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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationTue, 14 Dec 2010 10:07:08 +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/14/t129232116613xqr0qco4bq3r9.htm/, Retrieved Thu, 02 May 2024 15:30:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109342, Retrieved Thu, 02 May 2024 15:30:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [] [2010-12-11 16:17:47] [39e83c7b0ac936e906a817a1bb402750]
-    D    [Multiple Regression] [] [2010-12-14 10:07:08] [558c060a42ec367ec2c020fab85c25c7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2	4,5	1	7	42	3	1	3
1,8	69	2.547	4.603	624	3	5	4
0,7	27	11	180	180	4	4	4
3,9	19	0,023	0,3	35	1	1	1
1	30,4	160	169	392	4	5	4
3,6	28	3	26	63	1	2	1
1,4	50	52	440	230	1	1	1
1,5	7	0,425	6	112	5	4	4
0,7	30	465	423	281	5	5	5
2,1	3,5	0,075	1	42	1	1	1
4,1	6	0,785	4	42	2	2	2
1,2	10,4	0,2	5	120	2	2	2
0,5	20	28	115	148	5	5	5
3,4	3,9	0,12	1	16	3	1	2
1,5	41	85	325	310	1	3	1
3,4	9	0,101	4	28	5	1	3
0,8	7,6	1	6	68	5	3	4
0,8	46	521	655	336	5	5	5
2	24	0,01	0,25	50	1	1	1
1,9	100	62	1.320	267	1	1	1
1,3	3,2	0,023	0,4	19	4	1	3
5,6	5	2	6	12	2	1	1
3,1	6,5	4	11	120	2	1	1
1,8	12	0,48	16	140	2	2	2
0,9	20,2	10	115	170	4	4	4
1,8	13	2	11	17	2	1	2
1,9	27	192	180	115	4	4	4
0,9	18	3	12	31	5	5	5
2,6	4,7	0,28	2	21	3	1	3
2,4	9,8	4	50	52	1	1	1
1,2	29	7	179	164	2	3	2
0,9	7	0,75	12	225	2	2	2
0,5	6	4	21	225	3	2	3
0,6	20	56	175	151	5	5	5
2,3	4,5	0,9	3	60	2	1	2
0,5	7,5	2	12	200	3	1	3
2,6	2,3	0,104	3	46	3	2	2
0,6	24	4	58	210	4	3	4
6,6	3	4	4	14	2	1	1

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 8 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109342&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]8 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109342&T=0

As an alternative you can also use a QR Code:  
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 time8 seconds
R Server'George Udny Yule' @ 72.249.76.132






Multiple Linear Regression - Estimated Regression Equation
PS[t] = + 3.59872798429118 + 0.00168586791515148L[t] + 0.00505019021635358Wb[t] -0.00416766197027056Wbr[t] -0.00249985220101987Tg[t] + 0.76674401969889P[t] + 0.337375889226130S[t] -1.58803585821715D[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
PS[t] =  +  3.59872798429118 +  0.00168586791515148L[t] +  0.00505019021635358Wb[t] -0.00416766197027056Wbr[t] -0.00249985220101987Tg[t] +  0.76674401969889P[t] +  0.337375889226130S[t] -1.58803585821715D[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109342&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]PS[t] =  +  3.59872798429118 +  0.00168586791515148L[t] +  0.00505019021635358Wb[t] -0.00416766197027056Wbr[t] -0.00249985220101987Tg[t] +  0.76674401969889P[t] +  0.337375889226130S[t] -1.58803585821715D[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109342&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Estimated Regression Equation
PS[t] = + 3.59872798429118 + 0.00168586791515148L[t] + 0.00505019021635358Wb[t] -0.00416766197027056Wbr[t] -0.00249985220101987Tg[t] + 0.76674401969889P[t] + 0.337375889226130S[t] -1.58803585821715D[t] + e[t]






Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)3.598727984291180.4584567.849700
L0.001685867915151480.012150.13880.8905430.445272
Wb0.005050190216353580.0026851.8810.0693920.034696
Wbr-0.004167661970270560.002095-1.98910.0555740.027787
Tg-0.002499852201019870.002119-1.17980.2470430.123522
P0.766744019698890.3710812.06620.0472480.023624
S0.3373758892261300.2279421.48010.148940.07447
D-1.588035858217150.451945-3.51380.0013810.000691

\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) & 3.59872798429118 & 0.458456 & 7.8497 & 0 & 0 \tabularnewline
L & 0.00168586791515148 & 0.01215 & 0.1388 & 0.890543 & 0.445272 \tabularnewline
Wb & 0.00505019021635358 & 0.002685 & 1.881 & 0.069392 & 0.034696 \tabularnewline
Wbr & -0.00416766197027056 & 0.002095 & -1.9891 & 0.055574 & 0.027787 \tabularnewline
Tg & -0.00249985220101987 & 0.002119 & -1.1798 & 0.247043 & 0.123522 \tabularnewline
P & 0.76674401969889 & 0.371081 & 2.0662 & 0.047248 & 0.023624 \tabularnewline
S & 0.337375889226130 & 0.227942 & 1.4801 & 0.14894 & 0.07447 \tabularnewline
D & -1.58803585821715 & 0.451945 & -3.5138 & 0.001381 & 0.000691 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109342&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]3.59872798429118[/C][C]0.458456[/C][C]7.8497[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]L[/C][C]0.00168586791515148[/C][C]0.01215[/C][C]0.1388[/C][C]0.890543[/C][C]0.445272[/C][/ROW]
[ROW][C]Wb[/C][C]0.00505019021635358[/C][C]0.002685[/C][C]1.881[/C][C]0.069392[/C][C]0.034696[/C][/ROW]
[ROW][C]Wbr[/C][C]-0.00416766197027056[/C][C]0.002095[/C][C]-1.9891[/C][C]0.055574[/C][C]0.027787[/C][/ROW]
[ROW][C]Tg[/C][C]-0.00249985220101987[/C][C]0.002119[/C][C]-1.1798[/C][C]0.247043[/C][C]0.123522[/C][/ROW]
[ROW][C]P[/C][C]0.76674401969889[/C][C]0.371081[/C][C]2.0662[/C][C]0.047248[/C][C]0.023624[/C][/ROW]
[ROW][C]S[/C][C]0.337375889226130[/C][C]0.227942[/C][C]1.4801[/C][C]0.14894[/C][C]0.07447[/C][/ROW]
[ROW][C]D[/C][C]-1.58803585821715[/C][C]0.451945[/C][C]-3.5138[/C][C]0.001381[/C][C]0.000691[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109342&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109342&T=2

As an alternative you can also use a QR Code:  
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)3.598727984291180.4584567.849700
L0.001685867915151480.012150.13880.8905430.445272
Wb0.005050190216353580.0026851.8810.0693920.034696
Wbr-0.004167661970270560.002095-1.98910.0555740.027787
Tg-0.002499852201019870.002119-1.17980.2470430.123522
P0.766744019698890.3710812.06620.0472480.023624
S0.3373758892261300.2279421.48010.148940.07447
D-1.588035858217150.451945-3.51380.0013810.000691






Multiple Linear Regression - Regression Statistics
Multiple R0.760192943827821
R-squared0.577893311845608
Adjusted R-squared0.482578898391391
F-TEST (value)6.06302122525454
F-TEST (DF numerator)7
F-TEST (DF denominator)31
p-value0.000164664347328203
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.01105803783479
Sum Squared Residuals31.6893890319806

