The accompanying data set contains three variables, x₁, x₂, and x₃. 

a. The variable x₁ contains 3 categories: S, M, and L. Convert the category names into category scores (i.e., S = 1, M = 2, and L = 3). How many observations have a category score of 3? 

b. Transform x₂ into an appropriate number of dummy variables. How many dummy variables should be created? 

c. The variable x₃ contains four categories: A, B, C, and D. Reduce the number of categories by combining the two least-frequent categories into a new category E. How many observations are in the E category?