Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 13 Aug 2014 15:33:49 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Aug/13/t1407940493a7jl3vco3qxu2st.htm/, Retrieved Sat, 18 May 2024 05:29:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235523, Retrieved Sat, 18 May 2024 05:29:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMaxim Polderman
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [classical decompo...] [2014-08-13 14:33:49] [7ca0840e03a865d91d059c4387468671] [Current]
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Dataseries X:
24514
24442
24364
24222
25689
25618
24514
23780
23851
23851
23922
24072
24514
24735
25105
25397
26722
26573
25468
23851
24143
24442
24364
24735
24442
24955
25176
25247
26872
26573
25468
23851
24143
23922
24293
25105
25027
24884
25247
25468
26722
26793
25468
23559
23409
23851
23481
24663
24663
24222
24806
25176
26430
26793
25247
23409
23409
22818
22376
23338
22968
22084
22676
23189
24735
25326
23702
22526
22526
22084
21792
22376
21643
21493
21864
22376
23922
24222
22305
20909
20246
19584
19213
19947
19506
19584
19947
20246
21714
21935
19584
18480
17375
16635
16122
16855
16492
17076
17297
17518
18480
19064
16122
15388
13543
12367
11997
13030
12439
13179
13179
13251
14134
14725
11854
10821
9126
8022
7437
8905




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235523&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235523&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235523&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235523&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235523&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235523&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22444224514-72
32436424442.0047597012-78.0047597012162
42422224364.0051566576-142.005156657637
52568924222.00938752941466.9906124706
62561825688.9030217083-70.9030217082764
72451425618.0046871833-1104.00468718331
82378024514.0729823952-734.072982395188
92385123780.048527334370.9514726657253
102385123850.99530961370.00469038626397378
112392223850.999999689971.0000003100686
122407223921.9953064057150.004693594277
132451424071.9900836455442.00991635448
142473524513.9707800675221.029219932458
152510524734.9853884299370.014611570103
162539725104.9755394584292.024460541626
172672225396.98069515031325.01930484973
182657326721.912407-148.912407000025
192546826573.0098441467-1105.00984414673
202385125468.0730488431-1617.07304884306
212414323851.1068997855291.89310021446
222444224142.9807038341299.019296165898
232436424441.9802327429-77.9802327429425
242473524364.0051550362370.994844963767
252444224734.9754746581-292.97547465812
262495524442.0193677184512.980632281622
272517624954.9660884092221.033911590832
282524725175.985388119771.0146118802513
292687225246.99530543981625.0046945602
302657326871.8925758775-298.89257587746
312546826573.01975888-1105.01975887996
322385125468.0730494985-1617.07304949849
332414323851.1068997856291.893100214416
342392224142.9807038341-220.980703834102
352429323922.0146083628370.985391637154
362510524292.9754752831812.024524716948
372502725104.9463195261-77.9463195261269
382488425027.0051527943-143.005152794332
392524724884.0094536361362.99054636389
402546825246.976003798221.02399620202
412672225467.98538877521254.01461122477
422679326721.917100904671.0828990954396
432546826792.9953009255-1324.99530092554
442355925468.0875914132-1909.08759141315
452340923559.1262039796-150.126203979624
462385123409.0099243872441.990075612834
472348123850.9707813792-369.970781379154
482466323481.02445764411181.97554235585
492466324662.92186318850.0781368114949146
502422224662.9999948346-440.999994834616
512480624222.0291531696583.970846830383
522517624805.9613954618370.038604538204
532643025175.97553787231254.02446212773
542679326429.9171002533363.082899746652
552524726792.9759976928-1545.97599769278
562340925247.1021997755-1838.10219977553
