# Bernoulli standard deviation p <- seq(0,1,0.01) sd <- sqrt(p*(1-p)) plot(sd~p, main="Standard Deviation varies with p") zero <- 0-p one <- 1-p plot(zero~p, ylim=c(-1,1), main="Centered values versus p") points(one~p) zero.sd <- zero/sd one.sd <- one/sd plot(zero.sd~p, ylim=c(-10,10), main="Standardized values versus p") points(one.sd~p) zero.to.one <- one.sd - zero.sd plot(zero.to.one~p, ylab="std devs", main="Change of category in sd's") b <- rep(NA,99) bc <- rep(NA,99) bs <- rep(NA,99) for (i in 1:99){ x <- c(rep_len(0,i), rep_len(1,100-i)) xc <- x - mean(x) xs <- xc/sd(x) z <- rnorm(100) #y <- 3 + 7*x #y <- 3 + 7*x + rnorm(50) y <- 3 + 7*x + 7*z +rnorm(50) b[i] <- coef(lm(y~x+z))[2] bc[i] <- coef(lm(y~xc+z))[2] bs[i] <- coef(lm(y~xs+z))[2] } plot(b~p[2:100], ylim=c(0,7)) plot(bc~p[2:100], ylim=c(0,7)) plot(bs~p[2:100], ylim=c(0,7)) cor(y,x);cor(y,xc); cor(y,xs);