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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationWed, 22 Dec 2010 20:49:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/22/t129305090055i5dhafuizvyrm.htm/, Retrieved Sun, 05 May 2024 23:51:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114585, Retrieved Sun, 05 May 2024 23:51:29 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [] [2010-12-05 18:56:24] [b98453cac15ba1066b407e146608df68]
- R PD  [Multiple Regression] [2] [2010-12-22 20:47:35] [a7c91bc614e4e21e8b9c8593f39a36f1]
-           [Multiple Regression] [3] [2010-12-22 20:49:49] [062de5fc17e30860c0960288bdb996a8] [Current]
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Dataseries X:
6.3	2.0	4.5	1.000	6.600	42	3	1	3
2.1	1.8	69.0	2547.000	4603.000	624	3	5	4
9.1	0.7	27.0	10.550	179.500	180	4	4	4
15.8	3.9	19.0	0.023	0.300	35	1	1	1
5.2	1.0	30.4	160.000	169.000	392	4	5	4
10.9	3.6	28.0	3.300	25.600	63	1	2	1
8.3	1.4	50.0	52.160	440.000	230	1	1	1
11.0	1.5	7.0	0.425	6400.000	112	5	4	4
3.2	0.7	30.0	46.500	423.000	281	5	5	5
6.3	2.1	3.5	0.075	1.200	42	1	1	1
6.6	4.1	6.0	0.785	3.500	42	2	2	2
9.5	1.2	10.4	0.200	5.000	120	2	2	2
3.3	0.5	20.0	27.660	115.000	148	5	5	5
11.0	3.4	3.9	0.120	1.000	16	3	1	2
4.7	1.5	41.0	85.000	325.000	310	1	3	1
10.4	3.4	9.0	0.101	4.000	28	5	1	3
7.4	0.8	7.6	1.040	5.500	68	5	3	4
2.1	0.8	46.0	521.000	655.000	336	5	5	5
17.9	2.0	24.0	0.010	0.250	50	1	1	1
6.1	1.9	100.0	62.000	1320.000	267	1	1	1
11.9	1.3	3.2	0.023	0.400	19	4	1	3
13.8	5.6	5.0	1.700	6.300	12	2	1	1
14.3	3.1	6.5	3.500	10.800	120	2	1	1
15.2	1.8	12.0	0.480	15.500	140	2	2	2
10.0	0.9	20.2	10.000	115.000	170	4	4	4
11.9	1.8	13.0	1.620	11.400	17	2	1	2
6.5	1.9	27.0	192.000	180.000	115	4	4	4
7.5	0.9	18.0	2.500	12.100	31	5	5	5
10.6	2.6	4.7	0.280	1.900	21	3	1	3
7.4	2.4	9.8	4.235	50.400	52	1	1	1
8.4	1.2	29.0	6.800	179.000	164	2	3	2
5.7	0.9	7.0	0.750	12.300	225	2	2	2
4.9	0.5	6.0	3.600	21.000	225	3	2	3
3.2	0.6	20.0	5.550	175.000	151	5	5	5
11.0	2.3	4.5	0.900	2.600	60	2	1	2
4.9	0.5	7.5	2.000	12.300	200	3	1	3
13.2	2.6	2.3	0.104	2.500	46	3	2	2
9.7	0.6	24.0	4.190	58.000	210	4	3	4
12.8	6.6	3.0	3.500	3.900	14	2	1	1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114585&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114585&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114585&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
PS[t] = + 3.76393207604853 -0.00531741970536981SWS[t] + 0.00174503962468929L[t] + 0.00204744955906192Wb[t] -0.000115671074078297Wbr[t] -0.00689485090469952tg[t] + 0.967271429026893P[t] + 0.353700230106999S[t] -1.74310818493962D[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
PS[t] =  +  3.76393207604853 -0.00531741970536981SWS[t] +  0.00174503962468929L[t] +  0.00204744955906192Wb[t] -0.000115671074078297Wbr[t] -0.00689485090469952tg[t] +  0.967271429026893P[t] +  0.353700230106999S[t] -1.74310818493962D[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114585&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]PS[t] =  +  3.76393207604853 -0.00531741970536981SWS[t] +  0.00174503962468929L[t] +  0.00204744955906192Wb[t] -0.000115671074078297Wbr[t] -0.00689485090469952tg[t] +  0.967271429026893P[t] +  0.353700230106999S[t] -1.74310818493962D[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114585&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114585&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Estimated Regression Equation
