Hmmm. I agree that it doesn't match. What if by 'regression line' he means the regression line put through the sf-gdp data?
That is, you should be able to calculate sf as a fraction with
sf <- function(iq,c) ((1/2) * (1 + erf((iq-c)/(15*sqrt(2)))))
And then regress that against gdp, which will give you the various coefficients, and a much more sensible graph. (You can compare those to the SFs he calculates in the refinement, but those are with verbal IQ, which might require finding that dataset / trusting his, and have a separate IQ0.)
Comparing the two graphs, I find it interesting that the eight outliers Griffe mentions (Qatar, South Africa, Barbados, China, and then the NE Asian countries) are much more noticeable on the SF graph than the log(GDP) graph, and that the log(GDP) graph compresses the variation of the high-income countries, and gets most of its variation from the low-income countries; the situation is reversed in the SF graph. Since both our IQ and GDP estimates are better in high-income countries, that seems like a desirable property to have.
With outliers included, I'm getting R=.79 for SF and R=.74 for log(gdp). (I think, I'm not sure I'm calculating those correctly.)
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:
R> sf <- function(iq,f,c) ((c/2) * (1 + erf((iq-f)/(15*sqrt(2)))))
R> summary(nls(rGDPpc ~ sf(IQ,f,c), lynn, start=list(f=110,c=40000)))
Formula: rGDPpc ~ sf(IQ, f, c)
Parameters:
Estimate Std. Error t value Pr(>|t|)
f 99.64 3.07 32.44 < 2e-16
c 34779.17 6263.90 5.55 3.7e-07
Residual standard error: 5310 on 79 degrees of freedom
Number of iterations to
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