Um, you need to reverse y and x there. The question was about lm(y ~ x)....
> X <- cbind(1, y) > solve(crossprod(X)) Error in solve.default(crossprod(X)) : system is computationally singular: reciprocal condition number = 6.19587e-35 Actually, lm can QR perfectly OK, but it gets caught by its singularity detection: > qr <- qr(X, tol=1e-10) > qr # without the tol bit, you get same thing but $rank == 1 $qr y [1,] -3.0000000 -4.520117e+09 [2,] 0.3333333 -3.426530e+01 [3,] 0.3333333 -2.947103e-02 [4,] 0.3333333 4.252164e-01 [5,] 0.3333333 -3.665468e-01 [6,] 0.3333333 -3.488029e-01 [7,] 0.3333333 2.614064e-01 [8,] 0.3333333 4.086982e-01 [9,] 0.3333333 2.018556e-03 $rank [1] 2 $qraux [1] 1.333333 1.571779 $pivot [1] 1 2 attr(,"class") [1] "qr" > x = c(79.744, 123.904, 87.29601, 116.352, 67.71201, 72.96001, 101.632, > 108.928, 94.08) > qr.coef(qr,x) y -2.403345e+09 1.595099e+00 > lm(x~y) Call: lm(formula = x ~ y) Coefficients: (Intercept) y 94.73 NA > lm(x~y, tol=1e-10) Call: lm(formula = x ~ y, tol = 1e-10) Coefficients: (Intercept) y -2.403e+09 1.595e+00 > lm(x~I(y-mean(y))) Call: lm(formula = x ~ I(y - mean(y))) Coefficients: (Intercept) I(y - mean(y)) 94.734 1.595 > On 18 Apr 2019, at 17:56 , Fox, John <j...@mcmaster.ca> wrote: > > Dear Michael and Dingyuan Wang, > >> -----Original Message----- >> From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Michael >> Dewey >> Sent: Thursday, April 18, 2019 11:25 AM >> To: Dingyuan Wang <gumb...@aosc.io>; r-help@r-project.org >> Subject: Re: [R] lm fails on some large input >> >> Perhaps subtract 1506705766 from y? >> >> Saying some other software does it well implies you know what the _correct_ >> answer is here but I would question what that means with this sort of data- >> set. > > It's rather an interesting problem, though, because the naïve computation of > the LS solution works: > > plot(x, y) > X <- cbind(1, x) > b <- solve(t(X) %*% X) %*% t(X) %*% y > b > abline(b) > > That surprised me, because I expected that lm() computation, using the QR > decomposition, would be more numerically stable. > > Best, > John > > ----------------------------------------------------------------- > John Fox > Professor Emeritus > McMaster University > Hamilton, Ontario, Canada > Web: https://socialsciences.mcmaster.ca/jfox/ > > > >> >> On 17/04/2019 07:26, Dingyuan Wang wrote: >>> Hi, >>> >>> This input doesn't have any interesting properties except y is unix >>> time. Spreadsheets can do this well. >>> Is this a bug that lm can't do x ~ y? >>> >>> R version 3.5.2 (2018-12-20) -- "Eggshell Igloo" >>> Copyright (C) 2018 The R Foundation for Statistical Computing >>> Platform: x86_64-pc-linux-gnu (64-bit) >>> >>>> x = c(79.744, 123.904, 87.29601, 116.352, 67.71201, 72.96001, >>> 101.632, 108.928, 94.08) > y = c(1506705739.385, 1506705766.895, >>> 1506705746.293, 1506705761.873, 1506705734.743, 1506705735.351, >>> 1506705756.26, 1506705761.307, >>> 1506705747.372) >>>> m = lm(x ~ y) >>>> summary(m) >>> >>> Call: >>> lm(formula = x ~ y) >>> >>> Residuals: >>> Min 1Q Median 3Q Max >>> -27.0222 -14.9902 -0.6542 14.1938 29.1698 >>> >>> Coefficients: (1 not defined because of singularities) >>> Estimate Std. Error t value Pr(>|t|) >>> (Intercept) 94.734 6.511 14.55 4.88e-07 *** y >>> NA NA NA NA >>> --- >>> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >>> >>> Residual standard error: 19.53 on 8 degrees of freedom >>> >>>> summary(lm(y ~ x)) >>> >>> Call: >>> lm(formula = y ~ x) >>> >>> Residuals: >>> Min 1Q Median 3Q Max >>> -2.1687 -1.3345 -0.9466 1.3826 2.6551 >>> >>> Coefficients: >>> Estimate Std. Error t value Pr(>|t|) >>> (Intercept) 1.507e+09 3.294e+00 4.574e+08 < 2e-16 *** x >>> 6.136e-01 3.413e-02 1.798e+01 4.07e-07 *** >>> --- >>> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >>> >>> Residual standard error: 1.885 on 7 degrees of freedom Multiple >>> R-squared: 0.9788, Adjusted R-squared: 0.9758 >>> F-statistic: 323.3 on 1 and 7 DF, p-value: 4.068e-07 >>> >>> ______________________________________________ >>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >>> 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. >>> >>> --- >>> This email has been checked for viruses by AVG. >>> https://www.avg.com >>> >>> >> >> -- >> Michael >> http://www.dewey.myzen.co.uk/home.html >> >> ______________________________________________ >> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >> 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. > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.