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Freund & Littell: Table 5.5 1 DATA FOR ANALYSIS OF COVARIANCE: TWO-WAY STRUCTURE WITHOUT INTERACTION

        OBS    STORE    WEEK    DAY    P1    P2       Q1         Q2
          1      1        1      1     37    61    11.3208     0.0047
          2      1        1      2     37    37    12.9151     0.0037
          3      1        1      3     45    53    18.8947     7.5429
          4      1        1      4     41    41    14.6739     7.0652
          5      1        1      5     57    41     8.6493    21.2085
          6      1        1      6     49    33     9.5238    16.6667
          7      2        1      1     49    49     7.6923     7.1154
          8      2        1      2     53    53     0.0017     1.0000
          9      2        1      3     53    45     8.0477    24.2176
         10      2        1      4     53    53     6.7358     2.9361
         11      2        1      5     61    37     6.1441    40.5720
         12      2        1      6     49    65    21.7939     2.8324
         13      3        1      1     53    45     4.2553     6.0284
         14      3        1      2     57    57     0.0017     2.0906
         15      3        1      3     49    49    11.0196    13.9329
         16      3        1      4     53    53     6.2762     6.5551
         17      3        1      5     53    45    13.2316    10.6870
         18      3        1      6     53    53     5.0676     5.1351
         19      4        1      1     57    57     5.6235     3.9120
         20      4        1      2     49    49    14.9893     7.2805
         21      4        1      3     53    53    13.7233    16.3105
         22      4        1      4     53    45     6.0669    23.8494
         23      4        1      5     53    53     8.1602     4.1543
         24      4        1      6     61    37     1.4423    21.1538
         25      5        1      1     45    45     6.9971     6.9971
         26      5        1      2     53    45     5.2308     3.6923
         27      5        1      3     57    57     8.2560    10.6679
         28      5        1      4     49    49    14.5000    16.7500
         29      5        1      5     53    53    20.7627    15.2542
         30      5        1      6     53    45     3.6115    21.5442
         31      6        1      1     53    53    11.3475     4.9645
         32      6        1      2     53    45     9.4650    11.7284
         33      6        1      3     53    53    22.6103    14.8897
         34      6        1      4     61    37     0.0020    19.2000
         35      6        1      5     49    65    20.5997     2.3468
         36      6        1      6     37    37    28.1828    17.9543

Freund & Littell: Table 5.6 2 RESULTS OF ANALYSIS OF COVARIANCE: TWO-WAY STRUCTURE WITHOUT INTERACTION

                       General Linear Models Procedure
                           Class Level Information

                        Class    Levels    Values
                        STORE         6    1 2 3 4 5 6

                        DAY           6    1 2 3 4 5 6


                   Number of observations in data set = 36


Freund & Littell: Table 5.6 3 RESULTS OF ANALYSIS OF COVARIANCE: TWO-WAY STRUCTURE WITHOUT INTERACTION

                       General Linear Models Procedure

Dependent Variable: Q1
                                    Sum of           Mean
Source                  DF         Squares         Square   F Value     Pr > F
Model                   12     1225.369428     102.114119      5.75     0.0002

Error                   23      408.307781      17.752512

Corrected Total         35     1633.677209

                  R-Square            C.V.       Root MSE              Q1 Mean
                  0.750068        41.23841       4.213373             10.21711

Source                  DF       Type I SS    Mean Square   F Value     Pr > F
STORE                    5     313.4212672     62.6842534      3.53     0.0163
DAY                      5     250.3974714     50.0794943      2.82     0.0396
P1                       1     622.0086874    622.0086874     35.04     0.0001
P2                       1      39.5420018     39.5420018      2.23     0.1492

Source                  DF     Type III SS    Mean Square   F Value     Pr > F
STORE                    5     223.8339887     44.7667977      2.52     0.0583
DAY                      5     433.0972835     86.6194567      4.88     0.0035
P1                       1     538.1694631    538.1694631     30.32     0.0001
P2                       1      39.5420018     39.5420018      2.23     0.1492

