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An effect of model likelihood ratio test formally tests the hypothesis of whether the model fits the data better than no model.
It is common to test whether the model fits the data better than the null model that just fits the mean of the response.
A likelihood ratio G2 test formally tests whether the reduction is statistically significant. The null hypothesis states that all the parameters for the covariates are zero against the alternative that at least one parameter is not equal to zero. When the p-value is small, you can reject the null hypothesis and conclude that at least one parameter is not zero.