PS[t] = + 3.76393207604853 -0.00531741970536981SWS[t] + 0.00174503962468929L[t] + 0.00204744955906192Wb[t] -0.000115671074078297Wbr[t] -0.00689485090469952tg[t] + 0.967271429026893P[t] + 0.353700230106999S[t] -1.74310818493962D[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)3.763932076048530.8382664.49019.8e-054.9e-05
SWS-0.005317419705369810.054998-0.09670.923620.46181
L0.001745039624689290.0106290.16420.8706940.435347
Wb0.002047449559061920.0005533.70170.0008610.00043
Wbr-0.0001156710740782970.00015-0.77140.4464960.223248
tg-0.006894850904699520.002357-2.92570.0064920.003246
P0.9672714290268930.3481612.77820.0093360.004668
S0.3537002301069990.2000571.7680.0872320.043616
D-1.743108184939620.436761-3.9910.0003910.000196

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 3.76393207604853 & 0.838266 & 4.4901 & 9.8e-05 & 4.9e-05 \tabularnewline
SWS & -0.00531741970536981 & 0.054998 & -0.0967 & 0.92362 & 0.46181 \tabularnewline
L & 0.00174503962468929 & 0.010629 & 0.1642 & 0.870694 & 0.435347 \tabularnewline
Wb & 0.00204744955906192 & 0.000553 & 3.7017 & 0.000861 & 0.00043 \tabularnewline
Wbr & -0.000115671074078297 & 0.00015 & -0.7714 & 0.446496 & 0.223248 \tabularnewline
tg & -0.00689485090469952 & 0.002357 & -2.9257 & 0.006492 & 0.003246 \tabularnewline
P & 0.967271429026893 & 0.348161 & 2.7782 & 0.009336 & 0.004668 \tabularnewline
S & 0.353700230106999 & 0.200057 & 1.768 & 0.087232 & 0.043616 \tabularnewline
D & -1.74310818493962 & 0.436761 & -3.991 & 0.000391 & 0.000196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114585&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]3.76393207604853[/C][C]0.838266[/C][C]4.4901[/C][C]9.8e-05[/C][C]4.9e-05[/C][/ROW]
[ROW][C]SWS[/C][C]-0.00531741970536981[/C][C]0.054998[/C][C]-0.0967[/C][C]0.92362[/C][C]0.46181[/C][/ROW]
[ROW][C]L[/C][C]0.00174503962468929[/C][C]0.010629[/C][C]0.1642[/C][C]0.870694[/C][C]0.435347[/C][/ROW]
[ROW][C]Wb[/C][C]0.00204744955906192[/C][C]0.000553[/C][C]3.7017[/C][C]0.000861[/C][C]0.00043[/C][/ROW]
[ROW][C]Wbr[/C][C]-0.000115671074078297[/C][C]0.00015[/C][C]-0.7714[/C][C]0.446496[/C][C]0.223248[/C][/ROW]
[ROW][C]tg[/C][C]-0.00689485090469952[/C][C]0.002357[/C][C]-2.9257[/C][C]0.006492[/C][C]0.003246[/C][/ROW]
[ROW][C]P[/C][C]0.967271429026893[/C][C]0.348161[/C][C]2.7782[/C][C]0.009336[/C][C]0.004668[/C][/ROW]
[ROW][C]S[/C][C]0.353700230106999[/C][C]0.200057[/C][C]1.768[/C][C]0.087232[/C][C]0.043616[/C][/ROW]
[ROW][C]D[/C][C]-1.74310818493962[/C][C]0.436761[/C][C]-3.991[/C][C]0.000391[/C][C]0.000196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114585&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114585&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)3.763932076048530.8382664.49019.8e-054.9e-05
SWS-0.005317419705369810.054998-0.09670.923620.46181
L0.001745039624689290.0106290.16420.8706940.435347
Wb0.002047449559061920.0005533.70170.0008610.00043
Wbr-0.0001156710740782970.00015-0.77140.4464960.223248
tg-0.006894850904699520.002357-2.92570.0064920.003246
P0.9672714290268930.3481612.77820.0093360.004668
