1          options ps=256 ls=132 nocenter nodate nonumber;
3          DATA ONE;
4              TITLE1 'EXST7015: Multiple Regression from Snedecor & Cochran (1967)';
5            INPUT X1 X2 X3 Y;
6          **** LABEL Y ='Plant available phosphorus'
7                     X1='Inorganic phosphorus'
8                     X2='Hydrolized organic phosphorus'
9                     X3='Nonhydrolized phosphorus';
10         CARDS;
NOTE: The data set WORK.ONE has 18 observations and 4 variables.
NOTE: DATA statement used:
      real time           0.05 seconds
      cpu time            0.05 seconds
10       !        RUN;
29         ;
30         PROC PRINT DATA=ONE; TITLE2 'RAW DATA LISTING'; RUN;
NOTE: There were 18 observations read from the data set WORK.ONE.
NOTE: The PROCEDURE PRINT printed page 1.
NOTE: PROCEDURE PRINT used:
      real time           0.04 seconds
      cpu time            0.04 seconds
 
EXST7015: Multiple Regression from Snedecor & Cochran (1967)
RAW DATA LISTING
 
Obs     X1     X2     X3     Y
  1     0.4    53    158     64
  2     0.4    23    163     60
  3     3.1    19     37     71
  4     0.6    34    157     61
  5     4.7    24     59     54
  6     1.7    65    123     77
  7     9.4    44     46     81
  8    10.1    31    117     93
  9    11.6    29    173     93
 10    12.6    58    112     51
 11    10.9    37    111     76
 12    23.1    46    114     96
 13    23.1    50    134     77
 14    21.6    44     73     93
 15    23.1    56    168     95
 16     1.9    36    143     54
 17    26.8    58    202    168
 18    29.9    51    124     99
 
31      PROC REG DATA=ONE ALL LINEPRINTER; TITLE2 'PROC REG OUTPUT WITH ALL OPTIONS';
32            MODEL Y = X1 X2 X3 / INFLUENCE;
33              TEST X1=2; TEST X1=X2=X3;
34         RUN;
NOTE: 18 observations read.
NOTE: 18 observations used in computations.
34       !      OPTIONS PS=60 LS=120;
35            MODEL Y = X1 X2 X3 / PARTIAL;
36            PLOT RESIDUAL.*PREDICTED. / VREF=0;
37         RUN;
38         OPTIONS LS=80;
NOTE: The PROCEDURE REG printed pages 2-20.
NOTE: PROCEDURE REG used:

      real time           0.13 seconds
      cpu time            0.13 seconds


EXST7015: Multiple Regression from Snedecor & Cochran (1967)
PROC REG OUTPUT WITH ALL OPTIONS
 
The REG Procedure
 
                               Descriptive Statistics
                                           Uncorrected                      Standard
Variable             Sum           Mean             SS       Variance      Deviation
Intercept       18.00000        1.00000       18.00000              0              0
X1             215.00000       11.94444     4321.02000      103.11556       10.15458
X2             758.00000       42.11111          35076      185.63399       13.62476
X3            2214.00000      123.00000         307894     2092.47059       45.74353
Y             1463.00000       81.27778         131299      728.80065       26.99631
 
              Uncorrected Sums of Squares and Crossproducts
Variable    Intercept             X1             X2             X3              Y
Intercept          18            215            758           2214           1463
X1                215        4321.02        10139.5          27645        20706.2
X2                758        10139.5          35076          96598          63825
X3               2214          27645          96598         307894         187542
Y                1463        20706.2          63825         187542         131299
 
                                  Correlation
Variable                X1                X2                X3                 Y
X1                  1.0000            0.4616            0.1520            0.6934
X2                  0.4616            1.0000            0.3175            0.3545
X3                  0.1520            0.3175            1.0000            0.3617
Y                   0.6934            0.3545            0.3617            1.0000
 
                       Model Crossproducts X'X X'Y Y'Y
Variable    Intercept             X1             X2             X3              Y
Intercept          18            215            758           2214           1463
X1                215        4321.02        10139.5          27645        20706.2
X2                758        10139.5          35076          96598          63825
X3               2214          27645          96598         307894         187542
Y                1463        20706.2          63825         187542         131299
 
