For the model in the previous exercise with constraints ????1 = ????1 = 0, generalize the model by adding an interaction term ????ij.

a. Show the new full-rank model matrix. Specify the constraints that {????ij}

satisfy. Indicate how many parameters the ????ij term represents in ????.

b. Show how to write the linear predictor using indicator variables for the factor categories, with the model parameters as coefficients of those indicators and the interaction parameters as coefficients of products of indicators.