# Inference in logistic regression

When we test the significance of a particular coefficient in linear regression, we assume that the sampling distribution of this coefficient is normally distributed given that the residuals of the regression model is normally distributed following the central limit theorem. As such, we obtain the p-value for the coefficient from the standard normal distribution. My first question is whether my understanding is correct and if yes, my second question is if there is an equivalent way of explaining how we go about testing the significance of a coefficent in logistic regression (i.e., assumption, sampling distribution).

There are some consequences to all of this. For example, one uses the normal distribution to set the length of the confidence interval in logistic regression (or more generally the generalized linear models) rather than a $$t$$ distribution in the linear regression, and everything is approximate not exact.