3.122 3.983 0.366 0.451 0.352 0.450 6,12,36,48 3.182 3.914 3.126 3.989 0.363 0.446 0.352 0.450 6,24,36,48 3.929 4.832 3.579 4.567 0.418 0.514 0.348 0.444

  12,24,36 3.351 3.976 3.373 4.149 0.520 0.617 0.425 0.523 12,24,48 3.172 3.764 3.246 3.993 0.526 0.624 0.438 0.539 12,36,48 3.243 3.848 3.227 3.969 0.527 0.625 0.470 0.579 24,36,48 6.043 7.170 3.758 4.622 0.533 0.633 0.524 0.644

  6,12,24 3.771 4.474 3.270 4.023 0.366 0.435 0.352 0.433 6,12,36 3.479 4.128 3.248 3.995 0.365 0.433 0.354 0.435 6,12,48 3.185 3.780 3.130 3.850 0.374 0.444 0.353 0.434 6,24,36 4.186 4.966 3.673 4.518 0.421 0.500 0.354 0.436 6,24,48 3.935 4.669 3.582 4.407 0.433 0.514 0.363 0.447 6,36,48 4.113 4.880 3.768 4.635 0.449 0.533 0.389 0.478

  SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  14.90 16.48 5.079 5.817 1.335 1.477 1.334 1.528 6,12 4.516 5.172 4.181 4.961 0.858 0.983 0.665 0.789

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  11.96

  8.22 10.11 2.421 2.873 1.823 2.242 6,36,48

  12.53

  10.56

  9.89 12.16 2.415 2.865 1.728 2.125 6,24,48

  13.26

  11.17

  8.24 10.14 2.014 2.390 1.552 1.909 6,24,36

  14.19

  9.95 12.23 1.980 2.350 1.536 1.889 6,12,48

  11.84

  13.44

  11.33

  10.63 13.07 1.892 2.245 1.556 1.914 6,12,36

  13.18

  11.11

  10.61 12.59 2.609 2.988 2.608 3.095 6,12,24

  18.91

  16.51

  9.95 11.81 2.609 2.988 2.608 3.094 36,48

  9.98

  8.05 9.91 2.457 2.915 2.056 2.529 12,24,36

  14.01

  9.07 11.16 2.609 3.096 2.605 3.204 6,12,24,36

  11.89

  9.66

  8.22 10.49 1.883 2.316 1.549 1.976 6,12,36,48

  12.97

  10.54

  9.89 12.61 1.877 2.309 1.533 1.956 6,12,24,48

  13.65

  11.09

  16.31

  12.00

  13.75

  8.39 10.32 2.606 3.092 2.511 3.088 24,36,48

  12.50

  10.54

  8.60 10.57 2.601 3.086 2.358 2.901 12,36,48

  13.71

  11.56

  10.26 12.62 2.602 3.087 2.277 2.801 12,24,48

  14.24

  16.05

  97 24,48

  IR

  15.11

  25.95

  48

  11.78 13.49 2.611 2.888 2.609 2.988

  21.75

  19.66

  36

  11.79 13.50 2.611 2.888 2.610 2.990

  16.71

  24

  10.67 12.22 2.610 2.887 2.608 2.987 6,12

  12 12.46 13.78 11.63 13.32 2.609 2.886 2.546 2.916

  6 13.90 15.38 11.84 13.56 2.482 2.745 2.169 2.484

  12,24,36,48 4.282 5.267 2.844 3.629 1.334 1.641 1.055 1.346 6,12,24,36,48 3.628 4.629 2.743 3.634 0.774 0.988 0.642 0.851

  6,12,24,36 4.058 4.991 3.560 4.543 0.774 0.952 0.649 0.829 6,12,24,48 3.959 4.870 2.841 3.625 0.776 0.955 0.661 0.843 6,12,36,48 3.636 4.472 2.755 3.515 0.822 1.011 0.652 0.832 6,24,36,48 3.775 4.643 2.783 3.552 1.135 1.396 0.718 0.916

  12,24,36 4.732 5.615 3.623 4.456 1.335 1.584 1.072 1.319 12,24,48 4.690 5.565 2.910 3.579 1.334 1.583 1.125 1.383 12,36,48 4.302 5.104 2.846 3.500 1.334 1.583 1.231 1.514 24,36,48 7.133 8.464 3.661 4.503 1.334 1.583 1.331 1.638

