|Malcolm's map showing wheat origins|
Malcolm has kindly provided me with a set of measurments from the two major wheat producing counties (Cambridgeshire and Lincolnshire) to each of the counties. See Malcolm's map on the right. We know the price difference between the wheat exporting county and county of importation; the distance between the two; the mean elevation of the journey, and the standard deviation of the elevation of the journey. The last measurement is to proxy the 'roughness' of the journey. I figured that greater changes in the standard deviation would be more expensive for the horse and cart operators of that time, and so they would increase the prices accordingly. We only have about 35 observations, but the results are interesting. After some experimentation, I found that regressing the natural log of the price difference against the natural log of the distance produced an acceptable result (p=0.02). The scatter plot of log price difference on the x axis with log distance on the y axis is shown here, together with a trend line of predicted values.
|Regression of log price diff against log distance|