Using R, consider the dataset bodyfat Re-compute body fat percentage using the “

Question

Using R, consider the dataset bodyfat

Re-compute body fat percentage using the “Density” variable and Siri’s equation: (495/Density) – 450

D. Form a new predictor variable as the ratio of weight on height. Compute the correlation between the body fat percentage and weight/height ratio, and fit another simple regression model for body fat percentage versus the weight/height ratio (again, provide population model, parameter estimates…). Is the ratio a better predictor than weight or height separately? (Again, use the coefficients of determination R^2 ).

E. Do weight/height ratio and abdomen circumference seem to “capture” the same underlying information? (To address this, you will have to look at the relationship between the weight/height ratio and abdomen circumference, in particular their correlation, and possibly the regression of one on the other).

Density SiriBFperc Over45 Weight Height NeckC ChestC AbdomenC HipC ThighC KneeC AnkleC BicepsC Forearm WristC

1.0708 12.3 0 154.25 67.75 36.2 93.1 85.2 94.5 59 37.3 21.9 32 27.4 17.1

1.0853 6.1 0 173.25 72.25 38.5 93.6 83 98.7 58.7 37.3 23.4 30.5 28.9 18.2

1.0414 25.3 0 154 66.25 34 95.8 87.9 99.2 59.6 38.9 24 28.8 25.2 16.6

1.0751 10.4 0 184.75 72.25 37.4 101.8 86.4 101.2 60.1 37.3 22.8 32.4 29.4 18.2

1.034 28.7 0 184.25 71.25 34.4 97.3 100 101.9 63.2 42.2 24 32.2 27.7 17.7

1.0502 20.9 0 210.25 74.75 39 104.5 94.4 107.8 66 42 25.6 35.7 30.6 18.8

1.0549 19.2 0 181 69.75 36.4 105.1 90.7 100.3 58.4 38.3 22.9 31.9 27.8 17.7

1.0704 12.4 0 176 72.5 37.8 99.6 88.5 97.1 60 39.4 23.2 30.5 29 18.8

1.09 4.1 0 191 74 38.1 100.9 82.5 99.9 62.9 38.3 23.8 35.9 31.1 18.2

1.0722 11.7 0 198.25 73.5 42.1 99.6 88.6 104.1 63.1 41.7 25 35.6 30 19.2

1.083 7.1 0 186.25 74.5 38.5 101.5 83.6 98.2 59.7 39.7 25.2 32.8 29.4 18.5

1.0812 7.8 0 216 76 39.4 103.6 90.9 107.7 66.2 39.2 25.9 37.2 30.2 19

1.0513 20.8 0 180.5 69.5 38.4 102 91.6 103.9 63.4 38.3 21.5 32.5 28.6 17.7

1.0505 21.2 0 205.25 71.25 39.4 104.1 101.8 108.6 66 41.5 23.7 36.9 31.6 18.8

1.0484 22.1 0 187.75 69.5 40.5 101.3 96.4 100.1 69 39 23.1 36.1 30.5 18.2

1.0512 20.9 0 162.75 66 36.4 99.1 92.8 99.2 63.1 38.7 21.7 31.1 26.4 16.9

1.0333 29 0 195.75 71 38.9 101.9 96.4 105.2 64.8 40.8 23.1 36.2 30.8 17.3

1.0468 22.9 0 209.25 71 42.1 107.6 97.5 107 66.9 40 24.4 38.2 31.6 19.3

1.0622 16 0 183.75 67.75 38 106.8 89.6 102.4 64.2 38.7 22.9 37.2 30.5 18.5

1.061 16.5 0 211.75 73.5 40 106.2 100.5 109 65.8 40.6 24 37.1 30.1 18.2

1.0551 19.1 0 179 68 39.1 103.3 95.9 104.9 63.5 38 22.1 32.5 30.3 18.4

1.064 15.2 0 200.5 69.75 41.3 111.4 98.8 104.8 63.4 40.6 24.6 33 32.8 19.9

1.0631 15.6 0 140.25 68.25 33.9 86 76.4 94.6 57.4 35.3 22.2 27.9 25.9 16.7

