Estimating the IQ of Greg Cochran
Assuming he took two of these tests and scored in the 99.6th percentile, it’s safe to assume that he would probably do it again - so I’ll just correct for the measurement error in the scholastic portion of the correlation (about 0.95) which leads to a regression coefficient of 0.86 instead of 0.84. - which concludes with an estimate of 135 and a standard error of 7.5.
g <- rnorm(20000000, mean=0)
iq <- 0.86*g + rnorm(20000000)*sqrt(1-0.86^2)
subby1 <- data.frame(iq, g)
subby2 <- subset(subby1, (subby1$iq > 2.65 & subby1$iq < 2.75))
mean(subby2$g)
sd(subby2$g)
sd(iq)