##################    Interpolation of Tmax for 10 dates.  #######################################

###########################  TWO-STAGE REGRESSION  ###############################################

#This script interpolates station values for the Oregon case study using a two-stage regression. #

#For each input dates, it performs 1) Step 1: General Additive Model (GAM)                       #

#                                  2) Step 2: Kriging on residuals from step 1                   #

#                                                                                                #

#The script uses LST monthly averages as input variables and  loads the station data             # 

#from a shape file with projection information.                                                  #

#Note that this program:                                                                         #

#1)assumes that the shape file is in the current working.                                        # 

#2)relevant variables were extracted from raster images before performing the regressions        #

#  and stored shapefile                                                                          #

#This scripts predicts tmax using ing GAM and LST derived from MOD11A1.Interactions terms are    #

#also included and assessed using the RMSE,MAE,ME and R2 from validation dataset.                #

#There are #10 dates used for the GAM interpolation. The dates must be provided as a textfile.   #

#AUTHOR: Benoit Parmentier                                                                       #

#DATE: 05/31/212                                                                                 #

#PROJECT: NCEAS INPLANT: Environment and Organisms --TASK#364--                                  #

##################################################################################################

###Loading R library and packages                                                      

library(gtools)                                         # loading some useful tools 

library(mgcv)                                           # GAM package by Simon Wood

library(sp)                                             # Spatial pacakge with class definition by Bivand et al.

library(spdep)                                          # Spatial pacakge with methods and spatial stat. by Bivand et al.

library(rgdal)                                          # GDAL wrapper for R, spatial utilities

library(gstat)                                          # Kriging and co-kriging by Pebesma et al.

###Parameters and arguments

infile1<- "ghcn_or_tmax_b_04142012_OR83M.shp"             #GHCN shapefile containing variables                  

infile2<-"list_10_dates_04212012.txt"                      #List of 10 dates for the regression

#infile2<-"list_365_dates_04212012.txt"

infile3<-"LST_dates_var_names.txt"                        #LST dates name

infile4<-"models_interpolation_05142012.txt"              #Interpolation model names

infile5<-"mean_day244_rescaled.rst"                       #Raster or grid for the locations of predictions

path<-"/data/computer/parmentier/Data/IPLANT_project/data_Oregon_stations"         #Jupiter LOCATION on EOS

#path<-"H:/Data/IPLANT_project/data_Oregon_stations"                                 #Jupiter Location on XANDERS

setwd(path) 

prop<-0.3                                                                           #Proportion of testing retained for validation   

seed_number<- 100                                                                   #Seed number for random sampling

out_prefix<-"_05312012_2d_Kr_LST"                                                   #User defined output prefix

############ START OF THE SCRIPT ##################

###Reading the station data and setting up for models' comparison

filename<-sub(".shp","",infile1)             #Removing the extension from file.

ghcn<-readOGR(".", filename)                 #reading shapefile 

CRS<-proj4string(ghcn)                       #Storing projectionminformation (ellipsoid, datum,etc.)

mean_LST<- readGDAL(infile5)                 #Reading the whole raster in memory. This provides a grid for kriging

proj4string(mean_LST)<-CRS                   #Assigning coordinate information to prediction grid.

ghcn = transform(ghcn,Northness = cos(ASPECT)) #Adding a variable to the dataframe

ghcn = transform(ghcn,Eastness = sin(ASPECT))  #adding variable to the dataframe.

ghcn = transform(ghcn,Northness_w = sin(slope)*cos(ASPECT)) #Adding a variable to the dataframe

ghcn = transform(ghcn,Eastness_w = sin(slope)*sin(ASPECT))  #adding variable to the dataframe.

set.seed(seed_number)                        #Using a seed number allow results based on random number to be compared...

dates <-readLines(paste(path,"/",infile2, sep=""))

LST_dates <-readLines(paste(path,"/",infile3, sep=""))

models <-readLines(paste(path,"/",infile4, sep=""))

#Model assessment: specific diagnostic/metrics for GAM

results_AIC<- matrix(1,length(dates),length(models)+3)  

results_GCV<- matrix(1,length(dates),length(models)+3)

results_DEV<- matrix(1,length(dates),length(models)+3)

results_RMSE_f<- matrix(1,length(dates),length(models)+3)

