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Trailing-Edge - PDP-10 Archives - decuslib20-05 - decus/20-0149/mulreg.pri
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***********************************
*  Example  1  originates from:   *
*  reference [4],  page 472, 479  *
***********************************





"Model"   y  =  c * Log (x)  +  a  +  b * x;





"Input"   5 * ([x], 10 * [y]);





"Options" Transformed data matrix, Correlation matrix,
          Residual analysis, Process submodels (1, 2);
Transformed data matrix
=======================

obs.no.      c           a           b           dep.var.     repeats

     1          1.398       1.000      25.000       0.790      10.000
     2          1.699       1.000      50.000       0.984      10.000
     3          1.903       1.000      80.000       1.058      10.000
     4          2.114       1.000     130.000       1.163      10.000
     5          2.255       1.000     180.000       1.209      10.000
Control information
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

 c                          1.873843                 0.306746                 1.397940                 2.255273
 a                          1.000000                 0.000000                 1.000000                 1.000000
 b                         93.000000                56.387870                25.000000               180.000000
 dep.var.                   1.040800                 0.163655                 0.670000                 1.330000

Number of observations :    5





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

             c           a           b           dep.var.

 c           1.000000
 a               *       1.000000
 b           0.962417        *       1.000000
 dep.var.    0.907742        *       0.849838    1.000000





Multiple correlation coefficient     0.911959    (adjusted   0.908023)
================================





Proportion of variation explained    0.831669    (adjusted   0.824506)
=================================





Standard deviation of the error term              0.068558
====================================
Regression parameters
=====================
                                                                                                    right  tail
parameter                 estimate           standard deviation              F - ratio              probability

 c                      0.6499168512             0.1175695440                30.558070                 0.000001

 a                     -0.0899819314             0.1641470240                 0.300500                 0.586163

 b                     -0.0009361326             0.0006395700                 2.142390                 0.149935






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

             c           a           b

 c           1.000000
 a          -0.993392    1.000000
 b          -0.962417    0.929333    1.000000





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

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

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

total              50               55.475600

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

mean                1               54.163232             54.163232          11523.444701              0.000000
regression          2                1.091456              0.545728            116.105776              0.000000
residual           47                0.220912              0.004700

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

 lack of fit        2                0.005012              0.002506              0.522336              0.596686
 pure error        45                0.215900              0.004798

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


regression null hypothesis :  c = b = 0
Residual analysis
=================
                                                                                              standardized         studentized
obs.no.        observation        fitted value    standard deviation          residual            residual            residual

     1            0.790000            0.795160            0.020789           -0.005160           -0.118992           -0.078976
     2            0.984000            0.967401            0.013590            0.016599            0.382824            0.247021
     3            1.058000            1.071978            0.015165           -0.013978           -0.322363           -0.209059
     4            1.163000            1.162208            0.012847            0.000792            0.018260            0.011757
     5            1.209000            1.207254            0.019954            0.001746            0.040272            0.026622

                                                       sum of residuals :     0.000000

                  Upper bound for the right tail probability of the largest absolute studentized residual (no. 2) :   1.000000
Control information  -  submodel  1
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

 b           omitted

 c                          1.873843                 0.306746                 1.397940                 2.255273
 a                          1.000000                 0.000000                 1.000000                 1.000000
 dep.var.                   1.040800                 0.163655                 0.670000                 1.330000

Number of observations :    5





Multiple correlation coefficient     0.907742    (adjusted   0.905720)
================================





Proportion of variation explained    0.823996    (adjusted   0.820329)
=================================





Standard deviation of the error term              0.069370
====================================
Regression parameters
=====================
                                                                                                    right  tail
parameter                 estimate           standard deviation              F - ratio              probability

 c                      0.4842988398             0.0323066319               224.720913                 0.000000

 a                      0.1332999205             0.0613273100                 4.724458                 0.034701






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

             c           a

 c           1.000000
 a          -0.987122    1.000000





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

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

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

total              50               55.475600

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

mean                1               54.163232             54.163232          11255.564569              0.000000
regression          1                1.081386              1.081386            224.720852              0.000000
residual           48                0.230982              0.004812

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

 lack of fit        3                0.015082              0.005027              1.047838              0.380681
 pure error        45                0.215900              0.004798

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

 reduction          1                0.010070              0.010070              2.142390              0.149935

