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Table 3 Confidence interval of estimation (Confidence level is 95%)

From: Modeling the relationship between body weight and energy intake: A molecular diffusion-based approach

Week

Weight(kg)

Weight(kg)

Weight(kg)

Weight(kg)

Weight(kg)

Weight(kg)

Weight(kg)

Weight(kg)

Weight(kg)

Weight(kg)

Weight(kg)

Weight(kg)

S13

S14

S15

S16

S17

S18

S19

S20

S21

S22

S23

S24

Subject No.

            

122(p)

51.7

51.5

51

50

49.4

49

48.5

48.2

47.7

47.8

47.2

47.4

122(model)

51.588 ± 2.592

51.063 ± 2.443

50.504 ± 2.332

49.919 ± 2.241

49.476 ± 2.145

49.057 ± 2.059

48.728 ± 1.983

48.414 ± 1.919

48.17 ± 1.86

47.977 ± 1.817

47.858 ± 1.767

47.876 ± 1.745

123(p)

55.2

54.9

54.8

53.9

53.4

53

52

51.9

51.5

52.1

52.2

52.1

123(model)

55.229 ± 4.239

54.645 ± 3.992

54.029 ± 3.788

53.387 ± 3.637

52.889 ± 3.493

52.415 ± 3.364

52.032 ± 3.255

51.666 ± 3.143

51.369 ± 3.044

51.125 ± 2.952

50.956 ± 2.903

50.924 ± 2.881

119(p)

53.9

53.4

53.2

52.2

51.4

51

50.8

50.5

50.3

50.7

49.8

49.1

119(model)

53.95 ± 1.32

53.386 ± 1.244

52.79 ± 1.179

52.168 ± 1.149

51.69 ± 1.1

51.235 ± 1.068

50.871 ± 1.036

50.523 ± 1.001

50.245 ± 0.969

50.019 ± 0.94

49.868 ± 0.966

49.853 ± 0.941

120(p)

56.8

56

55.5

54.7

54

53.4

53

52.3

52.1

51.3

51.2

51.6

120(model)

57.099 ± 1.013

56.485 ± 0.975

55.839 ± 0.973

55.168 ± 0.949

54.641 ± 0.947

54.14 ± 0.975

53.729 ± 1.017

53.335 ± 1.051

53.012 ± 1.139

52.741 ± 1.188

52.547 ± 1.335

52.489 ± 1.436

129(p)

55.8

55.5

54.8

53.8

53.4

53.4

53.3

53.2

53

52.8

52.8

52.2

129(model)

55.524 ± 3.382

54.936 ± 3.191

54.314 ± 3.045

53.668 ± 2.915

53.165 ± 2.79

52.687 ± 2.681

52.3 ± 2.61

51.929 ± 2.572

51.628 ± 2.567

51.38 ± 2.575

51.207 ± 2.587

51.171 ± 2.62

130(p)

56.9

56.6

56.6

55.4

55.7

55.7

55.7

55.6

54.2

53.9

54.5

53.6

130(model)

56.902 ± 4.128

56.291 ± 3.888

55.648 ± 3.691

54.981 ± 3.561

54.457 ± 3.416

53.958 ± 3.349

53.55 ± 3.356

53.16 ± 3.422

52.839 ± 3.525

52.571 ± 3.48

52.379 ± 3.437

52.325 ± 3.48

126(p)

68.1

67.4

67.6

66

65.7

65.4

65.3

63

62

62.6

61.6

60.6

126(model)

68.316 ± 1.859

67.522 ± 1.757

66.699 ± 1.667

65.855 ± 1.677

65.156 ± 1.607

64.486 ± 1.571

63.91 ± 1.589

63.353 ± 1.691

62.869 ± 1.646

62.441 ± 1.649

62.09 ± 1.604

61.88 ± 1.576

127(p)

51.8

51.3

51.2

50.8

50.4

49.6

49.2

48.7

49.2

48.7

49.2

49.3

127(model)

