Can you identify each of the following designs from the design matrix?

Design A 
  

   x1  x2  x3  x4  x5  x6  x7  x8
a   1   1   1   1   1   1   1   1
b   1   1  -1   1  -1  -1  -1   1
c   1   1   0  -2   0  -2   0  -2
d  -1   1   1   1  -1  -1   1   1
e  -1   1  -1   1   1  -1  -1   1
f  -1   1   0  -2   0   2   0  -2
g   0  -2   1   1   0   0  -2  -2
h   0  -2  -1   1   0   0   2  -2
i   0  -2   0  -2   0   0   0   4
 
Design B 
  

   x1  x2  s1  s2
a   1   1   1   1  
b   1   1  -1   1  
c   1   1   0  -2   
d  -1   1   1   1  
e  -1   1  -1   1   
f  -1   1   0  -2  
g   0  -2   1   1  
h   0  -2  -1   1  
i   0  -2   0  -2  
 
Design C  
  

   x1  s1  s2  x2  x3  x4  x5
a   1   1   0   1   1   1   1
b   1   1   0  -1   1  -1   1
c   1   1   0   0  -2   0  -2
d   1  -1   0   1   1   1   1
e   1  -1   0  -1   1  -1   1
f   1  -1   0   0  -2   0  -2
g  -1   0   1   1   1  -1  -1
h  -1   0   1  -1   1   1  -1
i  -1   0   1   0  -2   0   2
j  -1   0  -1   1   1  -1  -1
k  -1   0  -1  -1   1   1  -1
l  -1   0  -1   0  -2   0   2
 
Design D  


   x1  x2  x3  
a   1   1   0    
b   1   1   0    
c   1  -1   0    
d   1  -1   0    
e  -1   0   1     
f  -1   0   1    
g  -1   0  -1    
h  -1   0  -1   
 
Design E  
  

   x1  x2  x3  
a   1   1   1    
b   1   1   1    
c  -1   1   1    
d  -1   1   1    
e   0  -2   1     
f   0  -2   1    
g   0   0  -3    
h   0   0  -3  

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Linear Statistical Models Course