Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up.
Sign up to join this community
Suppose I want to generate independent data $(y_{i},x_{i})$ such that the conditional mean of $y_{i}$ given $x_{i}$ is a quadratic function in $x_{i}$ and the $.25$ conditional quantile of $y_{i}$ given $x_{i}$ is a function different than the conditional mean function.
I can generate such data with the given conditional mean using R. But how to make the $.25$ conditional quantile function different than the regression function?
A simple approach would be to draw $X\sim U[0,1]$ and $Y\sim N(x^2,x)$, i.e., the variance of $Y$ is $x$. Then the $0.25$ quantile of $Y$ would be $z_{0.25}\sqrt{x}$. Here are simulated data, with the expectation as a black and the quantile as a red line:
R code:
set.seed(1)
xx <- runif(1e3)
yy <- rnorm(length(xx),xx^2,sqrt(xx))
plot(xx,yy,pch=19,las=1,cex=0.6)
xx_pred <- seq(.01,.99,by=.01)
lines(xx_pred,xx_pred^2,lwd=2)
lines(xx_pred,qnorm(0.25,xx_pred^2,sqrt(xx_pred)),col="red",lwd=2)
