AssessmentTask136103 - Exploration of Data Skills and Issues
Eduardo Martins Lynch - 12228680
Sunday, March 08, 2015
This report has the objective to functions that can be used on R Studio. The chosen dataset is a list of various body measurements of men and the percentage of body fat, based on estimative using body density.
It has been proven that the measurements of various body circumferences can be used to estimate the percentage of body fat, without any other method. This is extremely useful for people or professional because there is no cost to estimate it.
This dataset is highly recommended for classes and linear regression, therefore, the data would fit perfectly to the purpose of this report. The source was http://lib.stat.cmu.edu/datasets/bodyfat and because it was in a txt file, the data needed to be separated, collated in a spreadsheet and saved as csv file.
The variables are integers and continuous. They are listed below: Body Density, Percent of Body Fat, Age (years), Weight (lbs), Height (inches), Neck circumference (cm), Chest circumference (cm), Abdomen circumference (cm), Hip circumference (cm), Thigh circumference (cm), Knee circumference (cm), Ankle circumference (cm), Biceps (extended) circumference (cm), Forearm circumference (cm) e Wrist circumference (cm).
Firstly, the working directory needs to be choosen:
setwd("D:/UTS/36103 - Statistical Thinking for Data Science/Assign_36103_09032015")Then the dataset needs to be imported. The dataset has been named as “body”.
body <- read.csv("D:/UTS/36103 - Statistical Thinking for Data Science/Assign_36103_09032015/body.csv")It’s important to check the dataset and make sure there is no evident discrepancies.Any check need to be done because this dataset has been used previously. All variables and attributes can be seen below:
body## bodydensity bodyfat age weight height neck chest abdomen hip thigh
## 1 1.0708 12.3 23 154.25 67.75 36.2 93.1 85.2 94.5 59.0
## 2 1.0853 6.1 22 173.25 72.25 38.5 93.6 83.0 98.7 58.7
## 3 1.0414 25.3 22 154.00 66.25 34.0 95.8 87.9 99.2 59.6
## 4 1.0751 10.4 26 184.75 72.25 37.4 101.8 86.4 101.2 60.1
## 5 1.0340 28.7 24 184.25 71.25 34.4 97.3 100.0 101.9 63.2
## 6 1.0502 20.9 24 210.25 74.75 39.0 104.5 94.4 107.8 66.0
## 7 1.0549 19.2 26 181.00 69.75 36.4 105.1 90.7 100.3 58.4
## 8 1.0704 12.4 25 176.00 72.50 37.8 99.6 88.5 97.1 60.0
## 9 1.0900 4.1 25 191.00 74.00 38.1 100.9 82.5 99.9 62.9
## 10 1.0722 11.7 23 198.25 73.50 42.1 99.6 88.6 104.1 63.1
## 11 1.0830 7.1 26 186.25 74.50 38.5 101.5 83.6 98.2 59.7
## 12 1.0812 7.8 27 216.00 76.00 39.4 103.6 90.9 107.7 66.2
## 13 1.0513 20.8 32 180.50 69.50 38.4 102.0 91.6 103.9 63.4
## 14 1.0505 21.2 30 205.25 71.25 39.4 104.1 101.8 108.6 66.0
## 15 1.0484 22.1 35 187.75 69.50 40.5 101.3 96.4 100.1 69.0
## 16 1.0512 20.9 35 162.75 66.00 36.4 99.1 92.8 99.2 63.1
## 17 1.0333 29.0 34 195.75 71.00 38.9 101.9 96.4 105.2 64.8
## 18 1.0468 22.9 32 209.25 71.00 42.1 107.6 97.5 107.0 66.9
## 19 1.0622 16.0 28 183.75 67.75 38.0 106.8 89.6 102.4 64.2
## 20 1.0610 16.5 33 211.75 73.50 40.0 106.2 100.5 109.0 65.8
## 21 1.0551 19.1 28 179.00 68.00 39.1 103.3 95.9 104.9 63.5
## 22 1.0640 15.2 28 200.50 69.75 41.3 111.4 98.8 104.8 63.4
## 23 1.0631 15.6 31 140.25 68.25 33.9 86.0 76.4 94.6 57.4
## 24 1.0584 17.7 32 148.75 70.00 35.5 86.7 80.0 93.4 54.9
## 25 1.0668 14.0 28 151.25 67.75 34.5 90.2 76.3 95.8 58.4
## 26 1.0911 3.7 27 159.25 71.50 35.7 89.6 79.7 96.5 55.0
## 27 1.0811 7.9 34 131.50 67.50 36.2 88.6 74.6 85.3 51.7
## 28 1.0468 22.9 31 148.00 67.50 38.8 97.4 88.7 94.7 57.5
## 29 1.0910 3.7 27 133.25 64.75 36.4 93.5 73.9 88.5 50.1
## 30 1.0790 8.8 29 160.75 69.00 36.7 97.4 83.5 98.7 58.9
## 31 1.0716 11.9 32 182.00 73.75 38.7 100.5 88.7 99.8 57.5
## 32 1.0862 5.7 29 160.25 71.25 37.3 93.5 84.5 100.6 58.5
## 33 1.0719 11.8 27 168.00 71.25 38.1 93.0 79.1 94.5 57.3
## 34 1.0502 21.3 41 218.50 71.00 