Fitting Percentage of Body Fat to Simple Body Measurements: College Women

Figures & data

Fig. 1 Listed Age for the 184 women in Slack (1997).

Table 1 Errors/Likely errors in the dataset.

Observation	Error/Likely Error
31	Calf: 66.0 cm
34	Height, Weight, BMI inconsistent
42	Chest: 43.0 cm
120	Age: 1 year
124	Knee: 24.7 cm
135	Chest: 49.5 cm
136	Elbow: 15.5 cm

Fig. 2 Fat versus Age, Height, Hips, and Weight. The observation with Age equal to one is omitted from the upper left-hand scatterplot.

Fig. 3 Weight versus Hips.

Table 2 Variable correlations (rounded) with Fat.

Variable	Correlation
BMI	0.77
Waist	0.74
PThigh	0.72
Hips	0.71
Weight	0.70
Biceps	0.67
MThigh	0.63
Knee	0.63
Forearm	0.59
Elbow	0.57
DThigh	0.53
Neck	0.50
Wrist	0.50
Chest	0.44
Ankle	0.43
Calf	0.37
Age	−0.06
Height	0.01

Table 3 Best subsets, according to adjusted $R^2,$ for a fixed number of predictor variables. The highest adjusted $R^2$ occurs when using 9 predictor variables.

	Number of Variables
	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Adjusted $R^2$(%)	58	61	63	64	65	65	66	66.07	66.19	66.16	66	66	66	66	65	65
Weight						X		X	X	X	X	X	X	X	X	X
BMI	X	X	X	X	X	X	X	X	X	X	X	X	X	X	X	X
Neck											X	X	X	X	X	X
Chest							X	X	X	X	X	X	X	X	X	X
Calf										X	X	X	X	X	X	X
Biceps									X	X	X	X	X	X	X	X
Hips		X	X		X	X	X	X	X	X	X	X	X	X	X	X
Waist			X	X	X	X	X	X	X	X	X	X	X	X	X	X
Forearm													X	X	X	X
PThigh												X		X	X	X
MThigh																X
DThigh															X	X
Wrist				X	X		X	X	X	X	X	X	X	X	X	X
Knee				X	X	X	X	X	X	X	X	X	X	X	X	X
Elbow													X	X	X	X
Ankle						X	X	X	X	X	X	X	X	X	X	X

Fig. 4 Best subsets adjusted $R^2$ versus the number of predictor variables.

Table 4 Forward selection.

Model Predictors	Adjusted $R^2$
BMI	0.5848115
$+$ Hips	0.6148687
$+$ Waist	0.6284737
$+$ Wrist	0.6407330
$+$ Knee	0.6478705
$+$ Ankle	0.6538457
$+$ Chest	0.6593282
$+$ Weight	0.6607029
$+$ Biceps	0.6618973
$+$ Calf	0.6615658
$+$ Neck	0.6601704
$+$ PThigh	0.6585607
$+$ Forearm	0.6568581
$+$ Elbow	0.6552405
$+$ DThigh	0.6532010
$+$ MThigh	0.6511244

Table 5 Backward elimination.

Model predictors	Adjusted $R^2$	Largest Individual $p$-value
All except age, height (16 variables)	0.6511	MThigh: 0.998412
- Mthigh	0.6532	DThigh: 0.937797
- Dthigh	0.6552	PThigh: 0.662902
- PThigh	0.6569	Forearm: 0.65239
- Forearm	0.6585	Elbow: 0.700402
- Elbow	0.6602	Neck: 0.591129
- Neck	0.6616	Calf: 0.363670
- Calf	0.6619	Biceps: 0.205042
- Biceps	0.6607	Weight: 0.19230
- Weight	0.6593	Wrist: 0.05338
- Wrist	0.6540	Chest: 0.04077
- Chest	0.6477	Knee: 0.01902
- Knee	0.6386	Ankle: 0.01491
- Ankle	0.6285	Waist: 0.00634
- Waist	0.6149	Hips: 0.000136
- Hips	0.5848	BMI: < $2\times {10}^{-16}$

Table 6 Fitting percent body fat to BMI, Hips, Waist, and Ankle.

Coefficient	Estimate	$p$-value
Intercept	−26.1253	$1.61\times {10}^{-6}$
BMI	0.9256	$1.13\times {10}^{-5}$
Hips	0.2840	0.00026
Waist	0.2040	0.01111
Ankle	−0.6481	0.01491

Slack, Jason V. (1997), “Estimating Body Fat Percentage Using Circumference Measurements and Lifestyle Questionnaire Data: A Multivariate Study of 184 College Aged Females,” M.S. Thesis, Department of Physical Education, Brigham Young University. Available via OregonPDF in Health & Performance, https://www.oregonpdf.org/, Catalog ID: PE 3794.

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