On 21 Aug 2001, Atul wrote:
> How do we calculate the adjusted r-square when the error degrees of
> freedom are zero ? (Or in other words, number of samples is equal to
> the number of regression terms including the constant.)
> Such a situation leads to a zero in the denominator in the expression
> for calculating adjusted r-square.
Depends in part on the expression you use, but in any case you also get
a zero in the numerator. Cf. Draper & Smith, Eq. (2.6.11b): the
right-hand expression indeed contains (n-p) in the denominator, but it
also includes (1-R^2) in the numerator, which produces the indeterminate
quotient 0/0. In the middle expression of that equation, the quotient
(residual SS)/(n-p) appears, which is also 0/0.
All of which only emphasizes that the result of any analysis for which
the error d.f. = 0 is meaningless: whether r-square, or regression
coefficients, or error mean square, ... . Statistical conclusions
cannot, in general, be drawn from such an analysis.
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Donald F. Burrill [EMAIL PROTECTED]
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