[R] Interpretation of 'Intercept' in a 2-way factorial lm

From: Gustaf Granath <gustaf.granath_at_ebc.uu.se>
Date: Wed, 05 Dec 2007 20:31:43 +0100

Hi all,

I hope this question is not too trivial. I can't find an explanation anywhere (Stats and R books, R-archives) so now I have to turn to the R-list.


If you have a factorial design with two factors (say A and B with two levels each). What does the intercept coefficient with treatment.contrasts represent??

Here is an example without interaction where A has two levels A1 and A2, and B has two levels B1 and B2. So R takes as a baseline A1 and B1.

coef( summary ( lm ( fruit ~ A + B, data = test)))

                Estimate   Std. Error  t value       Pr(>|t|)

(Intercept) 2.716667 0.5484828 4.953058 7.879890e-04
A2 6.266667 0.6333333 9.894737 3.907437e-06 B2 5.166667 0.6333333 8.157895 1.892846e-05

I understand that the mean of A2 is +6.3 more than A1, and that B2 is 5.2 more than B1.

So the question is: Is the intercept A1 and B1 combined as one mean
("the baseline")? or is it something else? Does this number actually
tell me anything
useful (2.716)??

What does the model (y = intercept + ??) look like then? I can't understand how both factors (A and B) can have the same intercept?

Thanks in advance!!

Gustaf Granath

Dept of Plant Ecology
Uppsala University, Sweden

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