In sci.stat.consult Graeme Byrne <[EMAIL PROTECTED]> wrote:
> In short, you don't. If the number of terms in the model equals the number
> of observations you have much bigger problems than not being able to compute
> adjusted R^2. It should always be the case that the number of observations
> exceed the number of terms in the model otherwise you cannot calculate any
> of the standard regression diagnostics (F-stats, t-stats etc). My advice is
> get more data or remove terms from the model. If neither of these is an
> option you are stuck.
It's worse than not being able to calculate regression diagnostics. You
can't make *any* inferences beyond your observed data. Consider the
degenerate case of trying to fit a bivariate regression line when you have
only two observations. You'll *always* get a perfect fit because two
points mathematically define a line. But that perfect fit will tell you
absolutely nothing about the underlying relationship between the two
variables. It's consistent with *any* possible relationship, including
complete independence. You can't tell how far off your model is from the
observations because there simply isn't any room for it to be off ("room
for the model to be off" otherwise being known as "degrees of freedom").
A model with as many parameters as observations is equivalent to the
observations themselves, and therefore testing such a model against the
observations is the same thing as asking if the observations are equal to
themselves, which is circular reasoning.
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