Canada has 10 provinces and 3 territories for a total of 13 administrative regions. A researcher is studying the growth patterns and health of a particular animal species. He wants to include in his regression information about which administrative region each animal observed is from. (a) The researcher is contemplating using a "region" variable and assigning 12 of the regions a number, 1 through 12, leaving one region out to be the base case. Given concerns of perfect multicollinearity, will this approach work? (b) A friend of the researcher suggests creating 12 separate dummy variables, one for each region except one, and coding the variables with a 1 if the animal being observed is from that region, otherwise coding as a zero. Given concerns of perfect multicollinearity, will this approach work? How should the coefficient be interpreted?