  6,12,24 4.080 4.841 3.989 4.907 0.780 0.925 0.662 0.815 6,12,36 4.141 4.913 3.664 4.507 0.827 0.981 0.654 0.805 6,12,48 4.515 5.357 2.906 3.574 0.850 1.008 0.661 0.813 6,24,36 4.176 4.955 3.684 4.532 1.137 1.349 0.735 0.904 6,24,48 4.023 4.774 2.964 3.646 1.145 1.359 0.788 0.969 6,36,48 3.964 4.703 2.926 3.599 1.183 1.403 0.922 1.134

  12,24 4.783 5.478 4.152 4.926 1.335 1.529 1.141 1.353 12,36 4.736 5.424 3.858 4.577 1.335 1.529 1.234 1.465 12,48 4.934 5.651 3.100 3.678 1.335 1.529 1.251 1.484 24,36 7.434 8.514 4.813 5.711 1.335 1.529 1.332 1.581 24,48 7.157 8.196 4.210 4.995 1.335 1.528 1.332 1.581 36,48 9.538 10.92 4.902 5.817 1.334 1.528 1.331 1.580

  6,24 4.179 4.786 3.994 4.740 1.147 1.314 0.807 0.957 6,36 4.634 5.307 3.691 4.380 1.183 1.355 0.931 1.105 6,48 5.719 6.550 2.966 3.519 1.194 1.368 0.968 1.148

  SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  28.71

  11.99

  11.50 13.64 2.610 2.989 2.605 3.091

  13.79

  17.11

  14.94

  8.85 10.50 2.609 2.988 2.543 3.017 24,36

  14.19

  12.39

  10.60 12.58 2.608 2.987 2.524 2.995 12,48

  13.80

  12.05

  11.30 13.41 2.604 2.982 2.399 2.847 12,36

  12.04

  13.73

  15.84 8.25 9.785 2.468 2.827 2.147 2.547 12,24

  13.83

  9.99 11.85 2.457 2.814 2.086 2.475 6,48

  13.69

  11.95

  10.76 12.77 2.422 2.774 1.876 2.226 6,36

  12.80

  11.17

  11.45 13.59 2.024 2.319 1.574 1.867 6,24

  8.02 10.24 1.970 2.423 1.535 1.959

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  24

  5.71

  6.31

  5.17 5.93 0.374 0.414 0.267 0.306

  12

  4.42

  4.89

  4.39 5.03 0.493 0.545 0.369 0.423

  6.74

  7.28 9.65 0.576 0.735 0.491 0.650

  7.46

  4.56 5.22 0.529 0.585 0.476 0.545

  36

  8.61

  9.52

  5.40 6.19 0.529 0.585 0.501 0.574

  48

  6

  9.36

  11.64

  7.28 9.29 0.585 0.719 0.502 0.640 6,12,36,48

  11.37

  7.42 9.13 0.733 0.870 0.682 0.839 6,12,24,36

  7.39

  9.09

  7.29 9.30 0.589 0.725 0.528 0.673 6,12,24,48

  7.37

  9.06

  7.37

  7.34

  9.06

  7.32 9.34 0.577 0.710 0.491 0.626 6,24,36,48

  7.91

  9.73

  7.41 9.45 0.610 0.750 0.510 0.650 12,24,36,48

  7.37

  9.07

  7.34 9.36 0.705 0.867 0.602 0.768 6,12,24,36,48

  10.53

  6.18 7.08 0.528 0.584 0.520 0.595 6,12

  7.44 9.16 0.709 0.841 0.633 0.778 24,36,48

  9.49

  6.67

  7.64

  4.43 5.25 0.526 0.602 0.468 0.556 24,48

  6.68

  7.65

  4.48 5.31 0.526 0.602 0.470 0.558 36,48

  8.29

  5.17 6.13 0.527 0.604 0.491 0.583 6,12,24

  5.06

  4.33

  5.13

  4.27 5.25 0.282 0.334 0.247 0.304 6,12,36

  4.27

  5.07

  4.29 5.28 0.286 0.339 0.249 0.306 6,12,48

  4.34

  5.15

  4.39 5.21 0.479 0.549 0.362 0.430 24,36

  4.41

  4.36

  4.76 5.65 0.337 0.385 0.261 0.310

  4.99

  4.31 5.12 0.289 0.331 0.249 0.295 6,24

  4.77

  5.46

  4.41 5.24 0.301 0.345 0.250 0.296 6,36

  5.01

  5.74

  15 6,48

  4.35 5.16 0.469 0.537 0.356 0.422 12,48

  5.48

  6.27

  5.04 5.98 0.354 0.405 0.263 0.312 12,24

  4.42

  5.06

  4.29 5.09 0.437 0.501 0.326 0.386 12,36

  4.37

  5.01

  9.58

  8.81

  IR

  8.00

  48

  12.42

  13.74

  9.49 10.87 0.749 0.828 0.744 0.852 6,12

  7.43

  8.50

  7.37 8.75 0.590 0.675 0.534 0.634 6,24

  9.16

  12.60

  7.52 8.93 0.622 0.712 0.557 0.661 6,36

  8.19

  9.38

  8.04 9.54 0.642 0.735 0.563 0.668 6,48

  8.31

  9.52

  8.42 9.99 0.666 0.763 0.542 0.643 12,24

  8.58 9.83 0.749 0.829 0.746 0.854

  11.39

  8.51

  8.38 10.70 2.601 3.199 2.263 2.887 6,12,24,36,48

  SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  6,24,36,48

  9.77

  12.02

  7.90 10.08 2.411 2.966 1.711 2.184 12,24,36,48

  10.52

  12.93

  9.65

  36

  12.31

  7.87 10.42 1.877 2.395 1.530 2.026

  

Balita Perempuan

  6 8.315 9.198 8.580 9.826 0.668 0.738 0.583 0.668 12 7.498 8.293 7.578 8.678 0.739 0.817 0.678 0.776

  24

  9.88

  10.93

  7.59 8.69 0.750 0.830 0.730 0.836

  7.43

  7.39 8.76 0.717 0.821 0.650 0.771 12,36

  7.43

  7.44 9.15 0.612 0.727 0.540 0.664 6,36,48

  8.75

  7.37 9.07 0.587 0.697 0.517 0.636 6,24,36

  7.95

  9.43

  7.41 9.11 0.621 0.736 0.557 0.685 6,24,48

  7.91

  9.39

  8.08

  7.36 9.05 0.589 0.699 0.534 0.657 6,12,48

  9.58

  7.87 9.68 0.621 0.736 0.539 0.663 12,24,36

  7.43

  8.81

  7.34 9.03 0.717 0.850 0.650 0.799 12,24,48

  7.41

  8.79

  7.34 9.03 0.710 0.842 0.632 0.777 12,36,48

  7.37

  8.79

  7.46

  7.42 8.81 0.748 0.856 0.710 0.843 24,48

  8.54

  7.51 8.91 0.727 0.833 0.657 0.780 12,48

  7.43

  8.50

  7.57 8.98 0.739 0.846 0.635 0.754 24,36

  9.60

  11.00

  9.65

  7.41

  11.06

  7.47 8.87 0.748 0.856 0.685 0.812 36,48

  11.05

  12.65

  8.28 9.82 0.739 0.847 0.688 0.817 3 6,12,24

  7.39

  8.77

  7.31 9.00 0.589 0.699 0.533 0.656 6,12,36

  4.31 5.30 0.286 0.339 0.248 0.306

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  1.51 1.86 0.548 0.650 0.464 0.571 24,36,48

