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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationMon, 13 Dec 2010 14:07:54 +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/13/t1292249212nzlqo1zpj8uh9qy.htm/, Retrieved Mon, 06 May 2024 16:20:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108939, Retrieved Mon, 06 May 2024 16:20:35 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
6.3	2.0	4.5	1.000	6.600	42.0	3	1	3
2.1	1.8	69.0	2547.000	44.500	624.0	3	5	4
9.1	0.7	27.0	10.55	179.500	180.0	4	4	4
15.8	3.9	19.0	0.023	0.300	35.0	1	1	1
5.2	1.0	30.4	160.000	169.000	392.0	4	5	4
10.9	3.6	28.0	3.300	25.600	63.0	1	2	1
8.3	1.4	50.0	52.16	440.000	230.0	1	1	1
11.0	1.5	7.0	0.425	6.400	112.0	5	4	4
3.2	0.7	30.0	465.000	423.000	281.0	5	5	5
6.3	2.1	3.5	0.075	1.200	42.0	1	1	1
6.6	4.1	6.0	0.785	3.500	42.0	2	2	2
9.5	1.2	10.4	0.200	5.000	120.0	2	2	2
3.3	0.5	20.0	27.66	115.000	148.0	5	5	5
11.0	3.4	3.9	0.120	1.000	16.0	3	1	2
4.7	1.5	41.0	85.000	325.000	310.0	1	3	1
10.4	3.4	9.0	0.101	4.000	28.0	5	1	3
7.4	0.8	7.6	1.040	5.500	68.0	5	3	4
2.1	0.8	46.0	521.000	655.000	336.0	5	5	5
17.9	2.0	24.0	0.010	0.250	50.0	1	1	1
6.1	1.9	100.0	62.000	1320.000	267.0	1	1	1
11.9	1.3	3.2	0.023	0.400	19.0	4	1	3
13.8	5.6	5.0	1.700	6.300	12.0	2	1	1
14.3	3.1	6.5	3.500	10.800	120.0	2	1	1
15.2	1.8	12.0	0.480	15.500	140.0	2	2	2
10.0	0.9	20.2	10.000	115.000	170.0	4	4	4
11.9	1.8	13.0	1.620	11.400	17.0	2	1	2
6.5	1.9	27.0	192.000	180.000	115.0	4	4	4
7.5	0.9	18.0	2.500	12.300	31.0	5	5	5
10.6	2.6	4.7	0.280	1.900	21.0	3	1	3
7.4	2.4	9.8	4.235	50.400	52.0	1	1	1
8.4	1.2	29.0	6.800	179.000	164.0	2	3	2
5.7	0.9	7.0	0.750	12.300	225.0	2	2	2
4.9	0.5	6.0	3.600	21.000	225.0	3	2	3
3.2	0.6	20.0	55.500	175.000	151.0	5	5	5
11.0	2.3	4.5	0.900	2.600	60.0	2	1	2
4.9	0.5	7.5	2.000	12.300	200.0	3	1	3
13.2	2.6	2.3	0.104	2.500	46.0	3	2	2
9.7	0.6	24.0	4.190	58.000	210.0	4	3	4
12.8	6.6	3.0	3.500	3.900	14.0	2	1	1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 4 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108939&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108939&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108939&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 time4 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Multiple Linear Regression - Estimated Regression Equation
PS[t] = + 3.87981407295822 + 0.020765785908446SWS[t] -0.0231142531223470L[t] + 0.00244205751433088Wb[t] + 0.0018345999329572Wbr[t] -0.00728851229481563Tg[t] + 0.75342769278963P[t] + 0.379291376975431S[t] -1.58459751852480D[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
PS[t] =  +  3.87981407295822 +  0.020765785908446SWS[t] -0.0231142531223470L[t] +  0.00244205751433088Wb[t] +  0.0018345999329572Wbr[t] -0.00728851229481563Tg[t] +  0.75342769278963P[t] +  0.379291376975431S[t] -1.58459751852480D[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108939&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]PS[t] =  +  3.87981407295822 +  0.020765785908446SWS[t] -0.0231142531223470L[t] +  0.00244205751433088Wb[t] +  0.0018345999329572Wbr[t] -0.00728851229481563Tg[t] +  0.75342769278963P[t] +  0.379291376975431S[t] -1.58459751852480D[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108939&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108939&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] = + 3.87981407295822 + 0.020765785908446SWS[t] -0.0231142531223470L[t] + 0.00244205751433088Wb[t] + 0.0018345999329572Wbr[t] -0.00728851229481563Tg[t] + 0.75342769278963P[t] + 0.379291376975431S[t] -1.58459751852480D[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)3.879814072958220.8054394.8173.9e-052e-05
