Interpretation of 'Intercept' in a 2-way factorial lm
Gustaf Granath wrote:
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.
Question:
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?
Consider an AxB crosstable of (fitted) means. Upper left corner is intercept , add A2, B2, or both to get the other three cells.
O__ ---- Peter Dalgaard ?ster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907