  2.15

  1.42 1.75 0.546 0.647 0.411 0.506 12,24,48

  1.74

  2.07

  1.52 1.88 0.546 0.648 0.425 0.523 12,36,48

  1.73

  2.06

  4.05

  2.00 2.46 0.447 0.531 0.339 0.417 12,24,36

  4.81

  1.53 1.89 0.563 0.668 0.544 0.669 6,12,24,36

  1.60

  1.97

  1.42 1.81 0.364 0.448 0.283 0.361 6,12,24,48

  1.52

  1.87

  1.52 1.94 0.362 0.446 0.286 0.365 6,12,36,48

  1.81

  2.56

  1.87

  1.50 1.84 0.368 0.436 0.287 0.353 6,12,48

  6.37

  7.30

  2.98 3.53 0.564 0.646 0.553 0.656 50 6,12,24

  1.76

  2.09

  1.53 1.88 0.364 0.432 0.290 0.356 6,12,36

  1.60

  1.90

  1.56

  2.15

  1.85

  1.52 1.87 0.372 0.441 0.286 0.352 6,24,36

  1.93

  2.29

  1.48 1.83 0.428 0.508 0.297 0.365 6,24,48

  1.82

  2.16

  1.68 2.07 0.433 0.514 0.307 0.377 6,36,48

  1.52

  1.49 1.90 0.363 0.446 0.286 0.365 6,24,36,48

  4.79

  4.20

  8.69

  3.12 3.57 1.149 1.271 1.140 1.305

  85

  48

  13.27

  14.67

  3.37 3.86 1.169 1.293 1.128 1.292 6,12

  3.67

  2.43 2.88 0.954 1.092 0.814 0.966 6,24

  36

  2.66

  3.04

  2.42 2.88 1.029 1.178 0.853 1.012 6,36

  2.96

  3.39

  2.21 2.62 1.038 1.188 0.915 1.086 6,48

  5.10

  5.84

  7.86

  2.94 3.36 1.153 1.276 1.143 1.309

  1.82

  6

  2.24

  1.40 1.78 0.423 0.521 0.296 0.378 12,24,36,48

  1.73

  2.13

  1.36 1.73 0.542 0.666 0.410 0.523 6,12,24,36,48

  1.51

  1.93

  1.36 1.79 0.361 0.461 0.283 0.375

  6.15

  5.42

  6.80

  2.82 3.23 1.038 1.148 0.930 1.065

  12

  3.76

  4.16

  2.43 2.79 1.145 1.266 1.078 1.234

  24

  4.90

  1.99 2.36 0.563 0.645 0.547 0.649 36,48

  4.19

  IR

  5.22

  4.43 5.44 0.525 0.623 0.468 0.576 6,12,24,36

  4.27

  5.25

  4.26 5.44 0.282 0.346 0.243 0.310 6,12,24,48

  4.33

  5.32

  4.25 5.43 0.282 0.347 0.247 0.315 6,12,36,48

  4.25

  4.27 5.45 0.286 0.351 0.248 0.316 6,24,36,48

  6.66

  4.74

  5.84

  4.35 5.55 0.295 0.363 0.239 0.305 12,24,36,48

  4.30

  5.29

  4.27 5.45 0.432 0.531 0.303 0.386 6,12,24,36,48

  4.23

  5.40

  7.90

  4.31 5.31 0.469 0.556 0.356 0.437 24,36,48

  6

  4.92

  SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  6,24,36

  4.77

  5.66

  4.35 5.35 0.298 0.353 0.243 0.299 6,24,48

  4.77

  5.65

  4.37 5.37 0.301 0.357 0.249 0.306 6,36,48

  5.84

  5.16

  4.65 5.72 0.336 0.399 0.261 0.321 12,24,36

  4.34

  5.15

  4.27 5.26 0.434 0.515 0.310 0.382 12,24,48

  4.41

  5.24

  4.27 5.25 0.437 0.519 0.323 0.398 12,36,48

  4.35

  4.25 5.64 0.280 0.357 0.239 0.316

  3.61

  1.65 1.96 0.565 0.648 0.546 0.648 24,48

  2.30

  1.73 2.05 0.433 0.496 0.317 0.377 6,36

  2.18

  2.49

  2.01 2.38 0.448 0.513 0.347 0.412 6,48

  2.52

  2.88

  2.05 2.43 0.449 0.514 0.357 0.424 12,24

  2.01

  1.54 1.82 0.547 0.626 0.437 0.518 12,36

  1.99

  1.83

  2.10

  1.52 1.80 0.550 0.630 0.472 0.560 12,48

  1.74

  2.00

  1.54 1.82 0.548 0.628 0.480 0.569 24,36

  4.21

  4.83

  2.28

  1.53 1.82 0.372 0.426 0.290 0.344 6,24

  3.99

  2.10 2.41 0.566 0.626 0.547 0.626

  2.09 2.39 0.456 0.504 0.359 0.412

  12

  2.15

  2.37

  1.54 1.76 0.551 0.609 0.481 0.551

  24

  4.22

  4.67

  36

  2.32

  6.39

  7.07

  3.07 3.51 0.569 0.629 0.553 0.634

  48

  8.41

  9.30

  3.47 3.97 0.572 0.633 0.557 0.638 6,12

  2.03

  2.05 2.43 1.037 1.188 0.930 1.103

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  9.22

  6.60

  7.56

  4.56 5.40 2.355 2.697 2.329 2.763 24,36

  8.17

  9.36

  5.84 6.93 2.303 2.637 2.348 2.786 24,48

  8.05

  5.43 6.45 2.355 2.698 2.314 2.746 36,48

  6.35