39.8 111.7 100.5 108.3 67.1
## 35 1.0263 32.3 41 247.25 73.50 42.1 117.0 115.6 116.1 71.2
## 36 1.0101 40.1 49 191.75 65.00 38.4 118.5 113.1 113.8 61.9
## 37 1.0438 24.2 40 202.25 70.00 38.5 106.5 100.9 106.2 63.5
## 38 1.0346 28.4 50 196.75 68.25 42.1 105.6 98.8 104.8 66.0
## 39 1.0202 35.2 46 363.15 72.25 51.2 136.2 148.1 147.7 87.3
## 40 1.0258 32.6 50 203.00 67.00 40.2 114.8 108.1 102.5 61.3
## 41 1.0217 34.5 45 262.75 68.75 43.2 128.3 126.2 125.6 72.5
## 42 1.0250 32.9 44 205.00 29.50 36.6 106.0 104.3 115.5 70.6
## 43 1.0279 31.6 48 217.00 70.00 37.3 113.3 111.2 114.1 67.7
## 44 1.0269 32.0 41 212.00 71.50 41.5 106.6 104.3 106.0 65.0
## 45 1.0814 7.7 39 125.25 68.00 31.5 85.1 76.0 88.2 50.0
## 46 1.0670 13.9 43 164.25 73.25 35.7 96.6 81.5 97.2 58.4
## 47 1.0742 10.8 40 133.50 67.50 33.6 88.2 73.7 88.5 53.3
## 48 1.0665 5.6 39 148.50 71.25 34.6 89.8 79.5 92.7 52.7
## 49 1.0678 13.6 45 135.75 68.50 32.8 92.3 83.4 90.4 52.0
## 50 1.0903 4.0 47 127.50 66.75 34.0 83.4 70.4 87.2 50.6
## 51 1.0756 10.2 47 158.25 72.25 34.9 90.2 86.7 98.3 52.6
## 52 1.0840 6.6 40 139.25 69.00 34.3 89.2 77.9 91.0 51.4
## 53 1.0807 8.0 51 137.25 67.75 36.5 89.7 82.0 89.1 49.3
## 54 1.0848 6.3 49 152.75 73.50 35.1 93.3 79.6 91.6 52.6
## 55 1.0906 3.9 42 136.25 67.50 37.8 87.6 77.6 88.6 51.9
## 56 1.0473 22.6 54 198.00 72.00 39.9 107.6 100.0 99.6 57.2
## 57 1.0524 20.4 58 181.50 68.00 39.1 100.0 99.8 102.5 62.1
## 58 1.0356 28.0 62 201.25 69.50 40.5 111.5 104.2 105.8 61.8
## 59 1.0280 31.5 54 202.50 70.75 40.5 115.4 105.3 97.0 59.1
## 60 1.0430 24.6 61 179.75 65.75 38.4 104.8 98.3 99.6 60.6
## 61 1.0396 26.1 62 216.00 73.25 41.4 112.3 104.8 103.1 61.6
## 62 1.0317 29.8 56 178.75 68.50 35.6 102.9 94.7 100.8 60.9
## 63 1.0298 30.7 54 193.25 70.25 38.0 107.6 102.4 99.4 61.0
## 64 1.0403 25.8 61 178.00 67.00 37.4 105.3 99.7 99.7 60.8
## 65 1.0264 32.3 57 205.50 70.00 40.1 105.3 105.5 108.3 65.0
## 66 1.0313 30.0 55 183.50 67.50 40.9 103.0 100.3 104.2 64.8
## 67 1.0499 21.5 54 151.50 70.75 35.6 90.0 83.9 93.9 55.0
## 68 1.0673 13.8 55 154.75 71.50 36.9 95.4 86.6 91.8 54.3
## 69 1.0847 6.3 54 155.25 69.25 37.5 89.3 78.4 96.1 56.0
## 70 1.0693 12.9 55 156.75 71.50 36.3 94.4 84.6 94.3 51.2
## 71 1.0439 24.3 62 167.50 71.50 35.5 97.6 91.5 98.5 56.6
## 72 1.0788 8.8 55 146.75 68.75 38.7 88.5 82.8 95.5 58.9
## 73 1.0796 8.5 56 160.75 73.75 36.4 93.6 82.9 96.3 52.9
## 74 1.0680 13.5 55 125.00 64.00 33.2 87.7 76.0 88.6 50.9
## 75 1.0720 11.8 61 143.00 65.75 36.5 93.4 83.3 93.0 55.5
## 76 1.0666 18.5 61 148.25 67.50 36.0 91.6 81.8 94.8 54.5
## 77 1.0790 8.8 57 162.50 69.50 38.7 91.6 78.8 94.3 56.7
## 78 1.0483 22.2 69 177.75 68.50 38.7 102.0 95.0 98.3 55.0
## 79 1.0498 21.5 81 161.25 70.25 37.8 96.4 95.4 99.3 53.5
## 80 1.0560 18.8 66 171.25 69.25 37.4 102.7 98.6 100.2 56.5
## 81 1.0283 31.4 67 163.75 67.75 38.4 97.7 95.8 97.1 54.8
## 82 1.0382 26.8 64 150.25 67.25 38.1 97.1 89.0 96.9 54.8
## 83 1.0568 18.4 64 190.25 72.75 39.3 103.1 97.8 99.6 58.9
## 84 1.0377 27.0 70 170.75 70.00 38.7 101.8 94.9 95.0 56.0
## 85 1.0378 27.0 72 168.00 69.25 38.5 101.4 99.8 96.2 56.3
## 86 1.0386 26.6 67 167.00 67.50 36.5 98.9 89.7 96.2 54.7
## 87 1.0648 14.9 72 157.75 67.25 37.7 97.5 88.1 96.9 57.2
## 88 1.0462 23.1 64 160.00 65.75 36.5 104.3 90.9 93.8 57.8
## 89 1.0800 8.3 46 176.75 72.50 38.0 97.3 86.0 99.3 61.0
## 90 1.0666 14.1 48 176.00 73.00 36.7 96.7 86.5 98.3 60.4
## 91 1.0520 20.5 46 177.00 70.00 37.2 99.7 95.6 102.2 58.3
## 92 1.0573 18.2 44 179.75 69.50 39.2 101.9 93.2 100.6 58.9
## 93 1.0795 8.5 47 165.25 70.50 37.5 97.2 83.1 95.4 56.9
## 94 1.0424 24.9 46 192.50 71.75 38.0 106.6 97.5 100.6 58.9
## 95 1.0785 9.0 47 184.25 74.50 37.3 99.6 88.8 101.4 57.4
## 96 1.0991 17.4 53 224.50 77.75 41.1 113.2 99.2 107.5 61.7
## 97 1.0770 9.6 38 188.75 73.25 37.5 99.1 91.6 102.4 60.6
## 98 1.0730 11.3 50 162.50 66.50 38.7 99.4 86.7 96.2 62.1
## 99 1.0582 17.8 46 156.50 68.25 