Track in 40km radius of Holkham Hall

Malcolm has done a wizard job of calculating the amount of track on an annual basis within a 40km radius of Holkham Hall in Norfolk. The graph is here:

Our hypothesis is that the availability of track would reduce the costs of farming to the tenant farmer, but that the landowner would grab the savings in the form of higher land rents---the 'resource extraction' theory.The next step is for me to test this using a time-series regression, controlling for other variables such as the price of wheat and the price of livestock. We need to hold steady the other variables so that we can isolate the effect of the reduced transport cost. Rent is the dependent variable and then the amount of track and the various prices are the independent (or 'explanatory' variables). The equation looks like this:

 
The regression is a time-series, and so we have to remove the effects of auto-correlation over time. I've omitted all the subscripts for time for clarity. We can use ARIMA for the regression. This is exciting and a great way to spend the holiday! Thanks Malcolm for your speedy work. I'll be back with some statistical output shortly.