# SOCR Data BMI Regression

## Summary

This is a comprehensive dataset that lists estimates of the percentage of body fat determined by underwater weighing and various body circumference measurements for 252 men.

## Classroom use of this data set

This data set can be used to illustrate multiple regression techniques. Accurate measurement of body fat is inconvenient/costly and it is desirable to have easy methods of estimating body fat that are cost-effective and convenient.

References to the BMI index by country/region and per capita food consumption and undernourishment (calories) may be appropriate when discussing BMI.

## Siri's Equation

A variety of popular health books suggest that the readers assess their health, at least in part, by estimating their percentage of body fat. In Bailey (1994), for instance, the reader can estimate body fat from tables using their age and various skin-fold measurements obtained by using a caliper. Other texts give predictive equations for body fat using body circumference measurements (e.g. abdominal circumference) and/or skin-fold measurements ( Behnke and Wilmore, 1974, pp. 66-67; Wilmore, 1976, p. 247; or Katch and McArdle, 1977, pp. 120-132).

Percentage of body fat for an individual can be estimated once body density has been determined. Siri (1956) assumes that the body consists of two components - lean body tissue and fat tissue.

• Suppose we let:
• D = Body Density (gm/cm3)
• A = proportion of lean body tissue
• B = proportion of fat tissue (A+B=1)
• a = density of lean body tissue (gm/cm3)
• b = density of fat tissue (gm/cm3)
• Then, we have $D = {1 \over {A \over a} + {B\over b}}$ and solving for B we find

$B = {1\over D}\times{a b\over a-b} - {b\over a-b}$. Using the estimates a=1.10 gm/cm3 and b=0.90 gm/cm3 ( Katch and McArdle, 1977, p. 111 or Wilmore, 1976, p. 123) we come up with Siri's equation: Percentage of Body Fat $PBF = 100\times B = {495\over D} - 450$.

## Estimation of Body Density (BD)

Volume, and hence body density, can be accurately measured a variety of ways. The technique of underwater weighing computes body volume as the difference between body weight measured in air and weight measured during water submersion. In other words, body volume is equal to the loss of weight in water with the appropriate temperature correction for the water's density (Katch and McArdle, 1977, p. 113). Using this technique, $BD = {WA\over {WA-WW\over CF} - LV}$, where

• WA = Weight in air (kg)
• WW = Weight in water (kg)
• CF = Water correction factor. CF=1 at 4o C (Celsius) as one-gram of water occupies exactly one cm3 of space, and CF=0.997 at 25o C)
• LV = Residual Lung Volume (liters) Katch and McArdle (1977), p. 115.

Other methods of determining body volume are given in Behnke and Wilmore, 1974, p. 22.

## BMI Calculators

There are many body-mass-index calculators. Here are some examples:

## Data Description

The body density dataset includes the following 15 variables listed from left to right:

• Density determined from underwater weighing
• Percent body fat from Siri's (1956) equation
• Age (years)
• Weight (kg)
• Height (cm)
• Neck circumference (cm)
• Chest circumference (cm)
• Abdomen 2 circumference (cm)
• Hip circumference (cm)
• Thigh circumference (cm)
• Knee circumference (cm)
• Ankle circumference (cm)
• Biceps (extended) circumference (cm)
• Forearm circumference (cm)
• Wrist circumference (cm)
• Notes
• The measurement standards are listed in Benhke and Wilmore, 1974, pp. 45-48, where, for instance, the abdomen 2 circumference is measured laterally, at the level of the iliac crests, and anteriorly, at the umbilicus.
• These data are used to produce the predictive equations for lean body weight given in the abstract Generalized body composition prediction equation for men using simple measurement techniques, 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.
• The predictive equations were obtained from training data (the first 143 of the 252 cases that are listed in the spreadsheet below). The remaining 109 cases may be used for testing.
• These data were generously supplied by Dr. A. Garth Fisher who gave permission to freely distribute the data and use for non-commercial purposes.
• The data is also available in PDF format.
• The body-mass-index is defined by: $BMI = {Weight(kg)\over Height^2(m)}$.

