Quantile Regression for Cubics


#1

Hi,
I'm trying to create some quantile regression curves for multiple values of \tau, for a cubic equation. I have so far done the following

'''plot(Year,Diff, type="l", main="Plot of Quantile Regression Curves ", xlab="Years", ylab="Deaths per 100,000", font.lab=4, cex.main=1, col="orangered3", lwd=2)
x1<-Year^{3}
fitmedian<-rq(Diff~Year+x1,tau=0.5)
lines(Year,fitmedian$fitted.values,col="orangered1")'''

I've noticed that this does create Quantile regression curves in my plot, but was unsure if this is correct, since when I try and receive a summary(fitmedian), I am left with an error "Error in solve.default(crossprod(x)) :
system is computationally singular: reciprocal condition number = 1.672e-21". In contrast to this, when my model is
Diff~Year, that is the simple linear regression model, 'R' reports no error in obtaining a summary of the linear model.The question I am battling over is whether I am modelling my cubic the correct way or not?