Table 4 Age-, sex- and population stratification-adjusted univariate and bivariate genome-wide complex trait analysis (GCTA) for GCSE mathematics, science and English; N- number of individuals in the analyses; tr1- trait one; tr2- trait 2. Standard error in parentheses.

	Additive genetic effects			Genetic correlation	Residual (non-genetic) effects			Environmental (non-genetic residual) correlation*	Variance_tr1	Variance_tr2	N_tr1/N_tr2
	Genetic variance_tr1	Genetic variance_tr2	Genetic covariance	Genetic correlation	Residual variance_tr1	Residual variance)_tr2	Residual covariance	Environmental (non-genetic residual) correlation*	Variance_tr1	Variance_tr2	N_tr1/N_tr2
Maths-Science	0.21 (0.11)	0.19 (0.12)	0.19 (0.09)	0.96 (0.16)	0.71 (0.11)	0.80 (0.12)	0.49 (0.10)	0.65 (0.06)	0.92 (0.03)	0.99 (0.03)	2502/2381
Maths-English	0.19 (0.11)	0.15 (0.10)	0.17 (0.09)	1.00 (0.19)	0.74 (0.11)	0.75 (0.11)	0.46 (0.09)	0.62 (0.06)	0.93 (0.03)	0.90 (0.03)	2502/2529
Science-English	0.17 (0.11)	0.15 (0.10)	0.16 (0.09)	1.00 (0.28)	0.81 (0.12)	0.75 (0.11)	0.41 (0.09)	0.53 (0.07)	0.97 (0.03)	0.90 (0.03)	2381/2529
English-Maths g regressed	0.13 (0.11)	0.14 (0.11)	0.14 (0.09)	1.00 (0.33)	0.81 (0.11)	0.78 (0.11)	0.41 (0.09)	0.52 (0.07)	0.94 (0.03)	0.93 (0.03)	2491/2458
English-Science g regressed	0.14 (0.11)	0.11 (0.11)	0.12 (0.09)	1.00 (0.49)	0.80 (0.11)	0.86 (0.12)	0.35 (0.09)	0.42 (0.08)	0.93 (0.03)	0.97 (0.03)	2491/2345
Maths-Science g regressed	0.19 (0.11)	0.15 (0.12)	0.17 (0.09)	1.00 (0.26)	0.74 (0.11)	0.83 (0.12)	0.44 (0.09)	0.57 (0.07)	0.93 (0.03)	0.97 (0.03)	2458/2345

*The current version of GCTA does not report the ‘environmental’ (i.e., non-genetic residual) correlation or its standard error. The environmental correlation (residual correlation) was derived here from the GCTA estimates using the following algorithm: C(e)_tr12/(√V(e)_tr1 × √V(e)_tr2) and the standard error was calculated using: Var(re) = re × re × (VarVe1/(4 × Ve1 × Ve1) + VarVe2/(4 × Ve2 × Ve2) + VarCe/(Ce× Ce) + CovVe1Ve2/(2 × Ve1 × Ve2 − CovVe1Ce/(Ve1 × Ce) − CovVe2Ce/(Ve2 × Ce)); SE(re) = sqrt[Var(re)], where re is the environmental correlation, Ve1 is the residual variance for trait 1, Ce is the residual covariance between two traits, VarVe1 is the sampling variance for Ve1 (residual variance for trait 1), VarCe is the sampling variance for Ce, CovVe1Ve2 is the sampling covariance between Ve1 and Ve2 and CovVe1Ce is the sampling covariance between Ve1 and Ce²⁶.

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