1.0584 17.7 0 148.75 70 35.5 86.7 80 93.4 54.9 36.2 22.1 29.8 26.7 17.1

1.0668 14 0 151.25 67.75 34.5 90.2 76.3 95.8 58.4 35.5 22.9 31.1 28 17.6

1.0911 3.7 0 159.25 71.5 35.7 89.6 79.7 96.5 55 36.7 22.5 29.9 28.2 17.7

1.0811 7.9 0 131.5 67.5 36.2 88.6 74.6 85.3 51.7 34.7 21.4 28.7 27 16.5

1.0468 22.9 0 148 67.5 38.8 97.4 88.7 94.7 57.5 36 21 29.2 26.6 17

1.091 3.7 0 133.25 64.75 36.4 93.5 73.9 88.5 50.1 34.5 21.3 30.5 27.9 17.2

1.079 8.8 0 160.75 69 36.7 97.4 83.5 98.7 58.9 35.3 22.6 30.1 26.7 17.6

1.0716 11.9 0 182 73.75 38.7 100.5 88.7 99.8 57.5 38.7 33.9 32.5 27.7 18.4

1.0862 5.7 0 160.25 71.25 37.3 93.5 84.5 100.6 58.5 38.8 21.5 30.1 26.4 17.9

1.0719 11.8 0 168 71.25 38.1 93 79.1 94.5 57.3 36.2 24.5 29 30 18.8

1.0502 21.3 0 218.5 71 39.8 111.7 100.5 108.3 67.1 44.2 25.2 37.5 31.5 18.7

1.0263 32.3 0 247.25 73.5 42.1 117 115.6 116.1 71.2 43.3 26.3 37.3 31.7 19.7

1.0101 40.1 1 191.75 65 38.4 118.5 113.1 113.8 61.9 38.3 21.9 32 29.8 17

1.0438 24.2 0 202.25 70 38.5 106.5 100.9 106.2 63.5 39.9 22.6 35.1 30.6 19

1.0346 28.4 1 196.75 68.25 42.1 105.6 98.8 104.8 66 41.5 24.7 33.2 30.5 19.4

1.0202 35.2 1 363.15 72.25 51.2 136.2 148.1 147.7 87.3 49.1 29.6 45 29 21.4

1.0258 32.6 1 203 67 40.2 114.8 108.1 102.5 61.3 41.1 24.7 34.1 31 18.3

1.0217 34.5 0 262.75 68.75 43.2 128.3 126.2 125.6 72.5 39.6 26.6 36.4 32.7 21.4

1.025 32.9 0 205 29.5 36.6 106 104.3 115.5 70.6 42.5 23.7 33.6 28.7 17.4

1.0279 31.6 1 217 70 37.3 113.3 111.2 114.1 67.7 40.9 25 36.7 29.8 18.4

1.0269 32 0 212 71.5 41.5 106.6 104.3 106 65 40.2 23 35.8 31.5 18.8

1.0814 7.7 0 125.25 68 31.5 85.1 76 88.2 50 34.7 21 26.1 23.1 16.1

1.067 13.9 0 164.25 73.25 35.7 96.6 81.5 97.2 58.4 38.2 23.4 29.7 27.4 18.3

1.0742 10.8 0 133.5 67.5 33.6 88.2 73.7 88.5 53.3 34.5 22.5 27.9 26.2 17.3

1.0665 5.6 0 148.5 71.25 34.6 89.8 79.5 92.7 52.7 37.5 21.9 28.8 26.8 17.9

1.0678 13.6 0 135.75 68.5 32.8 92.3 83.4 90.4 52 35.8 20.6 28.8 25.5 16.3

1.0903 4 1 127.5 66.75 34 83.4 70.4 87.2 50.6 34.4 21.9 26.8 25.8 16.8

1.0756 10.2 1 158.25 72.25 34.9 90.2 86.7 98.3 52.6 37.2 22.4 26 25.8 17.3

1.084 6.6 0 139.25 69 34.3 89.2 77.9 91 51.4 34.9 21 26.7 26.1 17.2

1.0807 8 1 137.25 67.75 36.5 89.7 82 89.1 49.3 33.7 21.4 29.6 26 16.9

1.0848 6.3 1 152.75 73.5 35.1 93.3 79.6 91.6 52.6 37.6 22.6 38.5 27.4 18.5

1.0906 3.9 0 136.25 67.5 37.8 87.6 77.6 88.6 51.9 34.9 22.5 27.7 27.5 18.5

1.0473 22.6 1 198 72 39.9 107.6 100 99.6 57.2 38 22 35.9 30.2 18.9

1.0524 20.4 1 181.5 68 39.1 100 99.8 102.5 62.1 39.6 22.5 33.1 28.3 18.5

1.0356 28 1 201.25 69.5 40.5 111.5 104.2 105.8 61.8 39.8 22.7 37.7 30.9 19.2

1.028 31.5 1 202.5 70.75 40.5 115.4 105.3 97 59.1 38 22.5 31.6 28.8 18.2

1.043 24.6 1 179.75 65.75 38.4 104.8 98.3 99.6 60.6 37.7 22.9 34.5 29.6 18.5

