Looking at this further, by far the strongest effect is the latitude, and that looks more like a rectangular effect than a trigonometric one. Replacing the trigonometric fit with one that modelled a rectangulat latitude effect and no other yielded a model that explained most of the variation. By itself this looks better than the previous model.
The next biggest effect looks like it is due to variation in murphys constant. This looked vaguely quadratic.
The next biggest effect looked like it was due to variations in the value of Pi. It looked vaguely triangular, with the point ust below 3.15.
The next biggest effect looked like a vaguely sinusoidal variation due to the longitude.
Including all of these in a model yielded one with a standard deviation of 4.9, and predicted that the following 12 locations were the best:
76804 VALUE:87.95301643603202
16965 VALUE:88.18566645580597
104815 VALUE:88.34280034001172
8415 VALUE:88.39346893009704
18123 VALUE:88.50303192064138
107929 VALUE:88.5221749787355
99595 VALUE:88.59004262250107
80395 VALUE:88.59313676878352
42742 VALUE:88.72736581213306
40639 VALUE:88.80584599223495
65607 VALUE:90.36919375244607
94304 VALUE:90.63981001558145
This is currently my best estimate. As the predicted values are all < 100 I will have to file a report on this with the empires colonisation department in case there is every any interest in making another attempt, but I won’t risk the empresses’ rath by attempting to colonise any of them.
>!Grey turtles have a much lower weight than most 3.9->7.9
Greyish green turtles have a lower weight then the green ones, though the ranges overlap. Lowest 13 highest 42.9
There is a big spike in the number of green turtles with a weight of 20.4
Suggests we are dealing with multiple distinct species.
The spike in green turtles with a weight of 20.4 all have 6 shell segments.
No green turtle with 6 shell segments has a weight other than 20.4.
Therefore Harold has a weight of 20.4
All gray turtles have fangs, and no other coloured turtles do. Means we can ignore this as any effect will be entirely contained in the colour.
There appears to be a slight increase in weight with the number of wrinkles, scars, shell segments, and miscellaneous abnormalities, though the rate of increase depends on shell colour, and to a lesser extent on nostril size.
Fitting a linear model explains just under 80 percent of the variation for grey turtles, and a little over 50 percent for the rest.
There is no obvious pattern to the deviations, and there is clearly a lot of randomness as a lot of identical turtles have widely differing weights.
My best estimate for the weights of the turtles based on the linear model is as follows:
Abigail 20.0
Bertrand 17.3
Chartreuse 22.8
Dontanien 19.2
Espera 16.5
Flint 6.8
Gunther 25.5
Harold 20.4
Irene 21.7
Jacqueline 18.6
If I wanted to maximise my income from the constitutional despot I should bump up the estimates a bit, however I don’t need the money, and frankly my reputation as an honest scholar is worth more than a few gp. And who knows if enough people ignore perverse incentives like this he may stop offering them and become a less wrong constitutional despot? I can dream at least. As for the unflattering portrait, you can always judge someone by the quality of the pepole you have offended. Coming from him that is going to be seen as a compliment by the people that I care about, not an insult. So I will just give him my best estimates and move on.