data one;
   input yield rain;
   *rain=round(rain,1);
   rainclass=rain;
   cards;
24.5 9.6
33.7 12.9
27.9 9.9
27.5 8.7
21.7 6.8
31.9 12.5
36.8 13
29.9 10.1
30.2 10.1
32.0 10.1
34.0 10.8
19.4 7.8
36.0 16.2
30.2 14.1
32.4 10.6
36.4 10
36.9 11.5
31.5 13.6
30.5 12.1
32.3 12
34.9 9.3
30.1 7.7
36.9 11
26.8 6.9
30.5 9.5
33.3 16.5
29.7 9.3
35.0 9.4
29.9 8.7
35.2 9.5
38.3 11.6
35.2 12.1
35.5 8
36.7 10.7
26.8 13.9
38.0 11.3
31.7 11.6
32.6 10.4
;
run;
proc glm;
   class rainclass;
   *model yield=rain rain*rain rainclass/singular=.0001 xpx inverse;
   model yield=rain rain*rain rainclass/xpx inverse;
run;

/*
SAS has trouble inverting X'X for this problem.  Round-off error leads
to certain elements of X'X being non-zero when they're really 0.  There
is an option to change the minimum non-zero value, which is set by
default at .0000001, which the SAS documentation suggests may be too
small for some purposes.  I changed it in the code above and got the
right lack-of-fit test. 
 
http://v8doc.sas.com/sashtml/stat/chap30/sect19.htm#glmmodel
*/