                                        T for H0:    Pr > |T|   Std Error of
Parameter                  Estimate    Parameter=0                Estimate
INTERCEPT               51.69992598 B         5.28     0.0001     9.79102890
STORE     1             -7.64534544 B        -2.84     0.0093     2.69194262
          2             -5.60230134 B        -2.27     0.0326     2.46416803
          3             -7.36286500 B        -2.99     0.0066     2.46416803
          4             -4.36498683 B        -1.75     0.0926     2.48754811
          5             -5.02054195 B        -2.06     0.0508     2.43612070
          6              0.00000000 B          .        .          .
DAY       1             -5.83035696 B        -2.31     0.0299     2.51932612
          2             -4.89995640 B        -2.00     0.0572     2.44708728
          3              2.26981232 B         0.89     0.3808     2.54028046
          4             -2.65248389 B        -1.08     0.2895     2.44667613
          5              4.04703833 B         1.58     0.1271     2.55655708
          6              0.00000000 B          .        .          .
P1                      -0.83036517          -5.51     0.0001     0.15081325
P2                       0.14884659           1.49     0.1492     0.09973313

Freund & Littell: Table 5.6 4 RESULTS OF ANALYSIS OF COVARIANCE: TWO-WAY STRUCTURE WITHOUT INTERACTION

                       General Linear Models Procedure
NOTE: The X'X matrix has been found to be singular and a generalized inverse
      was used to solve the normal equations.   Estimates followed by the
      letter 'B' are biased, and are not unique estimators of the parameters.

Freund & Littell: Table 5.6 5 RESULTS OF ANALYSIS OF COVARIANCE: TWO-WAY STRUCTURE WITHOUT INTERACTION

                       General Linear Models Procedure

Dependent Variable: Q2
                                    Sum of           Mean
Source                  DF         Squares         Square   F Value     Pr > F
Model                   12     2043.267643     170.272304      5.54     0.0002

Error                   23      706.941361      30.736581

Corrected Total         35     2750.209004

                  R-Square            C.V.       Root MSE              Q2 Mean
                  0.742950        50.11649       5.544058             11.06234

Source                  DF       Type I SS    Mean Square   F Value     Pr > F
STORE                    5     171.0596752     34.2119350      1.11     0.3809
DAY                      5     787.2623701    157.4524740      5.12     0.0027
P1                       1     232.6061446    232.6061446      7.57     0.0114
P2                       1     852.3394531    852.3394531     27.73     0.0001

Source                  DF     Type III SS    Mean Square   F Value     Pr > F
STORE                    5     155.0992228     31.0198446      1.01     0.4348
DAY                      5     614.4094078    122.8818816      4.00     0.0093
P1                       1      83.9232576     83.9232576      2.73     0.1120
P2                       1     852.3394531    852.3394531     27.73     0.0001

                                        T for H0:    Pr > |T|   Std Error of
Parameter                  Estimate    Parameter=0                Estimate
INTERCEPT               29.51172740 B         2.29     0.0315    12.88327272
STORE     1             -3.67685687 B        -1.04     0.3100     3.54212323
          2              1.99126834 B         0.61     0.5452     3.24241191
          3             -3.71613799 B        -1.15     0.2635     3.24241191
          4              0.29713857 B         0.09     0.9285     3.27317599
          5              0.87910173 B         0.27     0.7863     3.20550656
          6              0.00000000 B          .        .          .
DAY       1             -4.33313895 B        -1.31     0.2041     3.31499026
          2             -8.07235144 B        -2.51     0.0197     3.21993665
          3              4.54900790 B         1.36     0.1867     3.34256249
          4             -1.00426138 B        -0.31     0.7579     3.21939564
          5              2.94200636 B         0.87     0.3909     3.36397966
          6              0.00000000 B          .        .          .
P1                       0.32790706           1.65     0.1120     0.19844373
P2                      -0.69106015          -5.27     0.0001     0.13123127

Freund & Littell: Table 5.6 6 RESULTS OF ANALYSIS OF COVARIANCE: TWO-WAY STRUCTURE WITHOUT INTERACTION

                       General Linear Models Procedure
NOTE: The X'X matrix has been found to be singular and a generalized inverse
      was used to solve the normal equations.   Estimates followed by the
      letter 'B' are biased, and are not unique estimators of the parameters.