1.0396 26.1 1 216 73.25 41.4 112.3 104.8 103.1 61.6 40.9 23.1 36.2 31.8 20.2

1.0317 29.8 1 178.75 68.5 35.6 102.9 94.7 100.8 60.9 38 22.1 32.5 29.8 18.3

1.0298 30.7 1 193.25 70.25 38 107.6 102.4 99.4 61 39.4 23.6 32.7 29.9 19.1

1.0403 25.8 1 178 67 37.4 105.3 99.7 99.7 60.8 40.1 22.7 33.6 29 18.8

1.0264 32.3 1 205.5 70 40.1 105.3 105.5 108.3 65 41.2 24.7 35.3 31.1 18.4

1.0313 30 1 183.5 67.5 40.9 103 100.3 104.2 64.8 40.2 22.7 34.8 30.1 18.7

1.0499 21.5 1 151.5 70.75 35.6 90 83.9 93.9 55 36.1 21.7 29.6 27.4 17.4

1.0673 13.8 1 154.75 71.5 36.9 95.4 86.6 91.8 54.3 35.4 21.5 32.8 27.4 18.7

1.0847 6.3 1 155.25 69.25 37.5 89.3 78.4 96.1 56 37.4 22.4 32.6 28.1 18.1

1.0693 12.9 1 156.75 71.5 36.3 94.4 84.6 94.3 51.2 37.4 21.6 27.3 27.1 17.3

1.0439 24.3 1 167.5 71.5 35.5 97.6 91.5 98.5 56.6 38.6 22.4 31.5 27.3 18.6

1.0788 8.8 1 146.75 68.75 38.7 88.5 82.8 95.5 58.9 37.6 21.6 30.3 27.3 18.3

1.0796 8.5 1 160.75 73.75 36.4 93.6 82.9 96.3 52.9 37.5 23.1 29.7 27.3 18.2

1.068 13.5 1 125 64 33.2 87.7 76 88.6 50.9 35.4 19.1 29.3 25.7 16.9

1.072 11.8 1 143 65.75 36.5 93.4 83.3 93 55.5 35.2 20.9 29.4 27 16.8

1.0666 18.5 1 148.25 67.5 36 91.6 81.8 94.8 54.5 37 21.4 29.3 27 18.3

1.079 8.8 1 162.5 69.5 38.7 91.6 78.8 94.3 56.7 39.7 24.2 30.2 29.2 18.1

1.0483 22.2 1 177.75 68.5 38.7 102 95 98.3 55 38.3 21.8 30.8 25.7 18.8

1.0498 21.5 1 161.25 70.25 37.8 96.4 95.4 99.3 53.5 37.5 21.5 31.4 26.8 18.3

1.056 18.8 1 171.25 69.25 37.4 102.7 98.6 100.2 56.5 39.3 22.7 30.3 28.7 19

1.0283 31.4 1 163.75 67.75 38.4 97.7 95.8 97.1 54.8 38.2 23.7 29.4 27.2 19

1.0382 26.8 1 150.25 67.25 38.1 97.1 89 96.9 54.8 38 22 29.9 25.2 17.7

1.0568 18.4 1 190.25 72.75 39.3 103.1 97.8 99.6 58.9 39 23 34.3 29.6 19

1.0377 27 1 170.75 70 38.7 101.8 94.9 95 56 36.5 24.1 31.2 27.3 19.2

1.0378 27 1 168 69.25 38.5 101.4 99.8 96.2 56.3 36.6 22 29.7 26.3 18

1.0386 26.6 1 167 67.5 36.5 98.9 89.7 96.2 54.7 37.8 33.7 32.4 27.7 18.2

1.0648 14.9 1 157.75 67.25 37.7 97.5 88.1 96.9 57.2 37.7 21.8 32.6 28 18.8

1.0462 23.1 1 160 65.75 36.5 104.3 90.9 93.8 57.8 39.5 23.3 29.2 28.4 18.1

1.08 8.3 1 176.75 72.5 38 97.3 86 99.3 61 38.4 23.8 30.2 29.3 18.8

1.0666 14.1 1 176 73 36.7 96.7 86.5 98.3 60.4 39.9 24.4 28.8 29.6 18.7

1.052 20.5 1 177 70 37.2 99.7 95.6 102.2 58.3 38.2 22.5 29.1 27.7 17.7

1.0573 18.2 0 179.75 69.5 39.2 101.9 93.2 100.6 58.9 39.7 23.1 31.4 28.4 18.8

1.0795 8.5 1 165.25 70.5 37.5 97.2 83.1 95.4 56.9 38.3 22.1 30.1 28.2 18.4

1.0424 24.9 1 192.5 71.75 38 106.6 97.5 100.6 58.9 40.5 24.5 33.3 29.6 19.1

1.0785 9 1 184.25 74.5 37.3 99.6 88.8 101.4 57.4 39.6 24.6 30.3 27.9 17.8

1.0991 17.4 1 224.5 77.75 41.1 113.2 99.2 107.5 61.7 42.3 23.2 32.9 30.8 20.4

1.077 9.6 0 188.75 73.25 37.5 99.1 91.6 102.4 60.6 39.4 22.9 31.6 30.1 18.5

