[R] Summary coefficients give NA values because of singularities

[Gathurst]

Hello,

I have a data set which I am using to find a model with the most significant
parameters included and most importantly, the p-values.  The full model is
of the form:
  sad[,1]~b_1 sad[,2]+b_2 sad[,3]+b_3 sad[,4]+b_4 sad[,5]+b_5 sad[,6]+b_6
sad[,7]+b_7 sad[,8]+b_8 sad[,9]+b_9 sad[,10],
where the 9 variables on the right hand side are all indicator variables. 
The thing I don't understand is the line ' sad[, 10]         NA         NA     
NA       NA ' as a result of 'Coefficients: (1 not defined because of
singularities)'.

I think the output is taking sad[,10] as the intercept, based on previous
attempts at figuring my issue out, which I find a bit wierd considering
sad[,10] is either 0 or 1.  How do I produce the correct output showing all
p-values?

My code and output is as follows:

sad<-matrix(1,ncol=11,nrow=486)
sad[,c(1:10)]<-d[,2][-357]
sad[,1]<-d[,29][-357]
sad[,2][sad[,2]!=1]<-0
sad[,3][sad[,3]!=2]<-0
sad[,4][sad[,4]!=3]<-0
sad[,5][sad[,5]!=4]<-0
sad[,6][sad[,6]!=5]<-0
sad[,7][sad[,7]!=6]<-0
sad[,8][sad[,8]!=7]<-0
sad[,9][sad[,9]!=8]<-0
sad[,10][sad[,10]!=9]<-0
sad[,2][sad[,2]==1]<-1
sad[,3][sad[,3]==2]<-1
sad[,4][sad[,4]==3]<-1
sad[,5][sad[,5]==4]<-1
sad[,6][sad[,6]==5]<-1
sad[,7][sad[,7]==6]<-1
sad[,8][sad[,8]==7]<-1
sad[,9][sad[,9]==8]<-1
sad[,10][sad[,10]==9]<-1
sad

summary(lm(sad[,1]~sad[,2]+sad[,3]
+sad[,4]+sad[,5]+sad[,6]
+sad[,7]+sad[,8]+sad[,9]+sad[,10]))

Call:
lm(formula = sad[, 1] ~ sad[, 2] + sad[, 3] + sad[, 4] + sad[, 
    5] + sad[, 6] + sad[, 7] + sad[, 8] + sad[, 9] + sad[, 10])

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3191 -0.3893  0.0519  0.7436  1.0519 

Coefficients: (1 not defined because of singularities)
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.34091    0.14495  29.947   <2e-16 ***
sad[, 2]    -0.16142    0.18128  -0.890   0.3737    
sad[, 3]    -0.23221    0.20275  -1.145   0.2527    
sad[, 4]     0.17832    0.19695   0.905   0.3657    
sad[, 5]     0.06450    0.21447   0.301   0.7638    
sad[, 6]    -0.15909    0.18713  -0.850   0.3957    
sad[, 7]    -0.39286    0.18171  -2.162   0.0311 *  
sad[, 8]    -0.08450    0.21146  -0.400   0.6896    
sad[, 9]    -0.02176    0.20170  -0.108   0.9141    
sad[, 10]         NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.9615 on 477 degrees of freedom
Multiple R-squared: 0.02984,    Adjusted R-squared: 0.01357 
F-statistic: 1.834 on 8 and 477 DF,  p-value: 0.06869 

Thanks in advance.

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