## Data Table

 UnderwaterDensity BodyFatSiriEqu Age Height Weight(kg) NeckCircumf ChestCircumf Abdomen2Circumf HipCircumf ThighCircumf KneeCircumf AnkleCircumf ExtendBicepsCircumf ForearmCircumf WristCircumf 1.0708 12.3 23 172.085 69.96662 36.2 93.1 85.2 94.5 59 37.3 21.9 32 27.4 17.1 1.0853 6.1 22 183.515 78.58488 38.5 93.6 83 98.7 58.7 37.3 23.4 30.5 28.9 18.2 1.0414 25.3 22 168.275 69.85322 34 95.8 87.9 99.2 59.6 38.9 24 28.8 25.2 16.6 1.0751 10.4 26 183.515 83.80119 37.4 101.8 86.4 101.2 60.1 37.3 22.8 32.4 29.4 18.2 1.034 28.7 24 180.975 83.57439 34.4 97.3 100 101.9 63.2 42.2 24 32.2 27.7 17.7 1.0502 20.9 24 189.865 95.3678 39 104.5 94.4 107.8 66 42 25.6 35.7 30.6 18.8 1.0549 19.2 26 177.165 82.10022 36.4 105.1 90.7 100.3 58.4 38.3 22.9 31.9 27.8 17.7 1.0704 12.4 25 184.15 79.83226 37.8 99.6 88.5 97.1 60 39.4 23.2 30.5 29 18.8 1.09 4.1 25 187.96 86.63614 38.1 100.9 82.5 99.9 62.9 38.3 23.8 35.9 31.1 18.2 1.0722 11.7 23 186.69 89.92469 42.1 99.6 88.6 104.1 63.1 41.7 25 35.6 30 19.2 1.083 7.1 26 189.23 84.48158 38.5 101.5 83.6 98.2 59.7 39.7 25.2 32.8 29.4 18.5 1.0812 7.8 27 193.04 97.97595 39.4 103.6 90.9 107.7 66.2 39.2 25.9 37.2 30.2 19 1.0513 20.8 32 176.53 81.87342 38.4 102 91.6 103.9 63.4 38.3 21.5 32.5 28.6 17.7 1.0505 21.2 30 180.975 93.09983 39.4 104.1 101.8 108.6 66 41.5 23.7 36.9 31.6 18.8 1.0484 22.1 35 176.53 85.16197 40.5 101.3 96.4 100.1 69 39 23.1 36.1 30.5 18.2 1.0512 20.9 35 167.64 73.82216 36.4 99.1 92.8 99.2 63.1 38.7 21.7 31.1 26.4 16.9 1.0333 29 34 180.34 88.79071 38.9 101.9 96.4 105.2 64.8 40.8 23.1 36.2 30.8 17.3 1.0468 22.9 32 180.34 94.9142 42.1 107.6 97.5 107 66.9 40 24.4 38.2 31.6 19.3 1.0622 16 28 172.085 83.3476 38 106.8 89.6 102.4 64.2 38.7 22.9 37.2 30.5 18.5 1.061 16.5 33 186.69 96.04818 40 106.2 100.5 109 65.8 40.6 24 37.1 30.1 18.2 1.0551 19.1 28 172.72 81.19303 39.1 103.3 95.9 104.9 63.5 38 22.1 32.5 30.3 18.4 1.064 15.2 28 177.165 90.94527 41.3 111.4 98.8 104.8 63.4 40.6 24.6 33 32.8 19.9 1.0631 15.6 31 173.355 63.61633 33.9 86 76.4 94.6 57.4 35.3 22.2 27.9 25.9 16.7 1.0584 17.7 32 177.8 67.47187 35.5 86.7 80 93.4 54.9 36.2 22.1 29.8 26.7 17.1 1.0668 14 28 172.085 68.60585 34.5 90.2 76.3 95.8 58.4 35.5 22.9 31.1 28 17.6 1.0911 3.7 27 181.61 72.23458 35.7 89.6 79.7 96.5 55 36.7 22.5 29.9 28.2 17.7 1.0811 7.9 34 171.45 59.6474 36.2 88.6 74.6 85.3 51.7 34.7 21.4 28.7 27 16.5 1.0468 22.9 31 171.45 67.13167 38.8 97.4 88.7 94.7 57.5 36 21 29.2 26.6 17 1.091 3.7 27 164.465 60.44118 36.4 93.5 73.9 88.5 50.1 34.5 21.3 30.5 27.9 17.2 1.079 8.8 29 175.26 72.91497 36.7 97.4 83.5 98.7 58.9 35.3 22.6 30.1 26.7 17.6 1.0716 11.9 32 187.325 82.55381 38.7 100.5 88.7 99.8 57.5 38.7 33.9 32.5 27.7 18.4 1.0862 5.7 29 180.975 72.68818 37.3 93.5 84.5 100.6 58.5 38.8 21.5 30.1 26.4 17.9 1.0719 11.8 27 180.975 76.20352 38.1 93 79.1 94.5 57.3 36.2 24.5 29 30 18.8 1.0502 21.3 41 180.34 99.10993 39.8 111.7 100.5 108.3 67.1 44.2 25.2 37.5 31.5 