S0.3537002301069990.2000571.7680.0872320.043616
D-1.743108184939620.436761-3.9910.0003910.000196







Multiple Linear Regression - Regression Statistics
Multiple R0.82293927732987
R-squared0.67722905417221
Adjusted R-squared0.591156801951466
F-TEST (value)7.86814608307638
F-TEST (DF numerator)8
F-TEST (DF denominator)30
p-value1.19270193654764e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.898736554903028
Sum Squared Residuals24.2318218535689

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.82293927732987 \tabularnewline
R-squared & 0.67722905417221 \tabularnewline
Adjusted R-squared & 0.591156801951466 \tabularnewline
F-TEST (value) & 7.86814608307638 \tabularnewline
F-TEST (DF numerator) & 8 \tabularnewline
F-TEST (DF denominator) & 30 \tabularnewline
p-value & 1.19270193654764e-05 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.898736554903028 \tabularnewline
Sum Squared Residuals & 24.2318218535689 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114585&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.82293927732987[/C][/ROW]
[ROW][C]R-squared[/C][C]0.67722905417221[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.591156801951466[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]7.86814608307638[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]8[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]30[/C][/ROW]
[ROW][C]p-value[/C][C]1.19270193654764e-05[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.898736554903028[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]24.2318218535689[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114585&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114585&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Regression Statistics
Multiple R0.82293927732987
R-squared0.67722905417221
Adjusted R-squared0.591156801951466
F-TEST (value)7.86814608307638
F-TEST (DF numerator)8
F-TEST (DF denominator)30
p-value1.19270193654764e-05
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.898736554903028
Sum Squared Residuals24.2318218535689







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
121.476175255057400.523824744942604
21.81.95108903504383-0.151089035043833
30.70.833877995578501-0.133877995578501
43.93.049628680120210.850371319879793
510.05974678834371540.940253211656285
63.63.2558168121050.344183187894998
71.41.85499693624803-0.454996936248027
81.51.484733053101430.0152669468985724
90.7-0.2025906713559160.902590671355916
102.13.02483446021604-0.924834460216041
114.12.606652953276981.49334704672302
121.22.05974097531031-0.859740975310309
130.50.693495101875079-0.193495101875079
143.43.371356669532010.0286433304679942
151.52.09478709544179-0.594787095441791
163.43.49175737093506-0.091757370935059
170.82.19551386218784-1.39551386218784
180.80.3966414511452630.403358548854737
1922.94374370000132-0.94374370000132
201.91.617194115832690.282805884167307
211.32.56869895547028-1.26869895547028
225.64.164425511086361.43557448891364
233.13.42290535233612-0.322905352336116
241.81.89368546789393-0.0936854678939286
250.90.8925092444633430.00749075553665705
261.82.41015276761843-0.610152767618431
271.91.667320482572680.232679517427322
280.91.43475813832965-0.534758138329648
292.61.597520717613571.00247928238643
