Question $1(35$ points$)($a$)(8$ points$)$ Briefly explain, what is a dummy variable? What is the purpose of dummy variables in a regression model? $($b$)(10$ 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$)(9$ points$)$ Briefly explain what is multicollinearity in the context of multiple regression model?