#Model assessment: general diagnostic/metrics 

results_RMSE <- matrix(1,length(dates),length(models)+3)

results_RMSE_kr <- matrix(1,length(dates),length(models)+3)

results_MAE <- matrix(1,length(dates),length(models)+3)

results_MAE_kr <- matrix(1,length(dates),length(models)+3)

results_ME <- matrix(1,length(dates),length(models)+3)

results_ME_kr <- matrix(1,length(dates),length(models)+3)    #ME corresponds to the bias

results_R2 <- matrix(1,length(dates),length(models)+3)       #Coef. of determination for the validation dataset

results_R2_kr <- matrix(1,length(dates),length(models)+3)

results_RMSE_f<- matrix(1,length(dates),length(models)+3)    #RMSE fit, RMSE for the training dataset

results_RMSE_f_kr<- matrix(1,length(dates),length(models)+3)

#Tracking relationship between LST AND LC

cor_LST_LC1<-matrix(1,10,1)      #correlation LST-LC1

cor_LST_LC3<-matrix(1,10,1)      #correlation LST-LC3

cor_LST_tmax<-matrix(1,10,1)     #correlation LST-tmax

#Screening for bad values

ghcn_all<-ghcn

ghcn_test<-subset(ghcn,ghcn$tmax>-150 & ghcn$tmax<400)

ghcn_test2<-subset(ghcn_test,ghcn_test$ELEV_SRTM>0)

ghcn<-ghcn_test2

#coords<- ghcn[,c('x_OR83M','y_OR83M')]

month_var<-c("mm_01","mm_02","mm_03","mm_04","mm_05","mm_06","mm_07","mm_08","mm_09", "mm_10", "mm_11", "mm_12")

ghcn.subsets <-lapply(dates, function(d) subset(ghcn, date==d)) #this creates a list of 10 or 365 subsets dataset based on dates

## looping through the dates...this is the main part of the code

#i=1 #for debugging

#j=1 #for debugging

for(i in 1:length(dates)){            # start of the for loop #1

  date<-strptime(dates[i], "%Y%m%d")   # interpolation date being processed

  month<-strftime(date, "%m")          # current month of the date being processed

  LST_month<-paste("mm_",month,sep="") # name of LST month to be matched

  ###Regression part 1: Creating a validation dataset by creating training and testing datasets

  mod_LST <-ghcn.subsets[[i]][,match(LST_month, names(ghcn.subsets[[i]]))]  #Match interpolation date and monthly LST average

  ghcn.subsets[[i]] = transform(ghcn.subsets[[i]],LST = mod_LST)            #Add the variable LST to the subset dataset

  n<-nrow(ghcn.subsets[[i]])

  ns<-n-round(n*prop)   #Create a sample from the data frame with 70% of the rows

  nv<-n-ns              #create a sample for validation with prop of the rows

  ind.training <- sample(nrow(ghcn.subsets[[i]]), size=ns, replace=FALSE) #This selects the index position for 70% of the rows taken randomly

  ind.testing <- setdiff(1:nrow(ghcn.subsets[[i]]), ind.training)

  data_s <- ghcn.subsets[[i]][ind.training, ]   #Training dataset currently used in the modeling

  data_v <- ghcn.subsets[[i]][ind.testing, ]    #Testing/validation dataset

  ####Regression part 2: GAM models (REGRESSION STEP1)

  #Model can be changed without affecting the script

  mod1<- gam(tmax~ s(lat) + s (lon) + s (ELEV_SRTM), data=data_s)

  mod2<- gam(tmax~ s(lat,lon,ELEV_SRTM), data=data_s)

  mod3<- gam(tmax~ s(lat) + s (lon) + s (ELEV_SRTM) +  s (Northness)+ s (Eastness) + s(DISTOC), data=data_s)

  mod4<- gam(tmax~ s(lat) + s (lon) + s(ELEV_SRTM) + s(Northness) + s (Eastness) + s(DISTOC) + s(LST), data=data_s)

  mod5<- gam(tmax~ s(lat,lon) +s(ELEV_SRTM) + s(Northness,Eastness) + s(DISTOC) + s(LST), data=data_s)

  mod6<- gam(tmax~ s(lat,lon) +s(ELEV_SRTM) + s(Northness,Eastness) + s(DISTOC) + s(LST,LC1), data=data_s)

  mod7<- gam(tmax~ s(lat,lon) +s(ELEV_SRTM) + s(Northness,Eastness) + s(DISTOC) + s(LST,LC3), data=data_s)

  mod8<- gam(tmax~ s(lat,lon) +s(ELEV_SRTM) + s(Northness,Eastness) + s(DISTOC) + s(LST) + s(LC1), data=data_s)