  9.54

  10.93

  5.72 6.79 2.336 2.676 2.285 2.711 97 6,12,24

  5.58

  6.62

  5.34 6.57 1.993 2.365 1.538 1.892 6,12,36

  5.21

  6.18

  5.07 6.01 2.327 2.666 2.283 2.709 12,48

  5.55

  6.46

  6.52

  17.34

  19.18

  5.90 6.76 2.356 2.606 2.350 2.691 6,12

  6.64

  7.61

  5.41 6.42 2.066 2.367 1.538 1.825 6,24

  5.69

  5.36 6.36 2.258 2.586 1.729 2.052 6,36

  5.42 6.43 2.364 2.708 2.134 2.532 12,36

  5.83

  6.67

  4.91 5.83 2.279 2.610 1.941 2.303 6,48

  8.39

  9.61

  4.45 5.28 2.280 2.612 2.055 2.438 12,24

  6.01

  6.88

  4.90 6.03 1.954 2.319 1.530 1.882 6,12,48

  7.66

  5.93 6.79 2.338 2.587 2.354 2.696

  5.60

  5.19

  6.38

  4.49 5.73 1.954 2.404 1.515 1.933 6,12,24,48

  5.56

  6.84

  4.27 5.45 1.989 2.447 1.476 1.883 6,12,36,48

  4.56

  4.37 5.57 1.942 2.389 1.472 1.878 6,24,36,48

  9.13

  4.85

  5.97

  4.44 5.66 2.127 2.616 1.597 2.037 12,24,36,48

  4.89

  6.01

  4.25 5.43 2.285 2.811 2.009 2.563 6,12,24,36,48

  4.55

  5.80

  5.34 6.57 2.288 2.715 2.282 2.807 6,12,24,36

  7.70

  4.41 5.43 2.030 2.408 1.494 1.838 6,24,36

  5.89

  5.44

  6.45

  4.78 5.88 2.146 2.546 1.620 1.993 6,24,48

  5.67

  6.72

  4.44 5.46 2.236 2.653 1.602 1.971 6,36,48

  4.97

  4.44 5.46 2.278 2.703 1.777 2.186 12,24,36

  4.46 5.48 2.322 2.756 2.152 2.647 24,36,48

  5.55

  6.58

  4.50 5.53 2.300 2.730 2.032 2.500 12,24,48

  6.01

  7.13

  4.29 5.28 2.355 2.794 2.014 2.478 12,36,48

  4.96

  5.89

  48

  12.24

  IR

  1.94 2.39 0.949 1.126 0.791 0.973 6,24,36

  3.04

  2.38 2.93 0.924 1.097 0.814 1.001 6,12,36

  2.35

  2.78

  2.16 2.66 0.924 1.096 0.805 0.990 6,12,48

  3.36

  3.99

  2.48

  3.07 3.65 1.141 1.306 1.126 1.337 6,12,24

  2.95

  2.20 2.71 1.007 1.194 0.789 0.971 6,24,48

  2.66

  3.15

  2.04 2.51 1.028 1.220 0.798 0.981 6,36,48

  2.51

  2.98

  2.05 2.52 1.035 1.229 0.868 1.068 12,24,36

  2.56

  7.93

  3.13

  2.23 2.64 1.140 1.306 1.071 1.270 12,48

  SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  12,24

  2.98

  3.41

  2.41 2.86 1.145 1.311 1.008 1.196 12,36

  2.65

  3.03

  3.50

  6.92

  4.00

  2.00 2.37 1.145 1.311 1.076 1.277 24,36

  4.90

  5.61

  2.89 3.43 1.149 1.316 1.139 1.352 24,48

  4.85

  5.56

  2.72 3.23 1.153 1.321 1.128 1.339 36,48

  2.64

  1.99 2.45 1.134 1.346 0.931 1.146 12,24,48

  11.06

  5.77 6.61 2.282 2.524 2.060 2.359

  1.88 2.40 1.124 1.382 0.930 1.186 6,12,24,36,48

  2.04

  2.61

  1.88 2.48 0.912 1.164 0.775 1.026

  6

  9.23

  10.20

  12

  2.38

  6.75

  7.46

  5.44 6.23 2.368 2.619 2.329 2.668

  24

  8.19

  9.06

  6.03 6.91 2.366 2.617 2.350 2.691

  36

  2.93

  2.04 2.60 0.994 1.223 0.786 1.003 12,24,36,48

  2.97

  2.29

  3.53

  1.90 2.33 1.145 1.358 0.948 1.166 12,36,48

  2.39

  2.84

  1.96 2.41 1.134 1.346 1.029 1.265 24,36,48

  4.74

  5.63

  2.64 3.25 1.140 1.353 1.123 1.382 6,12,24,36

  2.82

  2.78

  1.99 2.54 0.921 1.133 0.780 0.995 6,12,24,48

  2.56

  3.15

  1.89 2.41 0.924 1.137 0.778 0.993 6,12,36,48

  2.05

  2.52

  1.93 2.46 0.913 1.123 0.787 1.005 6,24,36,48

  2.26

  4.24 5.62 1.941 2.477 1.471 1.949 IR

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  

Lampiran 7. Program Estimasi Tinggi Badan dan Indeks Massa Tubuh Balita dengan

Pendekatan Estimator Spline Truncated Birespon

  mp<-function(x,eps=1e-006) { x<-as.matrix(x) xsvd<-svd(x) diago<-xsvd$d[xsvd$d>eps] if(length(diago)==1) { xplus<-as.matrix(xsvd$v[,1])%*%t(as.matrix(xsvd$u[,1])/diago) } else {

