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# Mass and Physical Measurements for Male Subjects

Keywords: multiple regression

## Description

For his MS305 data project, Michael Larner measured the weight and various physical measurements for 22 male subjects aged 16 - 30. Subjects were randomly chosen volunteers, all in reasonable good health. Subjects were requested to slightly tense each muscle being measured to ensure measurement consistency. Apart from Mass, all measurements are in cm.

 Variable Description Mass Weight in kg Fore Maximum circumference of forearm Bicep Maximum circumference of bicep Chest Distance around chest directly under the armpits Neck Distance around neck, approximately halfway up Waist Distance around waist, approximately trouser line Thigh Circumference of thigh, measured halfway between the knee and the top of the leg Calf Maximum circumference of calf Height Height from top to toe Shoulders Distance around shoulders, measured around the peak of the shoulder blades

Data file (tab-delimited text)

## Source

Larner, M. (1996). Mass and its Relationship to Physical Measurements. MS305 Data Project, Department of Mathematics, University of Queensland.

## Analysis

This is very well behaved data. One can log-transform all the variables, but the original scales are very nearly as good. There is no evidence of non-linearity or interaction.

```> leaps.mass <- leaps(physical[,2:11],Mass,nbest=3)
> df.mass <- data.frame(p=leaps.mass\$size,Cp=leaps.mass\$Cp)
> round(df.mass,2)
p     Cp
Waist  2  60.50
Fore  2  74.80
Shoulder  2 110.36
Fore,Waist  3  14.70
Waist,Calf  3  25.25
Shoulder,Waist  3  29.54
Fore,Waist,Height  4   7.45
Fore,Waist,Calf  4  11.18
Fore,Waist,Thigh  4  12.21
Fore,Waist,Height,Thigh  5   4.44
Fore,Waist,Height,Calf  5   6.10
Fore,Waist,Height,Calf,Thigh  6   4.82

> lm.mass <-lm(Mass~Fore+Waist+Height+Thigh)
> summary(lm.mass,cor=F)

Call: lm(formula = Mass ~ Fore + Waist + Height + Thigh)
Residuals:
Min      1Q  Median     3Q   Max
-3.882 -0.6756 -0.1017 0.9641 4.992

Coefficients:
Value Std. Error   t value  Pr(>|t|)
(Intercept) -113.3120   14.6391    -7.7404    0.0000
Fore    2.0356    0.4624     4.4020    0.0004
Waist    0.6469    0.1043     6.2015    0.0000
Height    0.2717    0.0855     3.1789    0.0055
Thigh    0.5401    0.2374     2.2750    0.0361

Residual standard error: 2.249 on 17 degrees of freedom
Multiple R-Squared: 0.9659
F-statistic: 120.5 on 4 and 17 degrees of freedom, the p-value is 3.079e-012 ```