Among the first numerical data analysis fruits of James Burns' archive research (see "Gunning for data", 22 February) are a set of surprisingly strong correlations between crewing levels, tonnage and gunnery on British naval ships during the Revolutionary and Napoleonic Wars period.
James comments on the correlations below, and his plots to illustrate them are reproduced here (click them for an enlarged view in a separate browser window or tab).
“The pairwise relationships between all three variables can be represented as linear, as shown in my scatter and trendline.
The plots also show that a third order polynomial (or cubic) model fits the relationship between tonnage and crew level even better. I explored other models, but found that a second order (quadratic) fit brought very little improvement, third order was the big step, and that there was no benefit from going beyond that to fourth, fifth or sixth order.
This is interesting because it means that crewing was a greater relative overhead cost of expansion in mid range vessels than in first rate ships of the line or in the smaller sloops and brigs.
Although the regression fit for gunnery power against tonnage can be slightly improved by moving to a quadratic model, the difference is not great enough (on this data set, at least) to justify the change.
The correlation of gunnery to crew is firmly linear, and shows no improvement at all if the polynomial order of the model is increased. This probably reflects the composition of fighting vessel crews of the period. There were no separate gunnery personnel, and watch rotation was suspended during military engagement, so total ship's the crew reflected the numbers required to man guns at action stations.”
