Multiple Regression, The Linear Predictor

In the previous two chapters we studied regression models where the linear predictor depended on a single explanatory variable, x. In Chapter 3, x was categorical and for a binary variable (Section 3.1) with values g0,g1 we added bI(xi = g1) {\rm{bI}}({\rm{xi}} = {\rm{g1}}) to the intercept a, whereas in general, for a variable with k + 1 levels (Section 3.2) we added instead the expression b1I(xi = g1) + b2I(xi = g2) + ··· + bkI(xi = gk), {\rm{b1I}}({\rm{xi}} = {\rm{ g1}}) + {\rm{ b2I}}({\rm{xi}} = {\rm{ g2}}) + {\rm{ }}\cdot\cdot\cdot{\rm{ }} + {\rm{ bkI}}({\rm{xi}} = {\rm{ gk}}), with dummy variables for all categories except the reference category (xi = 0).