I didn’t find anything that affects weight of fanged turtles independently of shell segment number. The apparent effect from wrinkles and scars appears to be mediated by shell segment number. Any non-shell-segment-number effects on weight are either subtle or confusingly change directions to mostly cancel out in the large scale statistics.
Using linear regression, if you force intercept=0, then you get a slope close to 0.5 (i.e. avg weight= 0.5*(number of shell segments) as suggested by qwertyasdef), and that’s tempting to go for for the round number, but if you don’t force intercept=0 then 0 intercept is well outside the error bars for the intercept (though it’s still low, 0.376-0.545 at 95% confidence). If you don’t force intercept=0 then the slope is more like 0.45 than 0.5. There is also a decent amount of variation which increases in a manner that could be plausibly linear with the number of shell segments (not really that great-looking a fit to a straight line with intercept 0 but plausibly close enough, I didn’t do the math). Plausibly this could be modeled by each shell segment having a weight drawn from a distribution (average 0.45) and the total weight being the sum of the weights for each segment. If we assume some distribution in discrete 0.1lb increments, the per-segment variance looks to be roughly the amount supplied by a d4.
So, I am now modeling fanged turtle weight as 0.5 base weight plus a contribution of 0.1*(1d4+2) for each segment. And no, I am not very confident that’s anything to do with the real answer, but it seems plausible at least and seems to fit pretty well.
The sole fanged turtle among the Tyrant’s pets, Flint, has a massive 14 shell segments and at that number of segments the cumulative probability of the weight being at or below the estimated value passes the 8⁄9 threshold at 7.3 lbs, so that’s my estimate for Flint.
In the non-fanged, more than 6 segment main subset:
Shell segment number doesn’t seem to be the dominant contributor here, all the numerical characteristics correlate with weight, will investigate further.
Abnormalities don’t seem to affect or be affected by anything but weight. This is not only useful to know for separating abnormality-related and other effects on weight, but also implies (I think) that nothing is downstream of weight causally, since that would make weight act as a link for correlations with other things.
This doesn’t rule out the possibility of some other variable (e.g age) that other weight-related characteristics might be downstream of. More investigation to come. I’m now holding reading others’ comments (beyond what I read at the time of my initial comment) until I have a more complete answer myself.
So had some results I didn’t feel were complete enough in to make a comment on (in the senses that subjectively I kept on feeling that there was some follow-on thing I should check to verify it or make sense of it), then got sidetracked by various stuff, including planning and now going on a trip sacred pilgrimage to see the eclipse. Anyway:
all of these results relate to the “main group” (non-fanged, 7-or-more segment turtles):
Everything seems to have some independent relation with weight (except nostril size afaik, but I didn’t particularly test nostril size). When you control for other stuff, wrinkles and scars (especially scars) become less important relative to segments.
The effect of abnormalities seems suspiciously close to 1 lb on average per abnormality (so, subjectively I think it might be 1). Adding abnormalities has an effect that looks like smoothing (in a biased manner so as to increase the average weight): the weight distribution peak gets spread out, but the outliers don’t get proportionately spread out. I had trouble finding a smoothing function* that I was satisfied exactly replicated the effect on the weight distribution however. This could be due to it not being a smoothing function, me not guessing the correct form, or me guessing the correct form and getting fooled by randomness into thinking it doesn’t quite fit.
For green turtles with zero miscellaneous abnormalities, the distribution of scars looked somewhat close to a Poisson distribution. For the same turtles, the distribution of wrinkles on the other hand looked similar but kind of spread out a bit...like the effect of a smoothing function. And they both get spread out more with different colours. Hmm. Same spreading happens to some extent with segments as the colours change.
On the other hand, segment distribution seemed narrower than Poisson, even one with a shifted axis, and the abnormality distribution definitely looks nothing like Poisson (peaks at 0, diminishes far slower than a 0-peak Poisson).
Anyway, on the basis of not very much clear evidence but on seeming plausibility, some wild speculation:
I speculate there is a hidden variable, age. Effect of wrinkles and greyer colour (among non-fanged turtles) could be a proxy for age, and not a direct effect (names of those characteristics are also suggestive). Scars is likely a weaker proxy for age and also no direct effect. I guess segments likely do have some direct effect, while also being a (weak, like scars) proxy for age. Abnormalities clearly have a direct effect. Have not properly tested interactions between these supposed direct effects (age, segments, abnormalities), but if abnormality effect doesn’t stack additively with the other effects, it would be harder for the 1-lb-per-abnormality size of the abnormality effect to be a non-coincidence.
So, further wild speculation: so age affect on weight could also be smoothing function (though, looks like high weight tail is thicker for greenish-gray—does that suggest it is not a smoothing function?
unknown: is there an inherent uncertainty in the weight given the characteristics, or does there merely appear to be because of the age proxies being unreliable indicators of age? is that even distinguishable?
* by smoothing function I think I mean another random variable that you add to the first one, this other random variable takes on a range of values within a relatively narrow range. (e.g. uniform distribution from 0.0 to 2.0, or e.g. 50% chance of being 0.2, 50% chance of being 1.8).
Anyway, this all feels figure-outable even though I haven’t figured it out yet. Some guesses where I throw out most of the above information (apart from prioritization of characteristics) because I haven’t organized it to generate an estimator, and just guess ad hoc based on similar datapoints, plus Flint and Harold copied from above:
updates:
In the fanged subset:
I didn’t find anything that affects weight of fanged turtles independently of shell segment number. The apparent effect from wrinkles and scars appears to be mediated by shell segment number. Any non-shell-segment-number effects on weight are either subtle or confusingly change directions to mostly cancel out in the large scale statistics.
