cupholder comments on Even if you have a nail, not all hammers are the same - Less Wrong
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The general advice here is
All of those points are true, but there's one I'd like to flag as true but potentially misleading:
Linear regression does assume this in that it tries to find the optimal linear combination of predictors to represent a dependent variable. However, there's nothing stopping a researcher from feeding in e.g. x and x squared as predictors, and thereby finding the best quadratic relationship between x and some dependent variable.