Re: regression line confidence interval

[<Bill.Venables@csiro.au>]

S is a programming language, with excellent graphical facilities, so why not write your own function?  Not only are you allowed to do that, but with S that's what you are supposed to do.  It can be quicker than google....

 

Here is a very simple first cut that treats the single predictor case in an obvious way:

 

showHourglass <- function(x, y) {

  dat <- data.frame(x = x, y = y)

  fm <- lm(y ~ x, dat)

  newdata = data.frame(x = seq(min(x), max(x), length = 500))

  pfm <- predict(fm, newdata = newdata, se = T)

  pfm$upper <- pfm$fit + 2*pfm$se

  pfm$lower <- pfm$fit - 2*pfm$se

  rg <- range(y, pfm$upper, pfm$lower)

  plot(x, y, ylim = rg, type = "n")

  points(x, y, pch = 1, col = 2)

  lines(newdata$x, pfm$upper, lty = 4, col = 3)

  lines(newdata$x, pfm$lower, lty = 4, col = 3)

  abline(coef(fm))

  invisible(fm)

}

 

Test drive:

 

x <- runif(50, 0, 10)

y <- x + rnorm(x)

showHourglass(x, y)

 

This gives the pointwise confidence interval for the mean (using '2' as the percentage point of the t-distribution).  If you want tolerance intervals (or prediction intervals for a single new observation) you need to be a bit more clever, but not much. 

 

Extend, generalize, tidy up, submit for others to use...  Easy.

 

Bill Venables.

-----Original Message-----
From: s-news-owner@lists.biostat.wustl.edu [mailto:s-news-owner@lists.biostat.wustl.edu] On Behalf Of Pierce, Ken
Sent: Wednesday, 27 April 2005 7:59 AM
To: s-news@lists.biostat.wustl.edu
Subject: [S] regression line confidence interval

I've been searching for some time now how to add the hourglass shape confidence intervals to a simple (or not so simple) regression line. I've tried to search the archive and google but it has been in vain. A simple case might be just a simple linear model object with a single predictor.

 

Thanks,

 

Ken 

 

~~~~~~~~~~~~~~~~~~~~~~~

Kenneth B. Pierce Jr.

Research Ecologist

Forestry Sciences Laboratory

3200 SW Jefferson Way

Corvallis, OR 97331

ken.pierce@oregonstate.edu

541 750-7393

~~~~~~~~~~~~~~~~~~~~~~~~