Thanks for the answer. The situation is that I don't know anything of y a priori. Of course I then would not do a regression on constant y's, but isn't it a problem of stability of the algorithm, if I get an adj RSquare of 0.6788 for a least square fit on this type of data? I think lm should give me a correct result even in case of y is perfectly fittable, because the situation is that I never know if my data could become so. If I have to offset y in this case, then my question becomes how noisy do my y's have to be, so that I can rely on the lm result, if I specify the formula y~x without offset. What if my y's become nearly linear (or nearly perfect fittable with another linear model). I think my question now becomes 'how to rely on lm's result if the formula is specified the way y~x without offset? or 'How do I prevent my result to become numerically incorrect if I may get nearly perfect fittable y's'.
Greetings Henrik -----Ursprüngliche Nachricht----- Von: Peter Ehlers [mailto:ehl...@ucalgary.ca] Gesendet: Freitag, 8. Januar 2010 19:44 An: Jan-Henrik Pötter Cc: r-help@r-project.org Betreff: Re: [R] how to get perfect fit of lm if response is constant You need to review the assumptions of linear models: y is assumed to be the realization of a random variable, not a constant (or, more precisely: there are assumed to be deviations that are N(0, sigma^2). If you 'know' that y is a constant, then you have two options: 1. don't do the regression because it makes no sense; 2. if you want to test lm()'s handling of the data: fm <- lm(y ~ x, data = df, offset = rep(1, nrow(df))) (or use: offset = y) -Peter Ehlers Jan-Henrik Pötter wrote: > Hello. > > Consider the response-variable of data.frame df is constant, so analytically > perfect fit of a linear model is expected. Fitting a regression line using > lm result in residuals, slope and std.errors not exactly zero, which is > acceptable in some way, but errorneous. But if you use summary.lm it shows > inacceptable error propagation in the calculation of the t value and the > corresponding p-value for the slope, as well R-Square – just consider the > adj R-Square of 0.6788! This result is independent of which mode used for > the input vectors. Is there any way to get the perfect fitted regression > curve using lm and prevent this error propagation? I consider rounding all > values of the lm-object afterwards to somewhat precision as a bad idea. > Unfortunately there is no option in lm for calculation precision. > > > >> df<-data.frame(x=1:10,y=1) > >> myl<-lm(y~x,data=df) > > > >> myl > > > > Call: > > lm(formula = y ~ x, data = df) > > > > Coefficients: > > (Intercept) x > > 1.000e+00 9.463e-18 > > > >> summary(myl) > > > > Call: > > lm(formula = y ~ x, data = df) > > > > Residuals: > > Min 1Q Median 3Q Max > > -1.136e-16 -1.341e-17 7.886e-18 2.918e-17 5.047e-17 > > > > Coefficients: > > Estimate Std. Error t value Pr(>|t|) > > (Intercept) 1.000e+00 3.390e-17 2.950e+16 <2e-16 *** > > x 9.463e-18 5.463e-18 1.732e+00 0.122 > > --- > > Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > > > Residual standard error: 4.962e-17 on 8 degrees of freedom > > Multiple R-squared: 0.7145, Adjusted R-squared: 0.6788 > > F-statistic: 20.02 on 1 and 8 DF, p-value: 0.002071 > > > > > [[alternative HTML version deleted]] > > > > ------------------------------------------------------------------------ > > ______________________________________________ > 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. -- Peter Ehlers University of Calgary 403.202.3921 ______________________________________________ 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.
