So, not that I think BMI is all that and a bag of chips, but a squared relation DOES actually make sense - when people gain weight they generally do it in two dimensions (they expand sideways and forwards/backwards) so you don't have to consider those dimensions as separate variables. Yes, I know, it's not monotonic and people will gain in different places first - butt, thighs, gut, whatever - but it all averages out to being the same in both horizontal dimensions, both of which are significantly smaller than the vertical dimension until we get to really extreme obesity.
Re: This is my burning ball of fury
So, not that I think BMI is all that and a bag of chips, but a squared relation DOES actually make sense - when people gain weight they generally do it in two dimensions (they expand sideways and forwards/backwards) so you don't have to consider those dimensions as separate variables. Yes, I know, it's not monotonic and people will gain in different places first - butt, thighs, gut, whatever - but it all averages out to being the same in both horizontal dimensions, both of which are significantly smaller than the vertical dimension until we get to really extreme obesity.