[R] Coefficients: (20 not defined because of singularities)

[Thomas Fischer]

Hello,

I am trying to run a linear regression analysis on my data set. For some 
reason most variables are removed due to singularities.

My linear regression looks this way (I am using only partial data, which 
is selected by flags):

fm<-lm(log(cplex6.time..sec..[flags]) ~ cplex6.cities[flags] + 
log(1/features.meanOver.frust[flags]) + 
log(1/features.meanOver.minDist[flags]) +
[...]
avg..steps.to.loc..Opt..norm..[flags] + NN.List.opt..tour.max.[flags])

As I am using inversion and logarithms I set all data to positiv values, 
before running lm():

cplex6.time..sec..[cplex6.time..sec..<=0.00001]=0.00001
features.meanOver.frust[features.meanOver.frust<=0.00001]=0.00001
features.meanOver.minDist[features.meanOver.minDist<=0.00001]=0.00001
[...]
features.varOver.varDist[features.varOver.varDist<=0.00001]=0.00001

Retrieving the summary of fm, I get the message, that some coefficients 
have been removed.

[...]
Coefficients: (20 not defined because of singularities)
                                                Estimate Std. Error t 
value
(Intercept)                                      87.2162    44.1148   
1.977
log(1/features.meanOver.frust[flags])            -2.5298     0.1515 
-16.702
log(1/features.meanOver.minDist[flags])         154.7170    11.3917  
13.582
log(1/features.meanOver.quant25Dist[flags])    -943.4625    71.3505 
-13.223
log(1/features.meanOver.quart1SpanDist[flags])  776.1049    60.0571  
12.923
log(1/features.meanOver.spanDist[flags])         -9.8069     0.1400 
-70.038
log(1/features.meanOver.varDist[flags])         -11.3211     0.6715 
-16.859
log(1/features.quant25Over.minDist[flags])      -46.9655     3.1438 
-14.939
avg..steps.to.loc..Opt..norm..[flags]             0.8324     1.0919   
0.762
                                               Pr(>|t|)
(Intercept)                                      0.0511 .
log(1/features.meanOver.frust[flags])            <2e-16 ***
log(1/features.meanOver.minDist[flags])          <2e-16 ***
log(1/features.meanOver.quant25Dist[flags])      <2e-16 ***
log(1/features.meanOver.quart1SpanDist[flags])   <2e-16 ***
log(1/features.meanOver.spanDist[flags])         <2e-16 ***
log(1/features.meanOver.varDist[flags])          <2e-16 ***
log(1/features.quant25Over.minDist[flags])       <2e-16 ***
avg..steps.to.loc..Opt..norm..[flags]            0.4478
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
[...]


The summary of one of the removed coefficients looks like this:

> summary(features.spanOver.quart1SpanDist[flags])
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
0.05584 0.05797 0.06366 0.06311 0.06674 0.07290
> summary(log(1/features.spanOver.quart1SpanDist[flags]))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  2.619   2.707   2.754   2.767   2.848   2.885

The summary of a coefficient that was kept looks this way:

> summary(features.quant25Over.minDist[flags])
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
0.001030 0.001030 0.001030 0.001032 0.001030 0.001040
> summary(log(1/features.quant25Over.minDist[flags]))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  6.869   6.878   6.878   6.877   6.878   6.878

So, I don't see the difference. Why has the first coefficient been 
removed and the second one kept?
Please help me.

I'm using R 1.6.2 on a Linux x86 machine.

Greetings,
Thomas Fischer