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


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

 reduction null hypothesis :  b = 0  (in the original model)
Residual analysis
=================
                                                                                              standardized         studentized
obs.no.        observation        fitted value    standard deviation          residual            residual            residual

     1            0.790000            0.810321            0.018238           -0.020321           -0.378175           -0.303615
     2            0.984000            0.956109            0.011321            0.027891            0.519060            0.407526
     3            1.058000            1.054964            0.009856            0.003036            0.056497            0.044211
     4            1.163000            1.157080            0.012506            0.005920            0.110169            0.086758
     5            1.209000            1.225526            0.015751           -0.016526           -0.307551           -0.244617

                                                       sum of residuals :    -0.000000

                  Upper bound for the right tail probability of the largest absolute studentized residual (no. 2) :   1.000000
Control information  -  submodel  2
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

 a           omitted
 b           omitted

 c                          1.873843                 0.306746                 1.397940                 2.255273
 dep.var.                   1.040800                 0.163655                 0.670000                 1.330000

Number of observations :    5





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





Multiple correlation coefficient     0.997711    (adjusted   0.997664)
================================





Proportion of variation explained    0.995427    (adjusted   0.995333)
=================================





Standard deviation of the error term              0.071958
====================================
Regression parameters
=====================
                                                                                                    right  tail
parameter                 estimate           standard deviation              F - ratio              probability

 c                      0.5536156656             0.0053607978             10664.926934                 0.000000






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

             c

 c           1.000000





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

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

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

total              50               55.475600

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

regression          1               55.221883             55.221883          10664.926934              0.000000
residual           49                0.253717              0.005178

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

 lack of fit        4                0.037817              0.009454              1.970525              0.115263
 pure error        45                0.215900              0.004798

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

 reduction          2                0.032804              0.016402              3.489644              0.038633

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


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

 reduction null hypothesis :  a = b = 0  (in the original model)
Residual analysis
=================
                                                                                              standardized         studentized
obs.no.        observation        fitted value    standard deviation          residual            residual            residual

     1            0.790000            0.773921            0.007494            0.016079            0.249818            0.224666
     2            0.984000            0.940576            0.009108            0.043424            0.674690            0.608353
     3            1.058000            1.053580            0.010202            0.004420            0.068669            0.062046
     4            1.163000            1.170312            0.011332           -0.007312           -0.113612           -0.102902
     5            1.209000            1.248554            0.012090           -0.039554           -0.614569           -0.557614

                                                       sum of residuals :     0.170553

                  Upper bound for the right tail probability of the largest absolute studentized residual (no. 2) :   1.000000





End of job :  1
***********************************
*  Example  2  originates from:   *
*  reference [9],  page 475, ff.  *
***********************************





"Model"   available  =  beta0  +  beta1 * inorganic  +  beta2 * organic;





"Input"   18 * [soil sample, available, inorganic, organic];





"Options" Transformed data matrix, Correlation matrix, Residual analysis;
Transformed data matrix
=======================

obs.no.      beta0       beta1       beta2       dep.var.

     1          1.000       0.400      53.000      64.000
     2          1.000       0.400      23.000      60.000
     3          1.000       3.100      19.000      71.000
     4          1.000       0.600      34.000      61.000
     5          1.000       4.700      24.000      54.000
     6          1.000       1.700      65.000      77.000
     7          1.000       9.400      44.000      81.000
     8          1.000      10.100      31.000      93.000
     9          1.000      11.600      29.000      93.000
    10          1.000      12.600      58.000      51.000

    11          1.000      10.900      37.000      76.000
    12          1.000      23.100      46.000      96.000
    13          1.000      23.100      50.000      77.000
    14          1.000      21.600      44.000      93.000
    15          1.000      23.100      56.000      95.000
    16          1.000       1.900      36.000      54.000
    17          1.000      26.800      58.000     168.000
    18          1.000      29.900      51.000      99.000
Control information
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

 beta0                      1.000000                 0.000000                 1.000000                 1.000000
 beta1                     11.944444                10.154583                 0.400000                29.900000
 beta2                     42.111111                13.624756                19.000000                65.000000
 dep.var.                  81.277778                26.996308                51.000000               168.000000

Number of observations :   18





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

             beta0       beta1       beta2       dep.var.

 beta0       1.000000
 beta1           *       1.000000
 beta2           *       0.461567    1.000000
 dep.var.        *       0.693403    0.354466    1.000000





