In an ATI study with three treatments, A 1 ,A 2 , and A 3 , and an attribute, X, effect coding was used to code the treatments as follows: in EI, subjects receiving treatment Al were identified (i.e.,...

In an ATI study with three treatments, A₁,A₂
, and A₃, and an attribute, X, effect coding was used to code the treatments as follows: in EI, subjects receiving treatment Al were identified (i.e., assigned 1 's); in vector E2, subjects receiving treatment A₂
were identified; subjects receiving treatment A₃
were assigned -1 's in both vectors. Product vectors were generated: XE1 and XE2. The overall regression equation was

Y'= 20.35 + 2.37X + 5.72El - 3.70E2 + 1.12XEl + .76XE2

(a) What are the separate regression equations for the three groups?

(b) What vectors should be included in a regression analysis if one wishes to calculate the common regression coefficient (be)?