Q. 6 (20 points) These data describe the daytime habits of two species of lizards, grahami and opalinus. They were collected by observing occupied sites or perches and recording the appropriate description, namely species involved, time of the day, height and length. Time of the day is recorded as early, mid- day or late (McCullagh and Nelder, 1989, p.129). They want to investigate the effect of these independent variables on the probability that a lizard caught at a site will be grahami. Here is the data. 1235 length height time y n short low early 54 67 short high early 44 49 long 4 long low early 25 43 high early 18 19 5 short low mid 77 98 6 short high mid 63 67 7 long low mid 64 97 8 long high mid 21 26 9 short low late 22 36 10 short high late 25 38 11 long low late 13 24 12 long high late 5 10 (a) (5 pts) First fit the full model with three-way interaction. If you were to simplify the model by removing a predictor, which would you remove? Why? (b) (10 pts) Use a model-building method to select the best model. Provide interpre- tation for the selected final model. (c) (5 pts) Conduct the goodness-of-fit test with the final model. Write down the conclusion.