x <- runif(100,-15,15)
xbeta <- 1+0.8*x
p <- f(xbeta)
y <- rep(0,100)
for (i in 1:100) y[i] <- 
  sample(c(0,1),1,prob=c(1-p[i],p[i]))
train <- data.frame(y=y,x=x)
model0 <- lm(y~.,data=train) 
plot(x,y,ylim=c(-1,2))
abline(a=model0$coef[1],b=model0$coef[2],lwd=4,col="blue")
model1 <- glm(as.factor(y)~.,data=train,family=binomial(link="logit"))
model1
plogit <- function(x){
  xbeta <- model1$coef[1]+model1$coef[2]*x
  exp(xbeta)/(1+exp(xbeta))}
curve(plogit,-15,15,add=TRUE,col="green",lwd=4)

model2 <- glm(as.factor(y)~.,data=train,family=binomial(link="probit"))
pprobit <- function(x){
  xbeta <- model2$coef[1]+model2$coef[2]*x
  pnorm(xbeta)
  }
curve(pprobit,-15,15,add=TRUE,col="sienna4",lwd=4)

poracle <- function(x){
  xbeta <- 1+0.8*x
  exp(xbeta)/(1+exp(xbeta))
}
curve(poracle,-15,15,add=TRUE,col="red",lwd=4)