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.760192943827821 \tabularnewline
R-squared & 0.577893311845608 \tabularnewline
Adjusted R-squared & 0.482578898391391 \tabularnewline
F-TEST (value) & 6.06302122525454 \tabularnewline
F-TEST (DF numerator) & 7 \tabularnewline
F-TEST (DF denominator) & 31 \tabularnewline
p-value & 0.000164664347328203 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.01105803783479 \tabularnewline
Sum Squared Residuals & 31.6893890319806 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109342&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.760192943827821[/C][/ROW]
[ROW][C]R-squared[/C][C]0.577893311845608[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.482578898391391[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]6.06302122525454[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]7[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]31[/C][/ROW]
[ROW][C]p-value[/C][C]0.000164664347328203[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]1.01105803783479[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]31.6893890319806[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109342&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109342&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Regression Statistics
Multiple R0.760192943827821
R-squared0.577893311845608
Adjusted R-squared0.482578898391391
F-TEST (value)6.06302122525454
F-TEST (DF numerator)7
F-TEST (DF denominator)31
p-value0.000164664347328203
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.01105803783479
Sum Squared Residuals31.6893890319806






Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
121.350697527562340.649302472437659
21.8-0.2162077442091522.01620774420915
30.70.5639821623793540.136017837620646
43.93.058214554135130.841785445864872
511.17544395981045-0.175443959810451
63.63.24869289660720.351307103392802
71.41.052978048853390.347021951146607
81.52.13876619473371-0.638766194733706
90.71.11268324397845-0.412683243978452
102.13.01192988255520-0.911929882555202
114.12.523311252193751.57668874780625
121.22.32861857609403-1.12861857609403
130.50.505011669859396-0.00501166985939576
143.43.023279826688140.376720173311857
151.52.15850624370848-0.658506243708485
163.42.934732768298880.465267231701118
170.81.91529918247594-1.11529918247594
180.80.3180783345778140.481921665422186
1923.02928884132129-1.02928884132129
201.92.92354876845506-1.02354876845506
211.32.19531905275739-0.89531905275739
225.63.845081576472541.75491842352746
233.13.56688841121648-0.46688841121648
241.82.23688869232548-0.436888692325475
250.90.8433646204177570.0566353795822429
261.82.23719509072015-0.43719509072015
271.91.640556984605650.259443015394354
280.91.09713706907745-0.197137069077445
292.61.420733770262361.17926622973764
302.42.81315888846639-0.413158888466388
311.21.89652622234123-0.696526222341228
320.92.03400611490253-1.13400611490253
330.51.18993256893983-0.689932568939826
340.60.3888577210980030.211142278901997
352.32.143157655321680.156842344678316
360.50.944990363911647-0.444990363911647
372.63.27454663423543-0.674546634235432
380.60.619656532235708-0.0196565322357083
396.63.855145840613452.74485415938655

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2 & 1.35069752756234 & 0.649302472437659 \tabularnewline
2 & 1.8 & -0.216207744209152 & 2.01620774420915 \tabularnewline
3 & 0.7 & 0.563982162379354 & 0.136017837620646 \tabularnewline
4 & 3.9 & 3.05821455413513 & 0.841785445864872 \tabularnewline
5 & 1 & 1.17544395981045 & -0.175443959810451 \tabularnewline
6 & 3.6 & 3.2486928966072 & 0.351307103392802 \tabularnewline
7 & 1.4 & 1.05297804885339 & 0.347021951146607 \tabularnewline
8 & 1.5 & 2.13876619473371 & -0.638766194733706 \tabularnewline
9 & 0.7 & 1.11268324397845 & -0.412683243978452 \tabularnewline
10 & 2.1 & 3.01192988255520 & -0.911929882555202 \tabularnewline
11 & 4.1 & 2.52331125219375 & 1.57668874780625 \tabularnewline
12 & 1.2 & 2.32861857609403 & -1.12861857609403 \tabularnewline
13 & 0.5 & 0.505011669859396 & -0.00501166985939576 \tabularnewline
14 & 3.4 & 3.02327982668814 & 0.376720173311857 \tabularnewline
15 & 1.5 & 2.15850624370848 & -0.658506243708485 \tabularnewline
16 & 3.4 & 2.93473276829888 & 0.465267231701118 \tabularnewline
17 & 0.8 & 1.91529918247594 & -1.11529918247594 \tabularnewline
18 & 0.8 & 0.318078334577814 & 0.481921665422186 \tabularnewline
19 & 2 & 3.02928884132129 & -1.02928884132129 \tabularnewline
20 & 1.9 & 2.92354876845506 & -1.02354876845506 \tabularnewline
21 & 1.3 & 2.19531905275739 & -0.89531905275739 \tabularnewline
22 & 5.6 & 3.84508157647254 & 1.75491842352746 \tabularnewline
23 & 3.1 & 3.56688841121648 & -0.46688841121648 \tabularnewline
24 & 1.8 & 2.23688869232548 & -0.436888692325475 \tabularnewline
25 & 0.9 & 0.843364620417757 & 0.0566353795822429 \tabularnewline
26 & 1.8 & 2.23719509072015 & -0.43719509072015 \tabularnewline
27 & 1.9 & 1.64055698460565 & 0.259443015394354 \tabularnewline
28 & 0.9 & 1.09713706907745 & -0.197137069077445 \tabularnewline
29 & 2.6 & 1.42073377026236 & 1.17926622973764 \tabularnewline
30 & 2.4 & 2.81315888846639 & -0.413158888466388 \tabularnewline
31 & 1.2 & 1.89652622234123 & -0.696526222341228 \tabularnewline
32 & 0.9 & 2.03400611490253 & -1.13400611490253 \tabularnewline
33 & 0.5 & 1.18993256893983 & -0.689932568939826 \tabularnewline
34 & 0.6 & 0.388857721098003 & 0.211142278901997 \tabularnewline
35 & 2.3 & 2.14315765532168 & 0.156842344678316 \tabularnewline
36 & 0.5 & 0.944990363911647 & -0.444990363911647 \tabularnewline
37 & 2.6 & 3.27454663423543 & -0.674546634235432 \tabularnewline
38 & 0.6 & 0.619656532235708 & -0.0196565322357083 \tabularnewline
39 & 6.6 & 3.85514584061345 & 2.74485415938655 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109342&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]1.35069752756234[/C][C]0.649302472437659[/C][/ROW]
[ROW][C]2[/C][C]1.8[/C][C]-0.216207744209152[/C][C]2.01620774420915[/C][/ROW]
[ROW][C]3[/C][C]0.7[/C][C]0.563982162379354[/C][C]0.136017837620646[/C][/ROW]