Multiple correlation coefficient     0.694487    (adjusted   0.642875)
================================





Proportion of variation explained    0.482313    (adjusted   0.413288)
=================================





Standard deviation of the error term             20.678399
====================================
Regression parameters
=====================
                                                                                                    right  tail
parameter                 estimate           standard deviation              F - ratio              probability

 beta0                 56.2510240854            16.3107373404                11.893610                 0.003581

 beta1                  1.7897741162             0.5567434145                10.334424                 0.005787

 beta2                  0.0866492500             0.4149429933                 0.043607                 0.837396






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

             beta0       beta1       beta2

 beta0       1.000000
 beta1       0.086771    1.000000
 beta2      -0.883117   -0.461567    1.000000





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

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

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

total              18           131299.000000

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

mean                1           118909.388889         118909.388889            278.088058              0.000000
regression          2             5975.668532           2987.834266              6.987514              0.007170
residual           15             6413.942579            427.596172

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


regression null hypothesis :  beta1 = beta2 = 0
Residual analysis
=================
                                                                                              standardized         studentized
obs.no.        observation        fitted value    standard deviation          residual            residual            residual

     1           64.000000           61.559344           10.596613            2.440656            0.129295            0.137448
     2           60.000000           58.959866            8.994436            1.040134            0.055101            0.055862
     3           71.000000           63.445660            9.817069            7.554340            0.400194            0.415085
     4           61.000000           60.270963            7.439813            0.729037            0.038621            0.037786
     5           54.000000           66.742544            8.277594          -12.742544           -0.675041           -0.672453
     6           77.000000           64.925841           14.017687           12.074159            0.639633            0.794248
     7           81.000000           76.887468            5.234633            4.112532            0.217863            0.205577
     8           93.000000           77.013869            6.457231           15.986131            0.846871            0.813778
     9           93.000000           79.525232            7.240620           13.474768            0.713830            0.695677
    10           51.000000           83.827834            8.070605          -32.827834           -1.739066           -1.724294

    11           76.000000           78.965584            5.239553           -2.965584           -0.157103           -0.148253
    12           96.000000          101.580672            7.461991           -5.580672           -0.295638           -0.289377
    13           77.000000          101.927269            7.367271          -24.927269           -1.320530           -1.290133
    14           93.000000           98.722712            7.026946           -5.722712           -0.303163           -0.294260
    15           95.000000          102.447164            7.905720           -7.447164           -0.394516           -0.389751
    16           54.000000           62.770968            6.954672           -8.770968           -0.464645           -0.450398
    17          168.000000          109.242627            9.235282           58.757373            3.112692            3.175816
    18           99.000000          114.184382           10.161448          -15.184382           -0.804398           -0.843133

                                                       sum of residuals :    -0.000000

                 Upper bound for the right tail probability of the largest absolute studentized residual (no. 17) :   0.001810





End of job :  2
***********************************
*  Example  3  originates from:   *
*  reference [3],  page 228, 339  *
***********************************





"Model"  Ln (Mean surface volume)  =  Lnalpha  +  beta * Ln (Feed rate)
	 +  gamma * Ln (Wheel velocity)  +  delta * Ln (Feed viscosity);





"Input"  35 * [Run number, Feed rate, Wheel velocity,
	       Feed viscosity, Mean surface volume];





"Options" Transformed data matrix, Residual analysis, Process submodels (1);
Transformed data matrix
=======================

obs.no.      Lnalpha     beta        gamma       delta       dep.var.

     1          1.000      -4.051       8.575      -2.226       3.235
     2          1.000      -2.765       8.594      -2.235       3.453
     3          1.000      -2.777       9.024      -2.235       3.246
     4          1.000      -4.440       9.287      -2.244       2.856
     5          1.000      -2.263       8.434      -2.283       3.643
     6          1.000      -4.440       9.333      -2.254       2.901
     7          1.000      -4.406       8.666      -2.254       3.277
     8          1.000      -4.406       8.987      -2.303       2.960
     9          1.000      -3.199       9.210      -2.244       3.105
    10          1.000      -3.199       8.795      -2.254       3.273

