Attached below is a dataset that lists estimates of the percentage of body fat determined by underwater weighing and various body circumference measurements for 252 men from K.W. Penrose, A.G. Nelson, A.G. Fisher, FACSM, Human Performance Research Center, Brigham Young University, Provo, Utah 84602 as listed in Medicine and Science in Sports and Exercise, vol.17, no. 2, April 1985, p.189.

Some experts claim BMI (Body Mass Index) as the most accurate and simple way to determine the effect of weight on your health.Meanwhile, in September 2000, the American Journal of Clinical Nutrition published a study showing that body-fat percentage may be a better measure of your risk of weight-related diseases than BMI.

An important question that arises is whether there is a relationship between 'Body Fat Percentage' and 'Body Mass Index' as a predictor.

Body Mass Index is defined asBMI =weight (kgs) / Height ²(m)

With the use of the statistical techniques used in this programme (especially simple linear regression), explain whether BMI can be used to explain the Body Fat percentage for an individual based on the dataset provided. Clearly explain and interpret your results.

Body Fat (%) Height (m) Weight(kg)

12.3 1.72085 69.96662

6.1 1.83515 78.58488

25.3 1.68275 69.85322

10.4 1.83515 83.80119

28.7 1.80975 83.57439

20.9 1.89865 95.3678

19.2 1.77165 82.10022

12.4 1.8415 79.83226

4.1 1.8796 86.63614

11.7 1.8669 89.92469

7.1 1.8923 84.48158

7.8 1.9304 97.97595

20.8 1.7653 81.87342

21.2 1.80975 93.09983

22.1 1.7653 85.16197

20.9 1.6764 73.82216

29 1.8034 88.79071

22.9 1.8034 94.9142

16 1.72085 83.3476

16.5 1.8669 96.04818

19.1 1.7272 81.19303

15.2 1.77165 90.94527

15.6 1.73355 63.61633

17.7 1.778 67.47187

14 1.72085 68.60585

3.7 1.8161 72.23458

7.9 1.7145 59.6474

22.9 1.7145 67.13167

3.7 1.64465 60.44118

8.8 1.7526 72.91497

11.9 1.87325 82.55381

5.7 1.80975 72.68818

11.8 1.80975 76.20352

21.3 1.8034 99.10993

32.3 1.8669 112.1507

40.1 1.651 86.97634

24.2 1.778 91.73906

28.4 1.73355 89.2443

35.2 1.83515 164.7221

32.6 1.7018 92.07925

34.5 1.74625 119.1814

32.9 1.7493 92.98644

31.6 1.778 98.42954

32 1.8161 96.16158

7.7 1.7272 56.81244

13.9 1.86055 74.50255

10.8 1.7145 60.55458

5.6 1.80975 67.35847

13.6 1.7399 61.57516

4 1.69545 57.83303

10.2 1.83515 71.78099

6.6 1.7526 63.16274

8 1.72085 62.25555

6.3 1.8669 69.28623

3.9 1.7145 61.80196

22.6 1.8288 89.81129

20.4 1.7272 82.32702

28 1.7653 91.28546

31.5 1.79705 91.85245

24.6 1.67005 81.53323

26.1 1.86055 97.97595

29.8 1.7399 81.07964

30.7 1.78435 87.65673

25.8 1.7018 80.73944

32.3 1.778 93.21323

30 1.7145 83.2342

21.5 1.79705 68.71924

13.8 1.8161 70.19342

6.3 1.75895 70.42022

12.9 1.8161 71.1006

24.3 1.8161 75.97672

8.8 1.74625 66.56468

8.5 1.87325 72.91497

13.5 1.6256 56.69905

11.8 1.67005 64.86371

18.5 1.7145 67.24507

8.8 1.7653 73.70876

22.2 1.7399 80.62604

21.5 1.78435 73.14177

18.8 1.75895 77.67769

31.4 1.72085 74.27575

26.8 1.70815 68.15225

18.4 1.84785 86.29595

27 1.778 77.4509

27 1.75895 76.20352

26.6 1.7145 75.74993

14.9 1.70815 71.5542

23.1 1.67005 72.57478

8.3 1.8415 80.17245

14.1 1.8542 79.83226

20.5 1.778 80.28585

18.2 1.7653 81.53323

8.5 1.7907 74.95614

24.9 1.82245 87.31653

9 1.8923 83.57439

17.4 1.97485 101.8315

9.6 1.86055 85.61556

11.3 1.6891 73.70876

17.8 1.73355 70.98721

