Old School: start with one X, and add them one by one until happy with the regression. Con: the smaller models that you're building on are probably biased, and may lead you in the wrong direction.
New School: start with all (your available) X's, and delete them one by one until happy with the regression. Con: when you start out your model looks like junk, and may continue to look like junk for a long time as you prune it.
Dr. Tufte prefers the latter method. The risks of omitting variables tend to be worse than those of including irrelevant ones ... so I lean towards using the extra computing power required by the New School method.
Neither method solves the problem of what variable to add/cut first, or whether to do them in groups or one by one.
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