                          X'X Inverse, Parameter Estimates, and SSE
Variable       Intercept             X1            X2            X3              Y
Intercept   0.8133156545   0.0019185269  -0.011398244  -0.002444578   43.652197791
X1          0.0019185269   0.0007249271  -0.000248347  -9.690816E-7   1.7847796802
X2          -0.011398244   -0.000248347  0.0004374839  -0.000032994   -0.083397057
X3          -0.002444578   -9.690816E-7  -0.000032994  0.0000312649    0.161132691
Y           43.652197791   1.7847796802  -0.083397057   0.161132691   5583.4996578
 
Analysis of Variance
                                    Sum of        Mean
Source                 DF        Squares         Square    F Value    Pr > F
Model                   3     6806.11145     2268.70382       5.69    0.0092
Error                  14     5583.49966      398.82140
Corrected Total        17          12390
 
Root MSE             19.97051    R-Square     0.5493
Dependent Mean       81.27778    Adj R-Sq     0.4528
Coeff Var            24.57069
 

 
 
 
                                                     Parameter Estimates
                                                                                                         Squared      Squared
                 Parameter     Standard                                               Standardized  Semi-partial      Partial
Variable   DF     Estimate        Error  t Value  Pr > |t|    Type I SS   Type II SS      Estimate   Corr Type I  Corr Type I
Intercept   1     43.65220     18.01021     2.42    0.0295       118909   2342.89647             0             .            .
X1          1      1.78478      0.53770     3.32    0.0051   5957.02249   4394.14983       0.67134       0.48081      0.48081
X2          1     -0.08340      0.41771    -0.20    0.8446     18.64604     15.89789      -0.04209       0.00150      0.00290
X3          1      0.16113      0.11167     1.44    0.1710    830.44292    830.44292       0.27303       0.06703      0.12947
 
                                          Parameter Estimates
                    Squared         Squared
               Semi-partial         Partial                      Variance
Variable   DF  Corr Type II    Corr Type II      Tolerance      Inflation       95% Confidence Limits
Intercept   1             .               .              .              0        5.02414       82.28026
X1          1       0.35466         0.44040        0.78692        1.27077        0.63154        2.93802
X2          1       0.00128         0.00284        0.72432        1.38060       -0.97929        0.81249
X3          1       0.06703         0.12947        0.89915        1.11216       -0.07837        0.40063
 
 
                             Covariance of Estimates
Variable          Intercept                X1                X2                X3
Intercept      324.36769134      0.7651495821      -4.545863489      -0.974950169
X1             0.7651495821      0.2891164632       -0.09904623       -0.00038649
X2             -4.545863489       -0.09904623      0.1744779464      -0.013158898
X3             -0.974950169       -0.00038649      -0.013158898      0.0124691254
 
                            Correlation of Estimates
Variable          Intercept                X1                X2                X3
Intercept            1.0000            0.0790           -0.6043           -0.4848
X1                   0.0790            1.0000           -0.4410           -0.0064
X2                  -0.6043           -0.4410            1.0000           -0.2821
X3                  -0.4848           -0.0064           -0.2821            1.0000
 
                  Sequential Parameter Estimates
   Intercept                X1                X2                X3
   81.277778                 0                 0                 0
   59.258959          1.843436                 0                 0
   56.251024          1.789774          0.086649                 0
   43.652198          1.784780         -0.083397          0.161133
 
 


