library(quantreg)
help(rq)
data(engel)
y = engel$foodexp
x = engel$income
fit1 <- rq(y ~ x, tau = 0.5)
fit1
summary(fit1, se = "nid") # Uses the Normal approximation


fit2 <- rq(y ~ x, tau = 0.95)
fit2
summary(fit2, se = "nid") # Uses the Normal approximation

# Several values of tau can be handled:
plot(x, y, cex = 0.25, type = "n", xlab = "Household Income", ylab = "Food Expenditure")
points(x, y, cex = 0.5, col = "black")
#abline(rq(y ~ x, tau = 0.5), col = "blue")
#abline(lm(y ~ x), lty = 2, col = "red")
#taus <- c(0.05, 0.1, 0.25, 0.75, 0.9, 0.95)
#for (i in 1:length(taus)) {abline(rq(y ~ x, tau = taus[i]), col = "gray")}
abline(rq(y ~ x, tau = 0.05), col = "blue")
abline(rq(y ~ x, tau = 0.95), col = "red")