How to visualize multivariate regression results
I personally like dotcharts of standardized regression coefficients, possibly with standard error bars to denote uncertainty. Make sure to standardize coefficients (and SEs!) appropriately so they "mean" something to your non-quantitative audience: "As you see, an increase of 1 unit in Z is associated with an increase of 0.3 units in X."

In R (without standardization):

set.seed(1)
foo &lt;- data.frame(X=rnorm(30),Y=rnorm(30),Z=rnorm(30))
model &lt;- lm(X~Y+Z,foo)

coefs &lt;- coefficients(model)
std.errs &lt;- summary(model)$coefficients[,2]

dotchart(coefs,pch=19,xlim=range(c(coefs+std.errs,coefs-std.errs)))
lines(rbind(coefs+std.errs,coefs-std.errs,NA),rbind(1:3,1:3,NA))
abline(v=0,lty=2)