# We began by doing a simple path analysis by hand:

> r12
[1] 0.65055
> r23
[1] 0.50615
> r13
[1] 0.6079
> a <- r12
> b <- (r13-r12*r23)/(1-r12^2)
> c <- (r23 - r12*r13)/(1-r12^2)
> a
[1] 0.65055
> b
[1] 0.4830643
> c
[1] 0.1918925


# Then we did a more complex analysis using sequential regression.  Here are the
# resulting paths:
> a <- -.07063
> b <- -.04727
> c <- -.20959
> d
[1] -0.02344
> e
[1] 0.64564
> f
[1] 0.25747
> g
[1] 0.13382
> h
[1] 0.15468
> i
[1] 0.35725

# We verified that the paths can recover the correlation between
# the FEMALE dummy and SALARY:
> b + a*i + d*h*i + c*e*h*i + d*g + c*e*g + c*f*i + c*j
[1] -0.2009633

# Then we looked at the correlation implied by specific paths
# in the diagram.
> d *g + d*g*h*i
[1] -0.003310075
> a*i
[1] -0.02523257
> c*j + c*f*i + c*e*h*i + c*e*g
[1] -0.1240287
> c*j + c*f*i
[1] -0.09844257