Dear there, I am wondering how to test whether a simple linear regression model (e.g. y=1.05x) is significantly different from a 1 to 1 line (i.e. y=x). Thanks. Regards, Jin [[alternative HTML version deleted]]
This is two tests: Whether the slope != 1 and whether the intercept != 0. To do this, include an offset in your model: fit <- lm(y ~ x + offset(x), data=dat) HTH, Simon. At 03:44 PM 3/08/2005, Jin.Li at csiro.au wrote:>Dear there, > >I am wondering how to test whether a simple linear regression model >(e.g. y=1.05x) is significantly different from a 1 to 1 line (i.e. y=x). >Thanks. > >Regards, > >Jin > > > [[alternative HTML version deleted]] > >______________________________________________ >R-help at stat.math.ethz.ch mailing list >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlSimon Blomberg, B.Sc.(Hons.), Ph.D, M.App.Stat. Centre for Resource and Environmental Studies The Australian National University Canberra ACT 0200 Australia T: +61 2 6125 7800 email: Simon.Blomberg_at_anu.edu.au F: +61 2 6125 0757 CRICOS Provider # 00120C
On Wed, 3 Aug 2005, Simon Blomberg wrote:> This is two tests: Whether the slope != 1 and whether the intercept != 0.Neither model given has an intercept ....> To do this, include an offset in your model: > > fit <- lm(y ~ x + offset(x), data=dat)but no intercept, so use summary(lm(y ~ 0 + x + offset(1.05*x), data=dat)) and look if the coefficient of x is significantly different from zero. E.g. x <- 1:10 set.seed(1) y <- 1.05*x + rnorm(10) summary(lm(y ~ 0 + x + offset(1.05*x))) Coefficients: Estimate Std. Error t value Pr(>|t|) x 0.03061 0.03910 0.783 0.454 is not.> > HTH, > > Simon. > > > At 03:44 PM 3/08/2005, Jin.Li at csiro.au wrote: >> >> I am wondering how to test whether a simple linear regression model >> (e.g. y=1.05x) is significantly different from a 1 to 1 line (i.e. y=x).-- 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
Thank you all for the reply. Regards, Jin -----Original Message----- From: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk] Sent: Wednesday, 3 August 2005 5:20 P To: Simon Blomberg Cc: Li, Jin (CSE, Atherton); r-help at stat.math.ethz.ch Subject: Re: [R] how to test this On Wed, 3 Aug 2005, Simon Blomberg wrote:> This is two tests: Whether the slope != 1 and whether the intercept !0.Neither model given has an intercept ....> To do this, include an offset in your model: > > fit <- lm(y ~ x + offset(x), data=dat)but no intercept, so use summary(lm(y ~ 0 + x + offset(1.05*x), data=dat)) and look if the coefficient of x is significantly different from zero. E.g. x <- 1:10 set.seed(1) y <- 1.05*x + rnorm(10) summary(lm(y ~ 0 + x + offset(1.05*x))) Coefficients: Estimate Std. Error t value Pr(>|t|) x 0.03061 0.03910 0.783 0.454 is not.> > HTH, > > Simon. > > > At 03:44 PM 3/08/2005, Jin.Li at csiro.au wrote: >> >> I am wondering how to test whether a simple linear regression model >> (e.g. y=1.05x) is significantly different from a 1 to 1 line (i.e.y=x). -- 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