Freund & Littell: Table 5.6 7 RESULTS OF ANALYSIS OF COVARIANCE: TWO-WAY STRUCTURE WITHOUT INTERACTION

                       General Linear Models Procedure
                             Least Squares Means

                DAY            Q1       Std Err     Pr > |T|
                           LSMEAN        LSMEAN   H0:LSMEAN=0
                1       5.5644085     1.7680823        0.0045
                2       6.4948090     1.7289576        0.0010
                3      13.6645778     1.7515037        0.0001
                4       8.7422815     1.7339188        0.0001
                5      15.4418038     1.7858075        0.0001
                6      11.3947654     1.7667250        0.0001

                DAY            Q2       Std Err     Pr > |T|
                           LSMEAN        LSMEAN   H0:LSMEAN=0
                1       7.7156596     2.3264855        0.0030
                2       3.9764471     2.2750042        0.0938
                3      16.5978064     2.3046709        0.0001
                4      11.0445371     2.2815323        0.0001
                5      14.9908049     2.3498087        0.0001
                6      12.0487985     2.3246995        0.0001

Freund & Littell: Table 5.10 8 RESULTS OF ANALYSIS OF COVARIANCE: TEST FOR HOMOGENEITY OF REGRESSION COEFFICIENTS

                       General Linear Models Procedure
                           Class Level Information

                        Class    Levels    Values
                        DAY           6    1 2 3 4 5 6


                   Number of observations in data set = 36


Freund & Littell: Table 5.10 9 RESULTS OF ANALYSIS OF COVARIANCE: TEST FOR HOMOGENEITY OF REGRESSION COEFFICIENTS

                       General Linear Models Procedure

Dependent Variable: Q1
                                    Sum of           Mean
Source                  DF         Squares         Square   F Value     Pr > F
Model                   11     1111.524578     101.047689      4.64     0.0008

Error                   24      522.152631      21.756360

Corrected Total         35     1633.677209

                  R-Square            C.V.       Root MSE              Q1 Mean
                  0.680382        45.65256       4.664371             10.21711

Source                  DF       Type I SS    Mean Square   F Value     Pr > F
P1                       1     516.5925608    516.5925608     23.74     0.0001
DAY                      5     430.5389236     86.1077847      3.96     0.0093
P1*DAY                   5     164.3930933     32.8786187      1.51     0.2236

Source                  DF     Type III SS    Mean Square   F Value     Pr > F
P1                       1     554.7873194    554.7873194     25.50     0.0001
DAY                      5     201.1729397     40.2345879      1.85     0.1412
P1*DAY                   5     164.3930933     32.8786187      1.51     0.2236



Freund & Littell: Table 5.10 10 RESULTS OF ANALYSIS OF COVARIANCE: TEST FOR HOMOGENEITY OF REGRESSION COEFFICIENTS ESTIMATED COEFFICIENTS FOR DAYS

                       General Linear Models Procedure
                           Class Level Information

                        Class    Levels    Values
                        DAY           6    1 2 3 4 5 6


                   Number of observations in data set = 36


Freund & Littell: Table 5.10 11 RESULTS OF ANALYSIS OF COVARIANCE: TEST FOR HOMOGENEITY OF REGRESSION COEFFICIENTS ESTIMATED COEFFICIENTS FOR DAYS

                       General Linear Models Procedure

Dependent Variable: Q1
                                    Sum of           Mean
Source                  DF         Squares         Square   F Value     Pr > F
Model                   11     1111.524578     101.047689      4.64     0.0008

Error                   24      522.152631      21.756360

Corrected Total         35     1633.677209

                  R-Square            C.V.       Root MSE              Q1 Mean
                  0.680382        45.65256       4.664371             10.21711

Source                  DF       Type I SS    Mean Square   F Value     Pr > F
P1                       1     516.5925608    516.5925608     23.74     0.0001
DAY                      5     430.5389236     86.1077847      3.96     0.0093
P1*DAY                   5     164.3930933     32.8786187      1.51     0.2236

Source                  DF     Type III SS    Mean Square   F Value     Pr > F
P1                       1     554.7873194    554.7873194     25.50     0.0001
DAY                      5     201.1729397     40.2345879      1.85     0.1412
P1*DAY                   5     164.3930933     32.8786187      1.51     0.2236