    11          1.000      -2.765       9.071      -2.263       3.250
    12          1.000      -3.199       8.389      -2.263       3.472
    13          1.000      -3.182       8.936      -2.244       3.223
    14          1.000      -2.293       8.476      -2.244       3.681
    15          1.000      -4.075       8.039      -2.244       3.572
    16          1.000      -3.189       9.138      -2.254       3.157
    17          1.000      -4.075       8.949      -2.323       3.096
    18          1.000      -4.075       8.575      -2.313       3.277
    19          1.000      -2.293       8.648      -2.323       3.681
    20          1.000      -2.777       8.732      -2.283       3.450

    21          1.000      -2.777       8.949      -2.283       3.292
    22          1.000      -4.075       9.230      -2.303       2.896
    23          1.000      -4.440       8.476      -2.283       3.346
    24          1.000      -3.199       8.795      -2.283       3.307
    25          1.000      -2.777       9.024      -2.283       3.250
    26          1.000      -4.075       8.949      -2.283       3.140
    27          1.000      -3.199       9.105      -0.489       3.153
    28          1.000      -4.075       9.220      -0.480       2.896
    29          1.000      -3.199       8.575      -0.399       3.431
    30          1.000      -2.777       8.987      -0.472       3.246

    31          1.000      -2.293       8.896      -0.489       3.367
    32          1.000      -4.440       8.764      -1.115       3.091
    33          1.000      -4.075       8.987      -1.076       2.934
    34          1.000      -4.440       9.180       0.612       2.885
    35          1.000      -3.199       8.748       0.663       3.346
Control information
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

 Lnalpha                    1.000000                 0.000000                 1.000000                 1.000000
 beta                      -3.454469                 0.748055                -4.439656                -2.263364
 gamma                      8.849891                 0.298180                 8.039157                 9.332558
 delta                     -1.778466                 0.899585                -2.322788                 0.662688
 dep.var.                   3.239746                 0.228501                 2.856470                 3.681351

Number of observations :   35





Multiple correlation coefficient     0.977342    (adjusted   0.975121)
================================





Proportion of variation explained    0.955197    (adjusted   0.950861)
=================================





Standard deviation of the error term              0.050652
====================================
Regression parameters
=====================
                                                                                                    right  tail
parameter                 estimate           standard deviation              F - ratio              probability

 Lnalpha                8.5495323331             0.2660238985              1032.864643                 0.000000

 beta                   0.1684244052             0.0118081196               203.445721                 0.000000

 gamma                 -0.5371370141             0.0300960773               318.530024                 0.000000

 delta                 -0.0144134670             0.0098170458                 2.155635                 0.152122






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

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

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

total              35              369.133526

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

mean                1              367.358289            367.358289         143182.007167              0.000000
regression          3                1.695702              0.565234            220.306257              0.000000
residual           31                0.079536              0.002566

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


regression null hypothesis :  beta = gamma = delta = 0
Residual analysis
=================
                                                                                              standardized         studentized
obs.no.        observation        fitted value    standard deviation          residual            residual            residual

     1            3.234749            3.293078            0.014784           -0.058329           -1.223587           -1.203971
     2            3.453157            3.499877            0.013574           -0.046720           -0.980073           -0.957386
     3            3.246491            3.266833            0.014411           -0.020342           -0.426727           -0.418915
     4            2.856470            2.845581            0.019237            0.010889            0.228428            0.232392
     5            3.642836            3.671117            0.019169           -0.028281           -0.593273           -0.603205
     6            2.901422            2.821409            0.020142            0.080013            1.678467            1.721617
     7            3.277145            3.185264            0.016296            0.091881            1.927422            1.915802
     8            2.960105            3.013233            0.015317           -0.053128           -1.114483           -1.100383
     9            3.104587            3.095864            0.015813            0.008723            0.182980            0.181266
    10            3.273364            3.319189            0.010115           -0.045825           -0.961298           -0.923297

    11            3.250374            3.244114            0.015389            0.006261            0.131334            0.129733
    12            3.471966            3.537118            0.016090           -0.065151           -1.366704           -1.356500
    13            3.222868            3.246139            0.010877           -0.023271           -0.488175           -0.470406
    14            3.681351            3.642772            0.018313            0.038579            0.809285            0.816897
    15            3.572346            3.577499            0.027704           -0.005154           -0.108113           -0.121538
    16            3.157000            3.136624            0.014274            0.020376            0.427441            0.419268
    17            3.095578            3.089933            0.012748            0.005644            0.118401            0.115136
    18            3.277145            3.290415            0.015136           -0.013270           -0.278377           -0.274531
    19            3.681351            3.551596            0.016891            0.129755            2.721926            2.717208
    20            3.449988            3.424209            0.012559            0.025778            0.540765            0.525330

