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Trying to rederive the constants doesn't help me, which is starting to make me wonder if he's really using the table he provided or misstated an equation or something:
If you double 34779 you get very close to his $69,321 so there might be something going wrong due to the 1/2 that appears in uses of the
erf
to make a cumulative distribution function, but I don't how a threshold of 99.64 IQ is even close to his 108!(The weird start values were found via trial-and-error in trying to avoid R's 'singular gradient error'; it doesn't appear to make a difference if you start with, say,
f=90
.)Most importantly, we appear to have figured out the answer to my original question: no, it is not easy. :P
So, I started off by deleting the eight outliers to make lynn2. I got an adjusted R^2 of 0.8127 for the exponential fit, and 0.7777 for the fit with iq0=108.2.
My nls came back with an optimal iq0 of 110, which is closer to the 108 I was expecting; the adjusted R^2 only increases to 0.7783, which is a minimal improvement, and still slightly worse than the exponential fit.
The value of the smart fraction cutoff appears to have a huge impact on the mapping... (read more)