[R] partial correlations

[Jonathan Baron]

There may well be a simple way to do partial correlations,
but I can't find it either.  Here are three ways:

1. Use the formula.  For r(xy,z),
xy <- cor(x,y)
xz <- cor(x,z)
yz <- cor(y,z)
(xy - xz*yz)/sqrt((1-xz^2)*(1-yz^2)

2. Correlate residuals.
cor(lm(x~z)$resid,lm(y~z)$resid)

The second method has the advantage that you can replace z with
many variables and partial them all.

3. From the coefficients of regressions.

a <- summary(lm(y ~ x + z))$coef[2,1]
b <- summary(lm(x ~ y + z))$coef[2,1]
sqrt(a*b)

The significance of the partial correlation should be the same as
the significance of the regression coefficient, e.g.,

summary(lm(y ~ x + z))
or
summary(lm(x ~ y + z))

and look at the first coefficient.

Jon Baron

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