[Rd] NIST StRD linear regression
Prof Brian Ripley
ripley at stats.ox.ac.uk
Mon Jul 31 08:52:01 CEST 2006
That is not an appropriate way to fit a degree-10 polynomial (in any
language, if fitting a degree-10 polynomial is in fact an appropriate
statistical analysis, which seems unlikely).
On Sun, 30 Jul 2006, Carnell, Rob C wrote:
> NIST maintains a repository of Statistical Reference Datasets at
> http://www.itl.nist.gov/div898/strd/. I have been working through the
> datasets to compare R's results to their references with the hope that
> if all works well, this could become a validation package.
What does it validate? The R user's understanding of numerical methods?
> All the linear regression datasets give results with some degree of
> accuracy except one. The NIST model includes 11 parameters, but R will
> not compute the estimates for all 11 parameters because it finds the
> data matrix to be singular.
>
> The code I used is below. Any help in getting R to estimate all 11
> regression parameters would be greatly appreciated.
>
> I am posting this to the R-devel list since I think that the discussion
> might involve the limitations of platform precision.
>
> I am using R 2.3.1 for Windows XP.
>
> rm(list=ls())
> require(gsubfn)
That is not needed.
> defaultPath <- "my path"
>
> data.base <- "http://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA"
>
> reg.data <- paste(data.base, "/Filip.dat", sep="")
>
> model <-
> "V1~V2+I(V2^2)+I(V2^3)+I(V2^4)+I(V2^5)+I(V2^6)+I(V2^7)+I(V2^8)+I(V2^9)+I
> (V2^10)"
>
> filePath <- paste(defaultPath, "//NISTtest.dat", sep="")
> download.file(reg.data, filePath, quiet=TRUE)
filePath <-
url("http://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA/Filip.dat")
will suffice.
> A <- read.table(filePath, skip=60, strip.white=TRUE)
> lm.data <- lm(formula(model), A)
>
> lm.data
lm(V1 ~ poly(V2, 10), A)
works.
> kappa(model.matrix(V1 ~ poly(V2, 10, raw=TRUE), A), exact=TRUE)
[1] 1.767963e+15
shows the design matrix is indeed numerically singular by the naive
method.
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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