35.9 95.1 88.2 92.8 54.7
## 100 1.0484 22.2 47 197.00 72.00 40.0 107.5 94.0 103.7 62.7
## 101 1.0506 21.2 49 198.50 73.50 40.1 106.5 95.0 101.7 59.0
## 102 1.0524 20.4 48 173.75 72.00 37.0 99.1 92.0 98.3 59.3
## 103 1.0530 20.1 41 172.75 71.25 36.3 96.7 89.2 98.3 60.0
## 104 1.0480 22.3 49 196.75 73.75 40.7 103.5 95.5 101.6 59.1
## 105 1.0412 25.4 43 177.00 69.25 39.6 104.0 98.6 99.5 59.5
## 106 1.0578 18.0 43 165.50 68.50 31.1 93.1 87.3 96.6 54.7
## 107 1.0547 19.3 43 200.25 73.50 38.6 105.2 102.8 103.6 61.2
## 108 1.0569 18.3 52 203.25 74.25 42.0 110.0 101.6 100.7 55.8
## 109 1.0593 17.3 43 194.00 75.50 38.5 110.1 88.7 102.1 57.5
## 110 1.0500 21.4 40 168.50 69.25 34.2 97.8 92.3 100.6 57.5
## 111 1.0538 19.7 43 170.75 68.50 37.2 96.3 90.6 99.3 61.9
## 112 1.0355 28.0 43 183.25 70.00 37.1 108.0 105.0 103.0 63.7
## 113 1.0486 22.1 47 178.25 70.00 40.2 99.7 95.0 98.6 62.3
## 114 1.0503 21.3 42 163.00 70.25 35.3 93.5 89.6 99.8 61.5
## 115 1.0384 26.7 48 175.25 71.75 38.0 100.7 92.4 97.5 59.3
## 116 1.0607 16.7 40 158.00 69.25 36.3 97.0 86.6 92.6 55.9
## 117 1.0529 20.1 48 177.25 72.75 36.8 96.0 90.0 99.7 58.8
## 118 1.0671 13.9 51 179.00 72.00 41.0 99.2 90.0 96.4 56.8
## 119 1.0404 25.8 40 191.00 74.00 38.3 95.4 92.4 104.3 64.6
## 120 1.0575 18.1 44 187.50 72.25 38.0 101.8 87.5 101.0 58.5
## 121 1.0358 27.9 52 206.50 74.50 40.8 104.3 99.2 104.1 58.5
## 122 1.0414 25.3 44 185.25 71.50 39.5 99.2 98.1 101.4 57.1
## 123 1.0652 14.7 40 160.25 68.75 36.9 99.3 83.3 97.5 60.5
## 124 1.0623 16.0 47 151.50 66.75 36.9 94.0 86.1 95.2 58.1
## 125 1.0674 13.8 50 161.00 66.50 37.7 98.9 84.1 94.0 58.5
## 126 1.0587 17.5 46 167.00 67.00 36.6 101.0 89.9 100.0 60.7
## 127 1.0373 27.2 42 177.50 68.75 38.9 98.7 92.1 98.5 60.7
## 128 1.0590 17.4 43 152.25 67.75 37.5 95.9 78.0 93.2 53.5
## 129 1.0515 20.8 40 192.25 73.25 39.8 103.9 93.5 99.5 61.7
## 130 1.0648 14.9 42 165.25 69.75 38.3 96.2 87.0 97.8 57.4
## 131 1.0575 18.1 49 171.75 71.50 35.5 97.8 90.1 95.8 57.0
## 132 1.0472 22.7 40 171.25 70.50 36.3 94.6 90.3 99.1 60.3
## 133 1.0452 23.6 47 197.00 73.25 37.8 103.6 99.8 103.2 61.2
## 134 1.0398 26.1 50 157.00 66.75 37.8 100.4 89.4 92.3 56.1
## 135 1.0435 24.4 41 168.25 69.50 36.5 98.4 87.2 98.4 56.0
## 136 1.0374 27.1 44 186.00 69.75 37.8 104.6 101.1 102.1 58.9
## 137 1.0491 21.8 39 166.75 70.75 37.0 92.9 86.1 95.6 58.8
## 138 1.0325 29.4 43 187.75 74.00 37.7 97.8 98.6 100.6 63.6
## 139 1.0481 22.4 40 168.25 71.25 34.3 98.3 88.5 98.3 58.1
## 140 1.0522 20.4 49 212.75 75.00 40.8 104.7 106.6 107.7 66.5
## 141 1.0422 24.9 40 176.75 71.00 37.4 98.6 93.1 101.6 59.1
## 142 1.0571 18.3 40 173.25 69.50 36.5 99.5 93.0 99.3 60.4
## 143 1.0459 23.3 52 167.00 67.75 37.5 102.7 91.0 98.9 57.1
## 144 1.0775 9.4 23 159.75 72.25 35.5 92.1 77.1 93.9 56.1
## 145 1.0754 10.3 23 188.15 77.50 38.0 96.6 85.3 102.5 59.1
## 146 1.0664 14.2 24 156.00 70.75 35.7 92.7 81.9 95.3 56.4
## 147 1.0550 19.2 24 208.50 72.75 39.2 102.0 99.1 110.1 71.2
## 148 1.0322 29.6 25 206.50 69.75 40.9 110.9 100.5 106.2 68.4
## 149 1.0873 5.3 25 143.75 72.50 35.2 92.3 76.5 92.1 51.9
## 150 1.0416 25.2 26 223.00 70.25 40.6 114.1 106.8 113.9 67.6
## 151 1.0776 9.4 26 152.25 69.00 35.4 92.9 77.6 93.5 56.9
## 152 1.0542 19.6 26 241.75 74.50 41.8 108.3 102.9 114.4 72.9
## 153 1.0758 10.1 27 146.00 72.25 34.1 88.5 72.8 91.1 53.6
## 154 1.0610 16.5 27 156.75 67.25 37.9 94.0 88.2 95.2 56.8
## 155 1.0510 21.0 27 200.25 73.50 38.2 101.1 100.1 105.0 62.1
## 156 1.0594 17.3 28 171.50 75.25 35.6 92.1 83.5 98.3 57.3
## 157 1.0287 31.2 28 205.75 69.00 38.5 105.6 105.0 106.4 68.6
## 158 1.0761 10.0 28 182.50 72.25 37.0 98.5 90.8 102.5 60.8
## 159 1.0704 12.5 30 136.50 68.75 35.9 88.7 76.6 89.8 50.1
## 160 1.0477 22.5 31 177.25 71.50 36.2 101.1 92.4 99.3 59.4
## 161 1.0775 9.4 31 151.25 72.25 35.0 94.0 81.2 91.5 52.5
## 162 1.0653 14.6 33 196.00 73.00 38.5 103.8 95.6 105.1 61.4
## 163 1.0690 13.0 33 184.25 