[ROW][C]4[/C][C]3.9[/C][C]3.05821455413513[/C][C]0.841785445864872[/C][/ROW]
[ROW][C]5[/C][C]1[/C][C]1.17544395981045[/C][C]-0.175443959810451[/C][/ROW]
[ROW][C]6[/C][C]3.6[/C][C]3.2486928966072[/C][C]0.351307103392802[/C][/ROW]
[ROW][C]7[/C][C]1.4[/C][C]1.05297804885339[/C][C]0.347021951146607[/C][/ROW]
[ROW][C]8[/C][C]1.5[/C][C]2.13876619473371[/C][C]-0.638766194733706[/C][/ROW]
[ROW][C]9[/C][C]0.7[/C][C]1.11268324397845[/C][C]-0.412683243978452[/C][/ROW]
[ROW][C]10[/C][C]2.1[/C][C]3.01192988255520[/C][C]-0.911929882555202[/C][/ROW]
[ROW][C]11[/C][C]4.1[/C][C]2.52331125219375[/C][C]1.57668874780625[/C][/ROW]
[ROW][C]12[/C][C]1.2[/C][C]2.32861857609403[/C][C]-1.12861857609403[/C][/ROW]
[ROW][C]13[/C][C]0.5[/C][C]0.505011669859396[/C][C]-0.00501166985939576[/C][/ROW]
[ROW][C]14[/C][C]3.4[/C][C]3.02327982668814[/C][C]0.376720173311857[/C][/ROW]
[ROW][C]15[/C][C]1.5[/C][C]2.15850624370848[/C][C]-0.658506243708485[/C][/ROW]
[ROW][C]16[/C][C]3.4[/C][C]2.93473276829888[/C][C]0.465267231701118[/C][/ROW]
[ROW][C]17[/C][C]0.8[/C][C]1.91529918247594[/C][C]-1.11529918247594[/C][/ROW]
[ROW][C]18[/C][C]0.8[/C][C]0.318078334577814[/C][C]0.481921665422186[/C][/ROW]
[ROW][C]19[/C][C]2[/C][C]3.02928884132129[/C][C]-1.02928884132129[/C][/ROW]
[ROW][C]20[/C][C]1.9[/C][C]2.92354876845506[/C][C]-1.02354876845506[/C][/ROW]
[ROW][C]21[/C][C]1.3[/C][C]2.19531905275739[/C][C]-0.89531905275739[/C][/ROW]
[ROW][C]22[/C][C]5.6[/C][C]3.84508157647254[/C][C]1.75491842352746[/C][/ROW]
[ROW][C]23[/C][C]3.1[/C][C]3.56688841121648[/C][C]-0.46688841121648[/C][/ROW]
[ROW][C]24[/C][C]1.8[/C][C]2.23688869232548[/C][C]-0.436888692325475[/C][/ROW]
[ROW][C]25[/C][C]0.9[/C][C]0.843364620417757[/C][C]0.0566353795822429[/C][/ROW]
[ROW][C]26[/C][C]1.8[/C][C]2.23719509072015[/C][C]-0.43719509072015[/C][/ROW]
[ROW][C]27[/C][C]1.9[/C][C]1.64055698460565[/C][C]0.259443015394354[/C][/ROW]
[ROW][C]28[/C][C]0.9[/C][C]1.09713706907745[/C][C]-0.197137069077445[/C][/ROW]
[ROW][C]29[/C][C]2.6[/C][C]1.42073377026236[/C][C]1.17926622973764[/C][/ROW]
[ROW][C]30[/C][C]2.4[/C][C]2.81315888846639[/C][C]-0.413158888466388[/C][/ROW]
[ROW][C]31[/C][C]1.2[/C][C]1.89652622234123[/C][C]-0.696526222341228[/C][/ROW]
[ROW][C]32[/C][C]0.9[/C][C]2.03400611490253[/C][C]-1.13400611490253[/C][/ROW]
[ROW][C]33[/C][C]0.5[/C][C]1.18993256893983[/C][C]-0.689932568939826[/C][/ROW]
[ROW][C]34[/C][C]0.6[/C][C]0.388857721098003[/C][C]0.211142278901997[/C][/ROW]
[ROW][C]35[/C][C]2.3[/C][C]2.14315765532168[/C][C]0.156842344678316[/C][/ROW]
[ROW][C]36[/C][C]0.5[/C][C]0.944990363911647[/C][C]-0.444990363911647[/C][/ROW]
[ROW][C]37[/C][C]2.6[/C][C]3.27454663423543[/C][C]-0.674546634235432[/C][/ROW]
[ROW][C]38[/C][C]0.6[/C][C]0.619656532235708[/C][C]-0.0196565322357083[/C][/ROW]
[ROW][C]39[/C][C]6.6[/C][C]3.85514584061345[/C][C]2.74485415938655[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109342&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109342&T=4