  xplus<-xsvd$v[,1:length(diago)]%*%diag(1/diago)%*% t(xsvd$u[,1:length(diago)])

  } return(xplus) } trun<-function(prediktor,knot,orde) { prediktor[prediktor<knot]<-knot b<-(prediktor-knot)^orde return(b)

  } spline<-function(data) { x<-data[,1] y1<-data[,2] y2<-data[,3] n<-nrow(data) #Error Tinggi Badan e1<-rep(0,n) p1<-as.numeric(readline("Orde Tinggi Badan = ")) k1<-as.numeric(readline("Banyak Knot Tinggi Badan = ")) w1<-rep(0,k1) cat("Jumlah Knot Tinggi Badan = ",k1,"\n") v11<-matrix(0,n,p1+1) for(i in 1:p1) { v11[,i]<-x^(i-1) v11[,p1+1]<-x^(p1)

  } v21<-matrix(0,n,k1) for(i in 1:k1) { v21[,i]<-trun(x,w1[i],p1) } X11<-cbind(v11,v21) betatopi1<-mp(t(X11)%*%X11)%*%t(X11)%*%y1 ytopi1<-X11%*%betatopi1 er1<-rep(0,n) er1=y1-ytopi1 H1<-X11%*%mp(t(X11)%*%X11)%*%t(X11) MSE1<-(t(y1-ytopi1)%*%(y1-ytopi1))/n GCV1<-MSE1/(1-(sum(diag(H1)))/n)^2 JKT1<-t(y1-(mean(y1)))%*%(y1-(mean(y1))) JKG1<-t(y1-ytopi1)%*%(y1-ytopi1)

  SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  IR

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  R1<-1-(JKG1/JKT1) cat("MSE Estimasi TB dengan Spline Truncated Unirespon =",MSE1,"\n") cat("GCV Estimasi TB dengan Spline Truncated Unirespon =",GCV1,"\n") cat("R-Square Estimasi TB dengan Spline Truncated Unirespon =",R1,"\n") cat("\n") #Error Indeks Massa Tubuh e2<-rep(0,n) p2<-as.numeric(readline("Orde Indeks Massa Tubuh = ")) k2<-as.numeric(readline("Banyak Knot Indeks Massa Tubuh = ")) w2<-rep(0,k2) cat("Jumlah Knot Indeks Massa Tubuh = ",k2,"\n") v12<-matrix(0,n,p2+1) for(i in 1:p2) { v12[,i]<-x^(i-1) v12[,p2+1]<-x^(p2)

  } v22<-matrix(0,n,k2) for(i in 1:k2) { v22[,i]<-trun(x,w2[i],p2) } X22<-cbind(v12,v22) betatopi2<-mp(t(X22)%*%X22)%*%t(X22)%*%y2 ytopi2<-X22%*%betatopi2 er2<-rep(0,n) er2=y2-ytopi2 H2<-X22%*%mp(t(X22)%*%X22)%*%t(X22) MSE2<-(t(y2-ytopi2)%*%(y2-ytopi2))/n GCV2<-MSE2/(1-(sum(diag(H2)))/n)^2 JKT2<-t(y2-(mean(y2)))%*%(y2-(mean(y2))) JKG2<-t(y2-ytopi2)%*%(y2-ytopi2) R2<-1-(JKG2/JKT2) cat("MSE Estimasi IMT dengan Spline Truncated Unirespon =",MSE2,"\n") cat("GCV Estimasi IMT dengan Spline Truncated Unirespon =",GCV2,"\n") cat("R-Square Estimasi IMT dengan Spline Truncated Unirespon =",R2,"\n") plot(x,y1,xlab="Usia",ylab="TB",type="p") lines(x,ytopi1,xlab="Usia",ylab="TB") title(main="U VS TB UNIRESPON") cat("\n") win.graph() plot(x,y2,xlab="Usia",ylab="IMT",type="p") lines(x,ytopi2,xlab="Usia",ylab="IMT") title(main="U VS IMT UNIRESPON") win.graph() #Membuat Matriks Pembobot W E<-rep(0,2,n) E<-cbind(er1,er2)

