Hospital size and length of stay A study shows that there is a positive correlation between x = size of a hospital (measured by its numbers of beds) and y = median number of days that patients remain in that hospital.

a. Does this mean that you can shorten a hospital stay by choosing a small hospital?

b. Identify a third variable that could be a common cause of x and y. Construct a hypothetical scatterplot (like Figure 3.22 for crime and education), identifying points according to their value on the third variable, to illustrate your argument.