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 <weixiaokuan@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
>
>
>
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>
>
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