Using linear regression, if you force intercept=0, then you get a slope close to 0.5 (i.e. avg weight= 0.5*(number of shell segments) as suggested by qwertyasdef), and that’s tempting to go for for the round number, but if you don’t force intercept=0 then 0 intercept is well outside the error bars for the intercept (though it’s still low, 0.376-0.545 at 95% confidence). If you don’t force intercept=0 then the slope is more like 0.45 than 0.5. There is also a decent amount of variation which increases in a manner that could be plausibly linear with the number of shell segments (not really that great-looking a fit to a straight line with intercept 0 but plausibly close enough, I didn’t do the math). Plausibly this could be modeled by each shell segment having a weight drawn from a distribution (average 0.45) and the total weight being the sum of the weights for each segment. If we assume some distribution in discrete 0.1lb increments, the per-segment variance looks to be roughly the amount supplied by a d4.
So, I am now modeling fanged turtle weight as 0.5 base weight plus a contribution of 0.1*(1d4+2) for each segment. And no, I am not very confident that’s anything to do with the real answer, but it seems plausible at least and seems to fit pretty well.
The sole fanged turtle among the Tyrant’s pets, Flint, has a massive 14 shell segments and at that number of segments the cumulative probability of the weight being at or below the estimated value passes the 8⁄9 threshold at 7.3 lbs, so that’s my estimate for Flint.
In the non-fanged, more than 6 segment main subset:
Shell segment number doesn’t seem to be the dominant contributor here, all the numerical characteristics correlate with weight, will investigate further.
Abnormalities don’t seem to affect or be affected by anything but weight. This is not only useful to know for separating abnormality-related and other effects on weight, but also implies (I think) that nothing is downstream of weight causally, since that would make weight act as a link for correlations with other things.
This doesn’t rule out the possibility of some other variable (e.g age) that other weight-related characteristics might be downstream of. More investigation to come. I’m now holding reading others’ comments (beyond what I read at the time of my initial comment) until I have a more complete answer myself.
So had some results I didn’t feel were complete enough in to make a comment on (in the senses that subjectively I kept on feeling that there was some follow-on thing I should check to verify it or make sense of it), then got sidetracked by various stuff, including planning and now going on a
tripsacred pilgrimage to see the eclipse. Anyway:all of these results relate to the “main group” (non-fanged, 7-or-more segment turtles):
Everything seems to have some independent relation with weight (except nostril size afaik, but I didn’t particularly test nostril size). When you control for other stuff, wrinkles and scars (especially scars) become less important relative to segments.
The effect of abnormalities seems suspiciously close to 1 lb on average per abnormality (so, subjectively I think it might be 1). Adding abnormalities has an effect that looks like smoothing (in a biased manner so as to increase the average weight): the weight distribution peak gets spread out, but the outliers don’t get proportionately spread out. I had trouble finding a smoothing function* that I was satisfied exactly replicated the effect on the weight distribution however. This could be due to it not being a smoothing function, me not guessing the correct form, or me guessing the correct form and getting fooled by randomness into thinking it doesn’t quite fit.
For green turtles with zero miscellaneous abnormalities, the distribution of scars looked somewhat close to a Poisson distribution. For the same turtles, the distribution of wrinkles on the other hand looked similar but kind of spread out a bit...like the effect of a smoothing function. And they both get spread out more with different colours. Hmm. Same spreading happens to some extent with segments as the colours change.
On the other hand, segment distribution seemed narrower than Poisson, even one with a shifted axis, and the abnormality distribution definitely looks nothing like Poisson (peaks at 0, diminishes far slower than a 0-peak Poisson).
Anyway, on the basis of not very much clear evidence but on seeming plausibility, some wild speculation:
I speculate there is a hidden variable, age. Effect of wrinkles and greyer colour (among non-fanged turtles) could be a proxy for age, and not a direct effect (names of those characteristics are also suggestive). Scars is likely a weaker proxy for age and also no direct effect. I guess segments likely do have some direct effect, while also being a (weak, like scars) proxy for age. Abnormalities clearly have a direct effect. Have not properly tested interactions between these supposed direct effects (age, segments, abnormalities), but if abnormality effect doesn’t stack additively with the other effects, it would be harder for the 1-lb-per-abnormality size of the abnormality effect to be a non-coincidence.
So, further wild speculation: so age affect on weight could also be smoothing function (though, looks like high weight tail is thicker for greenish-gray—does that suggest it is not a smoothing function?
unknown: is there an inherent uncertainty in the weight given the characteristics, or does there merely appear to be because of the age proxies being unreliable indicators of age? is that even distinguishable?
* by smoothing function I think I mean another random variable that you add to the first one, this other random variable takes on a range of values within a relatively narrow range. (e.g. uniform distribution from 0.0 to 2.0, or e.g. 50% chance of being 0.2, 50% chance of being 1.8).
Anyway, this all feels figure-outable even though I haven’t figured it out yet. Some guesses where I throw out most of the above information (apart from prioritization of characteristics) because I haven’t organized it to generate an estimator, and just guess ad hoc based on similar datapoints, plus Flint and Harold copied from above:
Abigail 21.6, Bertrand 19.3, Chartreuse 27.7, Dontanien 20.5, Espera 17.6, Flint 7.3, Gunther 28.9, Harold 20.4, Irene 26.1, Jacqueline 19.7