file <- "C:/Users/krizp/Documents/vyuka MFF/NMFM402 - Nezivotni pojisteni 2/Cviceni/CV5/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 models:
model.GammaLog <- glm(Claim ~ CarType + DriverAge, data = ClaimData, family = Gamma("log"))
model.NormalLog <- glm(Claim ~ CarType + DriverAge, data = ClaimData, family = gaussian("log"))
model.InverseGaussianLog <- glm(Claim ~ CarType + DriverAge, data = ClaimData, family = inverse.gaussian("log"))

#compare AIC of the models
AIC(model.GammaLog)
AIC(model.NormalLog)
AIC(model.InverseGaussianLog)


#backwards stepwise selection based on minimiztion of AIC for the chosen model
backwards <- step(model.InverseGaussianLog) 


# test if we can drop CarType by assessing the model differences with F test
model.reduced <- update(model.InverseGaussianLog, . ~ . - CarType)
anova(model.reduced, model.InverseGaussianLog, test = "F")


# test if we can drop DriverAge by assessing the model differences with F test
model.reduced <- update(model.InverseGaussianLog, . ~ . - DriverAge)
anova(model.reduced, model.InverseGaussianLog, test = "F")