Inthe Crabs data fileintroducedin Section 7.4.2, thevariable y indicates whetherafemale horseshoecrabhasatleastonesatellite(1 = yes,0 = no).

(a) Fitamain-effectslogisticmodelusingweightandcategoricalcolorasexplanatoryvari-

ables. Conductasignificancetestforthecoloreffect,andconstructa95%confidence intervalfortheweighteffect.

(b) Fitthemodelthatpermitsinteractionbetweencolorasafactorandweightintheireffects, showingtheestimatedeffectofweightforeachcolor.Testwhetherthismodelprovidesa significantlybetterfit.

(c) UseAICtodeterminewhichmodelsseemmostsensibleamongthemodelswith(i)inter-

action, (ii)maineffects,(iii)weightasthesolepredictor,(iv)colorasthesolepredictor, and (v)thenullmodel.