68.75 40.7 98.9 92.1 103.5 64.0
## 164 1.0644 15.1 34 140.00 70.50 36.0 89.2 83.4 89.6 52.4
## 165 1.0370 27.3 34 218.75 72.00 39.5 111.4 106.0 108.8 63.8
## 166 1.0549 19.2 35 217.00 73.75 40.5 107.5 95.1 104.5 64.8
## 167 1.0492 21.8 35 166.25 68.00 38.5 99.1 90.4 95.6 55.5
## 168 1.0525 20.3 35 224.75 72.25 43.9 108.2 100.4 106.8 63.3
## 169 1.0180 34.3 35 228.25 69.50 40.4 114.9 115.9 111.9 74.4
## 170 1.0610 16.5 35 172.75 69.50 37.6 99.1 90.8 98.1 60.1
## 171 1.0926 3.0 35 152.25 67.75 37.0 92.2 81.9 92.8 54.7
## 172 1.0983 0.7 35 125.75 65.50 34.0 90.8 75.0 89.2 50.0
## 173 1.0521 20.5 35 177.25 71.00 38.4 100.5 90.3 98.7 57.8
## 174 1.0603 16.9 36 176.25 71.50 38.7 98.2 90.3 99.9 59.2
## 175 1.0414 25.3 36 226.75 71.75 41.5 115.3 108.8 114.4 69.2
## 176 1.0763 9.9 37 145.25 69.25 36.0 96.8 79.4 89.2 50.3
## 177 1.0689 13.1 37 151.00 67.00 35.3 92.6 83.2 96.4 60.0
## 178 1.0316 29.9 37 241.25 71.50 42.1 119.2 110.3 113.9 69.8
## 179 1.0477 22.5 38 187.25 69.25 38.0 102.7 92.7 101.9 64.7
## 180 1.0603 16.9 39 234.75 74.50 42.8 109.5 104.5 109.9 69.5
## 181 1.0387 26.6 39 219.25 74.25 40.0 108.5 104.6 109.8 68.1
## 182 1.1089 0.0 40 118.50 68.00 33.8 79.3 69.4 85.0 47.2
## 183 1.0725 11.5 40 145.75 67.25 35.5 95.5 83.6 91.6 54.1
## 184 1.0713 12.1 40 159.25 69.75 35.3 92.3 86.8 96.1 58.0
## 185 1.0587 17.5 40 170.50 74.25 37.7 98.9 90.4 95.5 55.4
## 186 1.0794 8.6 40 167.50 71.50 39.4 89.5 83.7 98.1 57.3
## 187 1.0453 23.6 41 232.75 74.25 41.9 117.5 109.3 108.8 67.7
## 188 1.0524 20.4 41 210.50 72.00 38.5 107.4 98.9 104.1 63.5
## 189 1.0520 20.5 41 202.25 72.50 40.8 109.2 98.0 101.8 62.8
## 190 1.0434 24.4 41 185.00 68.25 38.0 103.4 101.2 103.1 61.5
## 191 1.0728 11.4 41 153.00 69.25 36.4 91.4 80.6 92.3 54.3
## 192 1.0140 38.1 42 244.25 76.00 41.8 115.2 113.7 112.4 68.5
## 193 1.0624 15.9 42 193.50 70.50 40.7 104.9 94.1 102.7 60.6
## 194 1.0429 24.7 42 224.75 74.75 38.5 106.7 105.7 111.8 65.3
## 195 1.0470 22.8 42 162.75 72.75 35.4 92.2 85.6 96.5 60.2
## 196 1.0411 25.5 42 180.00 68.25 38.5 101.6 96.6 100.6 61.1
## 197 1.0488 22.0 42 156.25 69.00 35.5 97.8 86.0 96.2 57.7
## 198 1.0583 17.7 42 168.00 71.50 36.5 92.0 89.7 101.0 62.3
## 199 1.0841 6.6 42 167.25 72.75 37.6 94.0 78.0 99.0 57.5
## 200 1.0462 23.6 43 170.75 67.50 37.4 103.7 89.7 94.2 58.5
## 201 1.0709 12.2 43 178.25 70.25 37.8 102.7 89.2 99.2 60.2
## 202 1.0484 22.1 43 150.00 69.25 35.2 91.1 85.7 96.9 55.5
## 203 1.0340 28.7 43 200.50 71.50 37.9 107.2 103.1 105.5 68.8
## 204 1.0854 6.0 44 184.00 74.00 37.9 100.8 89.1 102.6 60.6
## 205 1.0209 34.8 44 223.00 69.75 40.9 121.6 113.9 107.1 63.5
## 206 1.0610 16.6 44 208.75 73.00 41.9 105.6 96.3 102.0 63.3
## 207 1.0250 32.9 44 166.00 65.50 39.1 100.6 93.9 100.1 58.9
## 208 1.0254 32.8 47 195.00 72.50 40.2 102.7 101.3 101.7 60.7
## 209 1.0771 9.6 47 160.50 70.25 36.0 99.8 83.9 91.8 53.0
## 210 1.0742 10.8 47 159.75 70.75 34.5 92.9 84.4 94.0 56.0
## 211 1.0829 7.1 49 140.50 68.00 35.8 91.2 79.4 89.0 51.1
## 212 1.0373 27.2 49 216.25 74.50 40.2 115.6 104.0 109.0 63.7
## 213 1.0543 19.5 49 168.25 71.75 38.3 98.3 89.7 99.1 56.3
## 214 1.0561 18.7 50 194.75 70.75 39.0 103.7 97.6 104.2 60.0
## 215 1.0543 19.5 50 172.75 73.00 37.4 98.7 87.6 96.1 57.1
## 216 0.9950 47.5 51 219.00 64.00 41.2 119.8 122.1 112.8 62.5
## 217 1.0678 13.6 51 149.25 69.75 34.8 92.8 81.1 96.3 53.8
## 218 1.0819 7.5 51 154.50 70.00 36.9 93.3 81.5 94.4 54.7
## 219 1.0433 24.5 52 199.25 71.75 39.4 106.8 100.0 105.0 63.9
## 220 1.0646 15.0 53 154.50 69.25 37.6 93.9 88.7 94.5 53.7
## 221 1.0706 12.4 54 153.25 70.50 38.5 99.0 91.8 96.2 57.7
## 222 1.0399 26.0 54 230.00 72.25 42.5 119.9 110.4 105.5 64.2
## 223 1.0726 11.5 54 161.75 67.50 37.4 94.2 87.6 95.6 59.7
## 224 1.0874 5.2 55 142.25 67.25 35.2 92.7 82.8 91.9 54.4
## 225 1.0740 10.9 55 179.75 68.75 41.1 106.9 95.3 98.2 57.4
## 226 1.0703 12.5 55 126.50 66.75 33.4 88.8 78.2 87.5 50.8
## 227 1.0650 