library(ResourceSelection)
n <- 500; chisqs <- c()
for (i in 1:10000) {
    x <- rnorm(n)
    p <- plogis(0.1+0.5*x)
    y <- rbinom(n,1,p)
    x2 <- hoslem.test(y,p)$statistic
    chisqs <- cbind(chisqs,x2);
}
h <- hist(chisqs,50)
xs <- seq(0,25,0.01)
ys <- dchisq(xs,df=10)
lines(xs,ys*h$counts/h$density)

library(ResourceSelection)
n <- 500; chisqs <- c()
for (i in 1:10000) {
    x <- rnorm(n)
    p <- plogis(0.1+0.5*x)
    y <- rbinom(n,1,p)
    fit <- glm(y~x)
    x2 <- hoslem.test(y,fitted(fit))$statistic
    chisqs <- cbind(chisqs,x2);
}
h <- hist(chisqs,50)
xs <- seq(0,25,0.01)
ys <- dchisq(xs,df=8)
lines(xs,ys*h$counts/h$density)