# problem 1

tests.mds.2 <- cmdscale(tests.diss, eig=T)

par(pty="s")  # Creates a square plotting region
plot(tests.mds.2$points[,1], tests.mds.2$points[,2], type='n',
     xlab="Coordinate 1", ylab="Coordinate 2", xlim=c(-50,50), ylim=c(-50,50) )
text(tests.mds.2$points[,1], tests.mds.2$points[,2] , labels=row.names(tests.diss))



## Problem 2, HW 4b


recreation <- matrix(c(
61,49,25,21,
60,40,26,41,
60,37,33,52,
59,29,33,55,
48,16,28,57,
78,20,50,105), byrow=T, ncol=4, nrow=6,
dimnames = list(c('18-24','25-34','35-44','45-54','55-64','65+'),
                               c('exercise','sports','charity', 'gardening')))


# Enter name of data matrix / contingency table:
mymat <- recreation
rr <- nrow(mymat); cc <- ncol(mymat)
row.sums <- apply(mymat,1,sum)
col.sums <- apply(mymat,2,sum)
N<-sum(row.sums)

pijrow <- matrix(0,nrow=rr,ncol=cc); pijcol <- matrix(0,nrow=rr,ncol=cc)
distmat.row <- matrix(0,nrow=rr,ncol=rr); distmat.col <- matrix(0,nrow=cc,ncol=cc)

for (i in 1:rr){
pijcol[i,] <- mymat[i,]/row.sums[i]
}
for (j in 1:cc){
pijrow[,j] <- mymat[,j]/col.sums[j]
}

for (i in 1:rr){
for (ii in 1:(i-1)) {
my.hold <- sqrt( sum( (N/col.sums)*(pijcol[i,]-pijcol[ii,])^2 ) )
distmat.row[i,ii] <- my.hold; distmat.row[ii,i] <- my.hold
}
}

for (j in 1:cc){
for (jj in 1:(j-1)) {
my.hold <- sqrt( sum( (N/row.sums)*(pijrow[,j]-pijrow[,jj])^2 )  )
distmat.col[j,jj] <- my.hold; distmat.col[jj,j] <- my.hold
}
}

round(distmat.col,digits=2)
round(distmat.row,digits=2)

###################  END CODE ###########################
#########################################################

# A straightforward chi-square test for independence of rows and columns:

chisq.test(recreation)


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

# A quick way to do correspondence analysis using the "corresp" function
# in the MASS library:

library(MASS) # loading the MASS package

corresp(recreation,nf=2)  # The two-dimensional solution.

biplot(corresp(recreation,nf=2)); abline(h=0); abline(v=0)

corresp(recreation,nf=1)