SWS0.0207657859084460.0592490.35050.7284250.364212
L-0.02311425312234700.024253-0.9530.3481870.174093
Wb0.002442057514330880.0006493.76490.0007250.000363
Wbr0.00183459993295720.0016761.09460.2823840.141192
Tg-0.007288512294815630.002302-3.16670.0035280.001764
P0.753427692789630.3532112.13310.0412150.020608
S0.3792913769754310.1984211.91150.0655290.032764
D-1.584597518524800.426891-3.7120.0008370.000419

\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) & 3.87981407295822 & 0.805439 & 4.817 & 3.9e-05 & 2e-05 \tabularnewline
SWS & 0.020765785908446 & 0.059249 & 0.3505 & 0.728425 & 0.364212 \tabularnewline
L & -0.0231142531223470 & 0.024253 & -0.953 & 0.348187 & 0.174093 \tabularnewline
Wb & 0.00244205751433088 & 0.000649 & 3.7649 & 0.000725 & 0.000363 \tabularnewline
Wbr & 0.0018345999329572 & 0.001676 & 1.0946 & 0.282384 & 0.141192 \tabularnewline
Tg & -0.00728851229481563 & 0.002302 & -3.1667 & 0.003528 & 0.001764 \tabularnewline
P & 0.75342769278963 & 0.353211 & 2.1331 & 0.041215 & 0.020608 \tabularnewline
S & 0.379291376975431 & 0.198421 & 1.9115 & 0.065529 & 0.032764 \tabularnewline
D & -1.58459751852480 & 0.426891 & -3.712 & 0.000837 & 0.000419 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108939&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]3.87981407295822[/C][C]0.805439[/C][C]4.817[/C][C]3.9e-05[/C][C]2e-05[/C][/ROW]
[ROW][C]SWS[/C][C]0.020765785908446[/C][C]0.059249[/C][C]0.3505[/C][C]0.728425[/C][C]0.364212[/C][/ROW]
[ROW][C]L[/C][C]-0.0231142531223470[/C][C]0.024253[/C][C]-0.953[/C][C]0.348187[/C][C]0.174093[/C][/ROW]
[ROW][C]Wb[/C][C]0.00244205751433088[/C][C]0.000649[/C][C]3.7649[/C][C]0.000725[/C][C]0.000363[/C][/ROW]
[ROW][C]Wbr[/C][C]0.0018345999329572[/C][C]0.001676[/C][C]1.0946[/C][C]0.282384[/C][C]0.141192[/C][/ROW]
[ROW][C]Tg[/C][C]-0.00728851229481563[/C][C]0.002302[/C][C]-3.1667[/C][C]0.003528[/C][C]0.001764[/C][/ROW]
[ROW][C]P[/C][C]0.75342769278963[/C][C]0.353211[/C][C]2.1331[/C][C]0.041215[/C][C]0.020608[/C][/ROW]
[ROW][C]S[/C][C]0.379291376975431[/C][C]0.198421[/C][C]1.9115[/C][C]0.065529[/C][C]0.032764[/C][/ROW]
[ROW][C]D[/C][C]-1.58459751852480[/C][C]0.426891[/C][C]-3.712[/C][C]0.000837[/C][C]0.000419[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108939&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108939&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)3.879814072958220.8054394.8173.9e-052e-05
SWS0.0207657859084460.0592490.35050.7284250.364212
L-0.02311425312234700.024253-0.9530.3481870.174093
Wb0.002442057514330880.0006493.76490.0007250.000363
Wbr0.00183459993295720.0016761.09460.2823840.141192
Tg-0.007288512294815630.002302-3.16670.0035280.001764
P0.753427692789630.3532112.13310.0412150.020608
S0.3792913769754310.1984211.91150.0655290.032764
