## Fitness ofOLS Model

The assumptions of the OLS linear regression model strictly concern the error term (e) that can be represented by the pattern of residuals. The residuals from the fitted model are important for checking whether the assumptions of linear regression analysis are met (Quinn and Keough 2004). The residuals of the OLS models tended to be symmetrically distributed and centered on zero, suggesting that these models were well fit for the data in rice paddies under the F-D-F and the F-D-F-M (Fig. 9.3a-c). Power analyses for the model F-D-F-2 and the model F-D-F-M also showed that these linear relationships were strong enough to model the N2O data (Table 9.4). On the other hand, a stronger power for the model F-D-F-2 relative to the model F-D-F-1 suggested that it was better suited for the data, although both models had the similar determination coefficient (r2) (Table 9.4). However, great cares should be taken in using the r2 values for comparing the fitness of different models, such as the model F-D-F-1 and the reduced model F-D-F-2 in this study, since it is inappropriate for comparing models with different numbers of parameters (Scott and Wild 1991).

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