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.
Thank you for posting this. My findings are as follows:
Only 2 existing locations have > 100 performance. Both of these have:
- No strange smell
- Mint air
- Adequate Feng Shui
Most other high performers (But sub 100) have the same properties. Addittionally the weird sounds of the high performers are either:
- Eerie Silence
- Otherworldly Skittering
This suggests it would be sensible to restrict ourselve to locations with these properties. This alone increases the average performance from 23.12 to 46.92
High values of murphys constant are bad, though the affect seems to become small at around 3.5. There is some evidence to suggest that amongst the high performing section (But not the others) too low a value of murphys constant would be counterproductive, though it is a small affect. It may be a statistical fluctuation. Restricting to locations with a value < 3.5 would leave an average of 62.77
A value of pi below the normal value also looks harmful, though one that is too high also looks counterproductive. It looks like a relatively modest effect though and I don't wan to exclude too many possible locations, so I won't exclude any locations based on the value of pi.
There are few high performing ones between latitude -38 and +38.
There are few high performing ones around shortitude 0, and +-90
There are few high performing ones around deltitude 0, and +-90
But this might be caused by the small number of bases in these areas.
I then fitted a simple linear trigonometric model to the records that had the other properties that were identified with high performance. This gave the following model:
90.40498684665667+1.0177516945528096*sin(deltitude)+11.356095534597717*cos(deltitude)-0.17160136718146096*sin(shortitude)+14.734915658705445*cos(shortitude)-2.41427525418688*sin(latitude)-62.034325081735766*cos(latitude)+5.158741059290979*sin(longitude)+8.287780468342245*cos(longitude)
Standard deviation of error is 13.19479724158273 The no of records was 180
I found that the standard deviation error was reduced when degrees were converted to radians using the local value of pi, so that is what was used.
This predicts that the following 12 possible locations have the best performance:
38730 VALUE:110.47214318466737
103420 VALUE:110.67976641439135
91328 VALUE:111.69109272372066
26403 VALUE:112.35848311090837
7724 VALUE:112.40205758474453
21409 VALUE:113.21091851443907
89352 VALUE:113.88444725998731
3090 VALUE:113.89351821821175
65317 VALUE:121.11038526877846
57364 VALUE:123.12690147352956
26627 VALUE:132.5469987591373
91627 VALUE:134.17450784571542
In practice I think it is unlikely that all of them will be greater than 100, but it looks like it will probably be good enough to please the empress.
My best estimate is:
Hammer Hurler
Matchlock Marauder
Professor Pyro
This is also my entry for the PvP contest
I found this problem late. Could I have an extra day or two please?
I think this would have worked better if there had been less data. Looking at the other responses I'm not convinced that adding serval hundered thousand addittional rows did anything significant other than to extend the time needed to scan across this. This stopped me doing a more extensive analysis.
Also I found this one less interesting than the previous ones. I suspect a lot of this has to do with the introductory storyline which didn't make much sense to me. Possibly this was because I hadn't heard of the "homestuck" story before, and didn't have any relevant pre-existing context to relate this to.
I found this one much more difficult to get into than the other problmes in the series. Possibly irrationally I suspect this is because the back ground story was rather convoluted. I was able to load all the data, though it took about 20s to scan all over it which felt like an inconvenient delay.
Based on a rather cursory analysis I hope that the following two won't be too bad:
Page of Hope and Heir of Space
I haven't had a chance to analyse any effects that depend on Waking-Time yet. But based on the other data every other Snark that was hunted that matched one of B/G/H/P/Q/Y was successfully hunted so if this was for real I would play it safe and go with:
B G H P Q Y
To maximise value:
A B C D G H J K L M N P Q R V W Y
Looks like it will yield an expected value of just over 14, albeit with an uncomfortably low 84 percent chance of survival. This is my provisonal entry to the bonus task if I don't get a chance to analyse Waking-Time dependant effects.
Thank you for posting this. I didn't think this was too straightforward. Prior to reading the solution I actually thought it was one of the more difficult ones. Possibly because I focused on trying to copy the allocation helms early choices instead of on the ratings.
Some traits definitely go better with some houses, however I couldn't see much in the way of clear cut rules. I constructed the following highly provisional allocation by considering students that were sorted when the helm was still reasonably reliable, and then combining the probabilities of a student with each of the 5 ratings being sorted into each house, and selecting the one which on balance seemed most likely.
A Dragonslayer
B Thought-Talon
C Serpentyne
D Dragonslayer
E Humblescrumble
F Serpentyne
G Dragonslayer
H Humblescrumble
I Humblescrumble
J Thought-Talon
K Dragonslayer
L Dragonslayer
M Dragonslayer
N Dragonslayer
O Serpentyne
P Thought-Talon
Q Dragonslayer
R Humblescrumble
S Serpentyne
T Humblescrumble
>!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.