                                                       Output Statistics
           Dep Var Predicted    Std Error                                                   Std Error  Student
     Obs         Y     Value Mean Predict     95% CL Mean        95% CL Predict    Residual  Residual Residual   -2-1 0 1 2
       1   64.0000   65.4050      10.5752   42.7235   88.0865   16.9378  113.8723   -1.4050    16.941  -0.0829 |      |      |
       2   60.0000   68.7126      11.0062   45.1068   92.3185   19.8060  117.6192   -8.7126    16.664   -0.523 |     *|      |
       3   71.0000   53.5624      11.6962   28.4766   78.6481    3.9245  103.2002   17.4376    16.187    1.077 |      |**    |
       4   61.0000   67.1854       8.6364   48.6623   85.7085   20.5193  113.8515   -6.1854    18.007   -0.344 |      |      |
       5   54.0000   59.5460       9.4223   39.3371   79.7548   12.1854  106.9065   -5.5460    17.608   -0.315 |      |      |
       6   77.0000   61.0848      13.7970   31.4932   90.6765    9.0244  113.1453   15.9152    14.438    1.102 |      |**    |
       7   81.0000   64.1718      10.1592   42.3825   85.9610   16.1156  112.2279   16.8282    17.193    0.979 |      |*     |
       8   93.0000   77.9457       6.2695   64.4989   91.3925   33.0521  122.8393   15.0543    18.961    0.794 |      |*     |
       9   93.0000   89.8131       9.9864   68.3944  111.2318   41.9238  137.7024    3.1869    17.294    0.184 |      |      |
      10   51.0000   79.3503       8.3893   61.3571   97.3435   32.8919  125.8086  -28.3503    18.123   -1.564 |   ***|      |
      11   76.0000   77.9063       5.1132   66.9397   88.8730   33.6922  122.1205   -1.9063    19.305  -0.0987 |      |      |
      12   96.0000   99.4135       7.3614   83.6249  115.2021   53.7637  145.0632   -3.4135    18.564   -0.184 |      |      |
      13   77.0000  102.3025       7.1198   87.0320  117.5730   56.8294  147.7757  -25.3025    18.658   -1.356 |    **|      |
      14   93.0000   90.2967       8.9528   71.0949  109.4985   43.3570  137.2363    2.7033    17.851    0.151 |      |      |
      15   95.0000  107.2807       8.3375   89.3984  125.1629   60.8652  153.6961  -12.2807    18.147   -0.677 |     *|      |
      16   54.0000   67.0830       7.3513   51.3159   82.8500   21.4406  112.7253  -13.0830    18.568   -0.705 |     *|      |
      17  168.0000  119.1961      11.2752   95.0132  143.3789   70.0083  168.3838   48.8039    16.483    2.961 |      |***** |
      18   99.0000  112.7443       9.8642   91.5877  133.9009   64.9717  160.5169  -13.7443    17.364   -0.792 |     *|      |
 
Output Statistics
           Cook's                 Hat Diag         Cov                -------------------DFBETAS-------------------
     Obs        D     RStudent           H       Ratio      DFFITS    Intercept          X1          X2          X3
       1    0.001      -0.0799      0.2804      1.8655     -0.0499       0.0184      0.0389     -0.0292     -0.0126
       2    0.030      -0.5088      0.3037      1.7853     -0.3361      -0.1038      0.0829      0.1986     -0.2064
       3    0.151       1.0840      0.3430      1.4483      0.7832       0.7596     -0.0292     -0.3246     -0.4587
       4    0.007      -0.3324      0.1870      1.5994     -0.1594      -0.0176      0.0855      0.0327     -0.0885
       5    0.007      -0.3046      0.2226      1.6817     -0.1630      -0.1550      0.0089      0.0663      0.0863
       6    0.277       1.1115      0.4773      1.7897      1.0622      -0.3836     -0.7486      0.9230     -0.2049
       7    0.084       0.9772      0.2588      1.3667      0.5774       0.2736     -0.0944      0.2170     -0.5008
       8    0.017       0.7829      0.0986      1.2410      0.2589       0.1768      0.0437     -0.1658      0.0267
       9    0.003       0.1778      0.2501      1.7762      0.1027       0.0187      0.0226     -0.0717      0.0733
      10    0.131      -1.6594      0.1765      0.7574     -0.7682       0.1975      0.2350     -0.6252      0.2841
      11    0.000      -0.0952      0.0656      1.4354     -0.0252      -0.0154     -0.0019      0.0074      0.0036
      12    0.001      -0.1774      0.1359      1.5416     -0.0703      -0.0116     -0.0505      0.0070      0.0144
      13    0.067      -1.4021      0.1271      0.8773     -0.5350       0.0663     -0.3410     -0.0228     -0.0195
      14    0.001       0.1460      0.2010      1.6724      0.0732       0.0317      0.0399      0.0006     -0.0478
      15    0.024      -0.6631      0.1743      1.4261     -0.3046       0.1548     -0.1245     -0.0635     -0.1224
      16    0.019      -0.6913      0.1355      1.3467     -0.2737      -0.0470      0.1597      0.0298     -0.1113
      17    1.026       4.6666      0.3188      0.0386      3.1922      -1.8192      1.4167      0.1771      1.9528
      18    0.051      -0.7804      0.2440      1.4814     -0.4433       0.0137     -0.3603      0.0259      0.0449
 
