binom.prob=0.01
set.seed(8)
x=1:20000
y=sapply(x,function(x) sum(rbinom(x,1,binom.prob)))
plot(x,y,col=rgb(1,0,0,0.5),pch='.',main='binomial distribution');grid()
plot(x,y/x,col=rgb(1,0,0,1),pch='.',main='binomial distribution ratio');grid()

(summary(lm(y~x)))$r.squared #obviously high r squared, returns 0.97

(summary(lm(I(y/x)~x)))$r.squared #obviously low r squared, returns 0.00001977375

d=expand.grid(num=0:50,dem=1:50)
d=d[d$num<=d$dem,]
plot(d$dem,d$num/d$dem,col=rgb(1-d$dem/50,d$dem/50,0,1),pch=20,main='binomial distribution flower')