# [R] Interpreting summary.lm for a 2 factor anova

```Dear all,

Here is a small example : -```
```
> model <- aov(breaks ~ wool * tension, data = warpbreaks)
> summary.lm(model)

Call:
aov(formula = breaks ~ wool * tension, data = warpbreaks)

Residuals:
Min       1Q   Median       3Q      Max
-19.5556  -6.8889  -0.6667   7.1944  25.4444

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)      44.556      3.647  12.218 2.43e-16 ***
woolB           -16.333      5.157  -3.167 0.002677 **
tensionM        -20.556      5.157  -3.986 0.000228 ***
tensionH        -20.000      5.157  -3.878 0.000320 ***
woolB:tensionM   21.111      7.294   2.895 0.005698 **
woolB:tensionH   10.556      7.294   1.447 0.154327
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 10.94 on 48 degrees of freedom
Multiple R-squared:  0.3778,    Adjusted R-squared:  0.3129
F-statistic: 5.828 on 5 and 48 DF,  p-value: 0.0002772

> model.tables(model,"e")
Tables of effects

wool
wool
A       B
2.8889 -2.8889

tension
tension
L      M      H
8.241 -1.759 -6.481

wool:tension
tension
wool L      M      H
A  5.278 -5.278  0.000
B -5.278  5.278  0.000

> model.tables(model,"m")
Tables of means
Grand mean

28.14815

wool
wool
A      B
31.037 25.259

tension
tension
L     M     H
36.39 26.39 21.67

wool:tension
tension
wool L     M     H
A 44.56 24.00 24.56
B 28.22 28.78 18.78
>

I don't follow the output of summary.lm. I understand the output of
model.tables for effects and means. For instance what does 44.556 represent
? Is it the grand average ? The grand mean is 28.14815. Can someone help me
understand the output of summary.lm ?

Best Regards,
Ashim

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