Now I want to estimate the parameters of quantile regression, and I encounter the following problems. My main idea is :

y=\beta _0 +\beta _1 x_1+\beta_2x_2+\beta_3x_3+\epsilon, \epsilon\sim N(0,\sigma_1^2)

My model is following:

```
n=20
p=4 #include the constant
k=5 #the number of quantile
truebeta=c(0.2,0.8,0.5,-0.5)
obs_x=matrix(rnorm(n*p,2,0.5),nrow=n,ncol=(p-1))
sigma1=0.25
eps=rnorm(n,0,sigma1)
c=rep(1,n)
x=cbind(c,obs_x)
y=as.vector(x%*%truebeta+eps)
data=data.frame(cbind(y,obs_x))
names(data)=c("y","x1","x2","x3")
tau=c(0.05,0.25,0.5,0.75,0.95)
fit=rq(y~.,tau=tau,data=data)
fited=summary(fit)
beta_qr=fit$coefficients
```

For the \tau quantile regressions, I don’t know how to define the beta_qr .I hope that you can give me some advices