  VC<-rep(0,2,2)

  VC<-var(E) cat("Var-Covar TB dan IMT \n") print(VC) W1<-cbind(a,b)

  

SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  IR

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  W2<-cbind(b,d) W<-rbind(W1,W2) #Weighted Spline Truncated Birespon n<-length(x) y<-c(y1,y2) Xa<-matrix(0,n,(p2+k2+1)) Xb<-matrix(0,n,(p1+k1+1)) A<-cbind(X11,Xa) B<-cbind(Xb,X22) X<-rbind(A,B)

  IW<-mp(W) betatopi<-mp(t(X)%*%IW%*%X)%*%t(X)%*%IW%*%y ytopi<-X%*%betatopi H<-X%*%mp(t(X)%*%IW%*%X)%*%t(X)%*%IW MSE<-(t(y-ytopi)%*%IW%*%(y-ytopi))/n GCV<-MSE/(1-(sum(diag(H)))/n)^2 JKT<-t(y-(mean(y)))%*%(y-(mean(y))) JKG<-t(y-ytopi)%*%(y-ytopi) R<-1-(JKG/JKT) cat("\n") cat("=============================\n Nilai Betatopi Tinggi Badan \n =============================\n") for(i in 1:(p1+k1+1)) { cat("Beta",i-1,"=",betatopi[i],"\n") } cat("\n") cat("===================================\n") cat("Nilai Betatopi Indeks Massa Tubuh \n") cat("====================================\n") for(i in (p1+k1+2):length(betatopi)) { cat("Beta",i-(p1+k1+2),"=",betatopi[i],"\n") } Y1<-rep(0,n) Y2<-rep(0,n) Y1<-ytopi[1:n] Y2<-ytopi[(n+1):(2*n)] cat("\n") cat("HASIL ESTIMASI TINGGI BADAN DAN INDEKS MASSA TUBUH BALITA\n") cat("=========================================\n") cat("Usia \t\t TB \t\t IMT \n") cat("=========================================\n") for(i in 1:n) { cat(i-1,"\t\t",Y1[i],"\t",Y2[i],"\n") } cat("\n") cat("MSE Estimasi TB dan IMT dengan Spline Truncated Birespon =",MSE,"\n") cat("GCV Estimasi TB dan IMT dengan Spline Truncated Birespon =",GCV,"\n") cat("R-Square Estimasi TB dan IMT dengan Spline Truncated Birespon =",R,"\n") plot(x,y1,xlab="Usia",ylab="TB",type="p") lines(x,Y1,xlab="Usia",ylab="TB",col="red",lwd=3) title(main="PLOT USIA TERHADAP TINGGI BADAN") win.graph() plot(x,y2,xlab="Usia",ylab="IMT",type="p") lines(x,Y2,xlab="Usia",ylab="IMT",col="blue",lwd=3) title(main="PLOT USIA TERHADAP INDEKS MASSA TUBUH") }

  

SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  IR

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  Balita Laki-Laki:

1. P3

  Orde Tinggi Badan = 1 Banyak Knot Tinggi Badan = 3 Jumlah Knot Tinggi Badan = 3 Titik knots[ 1 ] = 12 Titik knots[ 2 ] = 36 Titik knots[ 3 ] = 48 MSE Estimasi TB dengan Spline Truncated Unirespon = 4.367902 GCV Estimasi TB dengan Spline Truncated Unirespon = 5.182705 R-Square Estimasi TB dengan Spline Truncated Unirespon = 0.9734129 Orde Indeks Massa Tubuh = 2 Banyak Knot Indeks Massa Tubuh = 3 Jumlah Knot Indeks Massa Tubuh = 3 Titik knots[ 1 ] = 6 Titik knots[ 2 ] = 12 Titik knots[ 3 ] = 48 MSE Estimasi IMT dengan Spline Truncated Unirespon = 0.3620817 GCV Estimasi IMT dengan Spline Truncated Unirespon = 0.4453904 R-Square Estimasi IMT dengan Spline Truncated Unirespon = 0.5301371 Var-Covar TB dan IMT [,1] [,2] [1,] 4.4407005 0.3429389 [2,] 0.3429389 0.3681164 ============================= Nilai Betatopi Tinggi Badan ============================= Beta 0 = 46.32181 Beta 1 = 1.810533 Beta 2 = -1.256006 Beta 3 = 0.2287139 Beta 4 = -0.6975229 =================================== Nilai Betatopi Indeks Massa Tubuh ==================================== Beta 0 = 11.59663 Beta 1 = 1.431151 Beta 2 = -0.1462756 Beta 3 = 0.170239 Beta 4 = -0.0234522 Beta 5 = -0.008828764 HASIL ESTIMASI TINGGI BADAN DAN INDEKS MASSA TUBUH BALITA ========================================= Usia TB IMT ========================================= 0 46.32181 11.59663 1 48.13234 12.88151 2 49.94288 13.87383 3 51.75341 14.57361 4 53.56394 14.98083 5 55.37448 15.0955 6 57.18501 14.91762 7 58.99554 14.61743 8 60.80608 14.36516 9 62.61661 14.16082 10 64.42714 14.00441