302.42.96385691244973-0.563856912449728
311.22.14176106450584-0.941761064505843
320.91.35033638889003-0.450336388890034
330.50.581837422015759-0.0818374220157593
340.60.621132916935961-0.0211329169359606
352.32.103170761410690.196829238589309
360.50.4008564430132640.0991435569867363
372.63.50351471994264-0.90351471994264
380.60.2659389239381070.334061076061893
396.64.156426169517052.44357383048295

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2 & 1.47617525505740 & 0.523824744942604 \tabularnewline
2 & 1.8 & 1.95108903504383 & -0.151089035043833 \tabularnewline
3 & 0.7 & 0.833877995578501 & -0.133877995578501 \tabularnewline
4 & 3.9 & 3.04962868012021 & 0.850371319879793 \tabularnewline
5 & 1 & 0.0597467883437154 & 0.940253211656285 \tabularnewline
6 & 3.6 & 3.255816812105 & 0.344183187894998 \tabularnewline
7 & 1.4 & 1.85499693624803 & -0.454996936248027 \tabularnewline
8 & 1.5 & 1.48473305310143 & 0.0152669468985724 \tabularnewline
9 & 0.7 & -0.202590671355916 & 0.902590671355916 \tabularnewline
10 & 2.1 & 3.02483446021604 & -0.924834460216041 \tabularnewline
11 & 4.1 & 2.60665295327698 & 1.49334704672302 \tabularnewline
12 & 1.2 & 2.05974097531031 & -0.859740975310309 \tabularnewline
13 & 0.5 & 0.693495101875079 & -0.193495101875079 \tabularnewline
14 & 3.4 & 3.37135666953201 & 0.0286433304679942 \tabularnewline
15 & 1.5 & 2.09478709544179 & -0.594787095441791 \tabularnewline
16 & 3.4 & 3.49175737093506 & -0.091757370935059 \tabularnewline
17 & 0.8 & 2.19551386218784 & -1.39551386218784 \tabularnewline
18 & 0.8 & 0.396641451145263 & 0.403358548854737 \tabularnewline
19 & 2 & 2.94374370000132 & -0.94374370000132 \tabularnewline
20 & 1.9 & 1.61719411583269 & 0.282805884167307 \tabularnewline
21 & 1.3 & 2.56869895547028 & -1.26869895547028 \tabularnewline
22 & 5.6 & 4.16442551108636 & 1.43557448891364 \tabularnewline
23 & 3.1 & 3.42290535233612 & -0.322905352336116 \tabularnewline
24 & 1.8 & 1.89368546789393 & -0.0936854678939286 \tabularnewline
25 & 0.9 & 0.892509244463343 & 0.00749075553665705 \tabularnewline
26 & 1.8 & 2.41015276761843 & -0.610152767618431 \tabularnewline
27 & 1.9 & 1.66732048257268 & 0.232679517427322 \tabularnewline
28 & 0.9 & 1.43475813832965 & -0.534758138329648 \tabularnewline
29 & 2.6 & 1.59752071761357 & 1.00247928238643 \tabularnewline
30 & 2.4 & 2.96385691244973 & -0.563856912449728 \tabularnewline
31 & 1.2 & 2.14176106450584 & -0.941761064505843 \tabularnewline
32 & 0.9 & 1.35033638889003 & -0.450336388890034 \tabularnewline
33 & 0.5 & 0.581837422015759 & -0.0818374220157593 \tabularnewline
34 & 0.6 & 0.621132916935961 & -0.0211329169359606 \tabularnewline
35 & 2.3 & 2.10317076141069 & 0.196829238589309 \tabularnewline
36 & 0.5 & 0.400856443013264 & 0.0991435569867363 \tabularnewline
37 & 2.6 & 3.50351471994264 & -0.90351471994264 \tabularnewline
38 & 0.6 & 0.265938923938107 & 0.334061076061893 \tabularnewline
39 & 6.6 & 4.15642616951705 & 2.44357383048295 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114585&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]2[/C][C]1.47617525505740[/C][C]0.523824744942604[/C][/ROW]
[ROW][C]2[/C][C]1.8[/C][C]1.95108903504383[/C][C]-0.151089035043833[/C][/ROW]
[ROW][C]3[/C][C]0.7[/C][C]0.833877995578501[/C][C]-0.133877995578501[/C][/ROW]
