# RPD -- Example 12.2 -- Poisson Variance Stabilization (Simulation)

simpoisson <- transform(data.frame(x = seq(1,30,by=0.05)),
                        y = rpois(length(x),x))
  # rpois(n,lambda) generates n indep. Poisson variates with mean(s) lambda


yx.mod <- lm(y ~ x, data=simpoisson)

plot(predict(yx.mod), residuals(yx.mod))


  # Try variance stabilizing transformation:

sqrty.x.mod <- lm(sqrt(y) ~ x, data=simpoisson)

dev.new()
plot(predict(sqrty.x.mod), residuals(sqrty.x.mod))


  # Attempt to restore straight-line mean relationship:

sqrty.sqrtx.mod <- lm(sqrt(y) ~ sqrt(x), data=simpoisson)

dev.new()
plot(predict(sqrty.sqrtx.mod), residuals(sqrty.sqrtx.mod))