## Example
test=matrix(scan("http://civil.colorado.edu/~balajir/CVEN5454/R-sessions/sess5/Prob-11-77-data.txt"), ncol=2, byrow=T)

Y = data[,2]
X = data[,1]

# fit a Kendall Thiel slope estimate..
# Chapter 10, pages 266-267  of Helsel and Hirsch

library(mblm)

zkt = mblm(Y ~ X)


zlin = lsfit(X, Y)    #Linear Regression



plot(X, Y, xlab="Monthly energy usage (kilowatt hours)", ylab="Peak hour demand (kilowatts)")

abline(zlin, col="red")

abline(zkt, col="blue")

####  Another example..

test=matrix(scan("http://civil.colorado.edu/~balajir/CVEN5454/R-sessions/sess5/Avg-SpringFlows-April1SWE-49-04.txt",skip=1), ncol=2, byrow=T)

Y=test[,1]		#Spring river flows
X=test[,2]		#April 1 Snow water equivalent

zkt = mblm(Y ~ X)


zlin = lsfit(X, Y)    #Linear Regression

plot(X, Y, xlab="Snow Water Equivalent)", ylab="Spring River flow")

abline(zlin, col="red")

abline(zkt, col="blue")

# clearly the blue line based on Kendall-Thiel slope is robust to outlier

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

# Kendall slope is tested using the Kendall Tau
# Chapter 8 pages 212-216  of Helsel and Hirsch

cor.test(X,Y,method = c("kendall"))

#Test on the Kendall's Tau statistic
#Same as doing the significance on the slope of the 
# Kendall-Thiel line

## you can use argument's spearman or pearson to perform test on the 
## Spearman's rank correlation or the traditional correlation (i.e. 
#Pearson's correlation)


#######################
# You can also use the library Kendall

library(Kendall)        #install library Kendall
help(Kendall)            # read the help on the command Kendall

zz = Kendall(X,Y)        #computes the Kendall tau correlation
zz$sl #gives you the p-value of the test. 

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

# Model Diagnostics
# Use the commands in the file
http://civil.colorado.edu/~balajir/CVEN5454/R-sessions/sess5/lsfit-diag-crossval-commands_elts.txt
or
in other files..

You can perform the diagnostics on the residuals from the Kendall-Thiel slope line and
also from the Linear regression

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