Appendix 2—table 1. The correlation matrix among Z, X, Y₂, and Y₁ without selecting on Y₁.

$\Sigma$	Z	X	Y2	Y1
Z	1	${\lambda }_z$	${\alpha }_z+{\alpha }_x{\lambda }_z$	${\beta }_z+{\beta }_x{\lambda }_z$
X	${\lambda }_z$	1	${\alpha }_x+{\alpha }_z{\lambda }_z$	${\beta }_x+{\beta }_z{\lambda }_z$
Y2	${\displaystyle {\alpha }_z+{\alpha }_x{\lambda }_z}$	${\alpha }_x+{\alpha }_z{\lambda }_z$	1	${\displaystyle ({\alpha }_z+{\alpha }_x{\lambda }_z){\beta }_z+{\beta }_x({\alpha }_x+{\alpha }_z{\lambda }_z)}$
Y1	${\beta }_z+{\beta }_x{\lambda }_z$	${\beta }_x+{\beta }_z{\lambda }_z$	${\displaystyle ({\alpha }_z+{\alpha }_x{\lambda }_z){\beta }_z+{\beta }_x({\alpha }_x+{\alpha }_z{\lambda }_z)}$	1