D-1.584597518524800.426891-3.7120.0008370.000419







Multiple Linear Regression - Regression Statistics
Multiple R0.834058740370982
R-squared0.69565398238923
Adjusted R-squared0.61449504435969
F-TEST (value)8.5715017874684
F-TEST (DF numerator)8
F-TEST (DF denominator)30
p-value5.31320069963037e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.872708087478808
Sum Squared Residuals22.8485821785276

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.834058740370982 \tabularnewline
R-squared & 0.69565398238923 \tabularnewline
Adjusted R-squared & 0.61449504435969 \tabularnewline
F-TEST (value) & 8.5715017874684 \tabularnewline
F-TEST (DF numerator) & 8 \tabularnewline
F-TEST (DF denominator) & 30 \tabularnewline
p-value & 5.31320069963037e-06 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.872708087478808 \tabularnewline
Sum Squared Residuals & 22.8485821785276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108939&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.834058740370982[/C][/ROW]
[ROW][C]R-squared[/C][C]0.69565398238923[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.61449504435969[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]8.5715017874684[/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]5.31320069963037e-06[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.872708087478808[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]22.8485821785276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108939&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108939&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 R0.834058740370982
R-squared0.69565398238923
Adjusted R-squared0.61449504435969
F-TEST (value)8.5715017874684
F-TEST (DF numerator)8
F-TEST (DF denominator)30
p-value5.31320069963037e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation0.872708087478808
Sum Squared Residuals22.8485821785276







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
121.500839185590370.49916081440963
21.81.90041716112323-0.100417161123231
30.70.6803262770579280.0196737229420718
43.93.06237284921150.837627150788498
51-0.2994197819057751.29941978190577
63.62.982223253657870.617776746342134
71.41.7028228537623-0.302822853762302
81.52.08881778084052-0.588817780840516
90.70.856965311357678-0.156965311357678
102.13.17412734734434-1.07412734734434
114.12.676646442232241.42335355776776
121.22.06798384488634-0.867983844886338
130.50.4264903437141880.0735096562858118
143.43.373982999186310.0260170008136889
151.51.88081424943918-0.380814249439178
163.43.083893956940040.316106043059960
170.81.94144628912481-1.14144628912481
180.80.6258091259345770.174190874065423
1922.88095857284094-0.880958572840935
201.91.870228300681540.0297716993184553
211.32.55447918153127-1.25447918153127
225.64.280607226727131.31939277327287
233.13.48181081538185-0.381810815381849
241.82.02354284907248-0.223542849072476
250.90.8094027012470240.090597298752976
261.82.44435922358036-0.644359223580361
271.91.544117168800800.355882831199198
280.91.16283550909251-0.262835509092515
292.61.728187071468130.871812928531874
302.43.0788860701858-0.678886070185799
311.22.00915117624407-0.809151176244073
320.91.31710423923805-0.417104239238050
