In a study of nesting horseshoe crabs, each female horseshoe crab had a male crab attached to her in her nest. The study investigated factors that affect whether the female crab had any other males, called satellites, residing near her. Explanatory variables that are thought to affect this included the female crab's color (C), spine condition (S), carapace width (W) and weight (Wt). The response outcome for each female crab is her number of satellites (Sa). There are 173 females in this study. Data are provided in the crab.txt. (a) Fit a Poisson model (M1) with log link with W as the single predictor. Check the goodness of fit and interpret your model. (b) Fit a model (M2) with W and Wt as predictors. Compare it with the model in (a). Interpret your results. (c) Check over dispersion in M2. Interpret the model after adjusting for over dispersion.