1.073 11.3 1 162.5 66.5 38.7 99.4 86.7 96.2 62.1 39.3 23.3 30.6 27.8 18.2

1.0582 17.8 1 156.5 68.25 35.9 95.1 88.2 92.8 54.7 37.3 21.9 31.6 27.5 18.2

1.0484 22.2 1 197 72 40 107.5 94 103.7 62.7 39 22.3 35.3 30.9 18.3

1.0506 21.2 1 198.5 73.5 40.1 106.5 95 101.7 59 39.4 22.3 32.2 31 18.6

1.0524 20.4 1 173.75 72 37 99.1 92 98.3 59.3 38.4 22.4 27.9 26.2 17

1.053 20.1 0 172.75 71.25 36.3 96.7 89.2 98.3 60 38.4 23.2 31 29.2 18.4

1.048 22.3 1 196.75 73.75 40.7 103.5 95.5 101.6 59.1 39.8 25.4 31 30.3 19.7

1.0412 25.4 0 177 69.25 39.6 104 98.6 99.5 59.5 36.1 22 30.1 27.2 17.7

1.0578 18 0 165.5 68.5 31.1 93.1 87.3 96.6 54.7 39 24.8 31 29.4 18.8

1.0547 19.3 0 200.25 73.5 38.6 105.2 102.8 103.6 61.2 39.3 23.5 30.5 28.5 18.1

1.0569 18.3 1 203.25 74.25 42 110 101.6 100.7 55.8 38.7 23.4 35.1 29.6 19.1

1.0593 17.3 0 194 75.5 38.5 110.1 88.7 102.1 57.5 40 24.8 35.1 30.7 19.2

1.05 21.4 0 168.5 69.25 34.2 97.8 92.3 100.6 57.5 36.8 22.8 32.1 26 17.3

1.0538 19.7 0 170.75 68.5 37.2 96.3 90.6 99.3 61.9 38 22.3 33.3 28.2 18.1

1.0355 28 0 183.25 70 37.1 108 105 103 63.7 40 23.6 33.5 27.8 17.4

1.0486 22.1 1 178.25 70 40.2 99.7 95 98.6 62.3 38.1 23.9 35.3 31.1 19.8

1.0503 21.3 0 163 70.25 35.3 93.5 89.6 99.8 61.5 37.8 21.9 30.7 27.6 17.4

1.0384 26.7 1 175.25 71.75 38 100.7 92.4 97.5 59.3 38.1 21.8 31.8 27.3 17.5

1.0607 16.7 0 158 69.25 36.3 97 86.6 92.6 55.9 36.3 22.1 29.8 26.3 17.3

1.0529 20.1 1 177.25 72.75 36.8 96 90 99.7 58.8 38.4 22.8 29.9 28 18.1

1.0671 13.9 1 179 72 41 99.2 90 96.4 56.8 38.8 23.3 33.4 29.8 19.5

1.0404 25.8 0 191 74 38.3 95.4 92.4 104.3 64.6 41.1 24.8 33.6 29.5 18.5

1.0575 18.1 0 187.5 72.25 38 101.8 87.5 101 58.5 39.2 24.5 32.1 28.6 18

1.0358 27.9 1 206.5 74.5 40.8 104.3 99.2 104.1 58.5 39.3 24.6 33.9 31.2 19.5

1.0414 25.3 0 185.25 71.5 39.5 99.2 98.1 101.4 57.1 40.5 23.2 33 29.6 18.4

1.0652 14.7 0 160.25 68.75 36.9 99.3 83.3 97.5 60.5 38.7 22.6 34.4 28 17.6

1.0623 16 1 151.5 66.75 36.9 94 86.1 95.2 58.1 36.5 22.1 30.6 27.5 17.6

1.0674 13.8 1 161 66.5 37.7 98.9 84.1 94 58.5 36.6 23.5 34.4 29.2 18

1.0587 17.5 1 167 67 36.6 101 89.9 100 60.7 36 21.9 35.6 30.2 17.6

1.0373 27.2 0 177.5 68.75 38.9 98.7 92.1 98.5 60.7 36.8 22.2 33.8 30.3 17.2

1.059 17.4 0 152.25 67.75 37.5 95.9 78 93.2 53.5 35.8 20.8 33.9 28.2 17.4

1.0515 20.8 0 192.25 73.25 39.8 103.9 93.5 99.5 61.7 39 21.8 33.3 29.6 18.1

1.0648 14.9 0 165.25 69.75 38.3 96.2 87 97.8 57.4 36.9 22.2 31.6 27.8 17.7

1.0575 18.1 1 171.75 71.5 35.5 97.8 90.1 95.8 57 38.7 23.2 27.5 26.5 17.6

1.0472 22.7 0 171.25 70.5 36.3 94.6 90.3 99.1 60.3 38.5 23 31.2 28.4 17.1

1.0452 23.6 1 197 73.25 37.8 103.6 99.8 103.2 61.2 38.1 22.6 33.5 28.6 17.9

1.0398 26.1 1 157 66.75 37.8 100.4 89.4 92.3 56.1 35.6 20.5 33.6 29.3 17.3

1.0435 24.4 0 168.25 69.5 36.5 98.4 87.2 98.4 56 36.9 23 34 29.8 18.1