330.50.515356921231035-0.0153569212310355
340.60.58061110541530.0193888945846996
352.32.290832378305300.00916762169470471
360.50.2637386605028180.236261339497182
372.63.61999936829082-1.01999936829082
380.6-0.0742536154953070.674253615495307
396.64.291485586160452.30851441383955

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 2 & 1.50083918559037 & 0.49916081440963 \tabularnewline
2 & 1.8 & 1.90041716112323 & -0.100417161123231 \tabularnewline
3 & 0.7 & 0.680326277057928 & 0.0196737229420718 \tabularnewline
4 & 3.9 & 3.0623728492115 & 0.837627150788498 \tabularnewline
5 & 1 & -0.299419781905775 & 1.29941978190577 \tabularnewline
6 & 3.6 & 2.98222325365787 & 0.617776746342134 \tabularnewline
7 & 1.4 & 1.7028228537623 & -0.302822853762302 \tabularnewline
8 & 1.5 & 2.08881778084052 & -0.588817780840516 \tabularnewline
9 & 0.7 & 0.856965311357678 & -0.156965311357678 \tabularnewline
10 & 2.1 & 3.17412734734434 & -1.07412734734434 \tabularnewline
11 & 4.1 & 2.67664644223224 & 1.42335355776776 \tabularnewline
12 & 1.2 & 2.06798384488634 & -0.867983844886338 \tabularnewline
13 & 0.5 & 0.426490343714188 & 0.0735096562858118 \tabularnewline
14 & 3.4 & 3.37398299918631 & 0.0260170008136889 \tabularnewline
15 & 1.5 & 1.88081424943918 & -0.380814249439178 \tabularnewline
16 & 3.4 & 3.08389395694004 & 0.316106043059960 \tabularnewline
17 & 0.8 & 1.94144628912481 & -1.14144628912481 \tabularnewline
18 & 0.8 & 0.625809125934577 & 0.174190874065423 \tabularnewline
19 & 2 & 2.88095857284094 & -0.880958572840935 \tabularnewline
20 & 1.9 & 1.87022830068154 & 0.0297716993184553 \tabularnewline
21 & 1.3 & 2.55447918153127 & -1.25447918153127 \tabularnewline
22 & 5.6 & 4.28060722672713 & 1.31939277327287 \tabularnewline
23 & 3.1 & 3.48181081538185 & -0.381810815381849 \tabularnewline
24 & 1.8 & 2.02354284907248 & -0.223542849072476 \tabularnewline
25 & 0.9 & 0.809402701247024 & 0.090597298752976 \tabularnewline
26 & 1.8 & 2.44435922358036 & -0.644359223580361 \tabularnewline
27 & 1.9 & 1.54411716880080 & 0.355882831199198 \tabularnewline
28 & 0.9 & 1.16283550909251 & -0.262835509092515 \tabularnewline
29 & 2.6 & 1.72818707146813 & 0.871812928531874 \tabularnewline
30 & 2.4 & 3.0788860701858 & -0.678886070185799 \tabularnewline
31 & 1.2 & 2.00915117624407 & -0.809151176244073 \tabularnewline
32 & 0.9 & 1.31710423923805 & -0.417104239238050 \tabularnewline
33 & 0.5 & 0.515356921231035 & -0.0153569212310355 \tabularnewline
34 & 0.6 & 0.5806111054153 & 0.0193888945846996 \tabularnewline
35 & 2.3 & 2.29083237830530 & 0.00916762169470471 \tabularnewline
36 & 0.5 & 0.263738660502818 & 0.236261339497182 \tabularnewline
37 & 2.6 & 3.61999936829082 & -1.01999936829082 \tabularnewline
38 & 0.6 & -0.074253615495307 & 0.674253615495307 \tabularnewline
39 & 6.6 & 4.29148558616045 & 2.30851441383955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108939&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]1.50083918559037[/C][C]0.49916081440963[/C][/ROW]
[ROW][C]2[/C][C]1.8[/C][C]1.90041716112323[/C][C]-0.100417161123231[/C][/ROW]
[ROW][C]3[/C][C]0.7[/C][C]0.680326277057928[/C][C]0.0196737229420718[/C][/ROW]
[ROW][C]4[/C][C]3.9[/C][C]3.0623728492115[/C][C]0.837627150788498[/C][/ROW]
