Interpreting parameters with factors and interactions Suppose we have a regression problem with a factor A with two levels (a 1 , a 2 ) and a factor B with three levels (b 1 , b 2 , b 3 ), so there...

Interpreting parameters with factors and interactions Suppose we have a regression problem with a factor A with two levels (a₁, a₂) and a factor B with three levels (b₁, b₂, b₃), so there are six treatment combinations. Suppose the response is Y, and further that E(Y|A = ai, B = bj) = μ_ij. The estimated μ_ij
are the quantities that are used in effects plots. The purpose of this problem is to relate the μ_ij
to the parameters that are actually fit in models with factors and interactions.