From: Brian McGill <brian.mcgill_at_mcgill.ca>

Date: Thu, 07 Feb 2008 17:56:07 -0500

Date: Thu, 07 Feb 2008 17:56:07 -0500

I am playing with the a 1-way anova with and without the "-1" option.

I have a simple cooked up example below but it behaves the same on a more complex real example.

How can a model that gets the same parameter estimates on the same data leading to the same residuals get different r2/F/p-value?

I suspect it depends on the difference in the model.matrix (see below) but this just confused me how it got the same parameter estimates without really clearing up why the r2's are different.

Any help on this is greatly appreciated!

* > x<-as.factor(c(1,1,1,2,2,2))
*

> y<-c(1.1,1.0,0.9,2.0,2.1,1.9)

> summary(lm(y~x))

Call:

lm(formula = y ~ x)

Residuals:

1 2 3 4 5 6 1.000e-01 -4.980e-16 -1.000e-01 8.538e-18 1.000e-01 -1.000e-01

Coefficients:

Estimate Std. Error t value Pr(>|t|) (Intercept) 1.00000 0.05774 17.32 6.52e-05 *** x2 1.00000 0.08165 12.25 0.000255 ***

--- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.1 on 4 degrees of freedom Multiple R-Squared: 0.974, Adjusted R-squared: 0.9675 F-statistic: 150 on 1 and 4 DF, p-value: 0.0002552Received on Thu 07 Feb 2008 - 23:00:31 GMT

> summary(lm(y~x-1))

Call: lm(formula = y ~ x - 1) Residuals: 1 2 3 4 5 6 1.000e-01 5.027e-16 -1.000e-01 4.405e-20 1.000e-01 -1.000e-01 Coefficients: Estimate Std. Error t value Pr(>|t|) x1 1.00000 0.05774 17.32 6.52e-05 *** x2 2.00000 0.05774 34.64 4.14e-06 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.1 on 4 degrees of freedom Multiple R-Squared: 0.9973, Adjusted R-squared: 0.996 F-statistic: 750 on 2 and 4 DF, p-value: 7.073e-06

> m2nc=lm(y~x-1)

> m2wc=lm(y~x)

> resid(m2nc)

1 2 3 4 5 6 1.000000e-01 5.026734e-16 -1.000000e-01 4.404571e-20 1.000000e-01 -1.000000e-01

> resid(m2wc)

1 2 3 4 5 6 1.000000e-01 -4.980012e-16 -1.000000e-01 8.538092e-18 1.000000e-01 -1.000000e-01

> model.matrix(m2nc)

x1 x2 1 1 0 2 1 0 3 1 0 4 0 1 5 0 1 6 0 1 attr(,"assign") [1] 1 1 attr(,"contrasts") attr(,"contrasts")$x [1] "contr.treatment"

> model.matrix(m2wc)

(Intercept) x2 1 1 0 2 1 0 3 1 0 4 1 1 5 1 1 6 1 1 attr(,"assign") [1] 0 1 attr(,"contrasts") attr(,"contrasts")$x [1] "contr.treatment" Brian McGill Dept of Biology McGill University Stewart Biology Bldg 1205 ave Docteur Penfield Montreal, QC H3A 1B1 CANADA (514) 398-6417 http://www.brianmcgill.org mail_at_brianmcgill.org [[alternative HTML version deleted]] ______________________________________________ R-help_at_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.

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