Three Clinics, Three Downward Slopes
Nine points $(x, y)$ come from three groups. Group 1: (0,6), (1,5), (2,4). Group 2: (2,6), (3,5), (4,4). Group 3: (4,8), (5,7), (6,6). Within each group the points lie exactly on a line of slope $-1$. What is the slope of the least-squares line fitted to all nine points pooled together? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
Source: Simpson's paradox in regression form (ecological fallacy); data original. Statement written for AxiomIQ.