51.982 ± 1.518

51.45 ± 1.435

50.885 ± 1.364

50.294 ± 1.312

49.845 ± 1.289

49.42 ± 1.274

49.085 ± 1.231

48.766 ± 1.19

48.515 ± 1.152

48.317 ± 1.165

48.193 ± 1.145

48.206 ± 1.205

22(p)

53.4

53

52.4

51.2

51.2

51.3

50.6

50.5

50

49.4

49.9

49.4

22(model)

53.261 ± 1.182

52.709 ± 1.117

52.123 ± 1.074

51.512 ± 1.037

51.044 ± 1.008

50.6 ± 0.971

50.246 ± 1.006

49.908 ± 0.988

49.639 ± 1.0

49.423 ± 0.985

49.282 ± 0.957

49.277 ± 0.973

23(p)

55

54.6

53.9

53.4

52.8

52.7

52.2

51.8

51.5

51.4

51.4

51.4

23(model)

55.229 ± 1.538

54.645 ± 1.457

54.029 ± 1.381

53.387 ± 1.318

52.889 ± 1.261

52.415 ± 1.211

52.032 ± 1.176

51.666 ± 1.139

51.369 ± 1.104

51.125 ± 1.073

50.956 ± 1.05

50.924 ± 1.041

19(p)

56.8

56.1

55.7

54.3

54

51.5

51.4

51.4

52.5

52.4

52.2

50.4

19(model)

56.902 ± 1.893

56.291 ± 1.784

55.648 ± 1.696

54.981 ± 1.615

54.457 ± 1.594

53.958 ± 1.551

53.55 ± 1.982

53.16 ± 2.207

52.839 ± 2.307

52.571 ± 2.243

52.379 ± 2.18

52.325 ± 2.123

20(p)

53

52.8

52.1

50.8

49.8

49.4

49.2

48.4

47.8

48.1

48.2

48

20(model)

53.36 ± 1.413

52.805 ± 1.353

52.218 ± 1.282

51.606 ± 1.223

51.136 ± 1.258

50.691 ± 1.414

50.335 ± 1.524

49.996 ± 1.582

49.726 ± 1.723

49.508 ± 1.909

49.365 ± 1.968

49.359 ± 1.986

29(p)

55.2

55.5

54.1

53.3

54.2

54

52.7

52.3

53

54.2

53.8

53.5

29(model)

53.95 ± 5.381

53.386 ± 5.136

52.79 ± 5.047

52.168 ± 4.87

51.69 ± 4.705

51.235 ± 4.722

50.871 ± 4.779

50.523 ± 4.709

50.245 ± 4.641

50.019 ± 4.69

49.868 ± 4.956

49.853 ± 5.142

30(p)

57

56.2

56

54.8

54.5

54.2

53.6

53.8

53.9

53.1

53.2

52.4

30(model)

57 ± 2.118

56.388 ± 1.995

55.743 ± 1.895

55.074 ± 1.811

54.549 ± 1.74

54.049 ± 1.67

53.639 ± 1.611

53.247 ± 1.556

52.925 ± 1.53

52.656 ± 1.556

52.463 ± 1.525

52.407 ± 1.522

26(p)

57.7

58

56.7

56.5

56

57.2

55.8

55.4

55.4

54.7

53.2

53.1

26(model)

57.492 ± 1.308

56.872 ± 1.24

56.22 ± 1.373

55.543 ± 1.339

55.01 ± 1.394

54.503 ± 1.444

54.086 ± 1.995

53.687 ± 2.116

53.358 ± 2.217

53.082 ± 2.362

52.881 ± 2.416

52.819 ± 2.355

27(p)

60.3

60

58.8

58.1

57.6

57.4

56.8

56.1

55.8

55.3

55.6

55.7

27(model)

60.149 ± 2.482

59.486 ± 2.34

58.792 ± 2.241

58.074 ± 2.135

57.501 ± 2.043

56.953 ± 1.961

56.497 ± 1.904

56.059 ± 1.845

55.692 ± 1.786

55.379 ± 1.732

55.142 ± 1.683

55.043 ± 1.651

4(p)