As an alternative you can also use a QR Code:  
QR Code


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

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
121.350697527562340.649302472437659
21.8-0.2162077442091522.01620774420915
30.70.5639821623793540.136017837620646
43.93.058214554135130.841785445864872
511.17544395981045-0.175443959810451
63.63.24869289660720.351307103392802
71.41.052978048853390.347021951146607
81.52.13876619473371-0.638766194733706
90.71.11268324397845-0.412683243978452
102.13.01192988255520-0.911929882555202
114.12.523311252193751.57668874780625
121.22.32861857609403-1.12861857609403
130.50.505011669859396-0.00501166985939576
143.43.023279826688140.376720173311857
151.52.15850624370848-0.658506243708485
163.42.934732768298880.465267231701118
170.81.91529918247594-1.11529918247594
180.80.3180783345778140.481921665422186
1923.02928884132129-1.02928884132129
201.92.92354876845506-1.02354876845506
211.32.19531905275739-0.89531905275739
225.63.845081576472541.75491842352746
233.13.56688841121648-0.46688841121648
241.82.23688869232548-0.436888692325475
250.90.8433646204177570.0566353795822429
261.82.23719509072015-0.43719509072015
271.91.640556984605650.259443015394354
280.91.09713706907745-0.197137069077445
292.61.420733770262361.17926622973764
302.42.81315888846639-0.413158888466388
311.21.89652622234123-0.696526222341228
320.92.03400611490253-1.13400611490253
330.51.18993256893983-0.689932568939826
340.60.3888577210980030.211142278901997
352.32.143157655321680.156842344678316
360.50.944990363911647-0.444990363911647
372.63.27454663423543-0.674546634235432
380.60.619656532235708-0.0196565322357083
396.63.855145840613452.74485415938655






Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
110.6729235081637320.6541529836725360.327076491836268
120.7034957269878960.5930085460242080.296504273012104
130.5895127075205950.820974584958810.410487292479405
140.4700667177509770.9401334355019530.529933282249023
150.3400337626702610.6800675253405230.659966237329739
160.2270620904306690.4541241808613380.772937909569331
170.2983037207497280.5966074414994550.701696279250272
180.2210822438613890.4421644877227780.778917756138611
190.3611525092222400.7223050184444810.63884749077776
200.3928273926647170.7856547853294330.607172607335283
210.598399734695370.803200530609260.40160026530463
220.7148490935114220.5703018129771550.285150906488578
230.6684626169161720.6630747661676550.331537383083828
240.5687696859811360.8624606280377290.431230314018864
250.446997226526610.893994453053220.55300277347339
260.3878933361914550.7757866723829110.612106663808545
270.4208174589660940.8416349179321870.579182541033906
280.2814689400405430.5629378800810860.718531059959457