18.7 1.0263 32.3 41 186.69 112.1507 42.1 117 115.6 116.1 71.2 43.3 26.3 37.3 31.7 19.7 1.0101 40.1 49 165.1 86.97634 38.4 118.5 113.1 113.8 61.9 38.3 21.9 32 29.8 17 1.0438 24.2 40 177.8 91.73906 38.5 106.5 100.9 106.2 63.5 39.9 22.6 35.1 30.6 19 1.0346 28.4 50 173.355 89.2443 42.1 105.6 98.8 104.8 66 41.5 24.7 33.2 30.5 19.4 1.0202 35.2 46 183.515 164.7221 51.2 136.2 148.1 147.7 87.3 49.1 29.6 45 29 21.4 1.0258 32.6 50 170.18 92.07925 40.2 114.8 108.1 102.5 61.3 41.1 24.7 34.1 31 18.3 1.0217 34.5 45 174.625 119.1814 43.2 128.3 126.2 125.6 72.5 39.6 26.6 36.4 32.7 21.4 1.025 32.9 44 74.93 92.98644 36.6 106 104.3 115.5 70.6 42.5 23.7 33.6 28.7 17.4 1.0279 31.6 48 177.8 98.42954 37.3 113.3 111.2 114.1 67.7 40.9 25 36.7 29.8 18.4 1.0269 32 41 181.61 96.16158 41.5 106.6 104.3 106 65 40.2 23 35.8 31.5 18.8 1.0814 7.7 39 172.72 56.81244 31.5 85.1 76 88.2 50 34.7 21 26.1 23.1 16.1 1.067 13.9 43 186.055 74.50255 35.7 96.6 81.5 97.2 58.4 38.2 23.4 29.7 27.4 18.3 1.0742 10.8 40 171.45 60.55458 33.6 88.2 73.7 88.5 53.3 34.5 22.5 27.9 26.2 17.3 1.0665 5.6 39 180.975 67.35847 34.6 89.8 79.5 92.7 52.7 37.5 21.9 28.8 26.8 17.9 1.0678 13.6 45 173.99 61.57516 32.8 92.3 83.4 90.4 52 35.8 20.6 28.8 25.5 16.3 1.0903 4 47 169.545 57.83303 34 83.4 70.4 87.2 50.6 34.4 21.9 26.8 25.8 16.8 1.0756 10.2 47 183.515 71.78099 34.9 90.2 86.7 98.3 52.6 37.2 22.4 26 25.8 17.3 1.084 6.6 40 175.26 63.16274 34.3 89.2 77.9 91 51.4 34.9 21 26.7 26.1 17.2 1.0807 8 51 172.085 62.25555 36.5 89.7 82 89.1 49.3 33.7 21.4 29.6 26 16.9 1.0848 6.3 49 186.69 69.28623 35.1 93.3 79.6 91.6 52.6 37.6 22.6 38.5 27.4 18.5 1.0906 3.9 42 171.45 61.80196 37.8 87.6 77.6 88.6 51.9 34.9 22.5 27.7 27.5 18.5 1.0473 22.6 54 182.88 89.81129 39.9 107.6 100 99.6 57.2 38 22 35.9 30.2 18.9 1.0524 20.4 58 172.72 82.32702 39.1 100 99.8 102.5 62.1 39.6 22.5 33.1 28.3 18.5 1.0356 28 62 176.53 91.28546 40.5 111.5 104.2 105.8 61.8 39.8 22.7 37.7 30.9 19.2 1.028 31.5 54 179.705 91.85245 40.5 115.4 105.3 97 59.1 38 22.5 31.6 28.8 18.2 1.043 24.6 61 167.005 81.53323 38.4 104.8 98.3 99.6 60.6 37.7 22.9 34.5 29.6 18.5 1.0396 26.1 62 186.055 97.97595 41.4 112.3 104.8 103.1 61.6 40.9 23.1 36.2 31.8 20.2 1.0317 29.8 56 173.99 81.07964 35.6 102.9 94.7 100.8 60.9 38 22.1 32.5 29.8 18.3 1.0298 30.7 54 178.435 87.65673 38 107.6 102.4 99.4 61 39.4 23.6 32.7 29.9 19.1 1.0403 25.8 61 170.18 80.73944 37.4 105.3 99.7 99.7 60.8 40.1 22.7 33.6 29 18.8 1.0264 32.3 57 177.8 93.21323 40.1 105.3 105.5 108.3 65 41.2 24.7 35.3 31.1 18.4 1.0313 30 55 171.45 83.2342 40.9 103 100.3 104.2 64.8 40.2 22.7 34.8 30.1 18.7 1.0499 21.5 54 179.705 68.71924 35.6 90 83.9 93.9 55 36.1 21.7 29.6 27.4 17.4 1.0673 13.8 55 181.61 70.19342 36.9 95.4 86.6 91.8 54.3 35.4 21.5 32.8 27.4 18.7 1.0847 6.3 54 175.895 70.42022 37.5 89.3 78.4 96.1 56 37.4 22.4 32.6 28.1 18.1 1.0693 12.9 55 181.61 71.1006 36.3 94.4 84.6 94.3 51.2 37.4 21.6 27.3 27.1 17.3 1.0439 24.3 62 181.61 