PREDICTING BODY COMPOSITION USING
SIMPLE MEASUREMENT TECHNIQUES
TIM JOHNSON, JAVIER NAVARRO, IDIONG IDONGESIT, MARK WEEKS
DATA
• IN 1985 A STUDY ABOUT PREDICTING BODY FAT DISTRIBUTION FROM EASILY
OBTAINABLE MEASUREMENTS WAS UNDERTAKEN. 252 MALE SUBJECTS
VOLUNTEERED FOR THE STUDY. OVER THE YEARS ONE INSTANCE WAS LOST.
• RECORDS WERE RECORDED FOR THE FOLLOWING VITAL STATISTICS:
1. Density
6. Neck
11. Knee
2. Percent Body Fat
7. Chest
12. Ankle
3. Age
8. Abdomen
13. Biceps
4. Weight (lbs)
9. Hip
14. Forearm
5. Height (inches)
10. Thigh
15. Wrist
(years)
Items 6-15 measured in centimeters
CALCULATIONS
DENSITY 𝑔𝑚/𝑐𝑚3
𝐷=
𝑊𝑎𝑖𝑟
𝑊𝑎𝑖𝑟 − 𝑊𝑤𝑎𝑡𝑒𝑟
𝑐. 𝑓. − 𝐿𝑢𝑛𝑔𝑣𝑜𝑙
where,
W is weight in water or air
c.f. is water temperature correction factor
~.997 at 76-78 degrees Fahrenheit
This method of determining D, density, is
considered the gold standard.
BODY FAT PERCENTAGE
𝐷= 1
(𝐴 𝑎 ) + (𝐵 𝑏 )
where,
A= proportion of lean body tissue
a= density of lean ~1.1 gm/cm3
B= proportion of fat body tissue
b= density of fat ~0.90 gm/cm3
AND % Body Fat = 495/D – 400
OR B = (1/D)*[ab/(a-b)]-[b/(a-b)]
EQUATION DEVELOPED FOR
LEAN BODY WEIGHT
LBW=17.298 <numerical offset>
+.89946(Weight)
-.2783(age) +.002617(age)2 <Age factor>
+17.819(Height) <Height factor>
-.6798(Waist-Wrist)
Stepwise multiple regression techniques were used to
develop this structural equation back in the 1980’s.
OVERVIEW OF THE DATA
HOW DOES AGE COMPARE TO DENSITY
HOW DOES HEIGHT COMPARE TO DENSITY?
AGE VS WEIGHT
HEIGHT VS WEIGHT
WEIGHT VS NECK
WEIGHT VS DENSITY
DENSITY VS WAIST
HOW DOES AGE COMPARE TO %BODY FAT
TRAINING SET DENSITY DISTRIBUTION
TRAINING SET %BODYFAT DISTRIBUTION
TEST SET’S %BODYFAT DISTRIBUTION
SIMPLE LINEAR REGRESSION
VISUALIZE ERRORS
HEALTH FREAK
CONSIDER THIS
• THE PREVIOUS NEARLY PERFECT PREDICTION LOOSES THE EASE OF PREDICTION USING
SIMPLE MEASUREMENT TECHNIQUES. THE FORMULA ALSO USES THE GOLD
STANDARD: DENSITY AS THE BASIS FOR THE PREDICTION.
• CAN SIMPLE MEASUREMENT TECHNIQUES PREDICTING %BODYFAT BE FOUND USING
WEKA?
• THE FOLLOWING SLIDES CHECK OUT THAT POSSIBILITY
• FIRST USING THE WAIST MEASUREMENT
• THEN USING THE WAIST AND THE WRIST MEASUREMENTS
• AND FINALLY USING ALL THE MEASUREMENTS BUT DENSITY
TRAINING SET WAIST
TRAINING SET WAIST & WRIST
TRAINING SET ALL BUT…
COULD WE DUPLICATE THE 1985 RESULTS?
ONE MEASUREMENT BODY FAT
TWO MEASUREMENT BODY FAT
ALL BUT PREDICT BODY FAT
1985
USING M5P RULES
Here we use machine learning to
develop rules: Weka detects two
using waist > or < 87.1 cm
circumference. Overall accuracy is
at a regression value of 85.33%
CLUSTERING—SIMPLE K MEANS
SUMMARY
• THE FORMULA WITH THE BEST RESULTS BASED ITS PREDICTIVE ABILITY UPON
THE DENSITY OF THE INDIVIDUAL IN AIR AND WATER.
• WE LOSE THE GOAL OF THE 1985 STUDY OF BEING ABLE TO PREDICT THE
PERCENT OF BODY FAT BASED ON EASILY ACCESSIBLE MEASUREMENTS.
• BY ELIMINATING THE DENSITY CATEGORY THE CALCULATION ENGINE IS
FORCED TO UTILIZE THE REMAINING CATEGORIES.
• THE RESULTING CORRELATION PROBABILITY SHOW THE ACCURACY ATTAINED
USING EASILY OBTAINABLE MEASUREMENTS WITHOUT OVER FITTING.
• SOME EVIDENCE OF CLUSTERING WAS FOUND AND COMPARED TO THE RULES.
REFERENCES
• “GENERALIZED BODY COMPOSITION PREDICTION EQUATION FOR MEN USING SIMPLE
MEASUREMENT TECHNIQUES” K. W. PENROSE, ET AL. FACSM, HUMAN PERFORMANCE
RESEARCH CENTER, BRIGHAM YOUNG UNIVERSITY, “MEDICINE AND SCIENCE IN SPORTS AND
EXERCISE, V17, NO. 2, APRIL 1985, P. 189.
• “BODYFAT”, R.W.JOHNSON, DEPT OF MATHEMATICS & COMPUTER SCIENCE, SOUTH DAKOTA
SCHOOL OF MINES AND TECHNOLOGY, HOSTED BY STATLIB, DEPARTMENT OF STATISTICS,
CARNEGIE MELLON UNIVERSITY, HTTP://LIB.STAT.CMU.EDU/MODULES.PHP, ACCESSED
3/23/2014.