A study of horseshoe crabs by zoologist Dr. Jane Brockmann at the University of Florida used logistic regression to predict the probability that a female crab had a male partner nesting nearby. One explanatory variable was x = weight of the female crab (in kilograms). The results were
The quartiles for weight were Q1 = 2.00, Q2 = 2.35, and Q3 = 2.85.
a. Find the estimated probability of a male partner at Q1 and at Q3.
b. Interpret the effect of weight by estimating how much the probability increases over the middle half of the sampled weights, between Q1 and Q3?