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An F-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 a null model that just fits the mean of the response. An analysis of variance table partitions the total variance in the response variable into the variation after fitting the full model (called the model error, or residual), the variation after fitting the null model, and the reduction by fitting the full model compared to the null model.
An F-test formally tests whether the reduction is statistically significant. The null hypothesis states that all the parameters except the intercept 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.