[ROW][C]5[/C][C]1[/C][C]-0.299419781905775[/C][C]1.29941978190577[/C][/ROW]
[ROW][C]6[/C][C]3.6[/C][C]2.98222325365787[/C][C]0.617776746342134[/C][/ROW]
[ROW][C]7[/C][C]1.4[/C][C]1.7028228537623[/C][C]-0.302822853762302[/C][/ROW]
[ROW][C]8[/C][C]1.5[/C][C]2.08881778084052[/C][C]-0.588817780840516[/C][/ROW]
[ROW][C]9[/C][C]0.7[/C][C]0.856965311357678[/C][C]-0.156965311357678[/C][/ROW]
[ROW][C]10[/C][C]2.1[/C][C]3.17412734734434[/C][C]-1.07412734734434[/C][/ROW]
[ROW][C]11[/C][C]4.1[/C][C]2.67664644223224[/C][C]1.42335355776776[/C][/ROW]
[ROW][C]12[/C][C]1.2[/C][C]2.06798384488634[/C][C]-0.867983844886338[/C][/ROW]
[ROW][C]13[/C][C]0.5[/C][C]0.426490343714188[/C][C]0.0735096562858118[/C][/ROW]
[ROW][C]14[/C][C]3.4[/C][C]3.37398299918631[/C][C]0.0260170008136889[/C][/ROW]
[ROW][C]15[/C][C]1.5[/C][C]1.88081424943918[/C][C]-0.380814249439178[/C][/ROW]
[ROW][C]16[/C][C]3.4[/C][C]3.08389395694004[/C][C]0.316106043059960[/C][/ROW]
[ROW][C]17[/C][C]0.8[/C][C]1.94144628912481[/C][C]-1.14144628912481[/C][/ROW]
[ROW][C]18[/C][C]0.8[/C][C]0.625809125934577[/C][C]0.174190874065423[/C][/ROW]
[ROW][C]19[/C][C]2[/C][C]2.88095857284094[/C][C]-0.880958572840935[/C][/ROW]
[ROW][C]20[/C][C]1.9[/C][C]1.87022830068154[/C][C]0.0297716993184553[/C][/ROW]
[ROW][C]21[/C][C]1.3[/C][C]2.55447918153127[/C][C]-1.25447918153127[/C][/ROW]
[ROW][C]22[/C][C]5.6[/C][C]4.28060722672713[/C][C]1.31939277327287[/C][/ROW]
[ROW][C]23[/C][C]3.1[/C][C]3.48181081538185[/C][C]-0.381810815381849[/C][/ROW]
[ROW][C]24[/C][C]1.8[/C][C]2.02354284907248[/C][C]-0.223542849072476[/C][/ROW]
[ROW][C]25[/C][C]0.9[/C][C]0.809402701247024[/C][C]0.090597298752976[/C][/ROW]
[ROW][C]26[/C][C]1.8[/C][C]2.44435922358036[/C][C]-0.644359223580361[/C][/ROW]
[ROW][C]27[/C][C]1.9[/C][C]1.54411716880080[/C][C]0.355882831199198[/C][/ROW]
[ROW][C]28[/C][C]0.9[/C][C]1.16283550909251[/C][C]-0.262835509092515[/C][/ROW]
[ROW][C]29[/C][C]2.6[/C][C]1.72818707146813[/C][C]0.871812928531874[/C][/ROW]
[ROW][C]30[/C][C]2.4[/C][C]3.0788860701858[/C][C]-0.678886070185799[/C][/ROW]
[ROW][C]31[/C][C]1.2[/C][C]2.00915117624407[/C][C]-0.809151176244073[/C][/ROW]
[ROW][C]32[/C][C]0.9[/C][C]1.31710423923805[/C][C]-0.417104239238050[/C][/ROW]
[ROW][C]33[/C][C]0.5[/C][C]0.515356921231035[/C][C]-0.0153569212310355[/C][/ROW]
[ROW][C]34[/C][C]0.6[/C][C]0.5806111054153[/C][C]0.0193888945846996[/C][/ROW]
[ROW][C]35[/C][C]2.3[/C][C]2.29083237830530[/C][C]0.00916762169470471[/C][/ROW]
[ROW][C]36[/C][C]0.5[/C][C]0.263738660502818[/C][C]0.236261339497182[/C][/ROW]
[ROW][C]37[/C][C]2.6[/C][C]3.61999936829082[/C][C]-1.01999936829082[/C][/ROW]
[ROW][C]38[/C][C]0.6[/C][C]-0.074253615495307[/C][C]0.674253615495307[/C][/ROW]
[ROW][C]39[/C][C]6.6[/C][C]4.29148558616045[/C][C]2.30851441383955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108939&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108939&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
121.500839185590370.49916081440963
21.81.90041716112323-0.100417161123231
30.70.6803262770579280.0196737229420718
43.93.06237284921150.837627150788498
51-0.2994197819057751.29941978190577
63.62.982223253657870.617776746342134
71.41.7028228537623-0.302822853762302
81.52.08881778084052-0.588817780840516