572340923409.1215113511-0.121511351080699
582281823409.0000080327-591.000008032748
592237622818.0390692147-442.03906921469
602333822376.0292218597961.970778140338
612296823337.9364070349-369.936407034947
622208422968.0244553718-884.02445537176
632267622084.0584401705591.941559829495
642318922675.9608685422513.039131457819
652473523188.9660845421546.03391545804
662532624734.8977963957591.1022036043
672370225325.9609240295-1623.96092402947
682252623702.107355122-1176.10735512204
692252622526.0777488835-0.0777488834719406
702208422526.0000051397-442.000005139744
712179222084.0292192773-292.029219277258
722237621792.0193051643583.980694835689
732164322375.9613948108-732.961394810776
742149321643.0484538506-150.048453850603
752186421493.0099192473370.990080752661
762237621863.9754749731512.024525026929
772392222375.96615161451546.03384838549
782422223921.8977964001300.102203599865
792230524221.9801611552-1916.98016115522
802090922305.1267257334-1396.12672573343
812024620909.0922936955-663.092293695499
821958420246.0438350166-662.04383501663
831921319584.0437657062-371.043765706214
841994719213.0245285759733.975471424121
851950619946.9514791119-440.951479111875
861958419506.029149962477.9708500376109
871994719583.994845584363.005154415972
882024619946.9760028323299.023997167715
892171420245.98023243221468.01976756782
902193521713.902953674221.097046326038
911958421934.9853839461-2350.9853839461
921848019584.1554164999-1104.15541649991
931737518480.0729923594-1105.07299235944
941663517375.0730530176-740.073053017597
951612216635.0489239807-513.048923980714
961685516122.0339161054732.966083894609
971649216854.9515458394-362.95154583942
981707616492.0239936238583.976006376186
991729717075.9613951207221.038604879283
1001751817296.9853878095221.014612190509
1011848017517.9853893956962.014610604427
1021906418479.9364041373584.063595862684
1031612219063.9613893304-2941.96138933044
1041538816122.1944841279-734.194484127864
1051354315388.0485353664-1845.04853536639
1061236713543.1219705522-1176.12197055222
1071199712367.0777498497-370.077749849654
1081303011997.02446471551032.97553528449
1091243913029.9317131262-590.931713126212
1101317912439.0390646999739.960935300078
1111317913178.9510834310.0489165689523361
1121325113178.999996766372.0000032337266
1131413413250.9952402986883.004759701433
1141472514133.9416272385591.058372761523
1151185414724.960926927-2870.96092692699
1161082111854.189790503-1033.18979050304
117912610821.0683010376-1695.06830103755
11880229126.11205581466-1104.11205581466
11974378022.072989493-585.072989493002
12089057437.03867739751467.9613226025

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 24442 & 24514 & -72 \tabularnewline
3 & 24364 & 24442.0047597012 & -78.0047597012162 \tabularnewline
4 & 24222 & 24364.0051566576 & -142.005156657637 \tabularnewline
5 & 25689 & 24222.0093875294 & 1466.9906124706 \tabularnewline
6 & 25618 & 25688.9030217083 & -70.9030217082764 \tabularnewline
7 & 24514 & 25618.0046871833 & -1104.00468718331 \tabularnewline
8 & 23780 & 24514.0729823952 & -734.072982395188 \tabularnewline
9 & 23851 & 23780.0485273343 & 70.9514726657253 \tabularnewline
10 & 23851 & 23850.9953096137 & 0.00469038626397378 \tabularnewline
11 & 23922 & 23850.9999996899 & 71.0000003100686 \tabularnewline
12 & 24072 & 23921.9953064057 & 150.004693594277 \tabularnewline
13 & 24514 & 24071.9900836455 & 442.00991635448 \tabularnewline
14 & 24735 & 24513.9707800675 & 221.029219932458 \tabularnewline
15 & 25105 & 24734.9853884299 & 370.014611570103 \tabularnewline
16 & 25397 & 25104.9755394584 & 292.024460541626 \tabularnewline
17 & 26722 & 25396.9806951503 & 1325.01930484973 \tabularnewline
18 & 26573 & 26721.912407 & -148.912407000025 \tabularnewline
19 & 25468 & 26573.0098441467 & -1105.00984414673 \tabularnewline
20 & 23851 & 25468.0730488431 & -1617.07304884306 \tabularnewline