[ROW][C]4[/C][C]3.9[/C][C]3.04962868012021[/C][C]0.850371319879793[/C][/ROW]
[ROW][C]5[/C][C]1[/C][C]0.0597467883437154[/C][C]0.940253211656285[/C][/ROW]
[ROW][C]6[/C][C]3.6[/C][C]3.255816812105[/C][C]0.344183187894998[/C][/ROW]
[ROW][C]7[/C][C]1.4[/C][C]1.85499693624803[/C][C]-0.454996936248027[/C][/ROW]
[ROW][C]8[/C][C]1.5[/C][C]1.48473305310143[/C][C]0.0152669468985724[/C][/ROW]
[ROW][C]9[/C][C]0.7[/C][C]-0.202590671355916[/C][C]0.902590671355916[/C][/ROW]
[ROW][C]10[/C][C]2.1[/C][C]3.02483446021604[/C][C]-0.924834460216041[/C][/ROW]
[ROW][C]11[/C][C]4.1[/C][C]2.60665295327698[/C][C]1.49334704672302[/C][/ROW]
[ROW][C]12[/C][C]1.2[/C][C]2.05974097531031[/C][C]-0.859740975310309[/C][/ROW]
[ROW][C]13[/C][C]0.5[/C][C]0.693495101875079[/C][C]-0.193495101875079[/C][/ROW]
[ROW][C]14[/C][C]3.4[/C][C]3.37135666953201[/C][C]0.0286433304679942[/C][/ROW]
[ROW][C]15[/C][C]1.5[/C][C]2.09478709544179[/C][C]-0.594787095441791[/C][/ROW]
[ROW][C]16[/C][C]3.4[/C][C]3.49175737093506[/C][C]-0.091757370935059[/C][/ROW]
[ROW][C]17[/C][C]0.8[/C][C]2.19551386218784[/C][C]-1.39551386218784[/C][/ROW]
[ROW][C]18[/C][C]0.8[/C][C]0.396641451145263[/C][C]0.403358548854737[/C][/ROW]
[ROW][C]19[/C][C]2[/C][C]2.94374370000132[/C][C]-0.94374370000132[/C][/ROW]
[ROW][C]20[/C][C]1.9[/C][C]1.61719411583269[/C][C]0.282805884167307[/C][/ROW]
[ROW][C]21[/C][C]1.3[/C][C]2.56869895547028[/C][C]-1.26869895547028[/C][/ROW]
[ROW][C]22[/C][C]5.6[/C][C]4.16442551108636[/C][C]1.43557448891364[/C][/ROW]
[ROW][C]23[/C][C]3.1[/C][C]3.42290535233612[/C][C]-0.322905352336116[/C][/ROW]
[ROW][C]24[/C][C]1.8[/C][C]1.89368546789393[/C][C]-0.0936854678939286[/C][/ROW]
[ROW][C]25[/C][C]0.9[/C][C]0.892509244463343[/C][C]0.00749075553665705[/C][/ROW]
[ROW][C]26[/C][C]1.8[/C][C]2.41015276761843[/C][C]-0.610152767618431[/C][/ROW]
[ROW][C]27[/C][C]1.9[/C][C]1.66732048257268[/C][C]0.232679517427322[/C][/ROW]
[ROW][C]28[/C][C]0.9[/C][C]1.43475813832965[/C][C]-0.534758138329648[/C][/ROW]
[ROW][C]29[/C][C]2.6[/C][C]1.59752071761357[/C][C]1.00247928238643[/C][/ROW]
[ROW][C]30[/C][C]2.4[/C][C]2.96385691244973[/C][C]-0.563856912449728[/C][/ROW]
[ROW][C]31[/C][C]1.2[/C][C]2.14176106450584[/C][C]-0.941761064505843[/C][/ROW]
[ROW][C]32[/C][C]0.9[/C][C]1.35033638889003[/C][C]-0.450336388890034[/C][/ROW]
[ROW][C]33[/C][C]0.5[/C][C]0.581837422015759[/C][C]-0.0818374220157593[/C][/ROW]
[ROW][C]34[/C][C]0.6[/C][C]0.621132916935961[/C][C]-0.0211329169359606[/C][/ROW]
[ROW][C]35[/C][C]2.3[/C][C]2.10317076141069[/C][C]0.196829238589309[/C][/ROW]
[ROW][C]36[/C][C]0.5[/C][C]0.400856443013264[/C][C]0.0991435569867363[/C][/ROW]
[ROW][C]37[/C][C]2.6[/C][C]3.50351471994264[/C][C]-0.90351471994264[/C][/ROW]
[ROW][C]38[/C][C]0.6[/C][C]0.265938923938107[/C][C]0.334061076061893[/C][/ROW]
[ROW][C]39[/C][C]6.6[/C][C]4.15642616951705[/C][C]2.44357383048295[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114585&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114585&T=4

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
121.476175255057400.523824744942604
21.81.95108903504383-0.151089035043833
30.70.833877995578501-0.133877995578501
43.93.049628680120210.850371319879793
510.05974678834371540.940253211656285
63.63.2558168121050.344183187894998
71.41.85499693624803-0.454996936248027
