#Correlation, significance and Monte carlo experiments 


#Correlation = normed regression

a<-1:1000
noise<-rnorm(1000)*500
b<-a + noise *1



plot(a,b)
cor(a,b)   #correlate a,b
cor.test(a,b)  #correlation + significance test



N<-30

a<-rnorm(N)
b<-rnorm(N)

cor(a,b)


#Now the same as a Monte Carlo experiment (some hundred times)

rsave<-vector()   #vector for saving 
for (i in 1:5000)
{
	a<-rnorm(N)
	b<-rnorm(N)
	rsave[i]<-cor(a,b)

}

hist(rsave)

#abs is used to get the p-values for a two-sided test
quantile(abs(rsave),probs=0.95)