1.0374 27.1 0 186 69.75 37.8 104.6 101.1 102.1 58.9 37.9 22.7 30.9 28.8 17.6

1.0491 21.8 0 166.75 70.75 37 92.9 86.1 95.6 58.8 36.1 22.4 32.7 28.3 17.1

1.0325 29.4 0 187.75 74 37.7 97.8 98.6 100.6 63.6 39.2 23.8 34.3 28.4 17.7

1.0481 22.4 0 168.25 71.25 34.3 98.3 88.5 98.3 58.1 38.4 22.5 31.7 27.4 17.6

1.0522 20.4 1 212.75 75 40.8 104.7 106.6 107.7 66.5 42.5 24.5 35.5 29.8 18.7

1.0422 24.9 0 176.75 71 37.4 98.6 93.1 101.6 59.1 39.6 21.6 30.8 27.9 16.6

1.0571 18.3 0 173.25 69.5 36.5 99.5 93 99.3 60.4 38.2 22 32 28.5 17.8

1.0459 23.3 1 167 67.75 37.5 102.7 91 98.9 57.1 36.7 22.3 31.6 27.5 17.9

1.0775 9.4 0 159.75 72.25 35.5 92.1 77.1 93.9 56.1 36.1 22.7 30.5 27.2 18.2

1.0754 10.3 0 188.15 77.5 38 96.6 85.3 102.5 59.1 37.6 23.2 31.8 29.7 18.3

1.0664 14.2 0 156 70.75 35.7 92.7 81.9 95.3 56.4 36.5 22 33.5 28.3 17.3

1.055 19.2 0 208.5 72.75 39.2 102 99.1 110.1 71.2 43.5 25.2 36.1 30.3 18.7

1.0322 29.6 0 206.5 69.75 40.9 110.9 100.5 106.2 68.4 40.8 24.6 33.3 29.7 18.4

1.0873 5.3 0 143.75 72.5 35.2 92.3 76.5 92.1 51.9 35.7 22 25.8 25.2 16.9

1.0416 25.2 0 223 70.25 40.6 114.1 106.8 113.9 67.6 42.7 24.7 36 30.4 18.4

1.0776 9.4 0 152.25 69 35.4 92.9 77.6 93.5 56.9 35.9 20.4 31.6 29 17.8

1.0542 19.6 0 241.75 74.5 41.8 108.3 102.9 114.4 72.9 43.5 25.1 38.5 33.8 19.6

1.0758 10.1 0 146 72.25 34.1 88.5 72.8 91.1 53.6 36.8 23.8 27.8 26.3 17.4

1.061 16.5 0 156.75 67.25 37.9 94 88.2 95.2 56.8 37.4 22.8 30.6 28.3 17.9

1.051 21 0 200.25 73.5 38.2 101.1 100.1 105 62.1 40 24.9 33.7 29.2 19.4

1.0594 17.3 0 171.5 75.25 35.6 92.1 83.5 98.3 57.3 37.8 21.7 32.2 27.7 17.7

1.0287 31.2 0 205.75 69 38.5 105.6 105 106.4 68.6 40 25.2 35.2 30.7 19.1

1.0761 10 0 182.5 72.25 37 98.5 90.8 102.5 60.8 38.5 25 31.6 28 18.6

1.0704 12.5 0 136.5 68.75 35.9 88.7 76.6 89.8 50.1 34.8 21.8 27 34.9 16.9

1.0477 22.5 0 177.25 71.5 36.2 101.1 92.4 99.3 59.4 39 24.6 30.1 28.2 18.2

1.0775 9.4 0 151.25 72.25 35 94 81.2 91.5 52.5 36.6 21 27 26.3 16.5

1.0653 14.6 0 196 73 38.5 103.8 95.6 105.1 61.4 40.6 25 31.3 29.2 19.1

1.069 13 0 184.25 68.75 40.7 98.9 92.1 103.5 64 37.3 23.5 33.5 30.6 19.7

1.0644 15.1 0 140 70.5 36 89.2 83.4 89.6 52.4 35.6 20.4 28.3 26.2 16.5

1.037 27.3 0 218.75 72 39.5 111.4 106 108.8 63.8 42 23.4 34 31.2 18.5

1.0549 19.2 0 217 73.75 40.5 107.5 95.1 104.5 64.8 41.3 25.6 36.4 33.7 19.4

1.0492 21.8 0 166.25 68 38.5 99.1 90.4 95.6 55.5 34.2 21.9 30.2 28.7 17.7

1.0525 20.3 0 224.75 72.25 43.9 108.2 100.4 106.8 63.3 41.7 24.6 37.2 33.1 19.8

1.018 34.3 0 228.25 69.5 40.4 114.9 115.9 111.9 74.4 40.6 24 36.1 31.8 18.8

1.061 16.5 0 172.75 69.5 37.6 99.1 90.8 98.1 60.1 39.1 23.4 32.5 29.8 17.4

1.0926 3 0 152.25 67.75 37 92.2 81.9 92.8 54.7 36.2 22.1 30.4 27.4 17.7

1.0983 0.7 0 125.75 65.5 34 90.8 75 89.2 50 34.8 22 24.8 25.9 16.9

