Estimating the IQ of Al Gore
score of 135 as a child, 1355 on the SAT
Steve Sailer claims that’s a z-score of roughly 2.46, which is good enough for me.
assuming correlation between SAT and IQ of 0.84, and longitudinal regression to the mean of 0.6
Simulations (tm) generate estimate of 135 with SE of 7.5
set.seed(1)
g <- rnorm(60000000, mean=0)
iq <- 0.6*g + rnorm(60000000)*sqrt(1-0.6^2)
sc <- 0.84*g + rnorm(60000000)*sqrt(1-0.84^2)
subby1 <- data.frame(iq, sc)
subby1$g = g
subby2 <- subset(subby1, (subby1$iq > 2.2 & subby1$iq < 2.5) & (subby1$sc > 2.3 & subby1$sc < 2.61))
mean(subby2$g)
sd(subby2$g)