In the horseshoe crab data, it was determined that weight modifies the association between crab color and having a satellite. (There is a significant weight x dark interaction term). Weight was coded in standard deviation units. logit(Y) = b0 + b1 (weight_std) + b2 (dark) + b3 (weight_std x dark) Our goal is to obtain a formula for the odds ratio comparing dark vs. non-dark crabs. 1a. Considering only crabs of mean weight (weight_std = 0), give a formula for the odds ratio comparing dark vs. non-dark crabs. 1b. Considering only crabs with weight 1SD above the mean (weight_std = 1), give a formula for the odds ratio comparing dark vs. non-dark crabs. (Hint: Multiply the odds ratio from 1a by the appropriate exponentiated interaction term.) 1c. What is the general formula for the odds ratio comparing dark to non-dark crabs? (Hint: consider crabs with weight_std = w. Your formula should be a function of w.)