GLM : Basics

Question 1

What do linear regression models assume?

Answer 1

Response variable is normally distributed with constant variance.

Question 2

What are the shortcomings of linear probability models?

Answer 2

1. Response doesn’t have a normal distribution so residual analysis is meaningless
2. Linear function may may assume values less than 0 or greater than 1, which are impossible for pi.
3. The variance is not constant; in fact, it is pi(1 - pi), a function of the mean

Question 3

What are the mean, the variance and the distribution of the response in a linear regression?

Answer 3

Mean of the response (yi) = systematic component

yi has a normal distribution with fixed variance