# fat: Body measurements to predict percentage of body fat in males In UsingR: Data Sets, Etc. for the Text "Using R for Introductory Statistics", Second Edition

## Description

A data set containing many physical measurements of 252 males. Most of the variables can be measured with a scale or tape measure. Can they be used to predict the percentage of body fat? If so, this offers an easy alternative to an underwater weighing technique.

## Usage

 `1` ```data(fat) ```

## Format

A data frame with 252 observations on the following 19 variables.

case

Case Number

body.fat

Percent body fat using Brozek's equation, 457/Density - 414.2

body.fat.siri

Percent body fat using Siri's equation, 495/Density - 450

density

Density (gm/cm\^2)

age

Age (yrs)

weight

Weight (lbs)

height

Height (inches)

BMI

ffweight

Fat Free Weight = (1 - fraction of body fat) * Weight, using Brozek's formula (lbs)

neck

Neck circumference (cm)

chest

Chest circumference (cm)

abdomen

Abdomen circumference (cm) "at the umbilicus and level with the iliac crest"

hip

Hip circumference (cm)

thigh

Thigh circumference (cm)

knee

Knee circumference (cm)

ankle

Ankle circumference (cm)

bicep

Extended biceps circumference (cm)

forearm

Forearm circumference (cm)

wrist

Wrist circumference (cm) "distal to the styloid processes"

## Details

From the source:

“The data are as received from Dr. Fisher. Note, however, that there are a few errors. The body densities for cases 48, 76, and 96, for instance, each seem to have one digit in error as can be seen from the two body fat percentage values. Also note the presence of a man (case 42) over 200 pounds in weight who is less than 3 feet tall (the height should presumably be 69.5 inches, not 29.5 inches)! The percent body fat estimates are truncated to zero when negative (case 182).”

## Source

This data set comes from the collection of the Journal of Statistics Education at http://www.amstat.org/publications/jse/datasets/fat.txt. The data set was contributed by Roger W. Johnson.

## References

The source of the data is attributed to Dr. A. Garth Fisher, Human Performance Research Center, Brigham Young University, Provo, Utah 84602,

## Examples

 ```1 2 3 4 5``` ```data(fat) f = body.fat ~ age + weight + height + BMI + neck + chest + abdomen + hip + thigh + knee + ankle + bicep + forearm + wrist res = lm(f, data=fat) summary(res) ```

### Example output

```Loading required package: MASS

Attaching package: 'Hmisc'

The following objects are masked from 'package:base':

format.pval, round.POSIXt, trunc.POSIXt, units

Attaching package: 'UsingR'

The following object is masked from 'package:survival':

cancer

Call:
lm(formula = f, data = fat)

Residuals:
Min       1Q   Median       3Q      Max
-10.2573  -2.5919  -0.1031   2.9040   9.2754

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.519e+01  1.611e+01  -0.943   0.3467
age          5.688e-02  3.003e-02   1.894   0.0594 .
weight      -8.130e-02  4.989e-02  -1.630   0.1045
height      -5.307e-02  1.034e-01  -0.513   0.6084
BMI          6.101e-02  2.780e-01   0.219   0.8265
neck        -4.450e-01  2.184e-01  -2.037   0.0427 *
chest       -3.087e-02  9.779e-02  -0.316   0.7526
abdomen      8.790e-01  8.545e-02  10.286   <2e-16 ***
hip         -2.031e-01  1.371e-01  -1.481   0.1398
thigh        2.274e-01  1.356e-01   1.677   0.0948 .
knee        -9.927e-04  2.298e-01  -0.004   0.9966
ankle        1.572e-01  2.076e-01   0.757   0.4496
bicep        1.485e-01  1.600e-01   0.928   0.3543
forearm      4.297e-01  1.849e-01   2.324   0.0210 *
wrist       -1.479e+00  4.967e-01  -2.978   0.0032 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.996 on 237 degrees of freedom
Multiple R-squared:  0.749,	Adjusted R-squared:  0.7342
F-statistic: 50.52 on 14 and 237 DF,  p-value: < 2.2e-16
```

UsingR documentation built on May 2, 2018, 1:03 a.m.