This is something which data analysts do all the time (especially when working with survey data which features missing responses.) It\'s common to first multiply impute a se
Another approach is to use the plyr package to do the looping. Using the example constructed by @chl, here is how you would do it
require(plyr)
# read csv files into list of data frames
data_frames = llply(csvdat, read.csv)
# run regression models on each data frame
regressions = llply(data_frames, lm, formula = y ~ .)
names(regressions) = csvdat