Troubleshooting
Problem
SPSS printed a negative number for Adjusted R Square. I thought that R Square should always be positive. What's wrong?
Resolving The Problem
Nothing. When R Square is small (relative to the ratio of parameters to cases), the Adjusted R Square will become negative. For example, if there are 5 independent variables and only 11 cases in the file, R^2 must exceed 0.5 in order for the Adjusted R^2 to remain positive.
Adjusted R Square is defined as
R^2 (adj) = R^2 - (1-R^2)p/(C-p*)
where
C is the sum of caseweights,
p is the number of independent variables,
p* is the number of coefficients in the model,
p* = p if the intercept is not included;
p* = p+1 otherwise.
[See SPSS Statistical Algorithms]
The smallest value that R^2 (adj) can have occurs when R^2 = 0; that
value is -p/(C-p*).
R^2 (adj) will be negative when
R^2 <= p/(C-p*+p),
that is, R^2 (adj) < 0 if and only if
R^2 <= p/C if the intercept is not included;
R^2 <= p/(C-1) otherwise
Related Information
Historical Number
15377
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Document Information
Modified date:
16 April 2020
UID
swg21476093