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PREDICTING BODY COMPOSITION USING SIMPLE MEASUREMENT TECHNIQUES TIM JOHNSON, JAVIER NAVARRO, IDIONG IDONGESIT, MARK WEEKS

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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.Density6.Neck11. Knee 2. Percent Body Fat7.Chest12. Ankle 3. Age (years)8.Abdomen13. Biceps 4. Weight (lbs)9.Hip14. Forearm 5. Height (inches)10. Thigh15. Wrist Items 6-15 measured in centimeters

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CALCULATIONS BODY FAT PERCENTAGE 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. where, A= proportion of lean body tissue a= density of lean ~1.1 gm/cm 3 B= proportion of fat body tissue b= density of fat ~0.90 gm/cm 3 AND % Body Fat = 495/D – 400 OR B = (1/D)*[ab/(a-b)]-[b/(a-b)]

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EQUATION DEVELOPED FOR LEAN BODY WEIGHT LBW=17.298 +.89946(Weight) -.2783(age) +.002617(age) 2 +17.819(Height) -.6798(Waist-Wrist) Stepwise multiple regression techniques were used to develop this structural equation back in the 1980’s.

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OVERVIEW OF THE DATA

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HOW DOES AGE COMPARE TO DENSITY

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HOW DOES HEIGHT COMPARE TO DENSITY?

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AGE VS WEIGHT

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HEIGHT VS WEIGHT

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WEIGHT VS NECK

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WEIGHT VS DENSITY

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DENSITY VS WAIST

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HOW DOES AGE COMPARE TO %BODY FAT

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TRAINING SET DENSITY DISTRIBUTION

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TRAINING SET %BODYFAT DISTRIBUTION

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TEST SET’S %BODYFAT DISTRIBUTION

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SIMPLE LINEAR REGRESSION

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VISUALIZE ERRORS

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HEALTH FREAK

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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

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TRAINING SET WAIST

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TRAINING SET WAIST & WRIST

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TRAINING SET ALL BUT…

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COULD WE DUPLICATE THE 1985 RESULTS?

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ONE MEASUREMENT BODY FAT

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TWO MEASUREMENT BODY FAT

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ALL BUT PREDICT BODY FAT

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1985

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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%

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CLUSTERING—SIMPLE K MEANS

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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.

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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.

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