  ####Regression part 3: Calculating and storing diagnostic measures

  #listmod can be created and looped over. In this case we loop around the GAM objects in memory...

  for (j in 1:length(models)){

    ##Model assessment: specific diagnostic/metrics for GAM

    name<-paste("mod",j,sep="")  #modj is the name of The "j" model (mod1 if j=1) 

    mod<-get(name)               #accessing GAM model ojbect "j"

    results_AIC[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_AIC[i,2]<- ns        #number of stations used in the training stage

    results_AIC[i,3]<- "AIC"

    results_AIC[i,j+3]<- AIC (mod)

    results_GCV[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_GCV[i,2]<- ns        #number of stations used in the training 

    results_GCV[i,3]<- "GCV"

    results_GCV[i,j+3]<- mod$gcv.ubre

    results_DEV[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_DEV[i,2]<- ns        #number of stations used in the training stage

    results_DEV[i,3]<- "DEV"

    results_DEV[i,j+3]<- mod$deviance

    results_RMSE_f[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_RMSE_f[i,2]<- ns        #number of stations used in the training stage

    results_RMSE_f[i,3]<- "RSME"

    results_RMSE_f[i,j+3]<- sqrt(sum((mod$residuals)^2)/nv)

    ##Model assessment: general diagnostic/metrics

    ##validation: using the testing data

    #Automate this using a data frame of size??

    y_mod<- predict(mod, newdata=data_v, se.fit = TRUE) #Using the coeff to predict new values.

    res_mod<- data_v$tmax - y_mod$fit                   #Residuals for the model

    RMSE_mod <- sqrt(sum(res_mod^2)/nv)                 #RMSE FOR REGRESSION STEP 1: GAM     

    MAE_mod<- sum(abs(res_mod))/nv                     #MAE, Mean abs. Error FOR REGRESSION STEP 1: GAM   

    ME_mod<- sum(res_mod)/nv                            #ME, Mean Error or bias FOR REGRESSION STEP 1: GAM

    R2_mod<- cor(data_v$tmax,y_mod$fit)^2              #R2, coef. of var FOR REGRESSION STEP 1: GAM

    results_RMSE[i,1]<- dates[i]    #storing the interpolation dates in the first column

    results_RMSE[i,2]<- ns          #number of stations used in the training stage

    results_RMSE[i,3]<- "RMSE"

    results_RMSE[i,j+3]<- RMSE_mod  #Storing RMSE for the model j

    results_MAE[i,1]<- dates[i]     #storing the interpolation dates in the first column

    results_MAE[i,2]<- ns           #number of stations used in the training stage

    results_MAE[i,3]<- "MAE"

    results_MAE[i,j+3]<- MAE_mod    #Storing MAE for the model j

    results_ME[i,1]<- dates[i]      #storing the interpolation dates in the first column

    results_ME[i,2]<- ns            #number of stations used in the training stage

    results_ME[i,3]<- "ME"

    results_ME[i,j+3]<- ME_mod      #Storing ME for the model j

    results_R2[i,1]<- dates[i]      #storing the interpolation dates in the first column

    results_R2[i,2]<- ns            #number of stations used in the training stage

    results_R2[i,3]<- "R2"

    results_R2[i,j+3]<- R2_mod      #Storing R2 for the model j

    #Saving residuals and prediction in the dataframes: tmax predicted from GAM

    pred<-paste("pred_mod",j,sep="")

    data_v[[pred]]<-as.numeric(y_mod$fit)

    data_s[[pred]]<-as.numeric(mod$fit) #Storing model fit values (predicted on training sample)

    name2<-paste("res_mod",j,sep="")

    data_v[[name2]]<-as.numeric(res_mod)

    data_s[[name2]]<-as.numeric(mod$residuals)

    #end of loop calculating RMSE

    }

  ###BEFORE Kringing the data object must be transformed to SDF

  coords<- data_v[,c('x_OR83M','y_OR83M')]

  coordinates(data_v)<-coords

  proj4string(data_v)<-CRS  #Need to assign coordinates...

  coords<- data_s[,c('x_OR83M','y_OR83M')]

  coordinates(data_s)<-coords

  proj4string(data_s)<-CRS  #Need to assign coordinates..

