Small Log to Check the Formula for Prediction Interval 
(as given on the handout RegrSheet.pdf)
against the Calculated Prediction Intervals in SAS.
======================================================

I begin by using the small simulated dataset already 
saved as SimSet0.sas7bdat. I am adding two artificial 
records, one with X value 1.5  and the other the same 
X as obs 10, with Y missing for both.

libname home ".";
options nocenter linesize=70;

data Simtmp; 
     set home.simset0;
     if _N_ = 1 then do;
          x = 1.5; y = .;
          output; end;
     if _N_ = 10 then do;
          y = .; output; end;
              
* Generated two records  ;

proc print; run; 

Obs       X       y
 1     1.50000    .
 2     0.31486    .


data SimSet0;
     set home.simset0 Simtmp;
proc reg data=simset0;
     model y = x;
     output out=PredTmp p = predmn 
          stdi = IndSE stdr = rsdSE
          L95 = lowpred U95 = hipred;

* Mean-square error sigma^2 hat =  0.79844
    with 73 degrees of freedom, and 
    (also from proc reg)
         ahat =    0.64567  , bhat = 2.01129

proc print data=PredTmp (firstobs=70);
   run;
 Obs    X         y      predmn   lowpred   hipred   rsdSE    IndSE

 70  0.09704   0.56500  0.84085  -0.97620  2.65789  0.87502  0.91171
 71  0.05941   1.48832  0.76517  -1.05641  2.58674  0.87264  0.91399
 72  0.97048   2.86848  2.59759   0.77650  4.41869  0.87289  0.91375
 73  0.42874   1.55990  1.50800  -0.28577  3.30176  0.88703  0.90003
 74  0.43740  -0.65496  1.52541  -0.26815  3.31897  0.88713  0.89993
 75  0.06559   0.62970  0.77759  -1.04321  2.59840  0.87305  0.91360
 76  1.50000    .       3.66260   1.74011  5.58510   .       0.96463
 77  0.31486    .       1.27893  -0.51942  3.07729   .       0.90234

NOTE that the IndSE (standard errors used in calculating the
prediction intervals) are a little bit higher than the rsdSE
standard errors used in calculating standardized residuals.
To see just how much, note from the formulas given in 
RegrSheet.pdf that

rsdSE^2   and   IndSE^2  
should lie equidistant from Sighat^2

We check this in a little data-step:

data checkSE;
   set PredTmp (keep = rsdSE IndSE);
    AvgVar = (rsdSE**2 + IndSE**2)/2; 
proc print data=checkSE (firstobs=70);
   run;

### The avgSE is constant .79844  to 5th decimal place
which DOES agree with sigma^2 above.

=================================================

Further features & options:

proc reg data=simset0;
     model y = x/ alpha=.01;
     output out=PredTmp2 p = predmn 
          stdi = IndSE stdr = rsdSE
          lcl = lowpred ucl = hipred;
run; 

Obs     X         y      predmn   lowpred   hipred   rsdSE    IndSE
 70  0.09704   0.56500  0.84085  -1.57052  3.25222  0.87502  0.91171
 71  0.05941   1.48832  0.76517  -1.65221  3.18254  0.87264  0.91399
 72  0.97048   2.86848  2.59759   0.18085  5.01433  0.87289  0.91375
 73  0.42874   1.55990  1.50800  -0.87247  3.88847  0.88703  0.90003
 74  0.43740  -0.65496  1.52541  -0.85479  3.90561  0.88713  0.89993
 75  0.06559   0.62970  0.77759  -1.63876  3.19395  0.87305  0.91360
 76  1.50000    .       3.66260   1.11130  6.21391   .       0.96463
 77  0.31486    .       1.27893  -1.10763  3.66549   .       0.90234

YOU CAN SEE THAT THE   alpha=.01  OPTION HERE HAD THE EFFECT 
OF WIDENING THE PREDICTION INTERVAL AND ENLARGING THE SE'S;
NOTE THAT YOU NEEDED TO SPECIFY THE PREDICTION LIMITS WITH UCL 
AND LCL  in order to use the option of customizing  ALPHA.