1.0521 20.5 0 177.25 71 38.4 100.5 90.3 98.7 57.8 37.3 22.4 31 28.7 17.7

1.0603 16.9 0 176.25 71.5 38.7 98.2 90.3 99.9 59.2 37.7 21.5 32.4 28.4 17.8

1.0414 25.3 0 226.75 71.75 41.5 115.3 108.8 114.4 69.2 42.4 24 35.4 21 20.1

1.0763 9.9 0 145.25 69.25 36 96.8 79.4 89.2 50.3 34.8 22.2 31 26.9 16.9

1.0689 13.1 0 151 67 35.3 92.6 83.2 96.4 60 38.1 22 31.5 26.6 16.7

1.0316 29.9 0 241.25 71.5 42.1 119.2 110.3 113.9 69.8 42.6 24.8 34.4 29.5 18.4

1.0477 22.5 0 187.25 69.25 38 102.7 92.7 101.9 64.7 39.5 24.7 34.8 30.3 18.1

1.0603 16.9 0 234.75 74.5 42.8 109.5 104.5 109.9 69.5 43.1 25.8 39.1 32.5 19.9

1.0387 26.6 0 219.25 74.25 40 108.5 104.6 109.8 68.1 42.8 24.1 35.6 29 19

1.1089 0 0 118.5 68 33.8 79.3 69.4 85 47.2 33.5 20.2 27.7 24.6 16.5

1.0725 11.5 0 145.75 67.25 35.5 95.5 83.6 91.6 54.1 36.2 21.8 31.4 28.3 17.2

1.0713 12.1 0 159.25 69.75 35.3 92.3 86.8 96.1 58 39.4 22.7 30 26.4 17.4

1.0587 17.5 0 170.5 74.25 37.7 98.9 90.4 95.5 55.4 38.9 22.4 30.5 28.9 17.7

1.0794 8.6 0 167.5 71.5 39.4 89.5 83.7 98.1 57.3 39.7 22.6 32.9 29.3 18.2

1.0453 23.6 0 232.75 74.25 41.9 117.5 109.3 108.8 67.7 41.3 24.7 37.2 31.8 20

1.0524 20.4 0 210.5 72 38.5 107.4 98.9 104.1 63.5 39.8 23.5 36.4 30.4 19.1

1.052 20.5 0 202.25 72.5 40.8 109.2 98 101.8 62.8 41.3 24.8 36.6 32.4 18.8

1.0434 24.4 0 185 68.25 38 103.4 101.2 103.1 61.5 40.4 22.9 33.4 29.2 18.5

1.0728 11.4 0 153 69.25 36.4 91.4 80.6 92.3 54.3 36.3 21.8 29.6 27.3 17.9

1.014 38.1 0 244.25 76 41.8 115.2 113.7 112.4 68.5 45 25.5 37.1 31.2 19.9

1.0624 15.9 0 193.5 70.5 40.7 104.9 94.1 102.7 60.6 38.6 24.7 34 30.1 18.7

1.0429 24.7 0 224.75 74.75 38.5 106.7 105.7 111.8 65.3 43.3 26 33.7 29.9 18.5

1.047 22.8 0 162.75 72.75 35.4 92.2 85.6 96.5 60.2 38.9 22.4 31.7 27.1 17.1

1.0411 25.5 0 180 68.25 38.5 101.6 96.6 100.6 61.1 38.4 24.1 32.9 29.8 18.8

1.0488 22 0 156.25 69 35.5 97.8 86 96.2 57.7 38.6 24 31.2 27.3 17.4

1.0583 17.7 0 168 71.5 36.5 92 89.7 101 62.3 38 22.3 30.8 27.8 16.9

1.0841 6.6 0 167.25 72.75 37.6 94 78 99 57.5 40 22.5 30.6 30 18.5

1.0462 23.6 0 170.75 67.5 37.4 103.7 89.7 94.2 58.5 39 24.1 33.8 28.8 18.8

1.0709 12.2 0 178.25 70.25 37.8 102.7 89.2 99.2 60.2 39.2 23.8 31.7 28.4 18.6

1.0484 22.1 0 150 69.25 35.2 91.1 85.7 96.9 55.5 35.7 22 29.4 26.6 17.4

1.034 28.7 0 200.5 71.5 37.9 107.2 103.1 105.5 68.8 38.3 23.7 32.1 28.9 18.7

1.0854 6 0 184 74 37.9 100.8 89.1 102.6 60.6 39 24 32.9 29.2 18.4

1.0209 34.8 0 223 69.75 40.9 121.6 113.9 107.1 63.5 40.3 21.8 34.8 30.7 17.4

1.061 16.6 0 208.75 73 41.9 105.6 96.3 102 63.3 39.8 24.1 37.3 23.1 19.4

1.025 32.9 0 166 65.5 39.1 100.6 93.9 100.1 58.9 37.6 21.4 33.1 29.5 17.3

1.0254 32.8 1 195 72.5 40.2 102.7 101.3 101.7 60.7 39.4 23.3 36.7 31.6 18.4

1.0771 9.6 1 160.5 70.25 36 99.8 83.9 91.8 53 36.2 22.5 31.4 27.5 17.7