75.97672 35.5 97.6 91.5 98.5 56.6 38.6 22.4 31.5 27.3 18.6 1.0788 8.8 55 174.625 66.56468 38.7 88.5 82.8 95.5 58.9 37.6 21.6 30.3 27.3 18.3 1.0796 8.5 56 187.325 72.91497 36.4 93.6 82.9 96.3 52.9 37.5 23.1 29.7 27.3 18.2 1.068 13.5 55 162.56 56.69905 33.2 87.7 76 88.6 50.9 35.4 19.1 29.3 25.7 16.9 1.072 11.8 61 167.005 64.86371 36.5 93.4 83.3 93 55.5 35.2 20.9 29.4 27 16.8 1.0666 18.5 61 171.45 67.24507 36 91.6 81.8 94.8 54.5 37 21.4 29.3 27 18.3 1.079 8.8 57 176.53 73.70876 38.7 91.6 78.8 94.3 56.7 39.7 24.2 30.2 29.2 18.1 1.0483 22.2 69 173.99 80.62604 38.7 102 95 98.3 55 38.3 21.8 30.8 25.7 18.8 1.0498 21.5 81 178.435 73.14177 37.8 96.4 95.4 99.3 53.5 37.5 21.5 31.4 26.8 18.3 1.056 18.8 66 175.895 77.67769 37.4 102.7 98.6 100.2 56.5 39.3 22.7 30.3 28.7 19 1.0283 31.4 67 172.085 74.27575 38.4 97.7 95.8 97.1 54.8 38.2 23.7 29.4 27.2 19 1.0382 26.8 64 170.815 68.15225 38.1 97.1 89 96.9 54.8 38 22 29.9 25.2 17.7 1.0568 18.4 64 184.785 86.29595 39.3 103.1 97.8 99.6 58.9 39 23 34.3 29.6 19 1.0377 27 70 177.8 77.4509 38.7 101.8 94.9 95 56 36.5 24.1 31.2 27.3 19.2 1.0378 27 72 175.895 76.20352 38.5 101.4 99.8 96.2 56.3 36.6 22 29.7 26.3 18 1.0386 26.6 67 171.45 75.74993 36.5 98.9 89.7 96.2 54.7 37.8 33.7 32.4 27.7 18.2 1.0648 14.9 72 170.815 71.5542 37.7 97.5 88.1 96.9 57.2 37.7 21.8 32.6 28 18.8 1.0462 23.1 64 167.005 72.57478 36.5 104.3 90.9 93.8 57.8 39.5 23.3 29.2 28.4 18.1 1.08 8.3 46 184.15 80.17245 38 97.3 86 99.3 61 38.4 23.8 30.2 29.3 18.8 1.0666 14.1 48 185.42 79.83226 36.7 96.7 86.5 98.3 60.4 39.9 24.4 28.8 29.6 18.7 1.052 20.5 46 177.8 80.28585 37.2 99.7 95.6 102.2 58.3 38.2 22.5 29.1 27.7 17.7 1.0573 18.2 44 176.53 81.53323 39.2 101.9 93.2 100.6 58.9 39.7 23.1 31.4 28.4 18.8 1.0795 8.5 47 179.07 74.95614 37.5 97.2 83.1 95.4 56.9 38.3 22.1 30.1 28.2 18.4 1.0424 24.9 46 182.245 87.31653 38 106.6 97.5 100.6 58.9 40.5 24.5 33.3 29.6 19.1 1.0785 9 47 189.23 83.57439 37.3 99.6 88.8 101.4 57.4 39.6 24.6 30.3 27.9 17.8 1.0991 17.4 53 197.485 101.8315 41.1 113.2 99.2 107.5 61.7 42.3 23.2 32.9 30.8 20.4 1.077 9.6 38 186.055 85.61556 37.5 99.1 91.6 102.4 60.6 39.4 22.9 31.6 30.1 18.5 1.073 11.3 50 168.91 73.70876 38.7 99.4 86.7 96.2 62.1 39.3 23.3 30.6 27.8 18.2 1.0582 17.8 46 173.355 70.98721 35.9 95.1 88.2 92.8 54.7 37.3 21.9 31.6 27.5 18.2 1.0484 22.2 47 182.88 89.3577 40 107.5 94 103.7 62.7 39 22.3 35.3 30.9 18.3 1.0506 21.2 49 186.69 90.03809 40.1 106.5 95 101.7 59 39.4 22.3 32.2 31 18.6 1.0524 20.4 48 182.88 78.81167 37 99.1 92 98.3 59.3 38.4 22.4 27.9 26.2 17 1.053 20.1 41 180.975 78.35808 36.3 96.7 89.2 98.3 60 38.4 23.2 31 29.2 18.4 1.048 22.3 49 187.325 89.2443 40.7 103.5 95.5 101.6 59.1 39.8 25.4 31 30.3 19.7 1.0412 25.4 43 175.895 80.28585 39.6 104 98.6 99.5 59.5 36.1 22 30.1 27.2 17.7 1.0578 18 43 173.99 75.06954 31.1 93.1 87.3 96.6 54.7 39 24.8 31 29.4 18.8 1.0547 19.3 43 186.69 90.83187 38.6 105.2 102.8 103.6 61.2 39.3 23.5 30.5 28.5 18.1 1.0569 