# What does it mean if magnitude of the variance of each measurement is allowed to be a function of its predicted value?

To better understand Logistic Regression and why it is called regression still, I was reading about Generalized Linear Models on Wikipedia, and I came across the below statement: "The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value."

I am not quite sure I understand the latter part as highlighted in the question. Is it possible this can be clarified for me please?

One simple example with a relationship between mean and variance is the Poisson distribution for count data. If data are distributed that way, the true mean and the variance are identical. For individual Bernoulli trials with probability of success $$p$$, which underlie logistic regression, the variance is $$p(1-p)$$. Those are different from the normal distribution, for which the mean and variance can be independent.