file <- "C:/Users/krizp/Documents/vyuka MFF/NMFM402 - Nezivotni pojisteni 2/Cviceni/CV6/reseni/data_claimSeverity.csv"
##change the path###


#read data:
ClaimData <- read.csv(file , header = TRUE, sep = ";")

#declare columns as factors, will not be treated as numerical variables in GLM:
ClaimData <- within(ClaimData , {
    CarType <- factor(CarType )
    DriverAge<- factor(DriverAge)
    })

#fitting the model:
model.InverseGaussianLog <- glm(Claim ~ CarType + DriverAge, data = ClaimData, family = inverse.gaussian("log"))
summary(model.InverseGaussianLog)

#coefficients estimated by MLE
model.InverseGaussianLog$coefficients

# 95% confidence interval for coefficients = solution to a)
confint(model.InverseGaussianLog)

#corresponding risk factors 
exp(model.InverseGaussianLog$coefficients)

#95% confidence intervals for risk factors = solution to b)
exp(confint(model.InverseGaussianLog))




#predictions on log link scale (for linear predictor) incl. standard error
logY <- predict(model.InverseGaussianLog, se.fit = TRUE)$fit
logY.stdErrors <- predict(model.InverseGaussianLog, se.fit = TRUE)$se.fit


#confidence intervals for claims in original scale = solution to c)
alpha <- 0.05
u <- qnorm(1-alpha/2, 0, 1)
lowerY <- exp(logY - u*logY.stdErrors)
upperY <- exp(logY + u*logY.stdErrors)

ClaimData["PredictClaim"] <-  exp(logY)
ClaimData["Claim_lowerBound"] <-  lowerY 
ClaimData["Claim_upperBound"] <-  upperY 
ClaimData