Hypothesis Testing in Logistic Regression In Linear Regression, the book Introduction to Statistical Learning argued that we should use the $F$ statistic to decide if s $\beta_1 = \beta_2 = ... = 0$ instead of looking at individual p-values for the $t$ statistic.
For instance, consider an example in which p = 100 and  $\beta_1 = \beta_2 = ... = 0$
is true, so no variable is truly associated with the response. In
this situation, about 5 % of the p-values associated with each variable will be below 0.05 by chance.
But when discussing Logistic Regression, we settled with looking at individual p-values of the coefficients,as also seen in this tutorial.
Is there a $F$ statistic counterpart for Logistic Regression?
Thanks
 A: The likelihood-ratio test on a model fit by maximum likelihood, (for example, a logistic regression or another generalized linear model), is a counterpart to the $F$ test on a linear regression model. Both allow for testing the overall model against the null model (in R, outcome ~ 1), as in your question, and generally for testing nested models against each other.
In R, the anova() function applied to 2 nested glm models will provide a likelihood-ratio test if you set test = "LR". Unlike anova() for linear regression with an $F$ test default, you need to specify the test.
For testing the full model against the null, you can construct the test yourself from the values of likelihoods or deviances and degrees of freedom typically reported for the full and null models. In R, from summary(model) you take the difference between the reported null and residual deviances, and test against chi-square with degrees of freedom equal to the difference between the null and residual degrees of freedom.
See the related UCLA IDRE page for a worked-through example and further information on testing things like combinations of predictors or different levels of a categorical predictor.
