algae <- read.table('Analysis.txt',
             header=F,
             dec='.',
            col.names=c('season','size','speed','mxPH','mnO2','Cl','NO3',
             'NH4','oPO4','PO4','Chla','a1','a2','a3','a4','a5','a6','a7'),
             na.strings=c('XXXXXXX'))
algae <- algae[-c(62,199),]
algae$season<-as.factor(algae$season)
algae$speed<-as.factor(algae$speed)
algae$size<-as.factor(algae$size)

algae.x<-myimputation(algae[,1:11],10)

algae1<-cbind(algae.x,algae$a1)
names(algae1)[12]<-"a1"
names(algae1)

#앞으로 모델링은 algae1 데이터를 이용 (We will use algae data for the analysis)
#이제 모델링 가능 (Now we can fit regression models)
# Linear model ; muliple linear regression 다중회귀모형
lm1<-lm(a1~., data=algae1)
#stepwise regression
lm1.final<-step(lm1,direction="both")

#tree model fitting
tr1<-tree(a1~., data=algae1)

#optimal tree search
tr1.cv<-cv.tree(tr1)
for (i in 2:10){
	tr1.cv$dev<-tr1.cv$dev+cv.tree(tr1)$dev
}
tr1.cv$dev<-tr1.cv$dev/10
plot(tr1.cv)
tr1.final<-prune.tree(tr1,best=3)
plot(tr1.final);text(tr1.final)

#compute prediction error in a training set
#최종모형은 lm1.final 과 tr1.final 에 저장되어 있음
#The final models are saved in lm1.final and tr1.final
#Regression에서는 MSE 또는 RMSE가 가장 많이 사용되는 measure
#RMSE or MSE is most frequently used performance measure in regression
#예측값 계산 (predicted value computation)

lm1.final.pred<-predict(lm1.final,algae1)
tr1.final.pred<-predict(tr1.final,algae1)

#MSE
lm1.mse<-mean((algae1$a1-lm1.final.pred)^2)
tr1.mse<-mean((algae1$a1-tr1.final.pred)^2)

#NMSE
# MSE/mean((y-ybar)^2)
mse.den<-mean((algae$a1-mean(algae$a1))^2)

lm1.nmse<-lm1.mse/mse.den
tr1.nmse<-tr1.mse/mse.den

lm1.nmse
tr1.nmse