1.0742 10.8 1 159.75 70.75 34.5 92.9 84.4 94 56 38.2 22.6 29 26.2 17.6

1.0829 7.1 1 140.5 68 35.8 91.2 79.4 89 51.1 35 21.7 30.9 28.8 17.4

1.0373 27.2 1 216.25 74.5 40.2 115.6 104 109 63.7 40.3 23.2 36.8 31 18.9

1.0543 19.5 1 168.25 71.75 38.3 98.3 89.7 99.1 56.3 38.8 23 29.5 27.9 18.6

1.0561 18.7 1 194.75 70.75 39 103.7 97.6 104.2 60 40.9 25.5 32.7 30 19

1.0543 19.5 1 172.75 73 37.4 98.7 87.6 96.1 57.1 38.1 21.8 28.6 26.7 18

0.995 47.5 1 219 64 41.2 119.8 122.1 112.8 62.5 36.9 23.6 34.7 29.1 18.4

1.0678 13.6 1 149.25 69.75 34.8 92.8 81.1 96.3 53.8 36.5 21.5 31.3 26.3 17.8

1.0819 7.5 1 154.5 70 36.9 93.3 81.5 94.4 54.7 39 22.6 27.5 25.9 18.6

1.0433 24.5 1 199.25 71.75 39.4 106.8 100 105 63.9 39.2 22.9 35.7 30.4 19.2

1.0646 15 1 154.5 69.25 37.6 93.9 88.7 94.5 53.7 36.2 22 28.5 25.7 17.1

1.0706 12.4 1 153.25 70.5 38.5 99 91.8 96.2 57.7 38.1 23.9 31.4 29.9 18.9

1.0399 26 1 230 72.25 42.5 119.9 110.4 105.5 64.2 42.7 27 38.4 32 19.6

1.0726 11.5 1 161.75 67.5 37.4 94.2 87.6 95.6 59.7 40.2 23.4 27.9 27 17.8

1.0874 5.2 1 142.25 67.25 35.2 92.7 82.8 91.9 54.4 35.2 22.5 29.4 26.8 17

1.074 10.9 1 179.75 68.75 41.1 106.9 95.3 98.2 57.4 37.1 21.8 34.1 31.1 19.2

1.0703 12.5 1 126.5 66.75 33.4 88.8 78.2 87.5 50.8 33 19.7 25.3 22 15.8

1.065 14.8 1 169.5 68.25 37.2 101.7 91.1 97.1 56.6 38.5 22.6 33.4 29.3 18.8

1.0418 25.2 1 198.5 74.25 38.3 105.3 96.7 106.6 64 42.6 23.4 33.2 30 18.4

1.0647 14.9 1 174.5 69.5 38.1 104 89.4 98.4 58.4 37.4 22.5 34.6 30.1 18.8

1.0601 17 1 167.75 68.5 37.4 98.6 93 97 55.4 38.8 23.2 32.4 29.7 19

1.0745 10.6 1 147.75 65.75 35.2 99.6 86.4 90.1 53 35 21.3 31.7 27.3 16.9

1.062 16.1 1 182.25 71.75 39.4 103.4 96.7 100.7 59.3 38.6 22.8 31.8 29.1 19

1.0636 15.4 1 175.5 71.5 38 100.2 88.1 97.8 57.1 38.9 23.6 30.9 29.6 18

1.0384 26.7 1 161.75 67.25 35.1 94.9 94.9 100.2 56.8 35.9 21 27.8 26.1 17.6

1.0403 25.8 1 157.75 67.5 40.4 97.2 93.3 94 54.3 35.7 21 31.3 28.7 18.3

1.0563 18.6 1 168.75 67.5 38.3 104.7 95.6 93.7 54.4 37.1 22.7 30.3 26.3 18.3

1.0424 24.8 1 191.5 72.25 40.6 104 98.2 101.1 59.3 40.3 23 32.6 28.5 19

1.0372 27.3 1 219.15 69.5 40.2 117.6 113.8 111.8 63.4 41.1 22.3 35.1 29.6 18.5

1.0705 12.4 1 155.25 69.5 37.9 95.8 82.8 94.5 61.2 39.1 22.3 29.8 28.9 18.3

1.0316 29.9 1 189.75 65.75 40.8 106.4 100.5 100.5 59.2 38.1 24 35.9 30.5 19.1

1.0599 17 1 127.5 65.75 34.7 93 79.7 87.6 50.7 33.4 20.1 28.5 24.8 16.5

1.0207 35 1 224.5 68.25 38.8 119.6 118 114.3 61.3 42.1 23.4 34.9 30.1 19.4

1.0304 30.4 1 234.25 72 41.4 119.7 109 109.1 63.7 42.4 24.6 35.6 30.7 19.5

1.0256 32.6 1 227.75 72.75 41.3 115.8 113.4 109.8 65.6 46 25.4 35.3 29.8 19.5

1.0334 29 1 199.5 68.5 40.7 118.3 106.1 101.6 58.2 38.8 24.1 32.1 29.3 18.5

1.0641 15.2 1 155.5 69.25 36.3 97.4 84.3 94.4 54.3 37.5 22.6 29.2 27.3 18.5

