Note:
- The indicator variable is named after the non-reference group.
- The variables are entered into the ultimate full model in this order – covariate, indicator variable, and interaction variable.
- The submodel for the “Diet-Curtailed” group is found by plugging in 0 for TAME in the full model and then simplifying. Essentially everything in the ultimate full model multiplied by TAME is dropped.
- The submodel for the “Tame” group is found by plugging in 1 for TAME in the full model and then simplifying. Essentially the word TAME is dropped and then the two constants (α and δ_{1}) are lumped together and the two items multiplied by the covariate (β and γ_{1}) are lumped together.
Growth of Pronghorn Antelopes
- The indicator variable is named “TAME” where TAME=1 if the pronghorn is in the “tame” group and TAME=0 if it is in the “diet-curtailed” group.
- The ultimate full model is μ_{WEIGHT} = α + βTIME + δ_{1}TAME + γ_{1}TAME×TIME.
- The submodels for both groups are below
- Diet-curtailed: μ_{WEIGHT} = α + βTIME
- Tame: μ_{WEIGHT} = (α+δ_{1}) + (β+γ_{1})TIME
- Interpretations of the coefficients are below.
- α is the intercept of diet-curtailed (reference) group
- β is the slope of diet-curtailed (reference) group
- δ_{1} is the difference in intercept of tame and diet-curtailed groups (i.e., tame-dietcurtailed)
- γ_{1} is the difference in slopes of tame and diet-curtailed groups (i.e., tame-dietcurtailed)
- The models for the “parallel lines test” are below.
- H_{0}: μ_{WEIGHT} = α + βTIME + δ_{1}TAME
- H_{A}: μ_{WEIGHT} = α + βTIME + δ_{1}TAME + γ_{1}TAME×TIME
- The models for the “intercepts test” (assuming parallel lines) are below.
- H_{0}: μ_{WEIGHT} = α + βTIME
- H_{A}: μ_{WEIGHT} = α + βTIME + δ_{1}TAME