The Black Death 1346-1353: The Complete History by Ole Benedictow was featured in the New England Journal of Medicine's March 2005 book review. The reviewer criticized the book's claim that the Black Death was the bubonic form of a rodent disease (Y. pestis) spread by fleas. Because the spread of Y. pestis depends on homebound rats, it is known to travel at a rate of only about 8 miles per year, whereas the Black Death "almost equalled that speed per day."9 For each of the two diseases, the speed of spreading corresponds to the slope of the line that relates distance to time, which is not exactly known but could be approximated by experts with interval estimates.
a. According to the critic of the theory that the Black Death and Y. pestis are one and the same, would confidence intervals for those two slopes overlap or not?
b. This problem involves three variables: distance covered, time, and type of disease. Tell whether each is quantitative or categorical, and whether it plays the role of explanatory or response variable.