1.0308 30.2 1 215.5 70.5 40.8 113.7 107.6 110 63.3 44 22.6 37.5 32.6 18.8

1.0736 11 1 134.25 67 34.9 89.2 83.6 88.8 49.6 34.8 21.5 25.6 25.7 18.5

1.0236 33.6 1 201 69.75 40.9 108.5 105 104.5 59.6 40.8 23.2 35.2 28.6 20.1

1.0328 29.3 1 186.75 66 38.9 111.1 111.5 101.7 60.3 37.3 21.5 31.3 27.2 18

1.0399 26 1 190.75 70.5 38.9 108.3 101.3 97.8 56 41.6 22.7 30.5 29.4 19.8

1.0271 31.9 1 207.5 70 40.8 112.4 108.5 107.1 59.3 42.2 24.6 33.7 30 20.9

Explanation / Answer

mport the dataset to R studio .

Compute the correlation between the body fat percentage and each of the variables weight, height and abdomen

Rcode:

cor(bodyfat_data$SiriBFperc,bodyfat_data$Weight)
cor(bodyfat_data$SiriBFperc,bodyfat_data$Height)
cor(bodyfat_data$SiriBFperc,bodyfat_data$AbdomenC)

Output:

0.612414

-0.08949538

0.8134323

there seems moderate positive relationship between

body fat percentage and weight,

there seems weak negative relationship between

body fat percentage and height,

There seems strong positive relationship between

body fat percentage and abdomen

scatterplot R code :

plot(bodyfat_data$Weight,bodyfat_data$SiriBFperc)
plot(bodyfat_data$Height,bodyfat_data$SiriBFperc)
plot(bodyfat_data$AbdomenC,bodyfat_data$SiriBFperc)

Solutionb:

then, fit three separate simple regression models for body fat percentage versus weight, height and abdomen circumference.

reg1 <- lm(bodyfat_data$SiriBFperc~bodyfat_data$Weight,data=bodyfat_data)
summary(reg1)
with(bodyfat_data,plot(bodyfat_data$Weight, bodyfat_data$SiriBFperc,data=bodyfat_data))
abline(reg1)
reg2 <- lm(bodyfat_data$SiriBFperc~bodyfat_data$Height,data=bodyfat_data)
  
summary(reg2)
with(bodyfat_data,plot(bodyfat_data$Height, bodyfat_data$SiriBFperc,data=bodyfat_data))
abline(reg2)
reg3 <- lm(bodyfat_data$SiriBFperc~bodyfat_data$AbdomenC,data=bodyfat_data)
summary(reg3)
with(bodyfat_data,plot(bodyfat_data$AbdomenC, bodyfat_data$SiriBFperc,data=bodyfat_data))
abline(reg3)

Output:

Regression1:

body fat percentage =-12.051+0.174(weight)

p <0.05

Weight is sginificant vrariable.

R sq=0.3751

37.51% variation in body fat percentage is explained by model not a good model.

Regression2:

body fat percentage =33.495--0.205(height)

R sq=0.008009=0.8%

0.8% variation in body fat percentage is explained by model not a good model.

p=0.15664.

p>0.05

height is not a signiifcant variable.

Regression3:

body fat percentage =-39.280+0.631(Abdomen_C)

R sq=0.6617

66.17% variation in body fat percentage is explained by model.

Comparatively good R2 value

p<0.05

Abdomen circumference is a significant variable.

weight and abdomen circumference appears to be the best predictor for body fat percentage.

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