* ch18eg1.sas;
* SAS program to illustrate residual plots,
* plus test of normality;
options ls=76 nodate;
;
data KFC;
  input y A j; * A=i;
  lines;
  11  1  1
  17  1  2
  16  1  3
  14  1  4
  15  1  5
  12  2  1
  10  2  2
  15  2  3
  19  2  4
  11  2  5
  23  3  1
  20  3  2
  18  3  3
  17  3  4
  27  4  1
  33  4  2
  22  4  3
  26  4  4
  28  4  5
;
* Fit the ANOVA model and save info for residual plots;
proc glm noprint;
  class A;
  model y = A;
  output out=B p=yhat r=e;
  title 'Kenton Food Company, (data from Table 16.1).';
;
* compute Blom's normal scores for the residuals;
proc rank normal=Blom;
 var e;
 ranks nscore;
;
proc print;
 title2 'KFC data, including normal scores.';
;
* Residual plots;
proc plot;
 plot e*yhat / vpos=19 vref=0;
 plot e*nscore / vpos=19 vref=0 href=0;
 title2 'Residual Plots.';
;
* Normality test;
proc corr nosimple;
 var e nscore;
 title2 'Testing Normality.';

 
                Kenton Food Company, (data from Table 16.1).               1
                     KFC data, including normal scores.

              Obs     y    A    j    yhat       e     nscore

                1    11    1    1    14.6    -3.6    -1.37597
                2    17    1    2    14.6     2.4     0.88413
                3    16    1    3    14.6     1.4     0.54695
                4    14    1    4    14.6    -0.6    -0.13058
                5    15    1    5    14.6     0.4     0.13058
                6    12    2    1    13.4    -1.4    -0.40115
                7    10    2    2    13.4    -3.4    -1.09680
                8    15    2    3    13.4     1.6     0.70547
                9    19    2    4    13.4     5.6     1.37597
               10    11    2    5    13.4    -2.4    -0.70547
               11    23    3    1    19.5     3.5     1.09680
               12    20    3    2    19.5     0.5     0.26344
               13    18    3    3    19.5    -1.5    -0.54695
               14    17    3    4    19.5    -2.5    -0.88413
               15    27    4    1    27.2    -0.2     0.00000
               16    33    4    2    27.2     5.8     1.84570
               17    22    4    3    27.2    -5.2    -1.84570
               18    26    4    4    27.2    -1.2    -0.26344
               19    28    4    5    27.2     0.8     0.40115


                Kenton Food Company, (data from Table 16.1).               2
                              Residual Plots.

            Plot of e*yhat.  Legend: A = 1 obs, B = 2 obs, etc.

 10 +
    |
    |
    |
    |
    |        A                                                      A
  5 +
    |
    |                                A
  e |            A
    |        A   A
    |                                A                              A
  0 +------------A--------------------------------------------------A-----
    |            A                                                  A
    |        A                       A
    |        A                       A
    |        A   A
    |
 -5 +                                                               A
    ---+-------+-------+-------+-------+-------+-------+-------+-------+--
      12      14      16      18      20      22      24      26      28

                                     yhat


                Kenton Food Company, (data from Table 16.1).               3
                              Residual Plots.

           Plot of e*nscore.  Legend: A = 1 obs, B = 2 obs, etc.

     10 +                              |
        |                              |
        |                              |
        |                              |
        |                              |
        |                              |                  A      A
      5 +                              |
        |                              |
        |                              |              A
      e |                              |           A
        |                              |       A A
        |                              |   A A
      0 +------------------------------A-A----------------------------
        |                          A A |
        |                      A A     |
        |                  A A         |
        |           A   A              |
        |                              |
     -5 +    A                         |
        ---+-------------+-------------+-------------+-------------+--
          -2            -1             0             1             2

                              Rank for Variable e


                Kenton Food Company, (data from Table 16.1).               4
                             Testing Normality.

                             The CORR Procedure

                      2  Variables:    e        nscore   


                 Pearson Correlation Coefficients, N = 19 
                        Prob > |r| under H0: Rho=0
 
                                              e        nscore

              e                         1.00000       0.98824
                                                       <.0001

              nscore                    0.98824       1.00000
              Rank for Variable e        <.0001