But you may also be struck by the shape of that trend line (Sen is quick to note, by the way, that he's not a statistician). It roughly suggests a political tip

But you may also be struck by the shape of that trend line (Sen is quick to note, by the way, that he's not a statistician). It roughly suggests a political tipping point somewhere around a population density of about 800-1,000 people per square mile. My guess would be that this is a linear fit using a least squares minimization. The fit is dominated by the upper right portion of the plot and has a relatively arbitrary x-intercept of around -10. Population density going negative doesn't make sense and shouldn't be a feature of a reasonable model. There's no tipping point, it's just how the line shows up on a log plot and it's almost entirely determined by the data with population density much great than 1000. I think it would make a more sense to plot population density on the x-axis because the scatter in the data is really coming from the Cook PVI rather than the population density and the Cook PVI can be interpreted as a dependent variable. We know very precisely what the populations are and we can also see that the magnitude of the Cook PVI scatter looks roughly constant as a function of population density. After this a simple least squares fit would be more reasonable to apply but again a line would not fit the data at all. Just by eye I would say that (Cook PVI)=AxLog[ (Population Density)xB ] would do a much better job modeling the distribution. Overall, it's a nice plot to motivate discussion but the fit doesn't really add anything to it and might even detract from it.