Draft

2024-05-23-resid-variances

Author

Gibran Hemani

Published

May 23, 2024

Background

pnorm(0.5457/0.099, low=F)

pf(2*0.0054*(1-0.0054)*0.5457^2 * 460000,)

Fval <- qf(3.7e-8, 1, 460000, low=F)


g <- rbinom(250000, 2, 0.005)
y <- g * 0.55 + rnorm(250000, 0, 4)
var(y)

summary(lm(y ~ g))

cor(y, g)^2

tval <- 0.56/0.079

vg <- mean(g)/2 * 2 * (1-mean(g)/2) * 0.56^2
rsq <- vg / var(y)
rsq

Fval <- rsq * 250000 / (1-rsq) / 1

tval^2

# rsq 
tval^2 / (tval^2 + 250000)

pf(Fval, 1, 250000, low=F)


se = var(y) / sqrt(2*p*(1-p) * N)

vyres <- 0.099 * sqrt(2*0.0054*(1-0.0054)*460000)

vyraw <- 0.00857 * sqrt(2*0.0054*(1-0.0054)*460000)

vyraw

0.037 / vyraw

0.54 / (vyres / 0.7)

6.95/0.7


5.4e-3


a = b - 0.3b
a = b(1-0.3)




g <- rbinom(250000, 2, 0.005)
prs <- rnorm(250000, 0, sqrt(10*0.3))
y <- g * 0.55 + prs + rnorm(250000, 0, sqrt(10*0.7))
var(y)

summary(lm(y ~ g))
summary(lm(y ~ g + prs))
yres <- residuals(lm(y ~ prs))
summary(lm(yres ~ g))

ysub <- y - prs
summary(lm(ysub ~ g))

sessionInfo()