library(openxlsx)

df<-read.xlsx("http://kanggc.iptime.org/book/data/describe-e.xlsx")


x<-cpi<-df$cpi
y<-rate<-df$rate
gdp<-df$GDP
deflator<-df$Deflator

n=length(x)

df_new<-cbind(cpi, rate, gdp, deflator)
df_new
summary(df_new)

(var<-var(df_new))

(sumx<-sum(x))
(sumy<-sum(y))
(mx=mean(x))
(my=mean(y))
(xy<-x*y)
(sumxy<-sum(xy))
(sumxsq<-sum(x^2))
(sumysq<-sum(y^2))

(varx<-(sumxsq-mx*sumx)/(n-1))
(vary<-(sumysq-my*sumy)/(n-1))

(sdx<-sqrt(varx))
(sdy<-sqrt(vary))

(covxy<-(sumxy-mx*sumy)/(n-1))
(corxy<-covxy/(sdx*sdy))

(vx<-var(x))
(vy<-var(y))

(sx<-sd(x))
(sy<-sd(y))

(cov(x,y))
(cor(x,y))

nx<-10*x
ny<-10*y

(vnx<-var(nx))
(vny<-var(ny))

(snx<-sd(nx))
(sny<-sd(ny))

(cov(nx,ny))
(cor(nx,ny))