Note c2-c5 are  Xi(1)  Xi(3)  Xi(5)  W
MTB > describe c2-c5

                N     MEAN   MEDIAN   TRMEAN    STDEV   SEMEAN
C2             40    44.16    43.90    44.09     7.24     1.14
C3             40    54.21    53.63    54.21     7.24     1.14
C4             40    64.27    63.21    64.49     9.24     1.46
C5             40   14.992   15.200   14.986    2.803    0.443

              MIN      MAX       Q1       Q3
C2          30.45    59.35    38.18    49.56
C3          39.87    67.71    48.61    60.45
C4          42.06    81.84    57.90    73.01
C5          9.462   20.399   13.288   16.837

MTB > print c1-c5


 ROW    C1        C2        C3        C4        C5

   1     1   37.5591   49.2905   61.0219   15.9725
   2     2   45.6543   51.5845   57.5147   15.3772
   3     3   40.9388   52.8798   64.8208   11.4790
   4     4   47.3594   55.4488   63.5382   16.8894
   5     5   52.7051   62.7035   72.7019   19.1783
   6     6   30.4523   46.3408   62.2293   11.8182
   7     7   43.6463   58.3700   73.0938   15.3287
   8     8   41.1555   49.2628   57.3700   13.2081
   9     9   44.1515   51.9980   59.8446   13.0904
  10    10   38.1596   46.5943   55.0289   10.3156
  11    11   37.6759   39.8673   42.0587   10.2613
  12    12   45.3005   54.3828   63.4651   15.5985
  13    13   39.3695   48.1535   56.9376   13.9009
  14    14   36.6637   43.7512   50.8387   13.5257
  15    15   53.3985   62.3164   71.2344   14.4470
  16    16   59.3546   62.8025   66.2505   20.1588
  17    17   53.1397   64.3491   75.5585   16.1145
  18    18   44.9017   58.8249   72.7481   15.0577
  19    19   41.7863   59.4402   77.0942   18.3338
  20    20   38.2456   48.9803   59.7150   13.7722
  21    21   47.2360   60.7889   74.3419   15.8823
  22    22   53.5713   67.7081   81.8449   18.2535
  23    23   35.5429   43.5109   51.4790   10.1454
  24    24   37.5435   50.2488   62.9541    9.4617
  25    25   37.0655   49.7070   62.3485   15.8149
  26    26   32.3981   44.6891   56.9800   11.6046
  27    27   45.2164   62.0766   78.9367   14.0775
  28    28   35.6718   47.4212   59.1706   12.1867
  29    29   38.3018   51.1347   63.9675   14.0722
  30    30   52.6135   55.5175   58.4216   16.6798
  31    31   38.3620   48.4903   58.6186   15.0716
  32    32   45.1399   51.4356   57.7314   13.9429
  33    33   53.8190   64.2745   74.7299   20.3992
  34    34   49.4558   61.4248   73.3937   15.9967
  35    35   56.2855   59.0422   61.7988   17.4674
  36    36   49.5883   57.5779   65.5674   17.2962
  37    37   41.4488   59.4312   77.4136   15.8574
  38    38   47.4177   57.4216   67.4255   18.9465
  39    39   56.9980   65.7324   74.4667   18.8964
  40    40   41.0608   43.5436   46.0265   13.7900

MTB > corr c2-c5

             C2       C3       C4
C3        0.842
C4        0.536    0.907
C5        0.766    0.765    0.598

MTB > regress c4 2 c2 c3

The regression equation is
C4 = -0.000003 - 1.00 C2 + 2.00 C3

Predictor       Coef       Stdev    t-ratio        p
Constant -0.00000309  0.00000000          *        *
C2          -1.00000     0.00000          *        *
C3           2.00000     0.00000          *        *

s = 0           R-sq = 100.0%    R-sq(adj) = 100.0%

Analysis of Variance

SOURCE       DF          SS          MS         F        p
Regression    2      3330.4      1665.2         *        *
Error        37         0.0         0.0
Total        39      3330.4

SOURCE       DF      SEQ SS
C2            1       956.1
C3            1      2374.3



MTB > GStd.
MTB > Plot c4 c3;
SUBC>   Symbol '*';
SUBC>   Title 'time 5 vs time 3'.

                               time 5 vs time 3
         -
 C4      -
         -                                                    *
         -                                      2   *
       75+                                        *     2  *
         -                                    **   * **
         -
         -                           *       2        *
         -                *     ***     **     *
       60+                  * *2    *
         -             *     * *   2      *
         -                 *
         -            2
         -
       45+            *
         -     *
         -
           --------+---------+---------+---------+---------+--------C3      
                42.0      48.0      54.0      60.0      66.0

MTB > GPro.
MTB > GStd.
MTB > Plot c4 c2;
SUBC>   Symbol '*';
SUBC>   Title 'time 5 vs time 1'.

