the nonlinearity of the effect of distance from 3.15
edit: I would definitely have seen anything as large as 3% like what your showing there. Not sure what the discrepancy is from.
, I will look again at that.
Your new selection of points is exactly the same as mine, though slightly different order. Your errors now look smaller than mine.
On Murphy:
It seemed to me a 3rd degree polynomial fits Murphy’s Constant’s effect very well (note, this is also including smaller terms than the highest order one—these other terms can suppress the growth at low values so it can grow enough later)
edit: looking into it, it’s still pretty good if I drop the linear and quadratic terms. Not only that but I can set the constant term to 1 and the cubic term to −0.004 and it still seems a decent fit.
...which along with the pi discrepancy makes me wonder if there’s some 1/x effect here, did I happen to model things the way around that abstractapplic set them up and are you modeling the 1/x of it?
Ah, that would be it. (And I should have realized before that the linear prediction using logs would be different in this way). No, my formulas don’t relate to the log. I take the log for some measurement purposes but am dividing out my guessed formula for the multiplicative effect of each thing on the total, rather than subtracting a formula that relates to the log of it.
So, I guess you could check to see if these formulas work satisfactorily for you:
log(1-0.004*(Murphy’s Constant)^3) and log(1-10*abs((Local Value of Pi)-3.15))
In my graphs, I don’t see an effect that looks clearly non-random. Like, it could be wiggled a little bit but not with a systematic effect more than around a factor of 0.003 or so and not more than I could believe is due to chance. (To reduce random noise, though, I ought to extend to the full dataset rather than the restricted set I am using).
Huh. On Pi I hadn’t noticed
the nonlinearity of the effect of distance from 3.15
edit: I would definitely have seen anything as large as 3% like what your showing there. Not sure what the discrepancy is from.
, I will look again at that.
Your new selection of points is exactly the same as mine, though slightly different order. Your errors now look smaller than mine.
On Murphy:
It seemed to me a 3rd degree polynomial fits Murphy’s Constant’s effect very well
(note, this is also including smaller terms than the highest order one—these other terms can suppress the growth at low values so it can grow enough later)edit: looking into it, it’s still pretty good if I drop the linear and quadratic terms. Not only that but I can set the constant term to 1 and the cubic term to −0.004 and it still seems a decent fit.
...which along with the pi discrepancy makes me wonder if there’s some 1/x effect here, did I happen to model things the way around that abstractapplic set them up and are you modeling the 1/x of it?
Hm. I’m trying to predict log of performance (technically negative log of performance) rather than performance directly, but I’d imagine you are too?
If you plot your residuals against pi/murphy, like the graphs I have above, do you see no remaining effect?
Ah, that would be it. (And I should have realized before that the linear prediction using logs would be different in this way). No, my formulas don’t relate to the log. I take the log for some measurement purposes but am dividing out my guessed formula for the multiplicative effect of each thing on the total, rather than subtracting a formula that relates to the log of it.
So, I guess you could check to see if these formulas work satisfactorily for you:
log(1-0.004*(Murphy’s Constant)^3) and log(1-10*abs((Local Value of Pi)-3.15))
In my graphs, I don’t see an effect that looks clearly non-random. Like, it could be wiggled a little bit but not with a systematic effect more than around a factor of 0.003 or so and not more than I could believe is due to chance. (To reduce random noise, though, I ought to extend to the full dataset rather than the restricted set I am using).