14.8 55 169.50 68.25 37.2 101.7 91.1 97.1 56.6
## 228 1.0418 25.2 55 198.50 74.25 38.3 105.3 96.7 106.6 64.0
## 229 1.0647 14.9 56 174.50 69.50 38.1 104.0 89.4 98.4 58.4
## 230 1.0601 17.0 56 167.75 68.50 37.4 98.6 93.0 97.0 55.4
## 231 1.0745 10.6 57 147.75 65.75 35.2 99.6 86.4 90.1 53.0
## 232 1.0620 16.1 57 182.25 71.75 39.4 103.4 96.7 100.7 59.3
## 233 1.0636 15.4 58 175.50 71.50 38.0 100.2 88.1 97.8 57.1
## 234 1.0384 26.7 58 161.75 67.25 35.1 94.9 94.9 100.2 56.8
## 235 1.0403 25.8 60 157.75 67.50 40.4 97.2 93.3 94.0 54.3
## 236 1.0563 18.6 62 168.75 67.50 38.3 104.7 95.6 93.7 54.4
## 237 1.0424 24.8 62 191.50 72.25 40.6 104.0 98.2 101.1 59.3
## 238 1.0372 27.3 63 219.15 69.50 40.2 117.6 113.8 111.8 63.4
## 239 1.0705 12.4 64 155.25 69.50 37.9 95.8 82.8 94.5 61.2
## 240 1.0316 29.9 65 189.75 65.75 40.8 106.4 100.5 100.5 59.2
## 241 1.0599 17.0 65 127.50 65.75 34.7 93.0 79.7 87.6 50.7
## 242 1.0207 35.0 65 224.50 68.25 38.8 119.6 118.0 114.3 61.3
## 243 1.0304 30.4 66 234.25 72.00 41.4 119.7 109.0 109.1 63.7
## 244 1.0256 32.6 67 227.75 72.75 41.3 115.8 113.4 109.8 65.6
## 245 1.0334 29.0 67 199.50 68.50 40.7 118.3 106.1 101.6 58.2
## 246 1.0641 15.2 68 155.50 69.25 36.3 97.4 84.3 94.4 54.3
## 247 1.0308 30.2 69 215.50 70.50 40.8 113.7 107.6 110.0 63.3
## 248 1.0736 11.0 70 134.25 67.00 34.9 89.2 83.6 88.8 49.6
## 249 1.0236 33.6 72 201.00 69.75 40.9 108.5 105.0 104.5 59.6
## 250 1.0328 29.3 72 186.75 66.00 38.9 111.1 111.5 101.7 60.3
## 251 1.0399 26.0 72 190.75 70.50 38.9 108.3 101.3 97.8 56.0
## 252 1.0271 31.9 74 207.50 70.00 40.8 112.4 108.5 107.1 59.3
## knee ankle biceps forearm wrist
## 1 37.3 21.9 32.0 27.4 17.1
## 2 37.3 23.4 30.5 28.9 18.2
## 3 38.9 24.0 28.8 25.2 16.6
## 4 37.3 22.8 32.4 29.4 18.2
## 5 42.2 24.0 32.2 27.7 17.7
## 6 42.0 25.6 35.7 30.6 18.8
## 7 38.3 22.9 31.9 27.8 17.7
## 8 39.4 23.2 30.5 29.0 18.8
## 9 38.3 23.8 35.9 31.1 18.2
## 10 41.7 25.0 35.6 30.0 19.2
## 11 39.7 25.2 32.8 29.4 18.5
## 12 39.2 25.9 37.2 30.2 19.0
## 13 38.3 21.5 32.5 28.6 17.7
## 14 41.5 23.7 36.9 31.6 18.8
## 15 39.0 23.1 36.1 30.5 18.2
## 16 38.7 21.7 31.1 26.4 16.9
## 17 40.8 23.1 36.2 30.8 17.3
## 18 40.0 24.4 38.2 31.6 19.3
## 19 38.7 22.9 37.2 30.5 18.5
## 20 40.6 24.0 37.1 30.1 18.2
## 21 38.0 22.1 32.5 30.3 18.4
## 22 40.6 24.6 33.0 32.8 19.9
## 23 35.3 22.2 27.9 25.9 16.7
## 24 36.2 22.1 29.8 26.7 17.1
## 25 35.5 22.9 31.1 28.0 17.6
## 26 36.7 22.5 29.9 28.2 17.7
## 27 34.7 21.4 28.7 27.0 16.5
## 28 36.0 21.0 29.2 26.6 17.0
## 29 34.5 21.3 30.5 27.9 17.2
## 30 35.3 22.6 30.1 26.7 17.6
## 31 38.7 33.9 32.5 27.7 18.4
## 32 38.8 21.5 30.1 26.4 17.9
## 33 36.2 24.5 29.0 30.0 18.8
## 34 44.2 25.2 37.5 31.5 18.7
## 35 43.3 26.3 37.3 31.7 19.7
## 36 38.3 21.9 32.0 29.8 17.0
## 37 39.9 22.6 35.1 30.6 19.0
## 38 41.5 24.7 33.2 30.5 19.4
## 39 49.1 29.6 45.0 29.0 21.4
## 40 41.1 24.7 34.1 31.0 18.3
## 41 39.6 26.6 36.4 32.7 21.4
## 42 42.5 23.7 33.6 28.7 17.4
## 43 40.9 25.0 36.7 29.8 18.4
## 44 40.2 23.0 35.8 31.5 18.8
## 45 34.7 21.0 26.1 23.1 16.1
## 46 38.2 23.4 29.7 27.4 18.3
## 47 34.5 22.5 27.9 26.2 17.3
## 48 37.5 21.9 28.8 26.8 17.9
## 49 35.8 20.6 28.8 25.5 16.3
## 50 34.4 21.9 26.8 25.8 16.8
## 51 37.2 22.4 26.0 25.8 17.3
## 52 34.9 21.0 26.7 26.1 17.2
## 53 33.7 21.4 29.6 26.0 16.9
## 54 37.6 22.6 38.5 27.4 18.5
## 55 34.9 22.5 27.7 27.5 18.5
## 56 38.0 22.0 35.9 30.2 18.9
## 57 39.6 22.5 33.1 28.3 18.5
## 58 39.8 22.7 37.7 30.9 19.2
## 59 38.0 22.5 31.6 28.8 18.2
## 60 37.7 22.9 34.5 29.6 18.5
## 61 40.9 23.1 36.2 31.8 20.2
## 62 38.0 22.1 32.5 29.8 18.3
## 63 39.4 23.6 32.7 29.9 19.1
## 64 40.1 22.7 33.6 29.0 18.8
## 65 41.2 24.7 35.3 31.1 18.4
## 66 40.2 22.7 34.8 30.1 18.7
## 67 36.1 21.7 29.6 27.4 17.4
## 68 35.4 21.5 32.8 27.4 18.7
## 69 37.4 22.4 32.6 28.1 18.1
## 70 37.4 21.6 27.3 27.1 17.3
## 71 38.6 22.4 31.5 27.3 18.6
## 72 37.6 21.6 30.3 27.3 18.3
## 73 37.5 23.1 29.7 27.3 18.2
## 74 35.4 