  #KRIGING ON GAM RESIDUALS: REGRESSION STEP2

  for (j in 1:length(models)){

    name<-paste("res_mod",j,sep="")

    data_s$residuals<-data_s[[name]]

    X11()

    hscat(residuals~1,data_s,(0:9)*20000) # 9 lag classes with 20,000m width

    v<-variogram(residuals~1, data_s)   

    plot(v)                               # This plot may be saved at a later stage...

    dev.off()

    v.fit<-fit.variogram(v,vgm(1,"Sph", 150000,1))

    res_krige<-krige(residuals~1, data_s,mean_LST, v.fit)#mean_LST provides the data grid/raster image for the kriging locations.

    res_krig1_s <- overlay(res_krige,data_s)             #This overlays the kriged surface tmax and the location of weather stations

    res_krig1_v <- overlay(res_krige,data_v)             #This overlays the kriged surface tmax and the location of weather stations

    name2<-paste("pred_kr_mod",j,sep="")

    #Adding the results back into the original dataframes.

    data_s[[name2]]<-res_krig1_s$var1.pred

    data_v[[name2]]<-res_krig1_v$var1.pred  

    #NEED TO ADD IT BACK TO THE PREDICTION FROM GAM

    gam_kr<-paste("pred_gam_kr",j,sep="")

    pred_gam<-paste("pred_mod",j,sep="")

    data_s[[gam_kr]]<-data_s[[pred_gam]]+ data_s[[name2]]

    data_v[[gam_kr]]<-data_v[[pred_gam]]+ data_v[[name2]]

    #Model assessment: RMSE and then krig the residuals....!

    res_mod_kr_s<- data_s$tmax - data_s[[gam_kr]]           #Residuals from kriging training

    res_mod_kr_v<- data_v$tmax - data_v[[gam_kr]]           #Residuals from kriging validation

    RMSE_mod_kr_s <- sqrt(sum(res_mod_kr_s^2,na.rm=TRUE)/(nv-sum(is.na(res_mod_kr_s))))         #RMSE from kriged surface training

    RMSE_mod_kr_v <- sqrt(sum(res_mod_kr_v^2,na.rm=TRUE)/(nv-sum(is.na(res_mod_kr_v))))         #RMSE from kriged surface validation

    MAE_mod_kr_s<- sum(abs(res_mod_kr_s),na.rm=TRUE)/(nv-sum(is.na(res_mod_kr_s)))        #MAE from kriged surface training                    #MAE, Mean abs. Error FOR REGRESSION STEP 1: GAM   

    MAE_mod_kr_v<- sum(abs(res_mod_kr_v),na.rm=TRUE)/(nv-sum(is.na(res_mod_kr_v)))        #MAE from kriged surface validation

    ME_mod_kr_s<- sum(res_mod_kr_s,na.rm=TRUE)/(nv-sum(is.na(res_mod_kr_s)))                    #ME, Mean Error or bias FOR REGRESSION STEP 1: GAM

    ME_mod_kr_v<- sum(res_mod_kr_v,na.rm=TRUE)/(nv-sum(is.na(res_mod_kr_v)))                    #ME, Mean Error or bias FOR REGRESSION STEP 1: GAM

    R2_mod_kr_s<- cor(data_s$tmax,data_s[[gam_kr]],use="complete.obs")^2                  #R2, coef. of determination FOR REGRESSION STEP 1: GAM

    R2_mod_kr_v<- cor(data_v$tmax,data_v[[gam_kr]],use="complete.obs")^2                  #R2, coef. of determinationFOR REGRESSION STEP 1: GAM

    #(nv-sum(is.na(res_mod2)))