90.70.856965311357678-0.156965311357678
102.13.17412734734434-1.07412734734434
114.12.676646442232241.42335355776776
121.22.06798384488634-0.867983844886338
130.50.4264903437141880.0735096562858118
143.43.373982999186310.0260170008136889
151.51.88081424943918-0.380814249439178
163.43.083893956940040.316106043059960
170.81.94144628912481-1.14144628912481
180.80.6258091259345770.174190874065423
1922.88095857284094-0.880958572840935
201.91.870228300681540.0297716993184553
211.32.55447918153127-1.25447918153127
225.64.280607226727131.31939277327287
233.13.48181081538185-0.381810815381849
241.82.02354284907248-0.223542849072476
250.90.8094027012470240.090597298752976
261.82.44435922358036-0.644359223580361
271.91.544117168800800.355882831199198
280.91.16283550909251-0.262835509092515
292.61.728187071468130.871812928531874
302.43.0788860701858-0.678886070185799
311.22.00915117624407-0.809151176244073
320.91.31710423923805-0.417104239238050
330.50.515356921231035-0.0153569212310355
340.60.58061110541530.0193888945846996
352.32.290832378305300.00916762169470471
360.50.2637386605028180.236261339497182
372.63.61999936829082-1.01999936829082
380.6-0.0742536154953070.674253615495307
396.64.291485586160452.30851441383955







Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
120.8491299877122250.301740024575550.150870012287775
130.7845483590719690.4309032818560630.215451640928031
140.6939939281153270.6120121437693450.306006071884673
150.5601246865024130.8797506269951730.439875313497587
160.4455383192855690.8910766385711370.554461680714431
170.4936164861180880.9872329722361750.506383513881912
180.4018405104525260.8036810209050520.598159489547474
190.3718248248684210.7436496497368430.628175175131579
200.2634627581584380.5269255163168760.736537241841562
210.4381427078076720.8762854156153440.561857292192328
220.505011840217020.989976319565960.49498815978298
230.439696610468520.879393220937040.56030338953148
240.3140357451445720.6280714902891440.685964254855428
250.2170890457442890.4341780914885790.78291095425571
260.1720083210166320.3440166420332630.827991678983368
270.1631114147729580.3262228295459170.836888585227042

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
12 & 0.849129987712225 & 0.30174002457555 & 0.150870012287775 \tabularnewline
13 & 0.784548359071969 & 0.430903281856063 & 0.215451640928031 \tabularnewline
14 & 0.693993928115327 & 0.612012143769345 & 0.306006071884673 \tabularnewline
15 & 0.560124686502413 & 0.879750626995173 & 0.439875313497587 \tabularnewline
16 & 0.445538319285569 & 0.891076638571137 & 0.554461680714431 \tabularnewline
17 & 0.493616486118088 & 0.987232972236175 & 0.506383513881912 \tabularnewline
18 & 0.401840510452526 & 0.803681020905052 & 0.598159489547474 \tabularnewline
19 & 0.371824824868421 & 0.743649649736843 & 0.628175175131579 \tabularnewline
20 & 0.263462758158438 & 0.526925516316876 & 0.736537241841562 \tabularnewline
21 & 0.438142707807672 & 0.876285415615344 & 0.561857292192328 \tabularnewline
22 & 0.50501184021702 & 0.98997631956596 & 0.49498815978298 \tabularnewline
23 & 0.43969661046852 & 0.87939322093704 & 0.56030338953148 \tabularnewline
24 & 0.314035745144572 & 0.628071490289144 & 0.685964254855428 \tabularnewline