                                        T for H0:    Pr > |T|   Std Error of
Parameter                  Estimate    Parameter=0                Estimate
P1:DAY1                 -0.22046200          -0.76     0.4569     0.29152321
P1:DAY2                 -0.62357044          -2.09     0.0470     0.29779324
P1:DAY3                 -0.61105263          -1.21     0.2380     0.50493300
P1:DAY4                 -0.79561535          -2.49     0.0200     0.31934767
P1:DAY5                 -1.19585217          -2.37     0.0263     0.50493300
P1:DAY6                 -1.22521219          -4.62     0.0001     0.26520381

                                        T for H0:    Pr > |T|   Std Error of
Parameter                  Estimate    Parameter=0                Estimate
INTERCEPT               73.27264926 B         5.43     0.0001    13.48372938
P1                      -1.22521219 B        -4.62     0.0001     0.26520381
DAY       1            -54.59726860 B        -2.77     0.0107    19.73544717
          2            -34.78566711 B        -1.72     0.0987    20.25104769
          3            -27.94299214 B        -0.95     0.3518    29.42841265
          4            -24.12339601 B        -1.13     0.2706    21.39333539

Freund & Littell: Table 5.10 12 RESULTS OF ANALYSIS OF COVARIANCE: TEST FOR HOMOGENEITY OF REGRESSION COEFFICIENTS ESTIMATED COEFFICIENTS FOR DAYS

                       General Linear Models Procedure

Dependent Variable: Q1

                                        T for H0:    Pr > |T|   Std Error of
Parameter                  Estimate    Parameter=0                Estimate
DAY       5              4.62658491 B         0.15     0.8812    30.62840858
          6              0.00000000 B          .        .          .
P1*DAY    1              1.00475019 B         2.55     0.0176     0.39410511
          2              0.60164175 B         1.51     0.1444     0.39876544
          3              0.61415957 B         1.08     0.2923     0.57034235
          4              0.42959684 B         1.03     0.3110     0.41510962
          5              0.02936002 B         0.05     0.9594     0.57034235
          6              0.00000000 B          .        .          .
NOTE: The X'X matrix has been found to be singular and a generalized inverse
      was used to solve the normal equations.   Estimates followed by the
      letter 'B' are biased, and are not unique estimators of the parameters.



TABLE 6.7 13 RESULTS OF MULTIVARIATE ANALYSIS OF COVARIANCE

                       General Linear Models Procedure
                           Class Level Information

                        Class    Levels    Values
                        STORE         6    1 2 3 4 5 6

                        DAY           6    1 2 3 4 5 6


                   Number of observations in data set = 36



                            E = Error SS&CP Matrix
                                      Q1                Q2

                    Q1      408.30778085      74.603491341
                    Q2      74.603491341      706.94136064

TABLE 6.7 14 RESULTS OF MULTIVARIATE ANALYSIS OF COVARIANCE

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

  Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r|
                        DF = 23           Q1        Q2

                        Q1          1.000000  0.138859
                                      0.0001    0.5176
                        Q2          0.138859  1.000000
                                      0.5176    0.0001



TABLE 6.7 15 RESULTS OF MULTIVARIATE ANALYSIS OF COVARIANCE

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

                     H = Type III SS&CP Matrix for STORE
                                      Q1                Q2

                    Q1       223.8339887      93.801032659
                    Q2      93.801032659      155.09922281

          Characteristic Roots and Vectors of: E Inverse * H, where
         H = Type III SS&CP Matrix for STORE   E = Error SS&CP Matrix

        Characteristic   Percent        Characteristic Vector  V'EV=1
             Root
                                                    Q1             Q2
            0.57364141     78.23            0.04622395     0.00941443
            0.15960375     21.77           -0.01899031     0.03679299


                Manova Test Criteria and F Approximations for
                  the Hypothesis of no Overall STORE Effect
         H = Type III SS&CP Matrix for STORE   E = Error SS&CP Matrix

                              S=2    M=1    N=10

 Statistic                     Value          F      Num DF    Den DF  Pr > F
 Wilks' Lambda              0.54800512     1.5437        10        44  0.1564
 Pillai's Trace             0.50216767     1.5422        10        46  0.1553
 Hotelling-Lawley Trace     0.73324516     1.5398        10        42  0.1594
 Roy's Greatest Root        0.57364141     2.6388         5        23  0.0501

         NOTE: F Statistic for Roy's Greatest Root is an upper bound.
                NOTE: F Statistic for Wilks' Lambda is exact.


