Using plot.rq in the quantreg package in R, we can plot the coefficient estimate distribution, and get something like this: enter image description here

What are the dotted red lines? Extensive googling has revealed that the middle one is the average of all 99 estimates, but still don't know about the dotted red line.

  • 6
    $\begingroup$ Extensive googling had it wrong: these are the OLS estimates and its SE $\endgroup$
    – user603
    Nov 4, 2012 at 9:31
  • $\begingroup$ @user603 (i) Do you have a reference for this? (ii) Do you mean the CI? Is this 95% or 99%? $\endgroup$
    – user14281
    Nov 4, 2012 at 11:05
  • 1
    $\begingroup$ @AndreSilva: thanks for bringing this question to the fore. Also, thanks for editing the plots in my answer. $\endgroup$
    – user603
    Feb 15, 2014 at 18:39

1 Answer 1


Here is a reproduction of the Engel regression from the quantreg vignette. To make the plot more readable, I focus on the second (slope) parameter:

xx   <- engel$income-mean(engel$income)
fit1 <- summary(rq(engel$foodexp~xx,tau=1:9/10))
plot(fit1, parm=2)

I can now overplot, in green, the usual OLS estimates and it's (5-95)% confidence interval:

fit2 <- lm(foodexp~xx, data=engel)
   col="green", lwd=3, lty=2)                                           #$
abline(h=summary(fit2)$coef[2] + qt(0.95,fit2$df)*summary(fit2)$coef[4], 
   col="green", lwd=3, lty=2)                                           #$
abline(h=summary(fit2)$coef[2] + qt(0.05,fit2$df)*summary(fit2)$coef[4], 
       col="green", lwd=3, lty=2)

and they match the dotted red lines on the original plot.

enter image description here


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