13.52 Cancer prediction A breast cancer study at a city hospital in New York used logistic regression to predict the probability that a female has breast cancer. One explanatory variable was x = radius of the tumor (in cm). The results are as follows:

The quartiles for the radius were Q1 = 1.00, Q2 = 1.35, and Q3 = 1.85.

a. Find the probability that a female has breast cancer at Q1 and Q3.

b. Interpret the effect of radius by estimating how much the probability increases over the middle half of the sampled radii, between Q1 and Q3.