    #Writing out results

    results_RMSE_kr[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_RMSE_kr[i,2]<- ns        #number of stations used in the training stage

    results_RMSE_kr[i,3]<- "RMSE"

    results_RMSE_kr[i,j+3]<- RMSE_mod_kr_v

    #results_RMSE_kr[i,3]<- res_mod_kr_v

    results_MAE_kr[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_MAE_kr[i,2]<- ns        #number of stations used in the training stage

    results_MAE_kr[i,3]<- "MAE"

    results_MAE_kr[i,j+3]<- MAE_mod_kr_v

    #results_RMSE_kr[i,3]<- res_mod_kr_v

    results_ME_kr[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_ME_kr[i,2]<- ns        #number of stations used in the training stage

    results_ME_kr[i,3]<- "ME"

    results_ME_kr[i,j+3]<- ME_mod_kr_v

    #results_RMSE_kr[i,3]<- res_mod_kr_v

    results_R2_kr[i,1]<- dates[i]  #storing the interpolation dates in the first column

    results_R2_kr[i,2]<- ns        #number of stations used in the training stage

    results_R2_kr[i,3]<- "R2"

    results_R2_kr[i,j+3]<- R2_mod_kr_v

    #results_RMSE_kr[i,3]<- res_mod_kr_v

    name3<-paste("res_kr_mod",j,sep="")

    #as.numeric(res_mod)

    #data_s[[name3]]<-res_mod_kr_s

    data_s[[name3]]<-as.numeric(res_mod_kr_s)

    #data_v[[name3]]<-res_mod_kr_v 

    data_v[[name3]]<-as.numeric(res_mod_kr_v)

    #Writing residuals from kriging

    }

  ###SAVING THE DATA FRAME IN SHAPEFILES AND TEXTFILES

  data_name<-paste("ghcn_v_",out_prefix,"_",dates[[i]],sep="")

  assign(data_name,data_v)

  #write.table(data_v, file= paste(path,"/",data_name,".txt",sep=""), sep=" ")

  #write out a new shapefile (including .prj component)

  #outfile<-sub(".shp","",data_name)   #Removing extension if it is present

  #writeOGR(data_v,".", outfile, driver ="ESRI Shapefile")

  data_name<-paste("ghcn_s_",out_prefix,"_",dates[[i]],sep="")

  assign(data_name,data_s)

  #write.table(data_s, file= paste(path,"/",data_name,".txt",sep=""), sep=" ")

  #outfile<-sub(".shp","",data_name)   #Removing extension if it is present

  #writeOGR(data_s,".", outfile, driver ="ESRI Shapefile")

  # end of the for loop1

  }

## Plotting and saving diagnostic measures

#Specific diagnostic measures related to the testing datasets

results_table_AIC<-as.data.frame(results_AIC)

results_table_GCV<-as.data.frame(results_GCV)

results_table_DEV<-as.data.frame(results_DEV)

results_table_RMSE_f<-as.data.frame(results_RMSE_f)

results_table_RMSE<-as.data.frame(results_RMSE)

results_table_MAE<-as.data.frame(results_MAE)

results_table_ME<-as.data.frame(results_ME)

results_table_R2<-as.data.frame(results_R2)

cname<-c("dates","ns","metric","mod1", "mod2","mod3", "mod4", "mod5", "mod6", "mod7","mod8")

colnames(results_table_RMSE)<-cname

colnames(results_table_MAE)<-cname

colnames(results_table_ME)<-cname

colnames(results_table_R2)<-cname

#Specific diagnostic measures

colnames(results_table_AIC)<-cname

colnames(results_table_GCV)<-cname

colnames(results_table_DEV)<-cname

colnames(results_table_RMSE_f)<-cname

#General diagnostic measures

results_table_RMSE_kr<-as.data.frame(results_RMSE_kr)

results_table_MAE_kr<-as.data.frame(results_MAE_kr)

results_table_ME_kr<-as.data.frame(results_ME_kr)

results_table_R2_kr<-as.data.frame(results_R2_kr)

cname<-c("dates","ns","metric","mod1k", "mod2k","mod3k", "mod4k", "mod5k", "mod6k", "mod7k","mod8k")

colnames(results_table_RMSE_kr)<-cname

colnames(results_table_MAE_kr)<-cname

colnames(results_table_ME_kr)<-cname

colnames(results_table_R2_kr)<-cname

#Summary of diagnostic measures are stored in a data frame

tb_diagnostic1<-rbind(results_table_RMSE,results_table_MAE, results_table_ME, results_table_R2)   #

tb_diagnostic1_kr<-rbind(results_table_RMSE_kr,results_table_MAE_kr, results_table_ME_kr, results_table_R2_kr)