50

49.4

48.6

47.9

48.3

48.3

47.5

47.3

47.1

47.1

47.3

47.4

4(model)

49.916 ± 1.246

49.417 ± 1.175

48.884 ± 1.114

48.325 ± 1.074

47.908 ± 1.056

47.514 ± 1.037

47.209 ± 1.082

46.92 ± 1.055

46.7 ± 1.038

46.531 ± 1.025

46.435 ± 1.03

46.476 ± 1.077

5(p)

63.7

62.8

62.3

60.7

60

59.6

58.8

58.6

58.1

57.8

57.2

57.1

5(model)

63.888 ± 2.476

63.165 ± 2.336

62.412 ± 2.226

61.636 ± 2.121

61.006 ± 2.099

60.402 ± 2.09

59.891 ± 2.057

59.399 ± 2.063

58.978 ± 2.036

58.612 ± 2.018

58.323 ± 1.997

58.173 ± 2.009

1(p)

64.4

62.6

60.6

59.2

58.8

57.7

57.3

56.6

56.5

56.6

58.2

57

1(model)

64.183 ± 2.634

63.456 ± 2.485

62.698 ± 2.416

61.917 ± 2.622

61.282 ± 2.953

60.674 ± 3.146

60.159 ± 3.416

59.662 ± 3.608

59.237 ± 3.807

58.867 ± 3.918

58.574 ± 3.95

58.42 ± 3.848

2(p)

58.8

58.2

58.2

57.1

56.5

56.2

54.6

55.1

55.2

57.2

57.9

55.9

2(model)

59.46 ± 0.854

58.808 ± 0.916

58.125 ± 0.948

57.418 ± 0.904

56.855 ± 0.884

56.318 ± 0.871

55.872 ± 0.841

55.444 ± 1.041

55.087 ± 1.022

54.783 ± 0.992

54.556 ± 1.483

54.466 ± 2.094

11(p)

54.1

53.5

53.2

52.5

51.8

51.9

50.8

50.3

50

49.5

49.9

49.6

11(model)

53.852 ± 0.897

53.29 ± 0.861

52.695 ± 0.827

52.075 ± 0.844

51.597 ± 0.843

51.144 ± 0.817

50.782 ± 0.883

50.435 ± 0.853

50.158 ± 0.828

49.934 ± 0.806

49.784 ± 0.809

49.771 ± 0.789

12(p)

67.6

67.8

67.7

66.2

65.2

65.1

64.9

63.8

62.9

61.8

61.6

63.2

12(model)

67.922 ± 1.654

67.135 ± 1.573

66.318 ± 1.548

65.48 ± 1.691

64.787 ± 1.67

64.123 ± 1.619

63.552 ± 1.643

63.001 ± 1.73

62.523 ± 1.72

62.1 ± 1.678

61.755 ± 1.636

61.551 ± 1.593

8(p)

50.7

50.2

50.3

50.5

49.9

48.8

47.8

47.7

48.8

48.9

48.3

47.5

8(model)

53.36 ± 4.876

52.805 ± 4.92

52.218 ± 4.943

51.606 ± 4.846

51.136 ± 4.68

50.691 ± 4.543

50.335 ± 4.49

49.996 ± 4.525

49.726 ± 4.524

49.508 ± 4.409

49.365 ± 4.292

49.359 ± 4.205

9(p)

59.6

59.9

59.6

58

57.3

57.6

57.1

57.5

57.4

57.2

56.6

58.1

9(model)

59.755 ± 3.082

59.099 ± 2.905

58.411 ± 2.799

57.699 ± 2.759

57.132 ± 2.646

56.59 ± 2.541

56.14 ± 2.506

55.708 ± 2.469

55.346 ± 2.548

55.039 ± 2.661

54.807 ± 2.774

54.714 ± 2.82

104(p)

55.8

54.9

53.8

52.9

52.6

52.3

51.8

51.4

51.1

51.4

51.4

51.6

104(model)

