Following Theil (1971), we define the incremental explanatory power of the
book value and residual earnings variables in terms of differences in the coefficient
of determination (R2). These differences are sometimes called the semi-partial
coefficient of determination (Cohen and Cohen, 1975, pp. 79±84). They are a
measure of the incremental explanatory power of one variable given the remaining
independent variables.
Define the R2 statistics from Equations (2), (3), and (4) as Rb
2, Rr
2, and R2
b,r, respectively.
Then the incremental explanatory power is defined as: