OF HOW you KHOW 3. (*) One very important type of qualitative variable is called a dummy or indicator variable. These variables indicate the presence or absence of an attribute (hence the name) using a 1 when present and a 0 otherwise. For example, we might call the variable M; to be a dummy variable for being married: R = M give at Tea [1, if person i is married otherwise 0, Page sont to support your In a very concrete way, dummy variables can be used as "building blocks" for qualitative variables. Consider the following variables from the survey in Question 1: R, which refers to RP MARSTAT, the marital status of the reference person in the survey: 1, if person i is married or common-law 2, if person i is single and never-married 3, if person i is separated, widowed, or divorced (a) (5 points) What kind of variable is R Explain. (b) (5 points) Suppose you made three dummies Mi, Si, and Di, which are indicators for being married, single, or divorced (respectively). How would these variables be defined in terms of the values of R. Write down an expression for each. 2 (2) (1) > of 4 (c) (5 points) Suppose a dataset called A has just Mi, Di and S. Does this have more information, less information, or the same information as a dataset (called B) with just R? Explain. (d) (5 points (bonus)) How many datasets using M, D, and S; are there with the same information as B? Explain your answer. Total for Question 3: 15