tb_diagnostic2<-rbind(results_table_AIC,results_table_GCV, results_table_DEV,results_table_RMSE_f)

write.table(tb_diagnostic1, file= paste(path,"/","results_GAM_Assessment_measure1",out_prefix,".txt",sep=""), sep=",")

write.table(tb_diagnostic1_kr, file= paste(path,"/","results_GAM_Assessment_measure1_kr_",out_prefix,".txt",sep=""), sep=",")

write.table(tb_diagnostic2, file= paste(path,"/","results_GAM_Assessment_measure2_",out_prefix,".txt",sep=""), sep=",")

# ##Visualization of results##

# 

# for(i in 1:length(dates)){

#   X11()

#   RMSE_kr<-results_table_RMSE_kr[i,]

#   RMSE_ga<-results_table_RMSE[i,]

#   

#   RMSE_kr<-RMSE_kr[,1:length(models)+2]

#   RMSE_ga<-RMSE_ga[,1:length(models)+2]

#   colnames(RMSE_kr)<-names(RMSE_ga)

#   height<-rbind(RMSE_ga,RMSE_kr)

#   rownames(height)<-c("GAM","GAM_KR")

#   height<-as.matrix(height)

#   barplot(height,ylim=c(14,36),ylab="RMSE in tenth deg C",beside=TRUE,

#           legend.text=rownames(height),

#           args.legend=list(x="topright"),

#           main=paste("RMSE for date ",dates[i], sep=""))

#   savePlot(paste("Barplot_results_RMSE_GAM_KR_",dates[i],out_prefix,".png", sep=""), type="png")

#   dev.off()

#   }

#   

# r1<-(results_table_RMSE[,3:10]) #selecting only the columns related to models and method 1

# r2<-(results_table_RMSE_kr[,3:10]) #selecting only the columns related to models and method 1

# mean_r1<-mean(r1)

# mean_r2<-mean(r2)

# median_r1<-sapply(r1, median)   #Calulcating the mean for every model (median of columns)

# median_r2<-sapply(r2, median)

# sd_r1<-sapply(r1, sd)

# sd_r2<-sapply(r2, sd)

# 

# barplot(mean_r1,ylim=c(23,26),ylab="RMSE in tenth deg C")

# barplot(mean_r2,ylim=c(23,26),ylab="RMSE in tenth deg C")

# barplot(median_r1,ylim=c(23,26),ylab="RMSE in tenth deg C",add=TRUE,inside=FALSE,beside=TRUE) # put both on the same plot

# barplot(median_r2,ylim=c(23,26),ylab="RMSE in tenth deg C",add=TRUE,inside=FALSE,beside=TRUE) # put both on the same plot

# 

# barplot(sd_r1,ylim=c(6,8),ylab="RMSE in tenth deg C") # put both on the same plot

# barplot(sd_r2,ylim=c(6,8),ylab="RMSE in tenth deg C") # put both on the same plot

# 

# height<-rbind(mean_r1,mean_r2)

# barplot(height,ylim=c(20,26),ylab="RMSE in tenth deg C",beside=TRUE,legend=rownames(height))

# barplot(height,ylim=c(20,26),ylab="RMSE in tenth deg C",beside=TRUE, col=c("darkblue","red"),legend=rownames(height)) # put both on the same plot

# 

# height<-rbind(median_r1,median_r2)

# barplot(height,ylim=c(20,26),ylab="RMSE in tenth deg C",beside=TRUE,legend=rownames(height))

# barplot(height,ylim=c(20,26),ylab="RMSE in tenth deg C",beside=TRUE, col=c("darkblue","red"),legend=rownames(height)) # put both on the same plot

# 

# height<-rbind(mean_r2,median_r2)

# barplot(height,ylim=c(20,26),ylab="RMSE in tenth deg C",beside=TRUE,legend=rownames(height))

# barplot(height,ylim=c(20,26),ylab="RMSE in tenth deg C",beside=TRUE, col=c("darkblue","red"),legend=rownames(height)) # put both on the same plot

#barplot2(mean_r,median_r,ylim=c(23,26),ylab="RMSE in tenth deg C") # put both on the same plot

#Collect var explained and p values for each var...

##### END OF SCRIPT ##########