doc30 are you an MD? Can you give me any valid scientific reason for the value for the height measurement to be squared rather than cubed?
The dimensions for the BMI are [mass][length]^-2.
From what I understand, this model correlates well to body fat %, at least compared to using [length]^-1 or [length]^-3. The response is more linear. However, I can see why you would be tempted to use [length]^-3 since that would be analagous to volume. Howver, human volume is not represented modeled by a cube of volume height^3.
The calculation in metric is:
[weight (kg) / height (m) / height (m)]
And in pounds/inches it is:
[weight (lb) / height (in) / height (in)] x 703
Where the 703 is the conversion factor to go from metric to pounds-inches.
To answer your question, I believe the BMI is an empirically determined model that best fits observation. However, it is a very poor model because it assumes constant muscle mass. THat's particularly bad for athletic men, who could easily be considered obese even if they have a 34" waist. For example, Bradd Pitt and Harrison Ford are considerd obese by BMI standards. The BMI is just a lazy way of stimating body fat content.