What is the expected form of the multiple regression equation for level 1 of factor A and level 3 of factor B in a two-factorial design?

In a two-factorial design, the expected form of the multiple regression equation represents the response variable (in this case, E(y)) in relation to the factors involved, which are typically coded as levels of those factors. The model includes an intercept (B0) and terms to account for the effects of the factors being studied.

In this context, when referring to level 1 of factor A and level 3 of factor B, you are essentially isolating the specific effects associated with those levels. Since factor levels generally have corresponding coefficients (often denoted as b1, b2, b3, etc.), the expected value of the response variable for a specific combination of levels can be simplified to represent just the intercept and the coefficient for the specific level of interest.

The correct formulation, E(y)=B0+B3, reflects that the expected value at level 3 of factor B is simply the base effect captured by B0, adjusted for the impact of being at level 3 of factor B. The presence of other factors or interactions does not alter the specific expected outcome for the particular combination of levels being evaluated; it is solely dependent on the intercept and the relevant coefficient for level 3 of factor B.

This model does not include additional