                      H = Type III SS&CP Matrix for DAY
                                      Q1                Q2

                    Q1       433.0972835      461.05135265
                    Q2      461.05135265      614.40940779


TABLE 6.7 16 RESULTS OF MULTIVARIATE ANALYSIS OF COVARIANCE

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

          Characteristic Roots and Vectors of: E Inverse * H, where
          H = Type III SS&CP Matrix for DAY   E = Error SS&CP Matrix

        Characteristic   Percent        Characteristic Vector  V'EV=1
             Root
                                                    Q1             Q2
            1.60708974     93.18            0.03517606     0.02300240
            0.11766505      6.82           -0.03549549     0.03021995


                Manova Test Criteria and F Approximations for
                   the Hypothesis of no Overall DAY Effect
          H = Type III SS&CP Matrix for DAY   E = Error SS&CP Matrix

                              S=2    M=1    N=10

 Statistic                     Value          F      Num DF    Den DF  Pr > F
 Wilks' Lambda              0.34318820     3.1108        10        44  0.0044
 Pillai's Trace             0.72170810     2.5971        10        46  0.0137
 Hotelling-Lawley Trace     1.72475478     3.6220        10        42  0.0015
 Roy's Greatest Root        1.60708974     7.3926         5        23  0.0003

         NOTE: F Statistic for Roy's Greatest Root is an upper bound.
                NOTE: F Statistic for Wilks' Lambda is exact.


                       H = Type III SS&CP Matrix for P1
                                      Q1                Q2

                    Q1      538.16946309      -212.5204331
                    Q2      -212.5204331      83.923257602

          Characteristic Roots and Vectors of: E Inverse * H, where
          H = Type III SS&CP Matrix for P1   E = Error SS&CP Matrix

        Characteristic   Percent        Characteristic Vector  V'EV=1
             Root
                                                    Q1             Q2
            1.57702428    100.00            0.04805515    -0.01539028
            0.00000000      0.00            0.01371085     0.03472024


TABLE 6.7 17 RESULTS OF MULTIVARIATE ANALYSIS OF COVARIANCE

                       General Linear Models Procedure
                      Multivariate Analysis of Variance

               Manova Test Criteria and Exact F Statistics for
                    the Hypothesis of no Overall P1 Effect
          H = Type III SS&CP Matrix for P1   E = Error SS&CP Matrix

                              S=1    M=0    N=10

 Statistic                     Value          F      Num DF    Den DF  Pr > F
 Wilks' Lambda              0.38804446    17.3473         2        22  0.0001
 Pillai's Trace             0.61195554    17.3473         2        22  0.0001
 Hotelling-Lawley Trace     1.57702428    17.3473         2        22  0.0001
 Roy's Greatest Root        1.57702428    17.3473         2        22  0.0001

                       H = Type III SS&CP Matrix for P2
                                      Q1                Q2

                    Q1      39.542001812      -183.5843354
                    Q2      -183.5843354      852.33945312

          Characteristic Roots and Vectors of: E Inverse * H, where
          H = Type III SS&CP Matrix for P2   E = Error SS&CP Matrix

        Characteristic   Percent        Characteristic Vector  V'EV=1
             Root
                                                    Q1             Q2
            1.42488733    100.00           -0.01960104     0.03666504
            0.00000000      0.00            0.04596829     0.00990105


               Manova Test Criteria and Exact F Statistics for
                    the Hypothesis of no Overall P2 Effect
          H = Type III SS&CP Matrix for P2   E = Error SS&CP Matrix

                              S=1    M=0    N=10

 Statistic                     Value          F      Num DF    Den DF  Pr > F
 Wilks' Lambda              0.41239029    15.6738         2        22  0.0001
 Pillai's Trace             0.58760971    15.6738         2        22  0.0001
 Hotelling-Lawley Trace     1.42488733    15.6738         2        22  0.0001
 Roy's Greatest Root        1.42488733    15.6738         2        22  0.0001