Sum of Residuals                           0
Sum of Squared Residuals          5583.49966
Predicted Residual SS (PRESS)          10683


EXST7015: Multiple Regression from Snedecor & Cochran (1967)
PROC REG OUTPUT WITH ALL OPTIONS
 
The REG Procedure
Model: MODEL1
 
Test 1 Results for Dependent Variable Y
                                Mean
Source             DF         Square    F Value    Pr > F
Numerator           1       63.89578       0.16    0.6950
Denominator        14      398.82140
 
       Test 1 Results using
          ACOV estimates
    DF    Chi-Square    Pr > ChiSq
     1          0.21        0.6480
 
Test 2 Results for Dependent Variable Y
                                Mean
Source             DF         Square    F Value    Pr > F
Numerator           2     1760.86020       4.42    0.0326
Denominator        14      398.82140
 
Test 2 Results using
          ACOV estimates
    DF    Chi-Square    Pr > ChiSq
     2         18.15        0.0001
 
 
           -----+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-----
  RESIDUAL |                                                                                                           |
           |                                                                                                           |
           |                                                                                                           |
        50 +                                                                                                           +
           |                                                                                                     1     |
           |                                                                                                           |
           |                                                                                                           |
           |                                                                                                           |
        40 +                                                                                                           +
           |                                                                                                           |
           |                                                                                                           |
           |                                                                                                           |
           |                                                                                                           |
        30 +                                                                                                           +
           |                                                                                                           |
           |                                                                                                           |
           |                                                                                                           |
           |                                                                                                           |
        20 +                                                                                                           +
R          |         1                                                                                                 |
e          |                    1   1                  1                                                               |
s          |                                                                                                           |
i          |                                                                                                           |
d       10 +                                                                                                           +
u          |                                                                                                           |
a          |                                                                                                           |
l          |                                                            1                                              |
           |                                                            1                                              |
         0 +                                                                                                           +
           |                          1                1                                                               |
           |                                                                         1                                 |
           |                 1          1                                                                              |
           |                              1                                                                            |
       -10 +                                                                                                           +
           |                                                                                    1                      |
           |                            1                                                               1              |
           |                                                                                                           |
           |                                                                                                           |
       -20 +                                                                                                           +
           |                                                                                                           |
           |                                                                                                           |
           |                                                                             1                             |
           |                                             1                                                             |
       -30 +                                                                                                           +
           |                                                                                                           |
           |                                                                                                           |
           -----+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-----
               50     55     60     65     70     75     80     85     90     95     100    105    110    115    120
                                                Predicted Value of Y           PRED
 
 


EXST7015: Multiple Regression from Snedecor & Cochran (1967)
PROC REG OUTPUT WITH ALL OPTIONS
 
The REG Procedure
Model: MODEL2
 
Partial Regression Residual Plot
 
    --+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---
 50 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                        1         |
    |                                                                                                                  |
 40 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |     1                                                                                                            |
    |                                                                                                                  |
 30 +                                                                                                                  +
    |                                                                    1                                             |
    |                                                                 1                                                |
    |                                                                                                                  |
    |                                                                                                                  |
 20 +                                                                                                                  +
    |                                                                                                                  |
  Y |                                                                                           1                      |
    |                                                                                                                  |
    |                                                              1                                                   |
 10 +                                                                                                                  +
    |                                                   1                                                              |
    |                                                          1                                                       |
    |             1                                                                                                    |
    |                                                                                                                  |
  0 +                                                1           1                                                     +
    |                                                                                                                  |
    |                                              1                                                                   |
    |                                                                                                                  |
    |                                                                                                                  |
-10 +                   1                            1                                                                 +
    |                                                                                                                  |
    |                                       1                                                                          |
    |                                                                                                                  |
    |                                                                                                                  |
-20 +                                                                                                                  +
    |                 1                                                                                                |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                    1                                                                             |
-30 +                                                                                                                  +
    |                                                                                                                  |
    |                             1                                                                                    |
    |                                                                                                                  |
    |                                                                                                                  |
-40 +                                                                                                                  +
    --+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---
    -0.4      -0.3      -0.2      -0.1       0.0       0.1       0.2       0.3       0.4       0.5       0.6       0.7
                                                         Intercept
 
