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Comparing the fits of the different enzyme inhibition models requires thinking both about enzyme mechanism and about statistics. Some notes:

The mixed model generalizes competitive, noncompetitive and uncompetitive. Each of those three models are special cases of the mixed-model.

Comparing R2 is an easy way to compare fits, but not a very good method.

Comparing the adjusted R2 is a better way to compare fits. To do this, you need to ask for reporting of adjusted R2 in the parameters dialog. But this is not a rigorous way to compare models.

Prism can compare models using two rigorous approaches, the extra sum-of-squares F test and the AICc approach.

The extra sum-of-squares F test is only valid when one model is a special case of (is nested within) the other model. The mixed model is a general equation that includes competitive, uncompetitive and noncompetitive inhibition as special cases, so it is OK to compare the mixed model with any of the other three by F test.  The competitive model is a special case of the uncompetitive or noncompetitive modes, so you can compare the competitive model with either uncompetitive or noncompetitive models by F test. The uncompetitive and noncompetitive models are not nested so cannot be compared by F test.

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