                               time 5 vs time 1
         -
 C4      -
         -                                            *
         -                        **    *
       75+                                  *         **    *
         -                            * *      *     **
         -
         -                       *          *   *               *
         -      *          ***           *  *              *
       60+              *   *2         *
         -         *           *  *     **           *
         -                   *
         -              * *
         -
       45+                       *
         -                  *
         -
           ----+---------+---------+---------+---------+---------+--C2      
            30.0      36.0      42.0      48.0      54.0      60.0

MTB > GPro.
MTB > GStd.
MTB > Plot c3 c2;
SUBC>   Symbol '*';
SUBC>   Title 'time 3 vs time 1'.

                               time 3 vs time 1
         -                                            *
 C3      -                                                  *
         -                                            **
         -                              *      *     **         *
       60+                        **        *              *
         -                            * *   *   *
         -                                  *        *
         -                               *
         -                   *   *     ***
       50+                 *2     *
         -              *    2 *
         -      *            *
         -         *    * *      *
         -
       40+                  *
         -
         -
           ----+---------+---------+---------+---------+---------+--C2      
            30.0      36.0      42.0      48.0      54.0      60.0


MTB > note let's look at exog variable in c5
MTB > regress c4 2 c5 c3

The regression equation is
C4 = 0.68 - 0.757 C5 + 1.38 C3

Predictor       Coef       Stdev    t-ratio        p
Constant       0.683       4.555       0.15    0.882
C5           -0.7570      0.3329      -2.27    0.029
C3            1.3822      0.1290      10.72    0.000

s = 3.752       R-sq = 84.4%     R-sq(adj) = 83.5%

Analysis of Variance

SOURCE       DF          SS          MS         F        p
Regression    2      2809.5      1404.8     99.80    0.000
Error        37       520.8        14.1
Total        39      3330.4

SOURCE       DF      SEQ SS
C5            1      1192.8
C3            1      1616.7

Unusual Observations
Obs.       C5         C4        Fit  Stdev.Fit   Residual    St.Resid
 19      18.3     77.094     68.962      0.947      8.132       2.24R 

R denotes an obs. with a large st. resid.

MTB > regress c4 2 c5 c2

The regression equation is
C4 = 31.2 + 1.50 C5 + 0.239 C2

Predictor       Coef       Stdev    t-ratio        p
Constant      31.213       7.546       4.14    0.000
C5            1.5004      0.6678       2.25    0.031
C2            0.2392      0.2587       0.92    0.361

s = 7.514       R-sq = 37.3%     R-sq(adj) = 33.9%

Analysis of Variance

SOURCE       DF          SS          MS         F        p
Regression    2     1241.10      620.55     10.99    0.000
Error        37     2089.28       56.47
Total        39     3330.38

SOURCE       DF      SEQ SS
C5            1     1192.84
C2            1       48.26

Unusual Observations
Obs.       C5         C4        Fit  Stdev.Fit   Residual    St.Resid
 27      14.1      78.94      63.15       1.45      15.79       2.14R 
 40      13.8      46.03      61.72       1.31     -15.70      -2.12R 

R denotes an obs. with a large st. resid.

MTB > regress c4 3 c5 c3 c2

The regression equation is
C4 = -0.000003 -0.000000 C5 + 2.00 C3 - 1.00 C2

Predictor       Coef       Stdev    t-ratio        p
Constant -0.00000312  0.00000000          *        *
C5       -0.00000004  0.00000000          *        *
C3           2.00000     0.00000          *        *
C2          -1.00000     0.00000          *        *

s = 0           R-sq = 100.0%    R-sq(adj) = 100.0%

Analysis of Variance

SOURCE       DF          SS          MS         F        p
Regression    3      3330.4      1110.1         *        *
Error        36         0.0         0.0
Total        39      3330.4

SOURCE       DF      SEQ SS
C5            1      1192.8
C3            1      1616.7
C2            1       520.8

MTB > GStd.
MTB > Plot C2 C5;
SUBC>   Symbol '*';
SUBC>   Title 'time=1 vs W'.

                                  time=1 vs W
       60+                                                        *
         -
 C2      -                                          *      *
         -                           *        *         *          *
         -                                      *            *
       50+                                   *     *
         -                                  *    *          *
         -                         2      **
         -                    *         * *
         -                     *  *         *            *
       40+            *            *
         -  *   **                **    *   **
         -      *         *      *
         -
         -             *
       30+              *
         -
           ----+---------+---------+---------+---------+---------+--C5      
            10.0      12.0      14.0      16.0      18.0      20.0

MTB > GPro.
MTB > GStd.
MTB > Plot C3 C5;
SUBC>   Symbol '*';
SUBC>   Title 'time=3 vs W'.

                                  time=3 vs W
         -                                              *
 C3      -                                                 *
         -                                    *                    *
         -                         * *       *               *    *
       60+                                  2       *    *
         -                              * *        *        *
         -                                      **
         -                                 *
         -            *       *    2      *
       50+  *                  *            **
         -                *       **    *
         -       *      *
         -      *      *         **
         -
       40+      *
         -
         -
           ----+---------+---------+---------+---------+---------+--C5      
            10.0      12.0      14.0      16.0      18.0      20.0

MTB > GPro.
MTB > GStd.
MTB > Plot C4 C5;
SUBC>   Symbol '*';
SUBC>   Title 'time=5 vs W'.