25 & 0.217089045744289 & 0.434178091488579 & 0.78291095425571 \tabularnewline
26 & 0.172008321016632 & 0.344016642033263 & 0.827991678983368 \tabularnewline
27 & 0.163111414772958 & 0.326222829545917 & 0.836888585227042 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108939&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]0.849129987712225[/C][C]0.30174002457555[/C][C]0.150870012287775[/C][/ROW]
[ROW][C]13[/C][C]0.784548359071969[/C][C]0.430903281856063[/C][C]0.215451640928031[/C][/ROW]
[ROW][C]14[/C][C]0.693993928115327[/C][C]0.612012143769345[/C][C]0.306006071884673[/C][/ROW]
[ROW][C]15[/C][C]0.560124686502413[/C][C]0.879750626995173[/C][C]0.439875313497587[/C][/ROW]
[ROW][C]16[/C][C]0.445538319285569[/C][C]0.891076638571137[/C][C]0.554461680714431[/C][/ROW]
[ROW][C]17[/C][C]0.493616486118088[/C][C]0.987232972236175[/C][C]0.506383513881912[/C][/ROW]
[ROW][C]18[/C][C]0.401840510452526[/C][C]0.803681020905052[/C][C]0.598159489547474[/C][/ROW]
[ROW][C]19[/C][C]0.371824824868421[/C][C]0.743649649736843[/C][C]0.628175175131579[/C][/ROW]
[ROW][C]20[/C][C]0.263462758158438[/C][C]0.526925516316876[/C][C]0.736537241841562[/C][/ROW]
[ROW][C]21[/C][C]0.438142707807672[/C][C]0.876285415615344[/C][C]0.561857292192328[/C][/ROW]
[ROW][C]22[/C][C]0.50501184021702[/C][C]0.98997631956596[/C][C]0.49498815978298[/C][/ROW]
[ROW][C]23[/C][C]0.43969661046852[/C][C]0.87939322093704[/C][C]0.56030338953148[/C][/ROW]
[ROW][C]24[/C][C]0.314035745144572[/C][C]0.628071490289144[/C][C]0.685964254855428[/C][/ROW]
[ROW][C]25[/C][C]0.217089045744289[/C][C]0.434178091488579[/C][C]0.78291095425571[/C][/ROW]
[ROW][C]26[/C][C]0.172008321016632[/C][C]0.344016642033263[/C][C]0.827991678983368[/C][/ROW]
[ROW][C]27[/C][C]0.163111414772958[/C][C]0.326222829545917[/C][C]0.836888585227042[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108939&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108939&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
120.8491299877122250.301740024575550.150870012287775
130.7845483590719690.4309032818560630.215451640928031
140.6939939281153270.6120121437693450.306006071884673
150.5601246865024130.8797506269951730.439875313497587
160.4455383192855690.8910766385711370.554461680714431
170.4936164861180880.9872329722361750.506383513881912
180.4018405104525260.8036810209050520.598159489547474
190.3718248248684210.7436496497368430.628175175131579
200.2634627581584380.5269255163168760.736537241841562
210.4381427078076720.8762854156153440.561857292192328
220.505011840217020.989976319565960.49498815978298
230.439696610468520.879393220937040.56030338953148
240.3140357451445720.6280714902891440.685964254855428
250.2170890457442890.4341780914885790.78291095425571
260.1720083210166320.3440166420332630.827991678983368
270.1631114147729580.3262228295459170.836888585227042







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=108939&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=108939&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108939&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):
par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
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')
}