 
 
Partial Regression Residual Plot
 
    ------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------
  Y |                                                                                                                  |
    |                                                                                                                  |
 80 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                       1                          |
    |                                                                                                                  |
 60 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 40 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 20 +                                                                                      1                           +
    |                                                         1       1                                                |
    |                                                                                         1              1         |
    |                                                  1                    1                                          |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
  0 +                                                             1                1                                   +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                        1                                                         |
    |                                                                                    1                             |
    |                                                                                                                  |
    |     1                                      1                                                                     |
-20 +                                                                                                                  +
    |                                 1                                                                                |
    |                                                                                                                  |
    |             1                     1                                                                              |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                             1                                                                    |
-40 +                                                                                                                  +
    |                                                                                                                  |
    ------+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-------
         -18   -16   -14   -12   -10   -8    -6    -4    -2     0     2     4     6     8    10    12    14    16
 
                                                             X1
 
 
EXST7015: Multiple Regression from Snedecor & Cochran (1967)
PROC REG OUTPUT WITH ALL OPTIONS
 
The REG Procedure
Model: MODEL2
 
Partial Regression Residual Plot
 
    -------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------
  Y |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 50 +                                                                                                                  +
    |                                                 1                                                                |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 40 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 30 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 20 +                                                                                                                  +
    |                       1                                                                                          |
    |                           1                                    1                                                 |
    |                                                                                                       1          |
    |                                                                                                                  |
 10 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |             1                                                                                                    |
    |                                              1                                                                   |
  0 +                                                                                                                  +
    |                                       1                                    1                                     |
    |                            1             1                                                                       |
    |                                      1                                                                           |
    |               1                                                                                                  |
-10 +                                                                                                                  +
    |                                          1           1                                                           |
    |                                           1                                                                      |
    |                                                                                                                  |
    |                                                                                                                  |
-20 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                               1                                                                  |
    |                                                                                                                  |
-30 +                                                                               1                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    -------+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+--------
          -20       -15       -10       -5         0         5        10        15        20        25        30
                                                             X2
 
 
Partial Regression Residual Plot
 
    -----+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-----
  Y |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 60 +                                                                                                       1          +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 50 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 40 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 30 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    |                                                                                                                  |
 20 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                1                                                 |
    |                                           1                                                             1        |
 10 +                                                                                                                  +
    |                 1                                                                                                |
    |     1                                                                                                            |
    |                                                                             1                                    |
  0 +                                                                                          1           1           +
    |                                                       1                                                          |
    |                       1                           1                                                              |
    |                                                                                 1                                |
-10 +                                                                               1                                  +
    |                             1                                                                                    |
    |                                                      1                                                           |
    |                                                                                                                  |
-20 +                                                                                                                  +
    |                                                                                                                  |
    |                                                              1                                                   |
    |                                                                                                                  |
-30 +                                                                                                                  +
    |                                         1                                                                        |
    |                                                                                                                  |
    |                                                                                                                  |
-40 +                                                                                                                  +
    |                                                                                                                  |
    |                                                                                                                  |
    -----+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+-----
        -80    -70    -60    -50    -40    -30    -20    -10     0     10     20     30     40     50     60     70
                                                             X3


39         PROC GLM;  TITLE2 'PROC GLM OUTPUT WITH CONFIDENCE LIMITS FOR THE MEAN';
40            MODEL Y = X1 X2 X3 / XPX I CLI ALPHA=0.01;     RUN;
41         OPTIONS LS=120;
NOTE: The PROCEDURE GLM printed pages 21-25.
NOTE: PROCEDURE GLM used:
      real time           0.09 seconds
      cpu time            0.09 seconds
NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA 27513-2414
NOTE: used:
      real time           0.99 seconds
      cpu time            0.63 seconds
 
 
 
EXST7015: Multiple Regression from Snedecor & Cochran (1967)
PROC GLM OUTPUT WITH CONFIDENCE LIMITS FOR THE MEAN
 
The GLM Procedure
Number of observations    18
 
 
                                The X'X Matrix
                 Intercept           X1           X2           X3            Y
Intercept               18          215          758         2214         1463
X1                     215      4321.02      10139.5        27645      20706.2
X2                     758      10139.5        35076        96598        63825
X3                    2214        27645        96598       307894       187542
Y                     1463      20706.2        63825       187542       131299
 
