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Keywords: multiple regression
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)
Larner, M. (1996). Mass and its Relationship to Physical Measurements. MS305 Data Project, Department of Mathematics, University of Queensland.
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,Head 5 6.83
Fore,Waist,Height,Thigh,Head 6 4.14
Fore,Waist,Height,Calf,Thigh 6 4.82
Fore,Waist,Height,Calf,Head 6 5.35
Fore,Waist,Height,Calf,Thigh,Head 7 4.38
Fore,Chest,Waist,Height,Calf,Head 7 4.81
Fore,Chest,Waist,Height,Thigh,Head 7 5.50
Fore,Chest,Waist,Height,Calf,Thigh,Head 8 5.47
Fore,Bicep,Waist,Height,Calf,Thigh,Head 8 6.07
Fore,Shoulder,Waist,Height,Calf,Thigh,Head 8 6.12
Fore,Chest,Neck,Waist,Height,Calf,Thigh,Head 9 7.13
Fore,Chest,Shoulder,Waist,Height,Calf,Thigh,Head 9 7.45
Fore,Bicep,Chest,Waist,Height,Calf,Thigh,Head 9 7.47
Fore,Bicep,Chest,Neck,Waist,Height,Calf,Thigh,Head 10 9.01
Fore,Chest,Neck,Shoulder,Waist,Height,Calf,Thigh,Head 10 9.10
Fore,Bicep,Chest,Shoulder,Waist,Height,Calf,Thigh,Head 10 9.45
Fore,Bicep,Chest,Neck,Shoulder,Waist,Height,Calf,Thigh,Head 11 11.00
> 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
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