Following the sentence, "We extract simulated coefficients and compute mean predictions..." there is this line of code:
However this code appears to be unnecessary. I think it should be deleted.
I believe it's leftover from the Introclass example HTML file, which shows how to "manually" do what predict() is doing.
sims <- as.matrix(fit_1)
predicted <- colMeans(sims[,1] + sims[,2] %*% t(introclass$midterm))