Refer to model (5.2) for the horseshoe crabs using x = width.

a. Show that (I) at the mean width (26.3), the estimated odds of a satellite equal 2.07; (ii) at x = 27.3, the estimated odds equal 3.40; and (iii) since exp(β̂ ) = 1.64, 3.40 = (1.64)2.07, and the odds increase by 64%.

b. Based on the 95% confidence interval for β, show that for x near where π = 0.5, the rate of increase in the probability of a satellite per 1-cm increase in x falls between about 0.07 and 0.17.