                              X'X Inverse Matrix
                 Intercept           X1           X2           X3            Y
Intercept     0.8133156545 0.0019185269 -0.011398244 -0.002444578 43.652197791
X1            0.0019185269 0.0007249271 -0.000248347 -9.690816E-7 1.7847796802
X2            -0.011398244 -0.000248347 0.0004374839 -0.000032994 -0.083397057
X3            -0.002444578 -9.690816E-7 -0.000032994 0.0000312649  0.161132691
Y             43.652197791 1.7847796802 -0.083397057  0.161132691 5583.4996578
 
 
The GLM Procedure
Dependent Variable: Y
 
                                      Sum of
Source                     DF        Squares    Mean Square   F Value   Pr > F
Model                       3     6806.11145     2268.70382      5.69   0.0092
Error                      14     5583.49966      398.82140
Corrected Total            17    12389.61111
 
R-Square     Coeff Var      Root MSE        Y Mean
0.549340      24.57069      19.97051      81.27778
 
Source                     DF      Type I SS    Mean Square   F Value   Pr > F
X1                          1    5957.022495    5957.022495     14.94   0.0017
X2                          1      18.646037      18.646037      0.05   0.8319
X3                          1     830.442921     830.442921      2.08   0.1710
 
Source                     DF    Type III SS    Mean Square   F Value   Pr > F
X1                          1    4394.149832    4394.149832     11.02   0.0051
X2                          1      15.897886      15.897886      0.04   0.8446
X3                          1     830.442921     830.442921      2.08   0.1710
 
 


                                  Standard
Parameter         Estimate           Error    t Value    Pr > |t|
Intercept      43.65219779     18.01021075       2.42      0.0295
X1              1.78477968      0.53769551       3.32      0.0051
X2             -0.08339706      0.41770557      -0.20      0.8446
X3              0.16113269      0.11166524       1.44      0.1710
 
 
EXST7015: Multiple Regression from Snedecor & Cochran (1967)
PROC GLM OUTPUT WITH CONFIDENCE LIMITS FOR THE MEAN
 
The GLM Procedure
 
Observation             Observed          Predicted           Residual
          1           64.0000000         65.4050308         -1.4050308
          2           60.0000000         68.7126060         -8.7126060
          3           71.0000000         53.5623803         17.4376197
          4           61.0000000         67.1853981         -6.1853981
          5           54.0000000         59.5459617         -5.5459617
          6           77.0000000         61.0848355         15.9151645
          7           81.0000000         64.1717601         16.8282399
          8           93.0000000         77.9456886         15.0543114
          9           93.0000000         89.8130830          3.1869170
         10           51.0000000         79.3502538        -28.3502538
         11           76.0000000         77.9063339         -1.9063339
         12           96.0000000         99.4134705         -3.4134705
         13           77.0000000        102.3025361        -25.3025361
         14           93.0000000         90.2966548          2.7033452
         15           95.0000000        107.2806653        -12.2806653
         16           54.0000000         67.0829599        -13.0829599
         17          168.0000000        119.1960675         48.8039325
         18           99.0000000        112.7443140        -13.7443140
 
                    99% Confidence Limits for
Observation         Individual Predicted Value
          1           -1.8647549     132.6748166
          2            0.8329702     136.5922418
          3          -15.3321646     122.4569252
          4            2.4154319     131.9553644
          5           -6.1877991     125.2797225
          6          -11.1721120     133.3417830
          7           -2.5274762     130.8709963
          8           15.6358585     140.2555187
          9           23.3454618     156.2807041
         10           14.8686997     143.8318080
         11           16.5396224     139.2730454
         12           36.0541644     162.7727767
         13           39.1883302     165.4167421
         14           25.1470643     155.4462453
         15           42.8586051     171.7027255
         16            3.7339941     130.4319258
         17           50.9262662     187.4658688
         18           46.4385986     179.0500294
 
Sum of Residuals                            0.00000
Sum of Squared Residuals                 5583.49966
Sum of Squared Residuals - Error SS         0.00000
PRESS Statistic                         10682.74523
First Order Autocorrelation                -0.16585
Durbin-Watson D                             2.29751



Modified: August 16, 2004
James P. Geaghan