On Tue, 30 May 2000, Niklas Hansen wrote:
> I'm a statistics student in sweden who needs some help.
> I'm running a best subsets (regression) and I get the following
> output:
< output deleted >
> What I would like to know is what does the statistic C-p mean?
> I would be very happy if someone could explain it to me...
C-p is usually written as C with subscript p . I don't recall who
invented it, but I remember encountering it in statistical journals
several decades ago. Minitab's Reference Manual (1989, for Release 7;
there are probably more modern references) has this to say:
[begin Minitab quote]
The C-p statistic is given by the formula
C-p = (SSEp/MSEm) - (n - 2p)
where SSEp is SSE [Sum of squares due to error] for the best model with
p parameters (including the intercept, if it is in the equation), and
MSEm is the mean square error for the model with all m predictors.
In general, we look for models where C-p is small and is also close to
p. If the model is adequate (i.e., fits the data well), then the
expected value of C-p is approximately equal to p, the number of
parameters in the model. A small value of C-p indicates that the
model is relatively precise (has small variance) in estimating the true
regression coefficients and predicting future responses. This precision
will not improve much by adding more predictors. Models with
considerable lack of fit have values of C-p larger than p.
See [9] for more on C-p.
[end of Minitab quote]
The reference [9] cited is
R.R. Hocking (1976). "A Biometrics Invited Paper: The Analysis and
Selection of Variables in Linear Regression," Biometrics 32, pp. 1-49.
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