19.1 29.3 25.7 16.9
## 75 35.2 20.9 29.4 27.0 16.8
## 76 37.0 21.4 29.3 27.0 18.3
## 77 39.7 24.2 30.2 29.2 18.1
## 78 38.3 21.8 30.8 25.7 18.8
## 79 37.5 21.5 31.4 26.8 18.3
## 80 39.3 22.7 30.3 28.7 19.0
## 81 38.2 23.7 29.4 27.2 19.0
## 82 38.0 22.0 29.9 25.2 17.7
## 83 39.0 23.0 34.3 29.6 19.0
## 84 36.5 24.1 31.2 27.3 19.2
## 85 36.6 22.0 29.7 26.3 18.0
## 86 37.8 33.7 32.4 27.7 18.2
## 87 37.7 21.8 32.6 28.0 18.8
## 88 39.5 23.3 29.2 28.4 18.1
## 89 38.4 23.8 30.2 29.3 18.8
## 90 39.9 24.4 28.8 29.6 18.7
## 91 38.2 22.5 29.1 27.7 17.7
## 92 39.7 23.1 31.4 28.4 18.8
## 93 38.3 22.1 30.1 28.2 18.4
## 94 40.5 24.5 33.3 29.6 19.1
## 95 39.6 24.6 30.3 27.9 17.8
## 96 42.3 23.2 32.9 30.8 20.4
## 97 39.4 22.9 31.6 30.1 18.5
## 98 39.3 23.3 30.6 27.8 18.2
## 99 37.3 21.9 31.6 27.5 18.2
## 100 39.0 22.3 35.3 30.9 18.3
## 101 39.4 22.3 32.2 31.0 18.6
## 102 38.4 22.4 27.9 26.2 17.0
## 103 38.4 23.2 31.0 29.2 18.4
## 104 39.8 25.4 31.0 30.3 19.7
## 105 36.1 22.0 30.1 27.2 17.7
## 106 39.0 24.8 31.0 29.4 18.8
## 107 39.3 23.5 30.5 28.5 18.1
## 108 38.7 23.4 35.1 29.6 19.1
## 109 40.0 24.8 35.1 30.7 19.2
## 110 36.8 22.8 32.1 26.0 17.3
## 111 38.0 22.3 33.3 28.2 18.1
## 112 40.0 23.6 33.5 27.8 17.4
## 113 38.1 23.9 35.3 31.1 19.8
## 114 37.8 21.9 30.7 27.6 17.4
## 115 38.1 21.8 31.8 27.3 17.5
## 116 36.3 22.1 29.8 26.3 17.3
## 117 38.4 22.8 29.9 28.0 18.1
## 118 38.8 23.3 33.4 29.8 19.5
## 119 41.1 24.8 33.6 29.5 18.5
## 120 39.2 24.5 32.1 28.6 18.0
## 121 39.3 24.6 33.9 31.2 19.5
## 122 40.5 23.2 33.0 29.6 18.4
## 123 38.7 22.6 34.4 28.0 17.6
## 124 36.5 22.1 30.6 27.5 17.6
## 125 36.6 23.5 34.4 29.2 18.0
## 126 36.0 21.9 35.6 30.2 17.6
## 127 36.8 22.2 33.8 30.3 17.2
## 128 35.8 20.8 33.9 28.2 17.4
## 129 39.0 21.8 33.3 29.6 18.1
## 130 36.9 22.2 31.6 27.8 17.7
## 131 38.7 23.2 27.5 26.5 17.6
## 132 38.5 23.0 31.2 28.4 17.1
## 133 38.1 22.6 33.5 28.6 17.9
## 134 35.6 20.5 33.6 29.3 17.3
## 135 36.9 23.0 34.0 29.8 18.1
## 136 37.9 22.7 30.9 28.8 17.6
## 137 36.1 22.4 32.7 28.3 17.1
## 138 39.2 23.8 34.3 28.4 17.7
## 139 38.4 22.5 31.7 27.4 17.6
## 140 42.5 24.5 35.5 29.8 18.7
## 141 39.6 21.6 30.8 27.9 16.6
## 142 38.2 22.0 32.0 28.5 17.8
## 143 36.7 22.3 31.6 27.5 17.9
## 144 36.1 22.7 30.5 27.2 18.2
## 145 37.6 23.2 31.8 29.7 18.3
## 146 36.5 22.0 33.5 28.3 17.3
## 147 43.5 25.2 36.1 30.3 18.7
## 148 40.8 24.6 33.3 29.7 18.4
## 149 35.7 22.0 25.8 25.2 16.9
## 150 42.7 24.7 36.0 30.4 18.4
## 151 35.9 20.4 31.6 29.0 17.8
## 152 43.5 25.1 38.5 33.8 19.6
## 153 36.8 23.8 27.8 26.3 17.4
## 154 37.4 22.8 30.6 28.3 17.9
## 155 40.0 24.9 33.7 29.2 19.4
## 156 37.8 21.7 32.2 27.7 17.7
## 157 40.0 25.2 35.2 30.7 19.1
## 158 38.5 25.0 31.6 28.0 18.6
## 159 34.8 21.8 27.0 34.9 16.9
## 160 39.0 24.6 30.1 28.2 18.2
## 161 36.6 21.0 27.0 26.3 16.5
## 162 40.6 25.0 31.3 29.2 19.1
## 163 37.3 23.5 33.5 30.6 19.7
## 164 35.6 20.4 28.3 26.2 16.5
## 165 42.0 23.4 34.0 31.2 18.5
## 166 41.3 25.6 36.4 33.7 19.4
## 167 34.2 21.9 30.2 28.7 17.7
## 168 41.7 24.6 37.2 33.1 19.8
## 169 40.6 24.0 36.1 31.8 18.8
## 170 39.1 23.4 32.5 29.8 17.4
## 171 36.2 22.1 30.4 27.4 17.7
## 172 34.8 22.0 24.8 25.9 16.9
## 173 37.3 22.4 31.0 28.7 17.7
## 174 37.7 21.5 32.4 28.4 17.8
## 175 42.4 24.0 35.4 21.0 20.1
## 176 34.8 22.2 31.0 26.9 16.9
## 177 38.1 22.0 31.5 26.6 16.7
## 178 42.6 24.8 34.4 29.5 18.4
## 179 39.5 24.7 34.8 30.3 18.1
## 180 43.1 25.8 39.1 32.5 19.9
## 181 42.8 24.1 35.6 29.0 19.0
## 182 33.5 20.2 27.7 24.6 16.5
## 183 36.2 21.8 31.4 28.3 17.2
## 184 39.4 22.7 30.0 26.4 17.4
## 185 38.9 22.4 30.5 28.9 17.7
## 186 39.7 22.6 32.9 29.3 18.2
## 187 41.3 24.7 37.2 31.8 20.0
## 188 39.8 23.5 36.4 30.4 19.1
## 189 41.3 24.8 36.6 32.4 18.8
## 190 40.4 22.9 33.4 29.2 18.5
## 191 36.3 21.8 29.6 27.3 17.9
## 192 45.0 25.5 37.1 31.2 19.9
## 193 38.6 24.7 34.0 30.1 18.7
## 194 43.3 26.0 33.7 29.9 18.5
## 195 38.9 22.4 31.7 27.1 17.1
## 196 38.4 24.1 32.9 29.8 