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"MODEL"  Y  =  A3 * X3  +  A2 * X2  +  A1 * X1;

"INPUT"  5 * [Y, X1, X2, X3];

"OPTIONS"  1, 2, 5, 8;
Transformed data matrix
=======================

obs.no.      A3          A2          A1          dep.var.

1          4.000       1.000       2.000       8.000
2          1.000       2.000      -1.000      10.000
3          4.000      -3.000       1.000       9.000
4          2.000       1.000       2.000       6.000
5          6.000       4.000       1.000      12.000
Control information
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

A3                         3.400000                 1.949359                 1.000000                 6.000000
A2                         1.000000                 2.549510                -3.000000                 4.000000
A1                         1.000000                 1.224745                -1.000000                 2.000000
dep.var.                   9.000000                 2.236068                 6.000000                12.000000

Number of observations :    5

There is no constant independent variable in the transformed (sub)model    (message)

Correlation matrix of the variables
===================================

A3          A2          A1          dep.var.

A3          1.000000
A2          0.150908    1.000000
A1          0.418854   -0.160128    1.000000
dep.var.    0.516185    0.438529   -0.547723    1.000000

Multiple correlation coefficient     0.936662    (adjusted   0.832670)
================================

Proportion of variation explained    0.877336    (adjusted   0.693339)
=================================

Standard deviation of the error term              5.105507
====================================
Regression parameters
=====================
right  tail
parameter                 estimate           standard deviation              F - ratio              probability

A3                     2.5446171560             0.9982125895                 6.498286                 0.125553

A2                     0.2665515256             1.0423373169                 0.065395                 0.822061

A1                    -1.3851468048             2.3646149361                 0.343140                 0.617320

Correlation matrix of the estimates
===================================

A3          A2          A1

A3          1.000000
A2         -0.452873    1.000000
A1         -0.751471    0.244757    1.000000

Analysis of variance
====================

source of                                                                                           right  tail
variation          df          sum of squares           mean square             F - ratio           probability

---------------------------------------------------------------------------------------------------------------

total               5              425.000000

---------------------------------------------------------------------------------------------------------------

regression          3              372.867588            124.289196              4.768212              0.178233
residual            2               52.132412             26.066206

---------------------------------------------------------------------------------------------------------------

regression null hypothesis :  A3 = A2 = A1 = 0
Control information  -  submodel  1
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

A1          omitted

A3                         3.400000                 1.949359                 1.000000                 6.000000
A2                         1.000000                 2.549510                -3.000000                 4.000000
dep.var.                   9.000000                 2.236068                 6.000000                12.000000

Number of observations :    5

There is no constant independent variable in the transformed (sub)model    (message)

Multiple correlation coefficient     0.925359    (adjusted   0.872057)
================================

Proportion of variation explained    0.856290    (adjusted   0.760483)
=================================

Standard deviation of the error term              4.512086
====================================
Regression parameters
=====================
right  tail
parameter                 estimate           standard deviation              F - ratio              probability

A3                     2.1052066559             0.5820385900                13.082354                 0.036325

A2                     0.4159957059             0.8931663715                 0.216927                 0.673122

Analysis of variance
====================

source of                                                                                           right  tail
variation          df          sum of squares           mean square             F - ratio           probability

---------------------------------------------------------------------------------------------------------------

total               5              425.000000

---------------------------------------------------------------------------------------------------------------

regression          2              363.923242            181.961621              8.937686              0.054479
residual            3               61.076758             20.358919

---------------------------------------------------------------------------------------------------------------

reduction          1                8.944346              8.944346              0.343140              0.617320

---------------------------------------------------------------------------------------------------------------

regression null hypothesis :  A3 = A2 = 0  (in the reduced model)

reduction null hypothesis :  A1 = 0  (in the original model)
Control information  -  submodel  2
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

A2          omitted
A1          omitted

A3                         3.400000                 1.949359                 1.000000                 6.000000
dep.var.                   9.000000                 2.236068                 6.000000                12.000000

Number of observations :    5

There is no constant independent variable in the transformed (sub)model    (message)

Multiple correlation coefficient     0.919727    (adjusted   0.898539)
================================

Proportion of variation explained    0.845898    (adjusted   0.807373)
=================================

Standard deviation of the error term              4.046392
====================================
Regression parameters
=====================
right  tail
parameter                 estimate           standard deviation              F - ratio              probability

A3                     2.2191780822             0.4735943538                21.956913                 0.009407

Analysis of variance
====================

source of                                                                                           right  tail
variation          df          sum of squares           mean square             F - ratio           probability

---------------------------------------------------------------------------------------------------------------

total               5              425.000000

---------------------------------------------------------------------------------------------------------------

regression          1              359.506849            359.506849             21.956913              0.009407
residual            4               65.493151             16.373288

---------------------------------------------------------------------------------------------------------------

reduction          2               13.360738              6.680369              0.256285              0.795998

---------------------------------------------------------------------------------------------------------------

regression null hypothesis :  A3 = 0  (in the reduced model)

reduction null hypothesis :  A2 = A1 = 0  (in the original model)

End of job :  1

"MODEL"  Y - 4 * X1  =  B2 * (X1 + X2) + B3 * X3;

"INPUT"  5 * [Y, X1, X2, X3];

"OPTIONS"  1, 2, 9;
Transformed data matrix
=======================

obs.no.      B2          B3          dep.var.

1          3.000       4.000       0.000
2          1.000       1.000      14.000
3         -2.000       4.000       5.000
4          3.000       2.000      -2.000
5          5.000       6.000       8.000
Control information
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

B2                         2.000000                 2.645751                -2.000000                 5.000000
B3                         3.400000                 1.949359                 1.000000                 6.000000
dep.var.                   5.000000                 6.403124                -2.000000                14.000000

Number of observations :    5

There is no constant independent variable in the transformed (sub)model    (message)

Correlation matrix of the variables
===================================

B2          B3          dep.var.

B2          1.000000
B3          0.339310    1.000000
dep.var.   -0.177084   -0.140202    1.000000

Proportion of variation explained    0.293057    (adjusted  -0.178239)
=================================

Standard deviation of the error term              8.252406
====================================
Regression parameters
=====================
right  tail
parameter                 estimate           standard deviation              F - ratio              probability

B2                    -0.2325836533             1.6513864104                 0.019836                 0.896920

B3                     1.1991223258             1.3390842284                 0.801883                 0.436516

Correlation matrix of the estimates
===================================

B2          B3

B2          1.000000
B3         -0.692631    1.000000

Analysis of variance
====================

source of                                                                                           right  tail
variation          df          sum of squares           mean square             F - ratio           probability

---------------------------------------------------------------------------------------------------------------

total               5              289.000000

---------------------------------------------------------------------------------------------------------------

regression          2               84.693363             42.346681              0.621811              0.594397
residual            3              204.306637             68.102212

---------------------------------------------------------------------------------------------------------------

reduction          1              152.174225            152.174225              5.837989              0.136963

---------------------------------------------------------------------------------------------------------------

regression null hypothesis :  B2 = B3 = 0

End of job :  2