    21            3.292126            3.307827            0.013565           -0.015701           -0.329363           -0.321724
    22            2.895912            2.938617            0.016603           -0.042705           -0.895839           -0.892395
    23            3.346389            3.281716            0.019666            0.064673            1.356676            1.385494
    24            3.306887            3.319607            0.010241           -0.012720           -0.266842           -0.256427
    25            3.250374            3.267523            0.014593           -0.017148           -0.359731           -0.353541
    26            3.139833            3.089357            0.012571            0.050476            1.058853            1.028699
    27            3.152736            3.127162            0.016604            0.025574            0.536468            0.534411
    28            2.895912            2.917634            0.018272           -0.021722           -0.455674           -0.459805
    29            3.430756            3.410283            0.019104            0.020473            0.429475            0.436419
    30            3.246491            3.261192            0.017683           -0.014701           -0.308384           -0.309713

    31            3.367296            3.392279            0.020625           -0.024983           -0.524074           -0.540015
    32            3.091042            3.110356            0.016548           -0.019313           -0.405145           -0.403428
    33            2.933857            3.051431            0.013053           -0.117574           -2.466405           -2.402326
    34            2.884801            2.862104            0.027070            0.022697            0.476118            0.530148
    35            3.346389            3.302140            0.026253            0.044249            0.928227            1.021480

                                                       sum of residuals :     0.000000

                 Upper bound for the right tail probability of the largest absolute studentized residual (no. 19) :   0.161110
Control information  -  submodel  1
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

 delta       omitted

 Lnalpha                    1.000000                 0.000000                 1.000000                 1.000000
 beta                      -3.454469                 0.748055                -4.439656                -2.263364
 gamma                      8.849891                 0.298180                 8.039157                 9.332558
 dep.var.                   3.239746                 0.228501                 2.856470                 3.681351

Number of observations :   35





Multiple correlation coefficient     0.975747    (adjusted   0.974211)
================================





Proportion of variation explained    0.952082    (adjusted   0.949087)
=================================





Standard deviation of the error term              0.051559
====================================
Regression parameters
=====================
                                                                                                    right  tail
parameter                 estimate           standard deviation              F - ratio              probability

 Lnalpha                8.6444323107             0.2626702491              1083.056676                 0.000000

 beta                   0.1684884827             0.0120193633               196.506767                 0.000000

 gamma                 -0.5449387793             0.0301534149               326.604694                 0.000000






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

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

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

total              35              369.133526

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

mean                1              367.358289            367.358289         138191.417269              0.000000
regression          2                1.690171              0.845086            317.901017              0.000000
residual           32                0.085067              0.002658

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

 reduction          1                0.005531              0.005531              2.155635              0.152122

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


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

 reduction null hypothesis :  delta = 0  (in the original model)
Residual analysis
=================
                                                                                              standardized         studentized
obs.no.        observation        fitted value    standard deviation          residual            residual            residual

     1            3.234749            3.288736            0.014744           -0.053986           -1.095063           -1.092714
     2            3.453157            3.495338            0.013453           -0.042181           -0.855592           -0.847461
     3            3.246491            3.258939            0.013610           -0.012448           -0.252494           -0.250309
     4            2.856470            2.835391            0.018263            0.021079            0.427577            0.437186
     5            3.642836            3.667170            0.019319           -0.024335           -0.493612           -0.509070
     6            2.901422            2.810729            0.019119            0.090693            1.839619            1.894046
     7            3.277145            3.179790            0.016148            0.097355            1.974757            1.988259
     8            2.960105            3.004546            0.014381           -0.044441           -0.901445           -0.897568
     9            3.104587            3.086354            0.014683            0.018233            0.369839            0.368910
    10            3.273364            3.312784            0.009289           -0.039420           -0.799600           -0.777283