18.8
## 197 38.6 24.0 31.2 27.3 17.4
## 198 38.0 22.3 30.8 27.8 16.9
## 199 40.0 22.5 30.6 30.0 18.5
## 200 39.0 24.1 33.8 28.8 18.8
## 201 39.2 23.8 31.7 28.4 18.6
## 202 35.7 22.0 29.4 26.6 17.4
## 203 38.3 23.7 32.1 28.9 18.7
## 204 39.0 24.0 32.9 29.2 18.4
## 205 40.3 21.8 34.8 30.7 17.4
## 206 39.8 24.1 37.3 23.1 19.4
## 207 37.6 21.4 33.1 29.5 17.3
## 208 39.4 23.3 36.7 31.6 18.4
## 209 36.2 22.5 31.4 27.5 17.7
## 210 38.2 22.6 29.0 26.2 17.6
## 211 35.0 21.7 30.9 28.8 17.4
## 212 40.3 23.2 36.8 31.0 18.9
## 213 38.8 23.0 29.5 27.9 18.6
## 214 40.9 25.5 32.7 30.0 19.0
## 215 38.1 21.8 28.6 26.7 18.0
## 216 36.9 23.6 34.7 29.1 18.4
## 217 36.5 21.5 31.3 26.3 17.8
## 218 39.0 22.6 27.5 25.9 18.6
## 219 39.2 22.9 35.7 30.4 19.2
## 220 36.2 22.0 28.5 25.7 17.1
## 221 38.1 23.9 31.4 29.9 18.9
## 222 42.7 27.0 38.4 32.0 19.6
## 223 40.2 23.4 27.9 27.0 17.8
## 224 35.2 22.5 29.4 26.8 17.0
## 225 37.1 21.8 34.1 31.1 19.2
## 226 33.0 19.7 25.3 22.0 15.8
## 227 38.5 22.6 33.4 29.3 18.8
## 228 42.6 23.4 33.2 30.0 18.4
## 229 37.4 22.5 34.6 30.1 18.8
## 230 38.8 23.2 32.4 29.7 19.0
## 231 35.0 21.3 31.7 27.3 16.9
## 232 38.6 22.8 31.8 29.1 19.0
## 233 38.9 23.6 30.9 29.6 18.0
## 234 35.9 21.0 27.8 26.1 17.6
## 235 35.7 21.0 31.3 28.7 18.3
## 236 37.1 22.7 30.3 26.3 18.3
## 237 40.3 23.0 32.6 28.5 19.0
## 238 41.1 22.3 35.1 29.6 18.5
## 239 39.1 22.3 29.8 28.9 18.3
## 240 38.1 24.0 35.9 30.5 19.1
## 241 33.4 20.1 28.5 24.8 16.5
## 242 42.1 23.4 34.9 30.1 19.4
## 243 42.4 24.6 35.6 30.7 19.5
## 244 46.0 25.4 35.3 29.8 19.5
## 245 38.8 24.1 32.1 29.3 18.5
## 246 37.5 22.6 29.2 27.3 18.5
## 247 44.0 22.6 37.5 32.6 18.8
## 248 34.8 21.5 25.6 25.7 18.5
## 249 40.8 23.2 35.2 28.6 20.1
## 250 37.3 21.5 31.3 27.2 18.0
## 251 41.6 22.7 30.5 29.4 19.8
## 252 42.2 24.6 33.7 30.0 20.9And those are the descriptive statistics for the variables.
summary(body)## bodydensity bodyfat age weight
## Min. :0.995 Min. : 0.00 Min. :22.00 Min. :118.5
## 1st Qu.:1.041 1st Qu.:12.47 1st Qu.:35.75 1st Qu.:159.0
## Median :1.055 Median :19.20 Median :43.00 Median :176.5
## Mean :1.056 Mean :19.15 Mean :44.88 Mean :178.9
## 3rd Qu.:1.070 3rd Qu.:25.30 3rd Qu.:54.00 3rd Qu.:197.0
## Max. :1.109 Max. :47.50 Max. :81.00 Max. :363.1
## height neck chest abdomen
## Min. :29.50 Min. :31.10 Min. : 79.30 Min. : 69.40
## 1st Qu.:68.25 1st Qu.:36.40 1st Qu.: 94.35 1st Qu.: 84.58
## Median :70.00 Median :38.00 Median : 99.65 Median : 90.95
## Mean :70.15 Mean :37.99 Mean :100.82 Mean : 92.56
## 3rd Qu.:72.25 3rd Qu.:39.42 3rd Qu.:105.38 3rd Qu.: 99.33
## Max. :77.75 Max. :51.20 Max. :136.20 Max. :148.10
## hip thigh knee ankle
## Min. : 85.0 Min. :47.20 Min. :33.00 Min. :19.1
## 1st Qu.: 95.5 1st Qu.:56.00 1st Qu.:36.98 1st Qu.:22.0
## Median : 99.3 Median :59.00 Median :38.50 Median :22.8
## Mean : 99.9 Mean :59.41 Mean :38.59 Mean :23.1
## 3rd Qu.:103.5 3rd Qu.:62.35 3rd Qu.:39.92 3rd Qu.:24.0
## Max. :147.7 Max. :87.30 Max. :49.10 Max. :33.9
## biceps forearm wrist
## Min. :24.80 Min. :21.00 Min. :15.80
## 1st Qu.:30.20 1st Qu.:27.30 1st Qu.:17.60
## Median :32.05 Median :28.70 Median :18.30
## Mean :32.27 Mean :28.66 Mean :18.23
## 3rd Qu.:34.33 3rd Qu.:30.00 3rd Qu.:18.80
## Max. :45.00 Max. :34.90 Max. :21.40The descriptive statistics for the first five variables:
summary(body[1:5])## bodydensity bodyfat age weight
## Min. :0.995 Min. : 0.00 Min. :22.00 Min. :118.5
## 1st Qu.:1.041 1st Qu.:12.47 1st Qu.:35.75 1st Qu.:159.0
## Median :1.055 Median :19.20 Median :43.00 Median :176.5
## Mean :1.056 Mean :19.15 Mean :44.88 Mean :178.9
## 3rd Qu.:1.070 3rd Qu.:25.30 3rd Qu.:54.00 3rd Qu.:197.0
## Max. :1.109 Max. :47.50 Max. :81.00 Max. :363.1
## height
## Min. :29.50
## 1st Qu.:68.25
## Median :70.00
## Mean :70.15
## 3rd Qu.:72.25
## Max. :77.75A list of correlation for all variables are shown below, however only some variables show high correlation coefficients.
