R help - Jun 2010 - Singularity in simple ANCOVA problem

I'm using R 2.10.1 with the latest version of all packages (updated today).

I'm confused as to why I'm getting a hard singularity in a simple set 
of experimental data:

 > blots
    ID Lot Age Conc
1   1   A   3 4.44
2   2   A   3 4.56
3   3   B  41 4.03
4   4   B  41 4.57
5   5   C 229 4.49
6   6   C 229 4.66
7   7   D 238 3.88
8   8   D 238 3.93
9   9   E 349 4.43
10 10   E 349 4.22
11 11   F 391 4.42
12 12   F 391 4.46

 > fit2<- lm(Conc ~ Age + Lot, data=blots)
 > summary(fit2)

Call:
lm(formula = Conc ~ Age + Lot, data = blots)

Residuals:
        Min         1Q     Median         3Q        Max
-2.700e-01 -6.625e-02  6.072e-17  6.625e-02  2.700e-01

Coefficients: (1 not defined because of singularities)
               Estimate Std. Error t value Pr(>|t|)
(Intercept)  4.5004639  0.1273234  35.347 3.42e-08 ***
Age         -0.0001546  0.0004605  -0.336   0.7485
LotB        -0.1941237  0.1706005  -1.138   0.2986
LotC         0.1099485  0.1554378   0.707   0.5059
LotD        -0.5586598  0.1558853  -3.584   0.0116 *
LotE        -0.1214948  0.1698331  -0.715   0.5013
LotF                NA         NA      NA       NA
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1

Residual standard error: 0.1787 on 6 degrees of freedom
Multiple R-squared: 0.7464,     Adjusted R-squared: 0.535
F-statistic: 3.532 on 5 and 6 DF,  p-value: 0.07811


Why the NA's here?
===============================================================Robert A.
LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"

You have only one Age value in each Lot.  Hence the Age is aliased with one
of the
5 degrees of freedom between lots.  You can see it in the picture

xyplot(Conc ~ Age|Lot, data=blots, pch=16)

There is no opportunity for a slope within each of the groups.

Rich

	[[alternative HTML version deleted]]

At 08:44 PM 6/20/2010, RICHARD M. HEIBERGER wrote:
>You have only one Age value in each Lot.  Hence the Age is aliased 
>with one of the
>5 degrees of freedom between lots.  You can see it in the picture
>
>xyplot(Conc ~ Age|Lot, data=blots, pch=16)
>
>There is no opportunity for a slope within each of the groups.
>
>Rich
Doh!

Thanks.

===============================================================Robert A.
LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"