                                  time=5 vs W
         -
 C4      -
         -                                              *
         -                         *        *            *
       75+                                  * *            *       *
         -                           *  * *  *               *
         -
         -            *                            *        *     *
         -  *           *          *       **    *  *
       60+                *   *   *     *    *
         -             *       *   2      *     *
         -       *
         -      *                *
         -
       45+                        *
         -      *
         -
           ----+---------+---------+---------+---------+---------+--C5      
            10.0      12.0      14.0      16.0      18.0      20.0

MTB > GPro.
MTB > corr c2-c5

             C2       C3       C4
C3        0.842
C4        0.536    0.907
C5        0.766    0.765    0.598

================================================================
================================================================
NOTE c22-c25 are  X(1)  X(3)  X(5)  W
MTB > corr c22-c25

            C22      C23      C24
C23       0.716
C24       0.491    0.741
C25       0.716    0.652    0.619

MTB > regress c24 2 c22 c23

The regression equation is
C24 = 5.05 - 0.121 C22 + 1.19 C23

Predictor       Coef       Stdev    t-ratio        p
Constant       5.054       9.052       0.56    0.580
C22          -0.1212      0.2360      -0.51    0.611
C23           1.1943      0.2358       5.07    0.000

s = 7.507       R-sq = 55.2%     R-sq(adj) = 52.7%

Analysis of Variance

SOURCE       DF          SS          MS         F        p
Regression    2      2565.3      1282.7     22.76    0.000
Error        37      2085.1        56.4
Total        39      4650.4

SOURCE       DF      SEQ SS
C22           1      1119.6
C23           1      1445.7

Unusual Observations
Obs.      C22        C24        Fit  Stdev.Fit   Residual    St.Resid
 37      37.5      80.05      75.71       3.58       4.34       0.66 X

X denotes an obs. whose X value gives it large influence.


MTB > note use W with fallible data
MTB > regress c24 2 c25 c23

The regression equation is
C24 = 3.04 + 0.924 C25 + 0.876 C23

Predictor       Coef       Stdev    t-ratio        p
Constant       3.038       8.705       0.35    0.729
C25           0.9240      0.5471       1.69    0.100
C23           0.8763      0.2100       4.17    0.000

s = 7.259       R-sq = 58.1%     R-sq(adj) = 55.8%

Analysis of Variance

SOURCE       DF          SS          MS         F        p
Regression    2      2700.8      1350.4     25.63    0.000
Error        37      1949.7        52.7
Total        39      4650.4

SOURCE       DF      SEQ SS
C25           1      1783.5
C23           1       917.2

Unusual Observations
Obs.      C25        C24        Fit  Stdev.Fit   Residual    St.Resid
 27      14.1      83.92      69.66       2.20      14.26       2.06R 

R denotes an obs. with a large st. resid.

MTB > regress c24 2 c25 c22

The regression equation is
C24 = 25.7 + 2.14 C25 + 0.145 C22

Predictor       Coef       Stdev    t-ratio        p
Constant      25.690       8.821       2.91    0.006
C25           2.1431      0.7181       2.98    0.005
C22           0.1447      0.2759       0.52    0.603

s = 8.770       R-sq = 38.8%     R-sq(adj) = 35.5%

Analysis of Variance

SOURCE       DF          SS          MS         F        p
Regression    2     1804.70      902.35     11.73    0.000
Error        37     2845.74       76.91
Total        39     4650.44

SOURCE       DF      SEQ SS
C25           1     1783.55
C22           1       21.16

Unusual Observations
Obs.      C25        C24        Fit  Stdev.Fit   Residual    St.Resid
 27      14.1      83.92      62.25       1.56      21.67       2.51R 
 40      13.8      42.67      61.03       1.58     -18.36      -2.13R 

R denotes an obs. with a large st. resid.

MTB > regress c24 3 c25 c23 c22

The regression equation is
C24 = 4.47 + 1.36 C25 + 1.04 C23 - 0.389 C22

Predictor       Coef       Stdev    t-ratio        p
Constant       4.467       8.602       0.52    0.607
C25           1.3637      0.6093       2.24    0.032
C23           1.0446      0.2338       4.47    0.000
C22          -0.3893      0.2542      -1.53    0.134

s = 7.131       R-sq = 60.6%     R-sq(adj) = 57.4%

Analysis of Variance

SOURCE       DF          SS          MS         F        p
Regression    3     2820.00      940.00     18.49    0.000
Error        36     1830.44       50.85
Total        39     4650.44

SOURCE       DF      SEQ SS
C25           1     1783.55
C23           1      917.21
C22           1      119.25

Unusual Observations
Obs.      C25        C24        Fit  Stdev.Fit   Residual    St.Resid
 17      16.1      78.98      63.54       2.54      15.44       2.32R 

R denotes an obs. with a large st. resid.

MTB > 