81.51.484733053101430.0152669468985724
90.7-0.2025906713559160.902590671355916
102.13.02483446021604-0.924834460216041
114.12.606652953276981.49334704672302
121.22.05974097531031-0.859740975310309
130.50.693495101875079-0.193495101875079
143.43.371356669532010.0286433304679942
151.52.09478709544179-0.594787095441791
163.43.49175737093506-0.091757370935059
170.82.19551386218784-1.39551386218784
180.80.3966414511452630.403358548854737
1922.94374370000132-0.94374370000132
201.91.617194115832690.282805884167307
211.32.56869895547028-1.26869895547028
225.64.164425511086361.43557448891364
233.13.42290535233612-0.322905352336116
241.81.89368546789393-0.0936854678939286
250.90.8925092444633430.00749075553665705
261.82.41015276761843-0.610152767618431
271.91.667320482572680.232679517427322
280.91.43475813832965-0.534758138329648
292.61.597520717613571.00247928238643
302.42.96385691244973-0.563856912449728
311.22.14176106450584-0.941761064505843
320.91.35033638889003-0.450336388890034
330.50.581837422015759-0.0818374220157593
340.60.621132916935961-0.0211329169359606
352.32.103170761410690.196829238589309
360.50.4008564430132640.0991435569867363
372.63.50351471994264-0.90351471994264
380.60.2659389239381070.334061076061893
396.64.156426169517052.44357383048295







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
120.7189959878450770.5620080243098460.281004012154923
130.7656568254871950.4686863490256110.234343174512805
140.6732288073008650.653542385398270.326771192699135
150.5381244514533130.9237510970933750.461875548546687
160.4079124122785240.8158248245570490.592087587721476
170.5071019363172420.9857961273655160.492898063682758
180.4003321563272580.8006643126545170.599667843672742
190.3721873331158740.7443746662317480.627812666884126
200.2645323598263740.5290647196527470.735467640173626
210.4510788227977170.9021576455954340.548921177202283
220.5408833492222930.9182333015554140.459116650777707
230.4661640298547480.9323280597094960.533835970145252
240.341159544394470.682319088788940.65884045560553
250.2357896767152570.4715793534305150.764210323284743
260.1806437149433590.3612874298867190.81935628505664
270.17902681478020.35805362956040.8209731852198

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
12 & 0.718995987845077 & 0.562008024309846 & 0.281004012154923 \tabularnewline
13 & 0.765656825487195 & 0.468686349025611 & 0.234343174512805 \tabularnewline
14 & 0.673228807300865 & 0.65354238539827 & 0.326771192699135 \tabularnewline
15 & 0.538124451453313 & 0.923751097093375 & 0.461875548546687 \tabularnewline
16 & 0.407912412278524 & 0.815824824557049 & 0.592087587721476 \tabularnewline
17 & 0.507101936317242 & 0.985796127365516 & 0.492898063682758 \tabularnewline
18 & 0.400332156327258 & 0.800664312654517 & 0.599667843672742 \tabularnewline
19 & 0.372187333115874 & 0.744374666231748 & 0.627812666884126 \tabularnewline
20 & 0.264532359826374 & 0.529064719652747 & 0.735467640173626 \tabularnewline
21 & 0.451078822797717 & 0.902157645595434 & 0.548921177202283 \tabularnewline
22 & 0.540883349222293 & 0.918233301555414 & 0.459116650777707 \tabularnewline
23 & 0.466164029854748 & 0.932328059709496 & 0.533835970145252 \tabularnewline
24 & 0.34115954439447 & 0.68231908878894 & 0.65884045560553 \tabularnewline