cor(body)## bodydensity bodyfat age weight height
## bodydensity 1.00000000 -0.98778240 -0.27763721 -0.59406188 0.09788114
## bodyfat -0.98778240 1.00000000 0.29145844 0.61241400 -0.08949538
## age -0.27763721 0.29145844 1.00000000 -0.01274609 -0.17164514
## weight -0.59406188 0.61241400 -0.01274609 1.00000000 0.30827854
## height 0.09788114 -0.08949538 -0.17164514 0.30827854 1.00000000
## neck -0.47296636 0.49059185 0.11350519 0.83071622 0.25370988
## chest -0.68259865 0.70262034 0.17644968 0.89419052 0.13489181
## abdomen -0.79895463 0.81343228 0.23040942 0.88799494 0.08781291
## hip -0.60933143 0.62520092 -0.05033212 0.94088412 0.17039426
## thigh -0.55309098 0.55960753 -0.20009576 0.86869354 0.14843561
## knee -0.49504035 0.50866524 0.01751569 0.85316739 0.28605321
## ankle -0.26489003 0.26596977 -0.10505810 0.61368542 0.26474369
## biceps -0.48710872 0.49327113 -0.04116212 0.80041593 0.20781557
## forearm -0.35164842 0.36138690 -0.08505555 0.63030143 0.22864922
## wrist -0.32571598 0.34657486 0.21353062 0.72977489 0.32206533
## neck chest abdomen hip thigh
## bodydensity -0.4729664 -0.6825987 -0.79895463 -0.60933143 -0.5530910
## bodyfat 0.4905919 0.7026203 0.81343228 0.62520092 0.5596075
## age 0.1135052 0.1764497 0.23040942 -0.05033212 -0.2000958
## weight 0.8307162 0.8941905 0.88799494 0.94088412 0.8686935
## height 0.2537099 0.1348918 0.08781291 0.17039426 0.1484356
## neck 1.0000000 0.7848350 0.75407737 0.73495788 0.6956973
## chest 0.7848350 1.0000000 0.91582767 0.82941992 0.7298586
## abdomen 0.7540774 0.9158277 1.00000000 0.87406618 0.7666239
## hip 0.7349579 0.8294199 0.87406618 1.00000000 0.8964098
## thigh 0.6956973 0.7298586 0.76662393 0.89640979 1.0000000
## knee 0.6724050 0.7194964 0.73717888 0.82347262 0.7991703
## ankle 0.4778924 0.4829879 0.45322269 0.55838682 0.5397971
## biceps 0.7311459 0.7279075 0.68498272 0.73927252 0.7614774
## forearm 0.6236603 0.5801727 0.50331609 0.54501412 0.5668422
## wrist 0.7448264 0.6601623 0.61983243 0.63008954 0.5586848
## knee ankle biceps forearm wrist
## bodydensity -0.49504035 -0.2648900 -0.48710872 -0.35164842 -0.3257160
## bodyfat 0.50866524 0.2659698 0.49327113 0.36138690 0.3465749
## age 0.01751569 -0.1050581 -0.04116212 -0.08505555 0.2135306
## weight 0.85316739 0.6136854 0.80041593 0.63030143 0.7297749
## height 0.28605321 0.2647437 0.20781557 0.22864922 0.3220653
## neck 0.67240498 0.4778924 0.73114592 0.62366027 0.7448264
## chest 0.71949640 0.4829879 0.72790748 0.58017273 0.6601623
## abdomen 0.73717888 0.4532227 0.68498272 0.50331609 0.6198324
## hip 0.82347262 0.5583868 0.73927252 0.54501412 0.6300895
## thigh 0.79917030 0.5397971 0.76147745 0.56684218 0.5586848
## knee 1.00000000 0.6116082 0.67870883 0.55589819 0.6645073
## ankle 0.61160820 1.0000000 0.48485454 0.41904999 0.5661946
## biceps 0.67870883 0.4848545 1.00000000 0.67825513 0.6321264
## forearm 0.55589819 0.4190500 0.67825513 1.00000000 0.5855883
## wrist 0.66450729 0.5661946 0.63212642 0.58558825 1.0000000Some variable are correlated, as an example, the variables “Body Density” and “Weight”, this significant correlation is reasonable and expected.
In other hands, some correlations presented high coefficients although not expected. One example is the high correlation coefficient for the variables “Weight” and “Circumference of the neck”
As explained, the objective of this study is to estimate the Body Density of male individuals based only on various body circumferences, for this, a linear regression is recommendaded:
bodymodel <- lm(bodydensity ~ age + weight + height + neck + chest + abdomen + hip + thigh + knee + ankle + biceps + forearm + wrist, data=body)The linear regression model shows an adjusted R-squared of 0.7238. This is a significant result and indicates that the calculation can be used with confidence. The results are here:
summary(bodymodel)##
## Call:
## lm(formula = bodydensity ~ age + weight + height + neck + chest +
## abdomen + hip + thigh + knee + ankle + biceps + forearm +
## wrist, data = body)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.021527 -0.007717 0.000096 0.006491 0.034114
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.139e+00 4.030e-02 28.248 < 2e-16 ***
## age -1.203e-04 7.515e-05 -1.601 0.11062
## weight 2.395e-04 1.243e-04 1.926 0.05528 .
## height 1.498e-04 2.230e-04 0.672 0.50243
## neck 1.075e-03 5.401e-04 1.991 0.04765 *
## chest 1.232e-04 2.303e-04 0.535 0.59339
## abdomen -2.277e-03 2.008e-04 -11.335 < 2e-16 ***
## hip 5.513e-04 3.390e-04 1.626 0.10521
## thigh -6.149e-04 3.354e-04 -1.833 0.06799 .
## knee -4.844e-05 5.622e-04 -0.086 0.93141
## ankle -6.314e-04 5.145e-04 -1.227 0.22094
## biceps -5.755e-04 3.976e-04 -1.448 0.14907
## forearm -1.017e-03 4.626e-04 -2.198 0.02891 *
## wrist 3.959e-03 1.243e-03 3.185 0.00164 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01 on 238 degrees of freedom
## Multiple R-squared: 0.7381, Adjusted R-squared: 0.7238
## F-statistic: 51.6 on 13 and 238 DF, p-value: < 2.2e-16I used my own measures to estimate my Body Fat and for this, I used the predict model below:
predbody <- predict.glm(bodymodel, data.frame(age=39, weight=171 ,height=5.7 ,neck=38 ,chest=104 ,abdomen=96 ,hip=102 , thigh=55 ,knee=39 ,ankle=24 ,biceps=37 ,forearm=27 ,wrist=18),type="response")This are the results:
summary(predbody)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.039 1.039 1.039 1.039 1.039 1.039In conclusion, this model allows individuals and professionals to estimate the body fat for men without using expensive techniques and this method is statistically accepted.
However this model is limited as it is based on men and excludes women, there is also other influences, such as: race, daily activities/habits, age range, genetics, etc.
I would to analyse other samples to identify similar patterns regarding this estimation.