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 δ1) are lumped together and the two items multiplied by the covariate (β and γ1) are lumped together.

Growth of Pronghorn Antelopes

  1. 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.
  2. The ultimate full model is μWEIGHT = α + βTIME + δ1TAME + γ1TAME×TIME.
  3. The submodels for both groups are below
    • Diet-curtailed: μWEIGHT = α + βTIME
    • Tame: μWEIGHT = (α+δ1) + (β+γ1)TIME
  4. Interpretations of the coefficients are below.
    • α is the intercept of diet-curtailed (reference) group
    • β is the slope of diet-curtailed (reference) group
    • δ1 is the difference in intercept of tame and diet-curtailed groups (i.e., tame-dietcurtailed)
    • γ1 is the difference in slopes of tame and diet-curtailed groups (i.e., tame-dietcurtailed)
  5. The models for the “parallel lines test” are below.
    • H0: μWEIGHT = α + βTIME + δ1TAME
    • HA: μWEIGHT = α + βTIME + δ1TAME + γ1TAME×TIME
  6. The models for the “intercepts test” (assuming parallel lines) are below.
    • H0: μWEIGHT = α + βTIME
    • HA: μWEIGHT = α + βTIME + δ1TAME