18.3 52 188.595 92.19265 42 110 101.6 100.7 55.8 38.7 23.4 35.1 29.6 19.1 1.0593 17.3 43 191.77 87.99692 38.5 110.1 88.7 102.1 57.5 40 24.8 35.1 30.7 19.2 1.05 21.4 40 175.895 76.43031 34.2 97.8 92.3 100.6 57.5 36.8 22.8 32.1 26 17.3 1.0538 19.7 43 173.99 77.4509 37.2 96.3 90.6 99.3 61.9 38 22.3 33.3 28.2 18.1 1.0355 28 43 177.8 83.1208 37.1 108 105 103 63.7 40 23.6 33.5 27.8 17.4 1.0486 22.1 47 177.8 80.85284 40.2 99.7 95 98.6 62.3 38.1 23.9 35.3 31.1 19.8 1.0503 21.3 42 178.435 73.93556 35.3 93.5 89.6 99.8 61.5 37.8 21.9 30.7 27.6 17.4 1.0384 26.7 48 182.245 79.49206 38 100.7 92.4 97.5 59.3 38.1 21.8 31.8 27.3 17.5 1.0607 16.7 40 175.895 71.66759 36.3 97 86.6 92.6 55.9 36.3 22.1 29.8 26.3 17.3 1.0529 20.1 48 184.785 80.39925 36.8 96 90 99.7 58.8 38.4 22.8 29.9 28 18.1 1.0671 13.9 51 182.88 81.19303 41 99.2 90 96.4 56.8 38.8 23.3 33.4 29.8 19.5 1.0404 25.8 40 187.96 86.63614 38.3 95.4 92.4 104.3 64.6 41.1 24.8 33.6 29.5 18.5 1.0575 18.1 44 183.515 85.04857 38 101.8 87.5 101 58.5 39.2 24.5 32.1 28.6 18 1.0358 27.9 52 189.23 93.66682 40.8 104.3 99.2 104.1 58.5 39.3 24.6 33.9 31.2 19.5 1.0414 25.3 44 181.61 84.02799 39.5 99.2 98.1 101.4 57.1 40.5 23.2 33 29.6 18.4 1.0652 14.7 40 174.625 72.68818 36.9 99.3 83.3 97.5 60.5 38.7 22.6 34.4 28 17.6 1.0623 16 47 169.545 68.71924 36.9 94 86.1 95.2 58.1 36.5 22.1 30.6 27.5 17.6 1.0674 13.8 50 168.91 73.02837 37.7 98.9 84.1 94 58.5 36.6 23.5 34.4 29.2 18 1.0587 17.5 46 170.18 75.74993 36.6 101 89.9 100 60.7 36 21.9 35.6 30.2 17.6 1.0373 27.2 42 174.625 80.51265 38.9 98.7 92.1 98.5 60.7 36.8 22.2 33.8 30.3 17.2 1.059 17.4 43 172.085 69.05944 37.5 95.9 78 93.2 53.5 35.8 20.8 33.9 28.2 17.4 1.0515 20.8 40 186.055 87.20313 39.8 103.9 93.5 99.5 61.7 39 21.8 33.3 29.6 18.1 1.0648 14.9 42 177.165 74.95614 38.3 96.2 87 97.8 57.4 36.9 22.2 31.6 27.8 17.7 1.0575 18.1 49 181.61 77.90449 35.5 97.8 90.1 95.8 57 38.7 23.2 27.5 26.5 17.6 1.0472 22.7 40 179.07 77.67769 36.3 94.6 90.3 99.1 60.3 38.5 23 31.2 28.4 17.1 1.0452 23.6 47 186.055 89.3577 37.8 103.6 99.8 103.2 61.2 38.1 22.6 33.5 28.6 17.9 1.0398 26.1 50 169.545 71.214 37.8 100.4 89.4 92.3 56.1 35.6 20.5 33.6 29.3 17.3 1.0435 24.4 41 176.53 76.31692 36.5 98.4 87.2 98.4 56 36.9 23 34 29.8 18.1 1.0374 27.1 44 177.165 84.36818 37.8 104.6 101.1 102.1 58.9 37.9 22.7 30.9 28.8 17.6 1.0491 21.8 39 179.705 75.63653 37 92.9 86.1 95.6 58.8 36.1 22.4 32.7 28.3 17.1 1.0325 29.4 43 187.96 85.16197 37.7 97.8 98.6 100.6 63.6 39.2 23.8 34.3 28.4 17.7 1.0481 22.4 40 180.975 76.31692 34.3 98.3 88.5 98.3 58.1 38.4 22.5 31.7 27.4 17.6 1.0522 20.4 49 190.5 96.50178 40.8 104.7 106.6 107.7 66.5 42.5 24.5 35.5 29.8 18.7 1.0422 24.9 40 180.34 80.17245 37.4 98.6 93.1 101.6 59.1 39.6 21.6 30.8 27.9 16.6 1.0571 18.3 40 176.53 78.58488 36.5 99.5 93 99.3 60.4 38.2 22 32 28.5 17.8 1.0459 23.3 52 172.085 75.74993 37.5 102.7 91 98.9 57.1 36.7 22.3 31.6 27.5 17.9 1.0775 9.4 23 183.515 72.46138 35.5 92.1 