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wnoise comments on Even if you have a nail, not all hammers are the same - Less Wrong
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For anyone interested, here is a decent algorithm for getting the "correct" number of lines in your linear regression.
http://www.cs.princeton.edu/~wayne/kleinberg-tardos/06dynamic-programming-2x2.pdf
Pages 5 and 6.
Welcome to LessWrong! Feel free to introduce yourself in the welcome thread.
That is a very good summary and review for those who want want to brush up on dynamic programming -- it gives several example problems and cost functions to be minimized, and shows how the optimal substructure fits in.
I do have to say that the bit for the tradeoff between overfitting and accuracy is not terribly useful for those trying to understand such things. It is a cookbook method, with no justification for why these particular error weightings are terribly useful.
EDIT: Of course, almost any regularization will help compared to nothing, and it does show a nice way to do this with dynamic programming, which can greatly speed things up over naive implementations.