#Dennis Moskov, Master Thesis
#Split by unique articles 
# MLR for model fitness
#reduced model
#conversion, selectivity and yield

#library(MASS)

#randomly shuffle the data
set.seed(77)                      # seed for reproducibility
DBs<-DB[sample(nrow(DB)),]

#initiate possible results
results<-rbind(c("Conversion","Selectivity","Yield"),c("X.MeOH","S.MeOH","Y.MeOH"),c(length(DBs)-2,length(DBs)-1,length(DBs)))

#loop through different outcomes
for (r in 1:3) {

#use desired outcome
useDB<-DBs[-c(1,as.numeric(results[3,-r]))]

#initiate results lists
res<-list()
res.names<-c("number","fitted","observed","residuals","residuals_squared")

#initiate matrices for regression and prediction values
reg<-matrix(, nrow = 10,ncol = 1)
colnames(reg, do.NULL = FALSE)
colnames(reg) <-  "overall"
rownames(reg) <- c("Sample","RSS","TSS","MSS","R","R","adj.R","MSE","RMSE","SDEC")
    
   	#multiple linear regression and prediction  
	form <- paste(names(useDB)[length(useDB)], "~", paste(names(useDB)[-length(useDB)], collapse=" + "))
  	fit<-lm(form, data=useDB)

        #stepwise variable selection
        step <- stepAIC(fit, direction="both")

	#predict
        pred<-predict(object=step, newdata=useDB)

    #save results
    res$number<-as.numeric(names(pred))
    res$fitted<-unname(pred)
    res$observed<-useDB[,length(useDB)]
    res$residuals<-res$observed-res$fitted
    res$residuals_squared<-(res$residuals)^2

    #values for model fitness
    reg["Sample",1]<-nrow(useDB)                 #number of datapoints in training set of the fold
    reg["RSS",1]<-sum(res$residuals_squared)  #Residual Sum of Squares
    reg["TSS",1]<-sum((res$observed-mean(res$observed))^2)                      #Total Sum of Squares
    reg["MSS",1]<-reg["TSS",1]-reg["RSS",1]                 #Model Sum of Squares
    reg["R",1]<-reg["MSS",1]/reg["TSS",1]                             #coefficient of determination
    reg["R",1]<-sqrt(reg["R",1])                           #multiple correlation coefficient
    reg["adj.R",1]<- 1-((1-reg["R",1])*((reg["Sample",1]-1)/(reg["Sample",1]-fit$rank)))      
	                         #Adjusted coefficient of determination
    reg["MSE",1]<-reg["RSS",1]/(reg["Sample",1]-(fit$rank+1))  #Mean square error
    reg["RMSE",1]<-sqrt(reg["MSE",1])                          #Root Mean square error (residual standard deviation)                      
    reg["SDEC",1]<-sqrt(reg["RSS",1]/reg["Sample",1])       #Standard Deviation Error in Calculation

 
#--------------------------------PLOT------------------------------------------------------------------------------------
#plot predicted vs. observed
x11()
plot(res$fitted,res$observed,pch=16, col="blue",xlim=c(0,1),ylim=c(0,1),xaxs="i",yaxs="i",xlab=paste("Fitted MeOH",results[1,r]), ylab=paste("Observed MeOH",results[1,r] ),main=paste("Fitted vs. Observed MeOH",results[1,r]))
abline(0,1)

x11()
plot(res$fitted,res$observed,pch=16, col="blue",xlim=c(min(0,min(res$fitted)),max(max(res$observed),max(res$fitted))),ylim=c(min(0,min(res$fitted)),max(max(res$observed),max(res$fitted))),xaxs="i",yaxs="i",xlab=paste("Fitted MeOH",results[1,r]), ylab=paste("Observed MeOH",results[1,r] ),main=paste("Fitted vs. Observed MeOH",results[1,r]))
abline(0,1)


#plot predicted vs. residuals
x11() 
plot(res$fitted,res$residuals, col="blue",xlim=c(0,1), ylim=c(-1,1),xaxs="i",yaxs="i",xlab=paste("Fitted MeOH",results[1,r]), ylab="Residuals",main=paste("Fitted MeOH",results[1,r],"vs. Residuals"),pch=16)
abline(h=0)

x11() 
plot(res$fitted,res$residuals, col="blue",xlim=c(min(res$fitted),max(res$fitted)), ylim=c(min(res$residuals),max(res$residuals)),xaxs="i",yaxs="i",xlab=paste("Fitted MeOH",results[1,r]), ylab="Residuals",main=paste("Fitted MeOH",results[1,r],"vs. Residuals"),pch=16)
abline(h=0)

#plot residual density
x11()
plot(density(res$residuals),xlab="Residuals", ylab="Density",main=paste("Density Plot of Residuals for",results[1,r]))

#--------------------------------DISPLAY------------------------------------------------------
View(reg,paste("Regression Values for MeOH",results[1,r]))

#---------------------------------SAVE------------------------------------------------------------------------------------

#plot predicted vs. observed
png(filename=paste(results[1,r]," fittedVSobs full.png"))
par(new=TRUE, pch=16)
plot(res$fitted,res$observed,pch=16, col="blue",xlim=c(0,1),ylim=c(0,1),xaxs="i",yaxs="i",xlab=paste("Fitted MeOH",results[1,r]), ylab=paste("Observed MeOH",results[1,r] ),main=paste("Fitted vs. Observed MeOH",results[1,r]))
abline(0,1)
dev.off()

png(filename=paste(results[1,r]," fittedVSobs croped.png"))
par(new=TRUE, pch=16)
plot(res$fitted,res$observed,pch=16, col="blue",xlim=c(min(0,min(res$fitted)),max(max(res$observed),max(res$fitted))),ylim=c(min(0,min(res$fitted)),max(max(res$observed),max(res$fitted))),xaxs="i",yaxs="i",xlab=paste("Fitted MeOH",results[1,r]), ylab=paste("Observed MeOH",results[1,r] ),main=paste("Fitted vs. Observed MeOH",results[1,r]))
abline(0,1)
dev.off()

#plot predicted vs. residuals
png(filename=paste(results[1,r]," fittedVSres full.png"))
plot(res$fitted,res$residuals, col="blue",xlim=c(0,1),ylim=c(-1,1),xaxs="i",yaxs="i",xlab=paste("Fitted MeOH",results[1,r]), ylab="Residuals",main=paste("Fitted MeOH",results[1,r],"vs. Residuals"),pch=16)
abline(h=0)
dev.off()

png(filename=paste(results[1,r]," fittedVSres croped.png"))
plot(res$fitted,res$residuals, col="blue",xlim=c(min(res$fitted),max(res$fitted)), ylim=c(min(res$residuals),max(res$residuals)),xaxs="i",yaxs="i",xlab=paste("Fitted MeOH",results[1,r]), ylab="Residuals",main=paste("Fitted MeOH",results[1,r],"vs. Residuals"),pch=16)
abline(h=0)
dev.off()

#plot residual density
png(filename=paste(results[1,r]," resDensity.png"))
plot(density(res$residuals),xlab="Residuals", ylab="Density",main=paste("Density Plot of Residuals for",results[1,r]))
dev.off()

#regression and prediction results
write.csv(reg, file =paste(results[1,r]," regression_values.csv"))
write.csv(res, file =paste(results[1,r]," results.csv"), row.names=FALSE)

capture.output(c(step$anova,levels(step$anova[[1]])), file = paste(results[1,r]," reduction.txt"))
}



