It is argued in this note that the coefficient of determination (R2) is not useful as a goodness-of-fit statistic if the covariance matrix of the random terms is not scalar and Ordinary Least Squares (OLS) estimation is used. It is further pointed out that the R2 is not well defined for the Generalized Least Squares (GLS) estimation procedure. GLS estimates are usually obtained by first transforming the original variables and then using OLS on the transformed variables. When this procedure is used, the R2 produced by computer programs is not defined and cannot be interpreted as the OLS R2.
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Blomquist et al. (1980) studied this question.
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