Hi: Perhaps this will clarify some things:
> model.matrix(m) (Intercept) factor1B factor1C factor2t2 factor2t3 1 1 0 0 0 0 2 1 1 0 0 0 3 1 0 1 0 0 4 1 0 0 1 0 5 1 1 0 1 0 6 1 0 1 1 0 7 1 0 0 0 1 8 1 1 0 0 1 9 1 0 1 0 1 Now tack on the predicted values from the model: > cbind(model.matrix(m), predict(m)) (Intercept) factor1B factor1C factor2t2 factor2t3 1 1 0 0 0 0 67.65502 2 1 1 0 0 0 134.24682 3 1 0 1 0 0 83.81768 4 1 0 0 1 0 52.71252 5 1 1 0 1 0 119.30431 6 1 0 1 1 0 68.87518 7 1 0 0 0 1 30.66079 8 1 1 0 0 1 97.25259 9 1 0 1 0 1 46.82345 In the first row, the subject is neither at levels B nor C of factor1, nor at level t2 of factor2. At what levels of factor1 and factor2 must this subject be? You'll see a pattern in how the predicted values are obtained from the level combinations in each observation, the model and its estimated coefficients. In the process, you'll learn how treatment contrasts work. Since I smell homework, this is as far as I'll go. HTH, Dennis On Wed, Apr 14, 2010 at 10:13 AM, Xiaokuan Wei <weixiaok...@yahoo.com>wrote: > Dear list, > > I have a question regarding the meaning of intercept term in a two-way > anova model without interaction term. > > for example (let's assume there is no interaction between factor1 and > factor2) : > > > df > val factor1 factor2 > 1 48.61533 A t1 > 2 171.13535 B t1 > 3 65.96884 C t1 > 4 63.71222 A t2 > 5 80.22049 B t2 > 6 96.95929 C t2 > 7 38.70078 A t3 > 8 99.44787 B t3 > 9 36.58818 C t3 > > the summary of regression : > > > summary(m) > Call: > lm(formula = val ~ factor1 + factor2, data = df) > Residuals: > 1 2 3 4 5 6 7 8 9 > -19.040 36.889 -17.849 11.000 -39.084 28.084 8.040 2.195 -10.235 > Coefficients: > Estimate Std. Error t value Pr(>|t|) > (Intercept) 67.66 25.42 2.661 0.0563 . > factor1B 66.59 27.85 2.391 0.0751 . > factor1C 16.16 27.85 0.580 0.5928 > factor2t2 -14.94 27.85 -0.537 0.6200 > factor2t3 -36.99 27.85 -1.328 0.2548 > --- > Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 > Residual standard error: 34.11 on 4 degrees of freedom > Multiple R-squared: 0.6669, Adjusted R-squared: 0.3338 > F-statistic: 2.002 on 4 and 4 DF, p-value: 0.2589 > > > This is contrast treatment, and my question is what the intercept (here is > 67.66) represent for? > > Thank you. > > > Xiaokuan > > > > [[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. > > [[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.
