- GLMs are linear in parameters, that's why “linear”. See also Distinction between linear and nonlinear model and Why is polynomial regression considered a special case of multiple linear regression? for more explanations.
- Why would GLMs be “general models” any more than any other models? You also got the name wrong, it stands for the generalized linear models, because it is a generalization of linear regression. General linear model in fact stands for something else.
- They are important because they are simple, yet versatile. They are easy to interpret, yet very flexible, and often work remarkably well for many problems.