22.2 1.8288 89.3577

21.2 1.8669 90.03809

20.4 1.8288 78.81167

20.1 1.80975 78.35808

22.3 1.87325 89.2443

25.4 1.75895 80.28585

18 1.7399 75.06954

19.3 1.8669 90.83187

18.3 1.88595 92.19265

17.3 1.9177 87.99692

21.4 1.75895 76.43031

19.7 1.7399 77.4509

28 1.778 83.1208

22.1 1.778 80.85284

21.3 1.78435 73.93556

26.7 1.82245 79.49206

16.7 1.75895 71.66759

20.1 1.84785 80.39925

13.9 1.8288 81.19303

25.8 1.8796 86.63614

18.1 1.83515 85.04857

27.9 1.8923 93.66682

25.3 1.8161 84.02799

14.7 1.74625 72.68818

16 1.69545 68.71924

13.8 1.6891 73.02837

17.5 1.7018 75.74993

27.2 1.74625 80.51265

17.4 1.72085 69.05944

20.8 1.86055 87.20313

14.9 1.77165 74.95614

18.1 1.8161 77.90449

22.7 1.7907 77.67769

23.6 1.86055 89.3577

26.1 1.69545 71.214

24.4 1.7653 76.31692

27.1 1.77165 84.36818

21.8 1.79705 75.63653

29.4 1.8796 85.16197

22.4 1.80975 76.31692

20.4 1.905 96.50178

24.9 1.8034 80.17245

18.3 1.7653 78.58488

23.3 1.72085 75.74993

9.4 1.83515 72.46138

10.3 1.9685 85.3434

14.2 1.79705 70.76041

19.2 1.84785 94.57401

29.6 1.77165 93.66682

5.3 1.8415 65.2039

25.2 1.78435 101.1511

9.4 1.7526 69.05944

19.6 1.8923 109.656

10.1 1.83515 66.22449

16.5 1.70815 71.1006

21 1.8669 90.83187

17.3 1.91135 77.79109

31.2 1.7526 93.32663

10 1.83515 82.78061

12.5 1.74625 61.91536

22.5 1.8161 80.39925

9.4 1.83515 68.60585

14.6 1.8542 88.9041

13 1.74625 83.57439

15.1 1.7907 63.50293

27.3 1.8288 99.22333

19.2 1.87325 98.42954

21.8 1.7272 75.40973

20.3 1.83515 101.9449

34.3 1.7653 103.5325

16.5 1.7653 78.35808

3 1.72085 69.05944

0.7 1.6637 57.03924

20.5 1.8034 80.39925

16.9 1.8161 79.94566

25.3 1.82245 102.8521

9.9 1.75895 65.88429

13.1 1.7018 68.49245

29.9 1.8161 109.4292

22.5 1.75895 84.93517

16.9 1.8923 106.4808

26.6 1.88595 99.45013

0 1.7272 53.7507 11.5

1.70815 66.11109 12.1

1.77165 72.23458 17.5

1.88595 77.3375 8.6

1.8161 75.97672 23.6

1.88595 105.5736 20.4

1.8288 95.48119 20.5

1.8415 91.73906 24.4

1.73355 83.91459 11.4

1.75895 69.39963 38.1

1.9304 110.7899 15.9

1.7907 87.77012 24.7

1.89865 101.9449 22.8

1.84785 73.82216 25.5

1.73355 81.64663 22

1.7526 70.87381 17.7

1.8161 76.20352 6.6

1.84785 75.86332 23.6

1.7145 77.4509 12.2

1.78435 80.85284 22.1

1.75895 68.03886 28.7

1.8161 90.94527 6 1.8796

83.461 34.8 1.77165

101.1511 16.6 1.8542

94.68741 32.9 1.6637

75.29633 32.8 1.8415

88.45051 9.6 1.78435

72.80158 10.8 1.79705

72.46138 7.1 1.7272

63.72973 27.2 1.8923

98.08935 19.5 1.82245

76.31692 18.7 1.79705

88.33711 19.5 1.8542

78.35808 47.5 1.6256

99.33673 13.6 1.77165

67.69866 7.5 1.778

70.08002 24.5 1.82245

90.37828 15 1.75895

70.08002 12.4 1.7907

69.51303 26 1.83515

104.3262 11.5 1.7145

73.36857 5.2 1.70815

64.52351 10.9 1.74625

81.53323 12.5 1.69545

57.37943 14.8 1.73355

76.88391 25.2 1.88595

90.03809 14.9 1.7653

79.15187 17 1.7399 76.09012

10.6 1.67005 67.01827

16.1 1.82245 82.66721

15.4 1.8161 79.60546

26.7 1.70815 73.36857

25.8 1.7145 71.5542

18.6 1.7145 76.54371

24.8 1.83515 86.86294

27.3 1.7653 99.40477

12.4 1.7653 70.42022

29.9 1.67005 86.06915

17 1.67005 57.83303

35 1.73355 101.8315

30.4 1.8288 106.254

32.6 1.84785 103.3057

29 1.7399 90.49168

15.2 1.75895 70.53361

30.2 1.7907 97.74916

11 1.7018 60.89478

33.6 1.77165 91.17207

29.3 1.6764 84.70838

26 1.7907 86.52274

31.9 1.778 94.12042