I'm on 64-bit vs your 32-bit. And if you haven't received this from other R-helpers already, here it is: FAQ 7.31. Machine precision is producing numbers very close to zero but not zero. Then division is practically a random number generator. Also, I'm certain that t and F are computed separately (i.e., not by computing t and then squaring) so that the relationship t^2 = F fails again due to the machine precision limitation in the intermediate calculations.
-----Original Message----- From: Vito M. R. Muggeo [mailto:vito.mug...@unipa.it] Sent: Wednesday, March 12, 2014 8:37 AM To: Andrews, Chris; r-help@r-project.org Subject: Re: [R] summary.lm() for zero variance response Hi Chris, Here my output (I have not yet installed R 3.0.3) > n=10;k=1;summary(lm(rep(k,n)~rnorm(n))) Call: lm(formula = rep(k, n) ~ rnorm(n)) Residuals: Min 1Q Median 3Q Max -1.465e-16 1.564e-18 1.764e-17 2.147e-17 3.492e-17 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.000e+00 2.021e-17 4.949e+16 <2e-16 *** rnorm(n) -1.620e-17 2.236e-17 -7.240e-01 0.489 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 5.637e-17 on 8 degrees of freedom Multiple R-squared: 0.6598, Adjusted R-squared: 0.6173 F-statistic: 15.52 on 1 and 8 DF, p-value: 0.004301 > sessionInfo() R version 3.0.2 (2013-09-25) Platform: i386-w64-mingw32/i386 (32-bit) Il 12/03/2014 13.25, Andrews, Chris ha scritto: > I get what I would expect. The tstat and the Fstat are both undefined (0/0); > as are the p-values > >> n=10;k=1;summary(lm(rep(k,n)~rnorm(n))) > > Call: > lm(formula = rep(k, n) ~ rnorm(n)) > > Residuals: > Min 1Q Median 3Q Max > 0 0 0 0 0 > > Coefficients: > Estimate Std. Error t value Pr(>|t|) > (Intercept) 1 0 Inf <2e-16 *** > rnorm(n) 0 0 NA NA > --- > Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 > > Residual standard error: 0 on 8 degrees of freedom > Multiple R-squared: NaN, Adjusted R-squared: NaN > F-statistic: NaN on 1 and 8 DF, p-value: NA > >> sessionInfo() > R version 3.0.2 (2013-09-25) > Platform: x86_64-w64-mingw32/x64 (64-bit) > > > -----Original Message----- > From: Vito M. R. Muggeo [mailto:vito.mug...@unipa.it] > Sent: Wednesday, March 12, 2014 6:27 AM > To: r-help@r-project.org > Subject: [R] summary.lm() for zero variance response > > dear all, > a student of mine brought to my attention the following, somewhat odd, > behaviour of summary.lm() when the response variance is zero (yes, > possibly meaningless from a practical viewpoint). Namely something like > > n=10;k=1;summary(lm(rep(k,n)~rnorm(n))) > > The values of k, n and the covariate do not matter. > > Two awkward points are > 1) the F stat is different from t squared > 2) more importantly, p-values from the F-stat are far smaller (and > "significant" at usual levels 0.05/0.01) than the p-values coming from > summary(..)$coef[,"Pr(>|t|)"] (i.e. the usual Wald test). Differences > are dramatic for n>1000 where p(tstat)\approx0.8 and p(Fstat)< 2.2e-16. > > I looked for "lm zero variance" or "lm deterministic data", or "lm zero > residuals" but without success. Also ?lm does not include any warning > about using it for zero variance data (as reported for instance in ?nls) > > Am I missing anything? > thanks, > vito > > -- ============================================== Vito M.R. Muggeo Dip.to Sc Statist e Matem `Vianelli' Università di Palermo viale delle Scienze, edificio 13 90128 Palermo - ITALY tel: 091 23895240 fax: 091 485726 http://dssm.unipa.it/vmuggeo 28th IWSM International Workshop on Statistical Modelling July 8-12, 2013, Palermo http://iwsm2013.unipa.it =============================================== ********************************************************** Electronic Mail is not secure, may not be read every day, and should not be used for urgent or sensitive issues ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.