  

SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  IR

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  11 66.23767 13.89593 12 68.04821 13.83537 13 68.60273 13.79928 14 69.15726 13.76422 15 69.71179 13.73018 16 70.26631 13.69717 17 70.82084 13.66517 18 71.37537 13.6342 19 71.92989 13.60425 20 72.48442 13.57532 21 73.03895 13.54742 22 73.59348 13.52053 23 74.148 13.49467 24 74.70253 13.46984 25 75.25706 13.44602 26 75.81158 13.42323 27 76.36611 13.40146 28 76.92064 13.38071 29 77.47516 13.36098 30 78.02969 13.34228 31 78.58422 13.3246 32 79.13874 13.30794 33 79.69327 13.2923 34 80.2478 13.27769 35 80.80232 13.2641 36 81.35685 13.25153 37 82.14009 13.23998 38 82.92333 13.22946 39 83.70657 13.21995 40 84.48981 13.21147 41 85.27305 13.20402 42 86.0563 13.19758 43 86.83954 13.19217 44 87.62278 13.18778 45 88.40602 13.18441 46 89.18926 13.18206 47 89.9725 13.18074 48 90.75574 13.18044 49 90.84146 13.17233 50 90.92718 13.14759 51 91.01289 13.10621 52 91.09861 13.0482 53 91.18433 12.97355 54 91.27005 12.88227 55 91.35576 12.77435 56 91.44148 12.64979 57 91.5272 12.5086 58 91.61292 12.35078 59 91.69864 12.17632 60 91.78435 11.98523 MSE Estimasi TB dan IMT dengan Spline Truncated Birespon = 1.966304 GCV Estimasi TB dan IMT dengan Spline Truncated Birespon = 2.926646 R-Square Estimasi TB dan IMT dengan Spline Truncated Birespon = 0.9978141

  SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  IR

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA

  U VS TB UNIRESPON _{90 14 15} U VS IMT UNIRESPON _{TB 60}

  80 _{70 IM T 12 13}

  50 _{10 20 Usia 30 40 50 60 10 20 Usia 30 40 50 60 90} PLOT USIA TERHADAP TINGGI BADAN PLOT USIA TERHADAP INDEKS MASSA TUBUH _{14 15 TB}

  80 _{60 70 IM T 13 50 10 20 Usia Usia 30 40 50 60}

  12 _{10 20 30 40 50 60}

2. P15

  Orde Tinggi Badan = 1 Banyak Knot Tinggi Badan = 2 Jumlah Knot Tinggi Badan = 2 Titik knots[ 1 ] = 12 Titik knots[ 2 ] = 48 MSE Estimasi TB dengan Spline Truncated Unirespon = 3.255013 GCV Estimasi TB dengan Spline Truncated Unirespon = 3.727886 R-Square Estimasi TB dengan Spline Truncated Unirespon = 0.9820574 Orde Indeks Massa Tubuh = 2 Banyak Knot Indeks Massa Tubuh = 2 Jumlah Knot Indeks Massa Tubuh = 2 Titik knots[ 1 ] = 6 Titik knots[ 2 ] = 12 MSE Estimasi IMT dengan Spline Truncated Unirespon = 0.3535375 GCV Estimasi IMT dengan Spline Truncated Unirespon = 0.4194876 R-Square Estimasi IMT dengan Spline Truncated Unirespon = 0.5124048 Var-Covar TB dan IMT [,1] [,2] [1,] 3.3092631 0.1108217 [2,] 0.1108217 0.3594298 ============================= Nilai Betatopi Tinggi Badan ============================= Beta 0 = 48.68564 Beta 1 = 1.787461

  

SKRIPSI RANCANGAN GRAFIK ACUAN... AMI ANDAYANI

  IR

• – PERPUSTAKAAN UNIVERSITAS AIRLANGGA