Refer to Problem 6.13 with Table 6.17.

a. Show that model (CE, CH, CL, EH, EL, HL) fits well. Show that model (CEH, CEL, CHL, EHL) also fits well but does not provide a significant improvement. Beginning with (CE, CH, CL, EH, EL, HL), show that back- ward elimination yields (CE, CL, EH, HL). Interpret its fit.

b. Based on the association graph for (CE, CL, EH, HL), (i) show that every path between C and H involves a variable in (E.L); (ii) explain why, col- lapsing over H, one obtains the same associations between C and E and between C and L, and collapsing over C, one obtains the same associations between H and E and between H and L; (iii) explain why the conditional independence patterns between C and H and between E and L are not collapsible.