I have a simple question that I cannot figure out. When specifying a regression model with categorical variables as an independent variable, it's possible to perform the coding in two ways. For a nominal variable with multiple levels (example: four countries), what is the difference in modelling the variable as 3 dummy variables (and an intercept) in comparison with coding it as four levels within one variable and setting a reference in a regression model and setting one of the categories as the reference? Are they equivalent and is there an advantage or disadvantage to either approach (is the regression equation the same?). Thanks for your responses.