I have been analysing data from about 700 parishes in the southwest of England, looking for patterns of how rent was set in the 1830s. The relationship between arable rent and wheat and barley yields is very strong, as we would expect. I started off the analysis with 96 parishes in Devon, in the far southwest of England. Here the relationship between rent and distance to market is very clear....further from market the lower the rent. Over the holidays, Malcolm helped me to increase the dataset, moving east towards London. The larger dataset was initially puzzling, because distance to market was no longer significant and had a positive sign. This morning I regressed distance to market against longitude and found that distance to market decreases as we move east towards London. In other words, there is a higher population density and so the farmer doesn't have to cart his produce so far to sell it. Here is a scatter plot with the regression trend line:
Now, I'll be the first to agree that this looks pretty much like wasps around a honey jar: BUT the relationship is statistically highly significant although with very little explanatory power (r-squared is small). I think this negative relationship goes towards explaining my initially confusing results. [Obvious when you think about it, which is (probably) what Newton thought after the apple landed on his head. ]
I did some more probing and found that the sign for market distance changes from negative and significant to either positive or not significant at about longitude= - 3.25. This is close to the eastern borders of our two western counties. Next step is to go to the 1841 census files and get population densities for the six counties we have been analysing. Clearly it wouldn't be a huge surprise if distance to market correlated with population density.