25 & 0.235789676715257 & 0.471579353430515 & 0.764210323284743 \tabularnewline
26 & 0.180643714943359 & 0.361287429886719 & 0.81935628505664 \tabularnewline
27 & 0.1790268147802 & 0.3580536295604 & 0.8209731852198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114585&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]12[/C][C]0.718995987845077[/C][C]0.562008024309846[/C][C]0.281004012154923[/C][/ROW]
[ROW][C]13[/C][C]0.765656825487195[/C][C]0.468686349025611[/C][C]0.234343174512805[/C][/ROW]
[ROW][C]14[/C][C]0.673228807300865[/C][C]0.65354238539827[/C][C]0.326771192699135[/C][/ROW]
[ROW][C]15[/C][C]0.538124451453313[/C][C]0.923751097093375[/C][C]0.461875548546687[/C][/ROW]
[ROW][C]16[/C][C]0.407912412278524[/C][C]0.815824824557049[/C][C]0.592087587721476[/C][/ROW]
[ROW][C]17[/C][C]0.507101936317242[/C][C]0.985796127365516[/C][C]0.492898063682758[/C][/ROW]
[ROW][C]18[/C][C]0.400332156327258[/C][C]0.800664312654517[/C][C]0.599667843672742[/C][/ROW]
[ROW][C]19[/C][C]0.372187333115874[/C][C]0.744374666231748[/C][C]0.627812666884126[/C][/ROW]
[ROW][C]20[/C][C]0.264532359826374[/C][C]0.529064719652747[/C][C]0.735467640173626[/C][/ROW]
[ROW][C]21[/C][C]0.451078822797717[/C][C]0.902157645595434[/C][C]0.548921177202283[/C][/ROW]
[ROW][C]22[/C][C]0.540883349222293[/C][C]0.918233301555414[/C][C]0.459116650777707[/C][/ROW]
[ROW][C]23[/C][C]0.466164029854748[/C][C]0.932328059709496[/C][C]0.533835970145252[/C][/ROW]
[ROW][C]24[/C][C]0.34115954439447[/C][C]0.68231908878894[/C][C]0.65884045560553[/C][/ROW]
[ROW][C]25[/C][C]0.235789676715257[/C][C]0.471579353430515[/C][C]0.764210323284743[/C][/ROW]
[ROW][C]26[/C][C]0.180643714943359[/C][C]0.361287429886719[/C][C]0.81935628505664[/C][/ROW]
[ROW][C]27[/C][C]0.1790268147802[/C][C]0.3580536295604[/C][C]0.8209731852198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114585&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114585&T=5

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
120.7189959878450770.5620080243098460.281004012154923
130.7656568254871950.4686863490256110.234343174512805
140.6732288073008650.653542385398270.326771192699135
150.5381244514533130.9237510970933750.461875548546687
160.4079124122785240.8158248245570490.592087587721476
170.5071019363172420.9857961273655160.492898063682758
180.4003321563272580.8006643126545170.599667843672742
190.3721873331158740.7443746662317480.627812666884126
200.2645323598263740.5290647196527470.735467640173626
210.4510788227977170.9021576455954340.548921177202283
220.5408833492222930.9182333015554140.459116650777707
230.4661640298547480.9323280597094960.533835970145252
240.341159544394470.682319088788940.65884045560553
250.2357896767152570.4715793534305150.764210323284743
260.1806437149433590.3612874298867190.81935628505664
270.17902681478020.35805362956040.8209731852198







Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114585&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114585&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114585&T=6

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level00OK
5% type I error level00OK
10% type I error level00OK



Parameters (Session):
Parameters (R input):
par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}