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Here are some data:

   Run     y
1    1 4.970
2    1 5.040
3    1 5.060
4    1 4.975
5    1 4.990
6    1 5.045
7    1 5.005
8    1 5.000
9    1 5.075
10   1 5.080
11   2 4.665
12   2 4.885
13   2 4.840
14   2 4.925
15   2 5.235
16   2 4.970
17   2 5.020
18   2 4.905
19   2 4.890
20   2 5.150

This dataset is called dat. Then I fit the model introduced here : a common mean for $y$ but a variance depending on the run (the data are much more dispersed in run 2). The SAS code is:

PROC MIXED DATA=dat;
CLASS Run; 
MODEL y= / solution CL outp=predicted ;
REPEATED  / group=Run;
RUN;QUIT;

I use PROC MIXED whereas the model has no random effect, because I don't know another SAS procedure to handle heteroscedasticity. For those more familiar with R the equivalent R code is:

library(nlme)
gls(y~1, data=dat, weights=varIdent(form= ~1|Run)))

As you have seen I have added the option outp=predicted in the SAS code in order to get prediction intervals for individual values. The result is strange: each observation has the same prediction interval, and this one coincides with the confidence interval about the mean. What's going on ?

EDIT: (later - also change the title). How could we define a prediction interval for this model ? We could imagine a new observation in run 1 or in run 2, but if we consider a third run we would need to assign a variance to the new observation, and there's no natural choice for that. So SAS should return nothing or it should return something derived from a particular convention which gives a sense to the "new observation".

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