Table 1.

Marginal distributions for age, height, and log(body mass) and the correlation between the height and log(body mass).

Population	Age	Height (cm)				Log(Body Mass (kg))				Correlation
		$H~N(\alpha +a_{1}A+a_2{A}^2,{\sigma }^2)$				$\text{log}(BM)~N(\alpha +a_{1}A+a_2{A}^2,{\sigma }^2)$
		α	a1	a2	σ	α	a1	a2	σ	ρ
UK
Male, White	U(16, 65)	176.0	0.15	−0.003	6.9	4.06	0.0168	−0.00017	0.17	0.41
Male, Asian		174.4	−0.086	0	6.3	3.96	0.0186	−0.00021	0.18	0.42
Male, Black		178.8	−0.113	0	7.4	4.10	0.0167	−0.0002	0.19	0.45
Female, White		163.9	0.052	−0.0017	6.3	4.00	0.0099	−0.00009	0.20	0.29
Female, Asian		162.0	−0.126	0	6.0	3.94	0.009	−0.00007	0.20	0.29
Female, Black		161.9	0.228	−0.0049	6.3	3.93	0.0147	−0.00013	0.19	0.36
US
Male, White	U(16, 65)	175.6	0.136	−0.002	6.6	3.96	0.0197	−0.00020	0.19	0.43
Male, Non-black hispanic		171.0	−0.03	0	6.4	3.86	0.0226	−0.00024	0.18	0.44
Male, Black		172.4	0.267	−0.0038	7.0	3.92	0.0233	−0.00026	0.22	0.28
Female, White		162.1	0.142	−0.0025	6.3	3.88	0.014	−0.00012	0.22	0.31
Female, Non-black hispanic		159.3	−0.066	0	6.0	3.79	0.020	−0.00021	0.21	0.29
Female, Black		162.3	0.108	−0.0019	6.4	3.87	0.020	−0.0002	0.25	0.46