setwd("C:\\Users\\authorized user\\Dropbox\\STAT445\\week4\\tutorials")


#####################################################
#Q8.19 page 476   National Track Records for Women
#####################################################

(Data.matrix<-read.csv("RecordsForFemales.csv"))


#RecordsForMen.csv
x=c(100,200,400,800,1500,3000,42195)

speed=function(a,b){return(a/b)}



Data.matrix[,5:8]=Data.matrix[,5:8]*60

data=matrix(unlist(diag(sapply(x,speed,Data.matrix[,2:8]))),ncol=7)


(eig=eigen(cor(data)))

(eig$values/sum(eig$values))

plot(eig$values)


(eig1=eigen(cov(data)))

#construct principal components
#from correlation matrix
PC=scale(data) %*% (eig$vectors)

index=order(PC[,1])
#rank the countries according to the PC1
Data.matrix[,1][index]


#construct principal components
#from covariance matrix
PC1= data %*% (eig1$vectors)

index1=order(PC1[,1])
#rank the countries according to the PC1
Data.matrix[,1][index1]



(eig1$values/sum(eig1$values))

plot(eig1$values)
#####################################################




#####################################################
#Q8.20 page 476   National Track Records for Men
#####################################################




(Data.matrix1<-read.csv("RecordsForMen.csv"))


#RecordsForMen.csv
x1=c(100,200,400,800,1500,5000,10000,42195)


Data.matrix1[,5:9]=Data.matrix1[,5:9]*60

data1=matrix(unlist(diag(sapply(x1,speed,Data.matrix1[,2:9]))),ncol=8)


(eig2=eigen(cor(data1)))

(eig2$values/sum(eig2$values))
plot(eig2$values)



#construct principal components
#from correlation matrix
PC_men=scale(data1) %*% (eig2$vectors)

index2=order(PC_men[,1])
#rank the countries according to the PC1
Data.matrix1[,1][index2]

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