56.016 ± 1.381

55.42 ± 1.308

54.791 ± 1.282

54.137 ± 1.358

53.627 ± 1.48

53.141 ± 1.529

52.746 ± 1.539

52.369 ± 1.563

52.061 ± 1.587

51.806 ± 1.606

51.626 ± 1.572

51.583 ± 1.533

105(p)

55.7

55

54.7

53.5

52.7

52.6

51.4

50.8

51.5

51.4

51.8

51.8

105(model)

55.918 ± 1.544

55.323 ± 1.462

54.695 ± 1.401

54.043 ± 1.334

53.534 ± 1.314

53.05 ± 1.342

52.657 ± 1.314

52.281 ± 1.423

51.974 ± 1.56

51.721 ± 1.53

51.542 ± 1.493

51.501 ± 1.458

101(p)

53.1

53.3

53.1

51.9

51.6

51.8

51.7

51.4

49.3

48.4

48.4

49.7

101(model)

53.064 ± 2.0

52.515 ± 1.884

51.933 ± 1.853

51.325 ± 1.898

50.859 ± 1.846

50.418 ± 1.818

50.067 ± 1.898

49.732 ± 2.015

49.467 ± 2.117

49.253 ± 2.054

49.114 ± 2.035

49.112 ± 2.007

102(p)

55.5

54.5

55.2

53.7

53.4

53.6

53

52.8

53

51.9

51.8

51.9

102(model)

55.721 ± 1.479

55.129 ± 1.401

54.505 ± 1.385

53.856 ± 1.383

53.35 ± 1.327

52.869 ± 1.274

52.478 ± 1.287

52.105 ± 1.271

51.801 ± 1.277

51.55 ± 1.365

51.374 ± 1.336

51.336 ± 1.315

111(p)

51.8

51.3

50.9

50.4

50.1

50.1

49.8

49.5

49.4

49.1

49

49.1

111(model)

51.588 ± 0.896

51.063 ± 0.855

50.504 ± 0.824

49.919 ± 0.82

49.476 ± 0.832

49.057 ± 0.869

48.728 ± 1.003

48.414 ± 1.113

48.17 ± 1.204

47.977 ± 1.308

47.858 ± 1.375

47.876 ± 1.435

112(p)

50.4

50.7

50.2

48.9

49

50.3

50.6

50.9

50.9

50.4

49

49

112(model)

50.014 ± 1.162

49.514 ± 1.124

48.979 ± 1.3

48.419 ± 1.438

48 ± 1.404

47.605 ± 1.455

47.299 ± 2.001

47.008 ± 2.567

46.786 ± 3.144

46.616 ± 3.632

46.519 ± 3.945

46.558 ± 4.001

108(p)

56.5

55.8

55.7

55.5

55

55.1

54.4

54.6

55.1

56.6

57.1

54.1

108(model)

56.804 ± 4.93

56.194 ± 4.648

55.553 ± 4.413

54.887 ± 4.204

54.364 ± 4.038

53.867 ± 3.891

53.461 ± 3.805

53.072 ± 3.705

52.752 ± 3.664

52.486 ± 3.728

52.295 ± 4.098

52.242 ± 4.545

109(p)

64.8

64.5

63.7

62.2

61.4

61.5

60.8

60.2

59.6

58.9

59.2

59.5

109(model)

64.675 ± 0.839

63.94 ± 0.795

63.174 ± 0.832

62.386 ± 0.852

61.744 ± 0.823

61.128 ± 0.812

60.605 ± 0.807

60.102 ± 0.785

59.669 ± 0.761

59.293 ± 0.739

58.993 ± 0.741

58.832 ± 0.727

  1. Note: 1)122(p) is actual experimental body weight value of subject 122, 122(model) is model body weight confidence interval of subject 122, etc.
  2. 2) In all 384 confidence intervals, 26 actual body weight values are outside the confidence interval, but 9 values from these 26 values are within the area of statistical handling error. So the unsatisfied rate of estimation is from 4.4% to 6.77%. It shows our model estimation is acceptable. 3)α is 5%. The confidence interval: estimated body weight ± t α / 2 ( n − 2 ) * S E , where SE is standard error, degree of freedom is n-2.