77.1 93.9 56.1 36.1 22.7 30.5 27.2 18.2 1.0754 10.3 23 196.85 85.3434 38 96.6 85.3 102.5 59.1 37.6 23.2 31.8 29.7 18.3 1.0664 14.2 24 179.705 70.76041 35.7 92.7 81.9 95.3 56.4 36.5 22 33.5 28.3 17.3 1.055 19.2 24 184.785 94.57401 39.2 102 99.1 110.1 71.2 43.5 25.2 36.1 30.3 18.7 1.0322 29.6 25 177.165 93.66682 40.9 110.9 100.5 106.2 68.4 40.8 24.6 33.3 29.7 18.4 1.0873 5.3 25 184.15 65.2039 35.2 92.3 76.5 92.1 51.9 35.7 22 25.8 25.2 16.9 1.0416 25.2 26 178.435 101.1511 40.6 114.1 106.8 113.9 67.6 42.7 24.7 36 30.4 18.4 1.0776 9.4 26 175.26 69.05944 35.4 92.9 77.6 93.5 56.9 35.9 20.4 31.6 29 17.8 1.0542 19.6 26 189.23 109.656 41.8 108.3 102.9 114.4 72.9 43.5 25.1 38.5 33.8 19.6 1.0758 10.1 27 183.515 66.22449 34.1 88.5 72.8 91.1 53.6 36.8 23.8 27.8 26.3 17.4 1.061 16.5 27 170.815 71.1006 37.9 94 88.2 95.2 56.8 37.4 22.8 30.6 28.3 17.9 1.051 21 27 186.69 90.83187 38.2 101.1 100.1 105 62.1 40 24.9 33.7 29.2 19.4 1.0594 17.3 28 191.135 77.79109 35.6 92.1 83.5 98.3 57.3 37.8 21.7 32.2 27.7 17.7 1.0287 31.2 28 175.26 93.32663 38.5 105.6 105 106.4 68.6 40 25.2 35.2 30.7 19.1 1.0761 10 28 183.515 82.78061 37 98.5 90.8 102.5 60.8 38.5 25 31.6 28 18.6 1.0704 12.5 30 174.625 61.91536 35.9 88.7 76.6 89.8 50.1 34.8 21.8 27 34.9 16.9 1.0477 22.5 31 181.61 80.39925 36.2 101.1 92.4 99.3 59.4 39 24.6 30.1 28.2 18.2 1.0775 9.4 31 183.515 68.60585 35 94 81.2 91.5 52.5 36.6 21 27 26.3 16.5 1.0653 14.6 33 185.42 88.9041 38.5 103.8 95.6 105.1 61.4 40.6 25 31.3 29.2 19.1 1.069 13 33 174.625 83.57439 40.7 98.9 92.1 103.5 64 37.3 23.5 33.5 30.6 19.7 1.0644 15.1 34 179.07 63.50293 36 89.2 83.4 89.6 52.4 35.6 20.4 28.3 26.2 16.5 1.037 27.3 34 182.88 99.22333 39.5 111.4 106 108.8 63.8 42 23.4 34 31.2 18.5 1.0549 19.2 35 187.325 98.42954 40.5 107.5 95.1 104.5 64.8 41.3 25.6 36.4 33.7 19.4 1.0492 21.8 35 172.72 75.40973 38.5 99.1 90.4 95.6 55.5 34.2 21.9 30.2 28.7 17.7 1.0525 20.3 35 183.515 101.9449 43.9 108.2 100.4 106.8 63.3 41.7 24.6 37.2 33.1 19.8 1.018 34.3 35 176.53 103.5325 40.4 114.9 115.9 111.9 74.4 40.6 24 36.1 31.8 18.8 1.061 16.5 35 176.53 78.35808 37.6 99.1 90.8 98.1 60.1 39.1 23.4 32.5 29.8 17.4 1.0926 3 35 172.085 69.05944 37 92.2 81.9 92.8 54.7 36.2 22.1 30.4 27.4 17.7 1.0983 0.7 35 166.37 57.03924 34 90.8 75 89.2 50 34.8 22 24.8 25.9 16.9 1.0521 20.5 35 180.34 80.39925 38.4 100.5 90.3 98.7 57.8 37.3 22.4 31 28.7 17.7 1.0603 16.9 36 181.61 79.94566 38.7 98.2 90.3 99.9 59.2 37.7 21.5 32.4 28.4 17.8 1.0414 25.3 36 182.245 102.8521 41.5 115.3 108.8 114.4 69.2 42.4 24 35.4 21 20.1 1.0763 9.9 37 175.895 65.88429 36 96.8 79.4 89.2 50.3 34.8 22.2 31 26.9 16.9 1.0689 13.1 37 170.18 68.49245 35.3 92.6 83.2 96.4 60 38.1 22 31.5 26.6 16.7 1.0316 29.9 37 181.61 109.4292 42.1 119.2 110.3 113.9 69.8 42.6 24.8 34.4 29.5 18.4 1.0477 22.5 38 175.895 84.93517 38 102.7 92.7 101.9 64.7 39.5 24.7 34.8 30.3 18.1 1.0603 16.9 39 189.23 106.4808 42.8 109.5 104.5 109.9 69.5 43.1 25.8 39.1 32.5 