please give well elabored answers for each part. If possible with suitable examples(wherever pissible).

Question 1 (30 points) (a) (8 points) Briefly explain, what is a dummy variable? What is the purpose of dummy variables in a regression model? (b) (8 points) How do we interpret regression coefficients associated with dummy variables? (c) (8 points) What is a dummy variable trap? How can we avoid it? (d) (6 points) How do we interpret slope cofficients in a multiple regression model