Hi:
Perhaps this will clarify some things:
model.matrix(m)
(Intercept) factor1B factor1C factor2t2 factor2t3
1 100 0 0
2 110 0 0
3 101 0 0
4 100 1 0
5 110 1 0
6 101 1 0
7 100 0 1
8 110 0 1
9 101 0 1
Now tack on the predicted values from the model:
cbind(model.matrix(m), predict(m))
(Intercept) factor1B factor1C factor2t2 factor2t3
1 100 0 0 67.65502
2 110 0 0 134.24682
3 101 0 0 83.81768
4 100 1 0 52.71252
5 110 1 0 119.30431
6 101 1 0 68.87518
7 100 0 1 30.66079
8 110 0 1 97.25259
9 101 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.comwrote:
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
valfactor1 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
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