# Re: [R] Odd anova(lm()) order phenomenon, looking for an explanation

From: Berwin A Turlach <berwin_at_maths.uwa.edu.au>
Date: Fri 31 Mar 2006 - 19:31:00 EST

G'day Andrew,

>>>>> "AR" == Andrew Robinson <A.Robinson@ms.unimelb.edu.au> writes:

AR> I would have expected any term to explain less Sum Sq if     AR> listed second than if listed first. Is my intuition awry? Yes. :-)

I would not expect that *any* term explains less Sum Sq if listed second, then life and (linear) modelling would be simple. The problem with multiple regression is that a covariate might look unimportant if used first (i.e. has small Sum Sq associated with it in the anova table), but if we first correct for other regressor, then this covariate becomes important all of a sudden (i.e. has large Sum Sq associated with it in the anova table).

What surprised me, was that you observed this phenomenon with respect to both regressors. If only one had displayed this behaviour, I would have readily explained it as above, but that both display it, I found surprising too.

AR> Does anyone have any modelling insight to help me interpret     AR> what I'm seeing?
Don't know if the following example, which shows the same behaviour, leads to any insight.

Response: y

```          Df Sum Sq Mean Sq  F value Pr(>F)
x1         1 0.0055  0.0055   0.1485 0.7008
x2         1 5.0071  5.0071 134.3499 <2e-16 ***
Residuals 97 3.6151  0.0373
```
```---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

> anova(lm(y~x2+x1))

Analysis of Variance Table

Response: y
Df Sum Sq Mean Sq  F value Pr(>F)
x2         1 4.9930  4.9930 133.9723 <2e-16 ***
x1         1 0.0196  0.0196   0.5261   0.47
Residuals 97 3.6151  0.0373
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Cheers,

Berwin

Berwin A Turlach                      Tel.: +61 (8) 6488 3338 (secr)
School of Mathematics and Statistics        +61 (8) 6488 3383 (self)
The University of Western Australia   FAX : +61 (8) 6488 1028
35 Stirling Highway
Crawley WA 6009                e-mail: berwin@maths.uwa.edu.au
Australia                        http://www.maths.uwa.edu.au/~berwin

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