19.9 1.0387 26.6 39 188.595 99.45013 40 108.5 104.6 109.8 68.1 42.8 24.1 35.6 29 19 1.1089 0 40 172.72 53.7507 33.8 79.3 69.4 85 47.2 33.5 20.2 27.7 24.6 16.5 1.0725 11.5 40 170.815 66.11109 35.5 95.5 83.6 91.6 54.1 36.2 21.8 31.4 28.3 17.2 1.0713 12.1 40 177.165 72.23458 35.3 92.3 86.8 96.1 58 39.4 22.7 30 26.4 17.4 1.0587 17.5 40 188.595 77.3375 37.7 98.9 90.4 95.5 55.4 38.9 22.4 30.5 28.9 17.7 1.0794 8.6 40 181.61 75.97672 39.4 89.5 83.7 98.1 57.3 39.7 22.6 32.9 29.3 18.2 1.0453 23.6 41 188.595 105.5736 41.9 117.5 109.3 108.8 67.7 41.3 24.7 37.2 31.8 20 1.0524 20.4 41 182.88 95.48119 38.5 107.4 98.9 104.1 63.5 39.8 23.5 36.4 30.4 19.1 1.052 20.5 41 184.15 91.73906 40.8 109.2 98 101.8 62.8 41.3 24.8 36.6 32.4 18.8 1.0434 24.4 41 173.355 83.91459 38 103.4 101.2 103.1 61.5 40.4 22.9 33.4 29.2 18.5 1.0728 11.4 41 175.895 69.39963 36.4 91.4 80.6 92.3 54.3 36.3 21.8 29.6 27.3 17.9 1.014 38.1 42 193.04 110.7899 41.8 115.2 113.7 112.4 68.5 45 25.5 37.1 31.2 19.9 1.0624 15.9 42 179.07 87.77012 40.7 104.9 94.1 102.7 60.6 38.6 24.7 34 30.1 18.7 1.0429 24.7 42 189.865 101.9449 38.5 106.7 105.7 111.8 65.3 43.3 26 33.7 29.9 18.5 1.047 22.8 42 184.785 73.82216 35.4 92.2 85.6 96.5 60.2 38.9 22.4 31.7 27.1 17.1 1.0411 25.5 42 173.355 81.64663 38.5 101.6 96.6 100.6 61.1 38.4 24.1 32.9 29.8 18.8 1.0488 22 42 175.26 70.87381 35.5 97.8 86 96.2 57.7 38.6 24 31.2 27.3 17.4 1.0583 17.7 42 181.61 76.20352 36.5 92 89.7 101 62.3 38 22.3 30.8 27.8 16.9 1.0841 6.6 42 184.785 75.86332 37.6 94 78 99 57.5 40 22.5 30.6 30 18.5 1.0462 23.6 43 171.45 77.4509 37.4 103.7 89.7 94.2 58.5 39 24.1 33.8 28.8 18.8 1.0709 12.2 43 178.435 80.85284 37.8 102.7 89.2 99.2 60.2 39.2 23.8 31.7 28.4 18.6 1.0484 22.1 43 175.895 68.03886 35.2 91.1 85.7 96.9 55.5 35.7 22 29.4 26.6 17.4 1.034 28.7 43 181.61 90.94527 37.9 107.2 103.1 105.5 68.8 38.3 23.7 32.1 28.9 18.7 1.0854 6 44 187.96 83.461 37.9 100.8 89.1 102.6 60.6 39 24 32.9 29.2 18.4 1.0209 34.8 44 177.165 101.1511 40.9 121.6 113.9 107.1 63.5 40.3 21.8 34.8 30.7 17.4 1.061 16.6 44 185.42 94.68741 41.9 105.6 96.3 102 63.3 39.8 24.1 37.3 23.1 19.4 1.025 32.9 44 166.37 75.29633 39.1 100.6 93.9 100.1 58.9 37.6 21.4 33.1 29.5 17.3 1.0254 32.8 47 184.15 88.45051 40.2 102.7 101.3 101.7 60.7 39.4 23.3 36.7 31.6 18.4 1.0771 9.6 47 178.435 72.80158 36 99.8 83.9 91.8 53 36.2 22.5 31.4 27.5 17.7 1.0742 10.8 47 179.705 72.46138 34.5 92.9 84.4 94 56 38.2 22.6 29 26.2 17.6 1.0829 7.1 49 172.72 63.72973 35.8 91.2 79.4 89 51.1 35 21.7 30.9 28.8 17.4 1.0373 27.2 49 189.23 98.08935 40.2 115.6 104 109 63.7 40.3 23.2 36.8 31 18.9 1.0543 19.5 49 182.245 76.31692 38.3 98.3 89.7 99.1 56.3 38.8 23 29.5 27.9 18.6 1.0561 18.7 50 179.705 88.33711 39 103.7 97.6 104.2 60 40.9 25.5 32.7 30 19 1.0543 19.5 50 185.42 78.35808 37.4 98.7 87.6 96.1 57.1 38.1 21.8 28.6 26.7 18 0.995 47.5 51 162.56 99.33673 41.2 119.8 122.1 112.8 62.5 36.9 23.6 34.7 29.1 18.4 1.0678 13.6 51 177.165 67.69866 