DF=read.csv(file="manyglacier.csv",header=T)
par(mfrow=c(3,1))
ts.plot(DF$Dis_CFS, main="Discharge in CFS",xlab="Year",ylab="")
ts.plot(DF$Temp_dF,main="Temperature",xlab="Year",ylab="")
ts.plot(DF$Prec_in, main="Precipitation",xlab="Year",ylab="")
par(mfrow=c(1,1))
pairs(cbind(DF$Dis_CFS,DF$Temp_dF,DF$Prec_in)) # scatter plot matrix
DF$Year=DF$Year-1949
cor(DF)
par(mfrow=c(5,1))
fit1=lm(Dis_CFS~Year  + Temp_dF + Prec_in, data=DF)
summary(fit1)
AIC(fit1)/59 #R gives n*AIC
acf(resid(fit1))

fit2=lm(Dis_CFS~Year  +I(log(Temp_dF)) + Prec_in, data=DF)
summary(fit2)
AIC(fit2)/59 #R gives n*AIC
acf(resid(fit2))

fit3=lm(Dis_CFS~ Temp_dF + Prec_in,data=DF)
summary(fit3)
AIC(fit3)/59 #R gives n*AIC
acf(resid(fit3))

fit4=lm(Dis_CFS~I(log(Temp_dF)) + Prec_in, data=DF)
summary(fit4)
AIC(fit4)/59 #R gives n*AIC
acf(resid(fit4))

fit5=lm(Dis_CFS~Temp_dF + I(Temp_dF^2) + Prec_in, data=DF)
summary(fit5)
AIC(fit5)/59 #R gives n*AIC
acf(resid(fit5))

anova(fit2,fit1)
anova(fit3,fit1)
anova(fit4,fit2)