Let X1,..., X4 be binary. Draw the independence graphs corresponding to the following log-linear models. Also, identify whether each is graphical and/or hierarchical (or neither).
(a) log f = 7+ 11x1 + 2x2 + 1.5x3 + 17x4
(b) log f = 7+ 11x1 + 2x2 + 1.5x3 + 17x4 + 12x2x3 + 78x2x4 + 3x3x4 + 32x2x3x4
(c) log f = 7+11x1 +2x2 +1.5x3 +17x4 +12x2x3 +3x3x4 + x1x4 +2x1x2
(d) log f = 7 + 5055x1x2x3x4