34.8 92.8 81.1 96.3 53.8 36.5 21.5 31.3 26.3 17.8 1.0819 7.5 51 177.8 70.08002 36.9 93.3 81.5 94.4 54.7 39 22.6 27.5 25.9 18.6 1.0433 24.5 52 182.245 90.37828 39.4 106.8 100 105 63.9 39.2 22.9 35.7 30.4 19.2 1.0646 15 53 175.895 70.08002 37.6 93.9 88.7 94.5 53.7 36.2 22 28.5 25.7 17.1 1.0706 12.4 54 179.07 69.51303 38.5 99 91.8 96.2 57.7 38.1 23.9 31.4 29.9 18.9 1.0399 26 54 183.515 104.3262 42.5 119.9 110.4 105.5 64.2 42.7 27 38.4 32 19.6 1.0726 11.5 54 171.45 73.36857 37.4 94.2 87.6 95.6 59.7 40.2 23.4 27.9 27 17.8 1.0874 5.2 55 170.815 64.52351 35.2 92.7 82.8 91.9 54.4 35.2 22.5 29.4 26.8 17 1.074 10.9 55 174.625 81.53323 41.1 106.9 95.3 98.2 57.4 37.1 21.8 34.1 31.1 19.2 1.0703 12.5 55 169.545 57.37943 33.4 88.8 78.2 87.5 50.8 33 19.7 25.3 22 15.8 1.065 14.8 55 173.355 76.88391 37.2 101.7 91.1 97.1 56.6 38.5 22.6 33.4 29.3 18.8 1.0418 25.2 55 188.595 90.03809 38.3 105.3 96.7 106.6 64 42.6 23.4 33.2 30 18.4 1.0647 14.9 56 176.53 79.15187 38.1 104 89.4 98.4 58.4 37.4 22.5 34.6 30.1 18.8 1.0601 17 56 173.99 76.09012 37.4 98.6 93 97 55.4 38.8 23.2 32.4 29.7 19 1.0745 10.6 57 167.005 67.01827 35.2 99.6 86.4 90.1 53 35 21.3 31.7 27.3 16.9 1.062 16.1 57 182.245 82.66721 39.4 103.4 96.7 100.7 59.3 38.6 22.8 31.8 29.1 19 1.0636 15.4 58 181.61 79.60546 38 100.2 88.1 97.8 57.1 38.9 23.6 30.9 29.6 18 1.0384 26.7 58 170.815 73.36857 35.1 94.9 94.9 100.2 56.8 35.9 21 27.8 26.1 17.6 1.0403 25.8 60 171.45 71.5542 40.4 97.2 93.3 94 54.3 35.7 21 31.3 28.7 18.3 1.0563 18.6 62 171.45 76.54371 38.3 104.7 95.6 93.7 54.4 37.1 22.7 30.3 26.3 18.3 1.0424 24.8 62 183.515 86.86294 40.6 104 98.2 101.1 59.3 40.3 23 32.6 28.5 19 1.0372 27.3 63 176.53 99.40477 40.2 117.6 113.8 111.8 63.4 41.1 22.3 35.1 29.6 18.5 1.0705 12.4 64 176.53 70.42022 37.9 95.8 82.8 94.5 61.2 39.1 22.3 29.8 28.9 18.3 1.0316 29.9 65 167.005 86.06915 40.8 106.4 100.5 100.5 59.2 38.1 24 35.9 30.5 19.1 1.0599 17 65 167.005 57.83303 34.7 93 79.7 87.6 50.7 33.4 20.1 28.5 24.8 16.5 1.0207 35 65 173.355 101.8315 38.8 119.6 118 114.3 61.3 42.1 23.4 34.9 30.1 19.4 1.0304 30.4 66 182.88 106.254 41.4 119.7 109 109.1 63.7 42.4 24.6 35.6 30.7 19.5 1.0256 32.6 67 184.785 103.3057 41.3 115.8 113.4 109.8 65.6 46 25.4 35.3 29.8 19.5 1.0334 29 67 173.99 90.49168 40.7 118.3 106.1 101.6 58.2 38.8 24.1 32.1 29.3 18.5 1.0641 15.2 68 175.895 70.53361 36.3 97.4 84.3 94.4 54.3 37.5 22.6 29.2 27.3 18.5 1.0308 30.2 69 179.07 97.74916 40.8 113.7 107.6 110 63.3 44 22.6 37.5 32.6 18.8 1.0736 11 70 170.18 60.89478 34.9 89.2 83.6 88.8 49.6 34.8 21.5 25.6 25.7 18.5 1.0236 33.6 72 177.165 91.17207 40.9 108.5 105 104.5 59.6 40.8 23.2 35.2 28.6 20.1 1.0328 29.3 72 167.64 84.70838 38.9 111.1 111.5 101.7 60.3 37.3 21.5 31.3 27.2 18 1.0399 26 72 179.07 86.52274 38.9 108.3 101.3 97.8 56 41.6 22.7 30.5 29.4 19.8 1.0271 31.9 74 177.8 94.12042 40.8 112.4 108.5 107.1 59.3 42.2 24.6 33.7 30 20.9

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