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R² is still calculated as the regression sum of squares divided by the total sum of squares. However, when there is no intercept in the model, the uncorrected, rather than corrected, sum of squares is used. The best reference for exactly how the calculations are being performed is the section on multiple correlation in Searle (1971, pp. 95-98). A good discussion of regression through the origin can also be found in SAS System for Regression. Note that PROC GLM calculates R² for the NOINT model in the same way.

For a discussion of the properties of different estimators of R², see Kvalseth (1985). It discusses eight different estimators of R², all of which are equivalent for a linear model with an intercept, in terms of both linear models without an intercept and nonlinear models.

The most important things to note are that the R² for a nointercept model is calculated differently from that for a linear model with an intercept and that the two should not be directly compared. For those wanting to make such a comparison, Myers (1990) suggests calculating R² for the NOINT model as follows:

1 - (error SS from noint model / corrected total SS).

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