file <- "C:/Users/krizp/Documents/vyuka MFF/NMFM402 - Nezivotni pojisteni 2/Cviceni/CV3/reseni/data.csv"
##change the path###


data <- read.csv(file , header = TRUE, sep = ",")
y <- data$y
X <- cbind(data$x_0,data$x_1)
N <- length(y)

steps <- 20 #number of iterations
betaApprox <- matrix(0, nrow = steps+1, ncol = 2)
betaApprox[1,]<-c(0,0) #initial guess
for (n in 1:steps)
	{
	beta <- betaApprox[n,]
	mu <- exp(X%*%beta)
	W <- diag(1,nrow = N)
	A <- diag(mu[,1], nrow = N) 
	H<- -1*t(X)%*%A%*%X
	betaNew <- beta - solve(H)%*%(t(X)%*%W%*%y - t(X)%*%W%*%mu)
	betaApprox[n+1,]<-betaNew
	}
betaApprox

plot(betaApprox[,1], betaApprox[,2],xlab="beta_0", ylab="beta_1")
lines(betaApprox[,1], betaApprox[,2])
points(1,1, pch = 8, col="red")