(a) How many dummy variables are required to represent the categorical variable? 2
oSMJoqqo 0 pue |aAo JoJ T =6x pue 3S|MUoUso 0 pue Z IDAJoJ I=Zx ououm xg+ Zx2g+TxTg+0g =(X) O E(y) = , + ,, + x where = 1 for level 1, = 2 for level 2, and = 3 for level 3.
O E(y) = o + 1 + 22 + + 44 where X = 1 for level 1 and 0 otherwise, X3 = 1 for level 2 and 0 otherwise, and x4 = 1 for level 3 and 0 otherwise.
(c) Interpret the parameter , in your regression equation.
, is the change in E(y) for a 1 unit change in x, holding the quantitative variable constant. , is the change in y for a 1 unit change in - , is the change in y for a 1 unit change in , holding the categorical variable constant.
O , is the change in E(y) for a 1 unit change in x, holding the categorical variable constant.
Interpret the parameter , in your regression equation. is the change in E(y) for a 1 unit change in X1. , represents two times the difference in the expected value of y for level 1 and level 3.
, is not included in the regression equation. , represents the difference in the expected value of y for level 1 and level 2.
Interpret the parameter in your regression equation. is the change in (y) for a 1 unit change in represents the difference in the expected value of y for level 1 and level 3.
is not included in the regression equation. 3 represents the difference in the expected value of y for level 1 and level 2.
Interpret the parameter , in your regression equation.