# Purpose: to show weighted least squares
# http://stat.cmu.edu/~cshalizi/350/lectures/18/lecture-18.pdf
n = 100
x = rnorm(n,0,3)
y = 3-2*x + rnorm(n,0,sapply(x,function(x){1+0.5*x^2}))
plot(x,y)
abline(a=3,b=-2,col='red')
fit.ols = lm(y~x)
abline(fit.ols$coefficients,lty=1, col='grey')
fit.wls = lm(y~x, weights=1/(1+0.5*x^2))
abline(fit.wls$coefficients,lty=1, col='black')
summary(fit.ols)
summary(fit.wls)