    11            3.250374            3.235443            0.014465            0.014931            0.302866            0.301712
    12            3.471966            3.533738            0.016210           -0.061771           -1.252973           -1.262069
    13            3.222868            3.238771            0.009822           -0.015903           -0.322584           -0.314204
    14            3.681351            3.639046            0.018461            0.042305            0.858113            0.878776
    15            3.572346            3.577070            0.028198           -0.004725           -0.095835           -0.109457
    16            3.157000            3.127544            0.013095            0.029456            0.597494            0.590683
    17            3.095578            3.081275            0.011505            0.014303            0.290113            0.284576
    18            3.277145            3.284817            0.014911           -0.007672           -0.155626           -0.155449
    19            3.681351            3.545399            0.016648            0.135953            2.757671            2.786075
    20            3.449988            3.417901            0.012012            0.032087            0.650846            0.639938

    21            3.292126            3.299829            0.012646           -0.007702           -0.156232           -0.154093
    22            2.895912            2.928056            0.015231           -0.032144           -0.652013           -0.652569
    23            3.346389            3.277298            0.019783            0.069091            1.401447            1.451105
    24            3.306887            3.312784            0.009289           -0.005897           -0.119624           -0.116286
    25            3.250374            3.258939            0.013610           -0.008564           -0.173721           -0.172218
    26            3.139833            3.081275            0.011505            0.058558            1.187784            1.165114
    27            3.152736            3.143769            0.012373            0.008967            0.181893            0.179159
    28            2.895912            2.933425            0.015036           -0.037513           -0.760916           -0.760637
    29            3.430756            3.432323            0.012027           -0.001567           -0.031791           -0.031260
    30            3.246491            3.279000            0.013097           -0.032509           -0.659420           -0.651909

    31            3.367296            3.410576            0.016728           -0.043280           -0.877901           -0.887443
    32            3.091042            3.120529            0.015296           -0.029487           -0.598106           -0.598860
    33            2.933857            3.060447            0.011724           -0.126590           -2.567757           -2.521296
    34            2.884801            2.893928            0.016507           -0.009128           -0.185143           -0.186866
    35            3.346389            3.338135            0.009558            0.008254            0.167433            0.162920

                                                       sum of residuals :     0.000000

                 Upper bound for the right tail probability of the largest absolute studentized residual (no. 19) :   0.125816





End of job :  3
**************************************
*  Example  4  originates from:      *
*  reference [1],  page 88, 93, ff.  *
**************************************





"Model"  y  =  alfa0  +  alfa1 * x;





"Input"  5 * ([x], n, n * [y]);





"Option" Transformed data matrix, Print input data;






"Data"

       1.000       4.000       1.100       0.700       1.800       0.400       3.000       5.000       3.000       1.400       4.900
       4.400       4.500       5.000       3.000       7.300       8.200       6.200      10.000       4.000      12.000      13.100
      12.600      13.200      15.000       4.000      18.700      19.700      17.400      17.100
Transformed data matrix
=======================

obs.no.      alfa0       alfa1       dep.var.     repeats

     1          1.000       1.000       1.000       4.000
     2          1.000       3.000       3.640       5.000
     3          1.000       5.000       7.233       3.000
     4          1.000      10.000      12.725       4.000
     5          1.000      15.000      18.225       4.000
Control information
===================

transformed variable
denoted by parameter          mean           standard deviation                minimum                  maximum

 alfa0                      1.000000                 0.000000                 1.000000                 1.000000
 alfa1                      6.700000                 5.262579                 1.000000                15.000000
 dep.var.                   8.385000                 6.545571                 0.400000                19.700000

Number of observations :    5





Multiple correlation coefficient     0.987051    (adjusted   0.986326)
================================





Proportion of variation explained    0.974269    (adjusted   0.972840)
=================================





Standard deviation of the error term              1.078736
====================================
Regression parameters
=====================
                                                                                                    right  tail
parameter                 estimate           standard deviation              F - ratio              probability

 alfa0                  0.1594830832             0.3968072487                 0.161536                 0.692478

 alfa1                  1.2276890919             0.0470261690               681.549798                 0.000000






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

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

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

total              20             2220.210000

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

mean                1             1406.164500           1406.164500           1208.387113              0.000000
regression          1              793.099430            793.099430            681.549798              0.000000
residual           18               20.946070              1.163671

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

 lack of fit        3                4.252403              1.417468              1.273658              0.319196
 pure error        15               16.693667              1.112911

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


regression null hypothesis :  alfa1 = 0





End of job :  4
**************************
*  Marten van Gelderen   *
*  Mathematisch Centrum  *
**************************