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
11 & 0.672923508163732 & 0.654152983672536 & 0.327076491836268 \tabularnewline
12 & 0.703495726987896 & 0.593008546024208 & 0.296504273012104 \tabularnewline
13 & 0.589512707520595 & 0.82097458495881 & 0.410487292479405 \tabularnewline
14 & 0.470066717750977 & 0.940133435501953 & 0.529933282249023 \tabularnewline
15 & 0.340033762670261 & 0.680067525340523 & 0.659966237329739 \tabularnewline
16 & 0.227062090430669 & 0.454124180861338 & 0.772937909569331 \tabularnewline
17 & 0.298303720749728 & 0.596607441499455 & 0.701696279250272 \tabularnewline
18 & 0.221082243861389 & 0.442164487722778 & 0.778917756138611 \tabularnewline
19 & 0.361152509222240 & 0.722305018444481 & 0.63884749077776 \tabularnewline
20 & 0.392827392664717 & 0.785654785329433 & 0.607172607335283 \tabularnewline
21 & 0.59839973469537 & 0.80320053060926 & 0.40160026530463 \tabularnewline
22 & 0.714849093511422 & 0.570301812977155 & 0.285150906488578 \tabularnewline
23 & 0.668462616916172 & 0.663074766167655 & 0.331537383083828 \tabularnewline
24 & 0.568769685981136 & 0.862460628037729 & 0.431230314018864 \tabularnewline
25 & 0.44699722652661 & 0.89399445305322 & 0.55300277347339 \tabularnewline
26 & 0.387893336191455 & 0.775786672382911 & 0.612106663808545 \tabularnewline
27 & 0.420817458966094 & 0.841634917932187 & 0.579182541033906 \tabularnewline
28 & 0.281468940040543 & 0.562937880081086 & 0.718531059959457 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109342&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]11[/C][C]0.672923508163732[/C][C]0.654152983672536[/C][C]0.327076491836268[/C][/ROW]
[ROW][C]12[/C][C]0.703495726987896[/C][C]0.593008546024208[/C][C]0.296504273012104[/C][/ROW]
[ROW][C]13[/C][C]0.589512707520595[/C][C]0.82097458495881[/C][C]0.410487292479405[/C][/ROW]
[ROW][C]14[/C][C]0.470066717750977[/C][C]0.940133435501953[/C][C]0.529933282249023[/C][/ROW]
[ROW][C]15[/C][C]0.340033762670261[/C][C]0.680067525340523[/C][C]0.659966237329739[/C][/ROW]
[ROW][C]16[/C][C]0.227062090430669[/C][C]0.454124180861338[/C][C]0.772937909569331[/C][/ROW]
[ROW][C]17[/C][C]0.298303720749728[/C][C]0.596607441499455[/C][C]0.701696279250272[/C][/ROW]
[ROW][C]18[/C][C]0.221082243861389[/C][C]0.442164487722778[/C][C]0.778917756138611[/C][/ROW]
[ROW][C]19[/C][C]0.361152509222240[/C][C]0.722305018444481[/C][C]0.63884749077776[/C][/ROW]
[ROW][C]20[/C][C]0.392827392664717[/C][C]0.785654785329433[/C][C]0.607172607335283[/C][/ROW]
[ROW][C]21[/C][C]0.59839973469537[/C][C]0.80320053060926[/C][C]0.40160026530463[/C][/ROW]
[ROW][C]22[/C][C]0.714849093511422[/C][C]0.570301812977155[/C][C]0.285150906488578[/C][/ROW]
[ROW][C]23[/C][C]0.668462616916172[/C][C]0.663074766167655[/C][C]0.331537383083828[/C][/ROW]
[ROW][C]24[/C][C]0.568769685981136[/C][C]0.862460628037729[/C][C]0.431230314018864[/C][/ROW]
[ROW][C]25[/C][C]0.44699722652661[/C][C]0.89399445305322[/C][C]0.55300277347339[/C][/ROW]
[ROW][C]26[/C][C]0.387893336191455[/C][C]0.775786672382911[/C][C]0.612106663808545[/C][/ROW]
[ROW][C]27[/C][C]0.420817458966094[/C][C]0.841634917932187[/C][C]0.579182541033906[/C][/ROW]
[ROW][C]28[/C][C]0.281468940040543[/C][C]0.562937880081086[/C][C]0.718531059959457[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109342&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109342&T=5

As an alternative you can also use a QR Code:  
QR Code


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

Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
110.6729235081637320.6541529836725360.327076491836268
120.7034957269878960.5930085460242080.296504273012104
130.5895127075205950.820974584958810.410487292479405
140.4700667177509770.9401334355019530.529933282249023
150.3400337626702610.6800675253405230.659966237329739
160.2270620904306690.4541241808613380.772937909569331
170.2983037207497280.5966074414994550.701696279250272
180.2210822438613890.4421644877227780.778917756138611
190.3611525092222400.7223050184444810.63884749077776
200.3928273926647170.7856547853294330.607172607335283
210.598399734695370.803200530609260.40160026530463
220.7148490935114220.5703018129771550.285150906488578
230.6684626169161720.6630747661676550.331537383083828
240.5687696859811360.8624606280377290.431230314018864
250.446997226526610.893994453053220.55300277347339
260.3878933361914550.7757866723829110.612106663808545
270.4208174589660940.8416349179321870.579182541033906
280.2814689400405430.5629378800810860.718531059959457






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=109342&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=109342&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109342&T=6

As an alternative you can also use a QR Code:  
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


Figures (Output of Computation)

Figure 1
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Figure 2
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Figure 4
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Figure 5
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Figure 6
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Figure 7
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Figure 8
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Figure 9
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Figure 10
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Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; 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')
}