21 & 24143 & 23851.1068997855 & 291.89310021446 \tabularnewline
22 & 24442 & 24142.9807038341 & 299.019296165898 \tabularnewline
23 & 24364 & 24441.9802327429 & -77.9802327429425 \tabularnewline
24 & 24735 & 24364.0051550362 & 370.994844963767 \tabularnewline
25 & 24442 & 24734.9754746581 & -292.97547465812 \tabularnewline
26 & 24955 & 24442.0193677184 & 512.980632281622 \tabularnewline
27 & 25176 & 24954.9660884092 & 221.033911590832 \tabularnewline
28 & 25247 & 25175.9853881197 & 71.0146118802513 \tabularnewline
29 & 26872 & 25246.9953054398 & 1625.0046945602 \tabularnewline
30 & 26573 & 26871.8925758775 & -298.89257587746 \tabularnewline
31 & 25468 & 26573.01975888 & -1105.01975887996 \tabularnewline
32 & 23851 & 25468.0730494985 & -1617.07304949849 \tabularnewline
33 & 24143 & 23851.1068997856 & 291.893100214416 \tabularnewline
34 & 23922 & 24142.9807038341 & -220.980703834102 \tabularnewline
35 & 24293 & 23922.0146083628 & 370.985391637154 \tabularnewline
36 & 25105 & 24292.9754752831 & 812.024524716948 \tabularnewline
37 & 25027 & 25104.9463195261 & -77.9463195261269 \tabularnewline
38 & 24884 & 25027.0051527943 & -143.005152794332 \tabularnewline
39 & 25247 & 24884.0094536361 & 362.99054636389 \tabularnewline
40 & 25468 & 25246.976003798 & 221.02399620202 \tabularnewline
41 & 26722 & 25467.9853887752 & 1254.01461122477 \tabularnewline
42 & 26793 & 26721.9171009046 & 71.0828990954396 \tabularnewline
43 & 25468 & 26792.9953009255 & -1324.99530092554 \tabularnewline
44 & 23559 & 25468.0875914132 & -1909.08759141315 \tabularnewline
45 & 23409 & 23559.1262039796 & -150.126203979624 \tabularnewline
46 & 23851 & 23409.0099243872 & 441.990075612834 \tabularnewline
47 & 23481 & 23850.9707813792 & -369.970781379154 \tabularnewline
48 & 24663 & 23481.0244576441 & 1181.97554235585 \tabularnewline
49 & 24663 & 24662.9218631885 & 0.0781368114949146 \tabularnewline
50 & 24222 & 24662.9999948346 & -440.999994834616 \tabularnewline
51 & 24806 & 24222.0291531696 & 583.970846830383 \tabularnewline
52 & 25176 & 24805.9613954618 & 370.038604538204 \tabularnewline
53 & 26430 & 25175.9755378723 & 1254.02446212773 \tabularnewline
54 & 26793 & 26429.9171002533 & 363.082899746652 \tabularnewline
55 & 25247 & 26792.9759976928 & -1545.97599769278 \tabularnewline
56 & 23409 & 25247.1021997755 & -1838.10219977553 \tabularnewline
57 & 23409 & 23409.1215113511 & -0.121511351080699 \tabularnewline
58 & 22818 & 23409.0000080327 & -591.000008032748 \tabularnewline
59 & 22376 & 22818.0390692147 & -442.03906921469 \tabularnewline
60 & 23338 & 22376.0292218597 & 961.970778140338 \tabularnewline
61 & 22968 & 23337.9364070349 & -369.936407034947 \tabularnewline
62 & 22084 & 22968.0244553718 & -884.02445537176 \tabularnewline
63 & 22676 & 22084.0584401705 & 591.941559829495 \tabularnewline
64 & 23189 & 22675.9608685422 & 513.039131457819 \tabularnewline
65 & 24735 & 23188.966084542 & 1546.03391545804 \tabularnewline
66 & 25326 & 24734.8977963957 & 591.1022036043 \tabularnewline
67 & 23702 & 25325.9609240295 & -1623.96092402947 \tabularnewline
68 & 22526 & 23702.107355122 & -1176.10735512204 \tabularnewline
69 & 22526 & 22526.0777488835 & -0.0777488834719406 \tabularnewline
70 & 22084 & 22526.0000051397 & -442.000005139744 \tabularnewline
71 & 21792 & 22084.0292192773 & -292.029219277258 \tabularnewline
72 & 22376 & 21792.0193051643 & 583.980694835689 \tabularnewline
73 & 21643 & 22375.9613948108 & -732.961394810776 \tabularnewline
74 & 21493 & 21643.0484538506 & -150.048453850603 \tabularnewline
75 & 21864 & 21493.0099192473 & 370.990080752661 \tabularnewline
76 & 22376 & 21863.9754749731 & 512.024525026929 \tabularnewline
77 & 23922 & 22375.9661516145 & 1546.03384838549 \tabularnewline
78 & 24222 & 23921.8977964001 & 300.102203599865 \tabularnewline
79 & 22305 & 24221.9801611552 & -1916.98016115522 \tabularnewline
80 & 20909 & 22305.1267257334 & -1396.12672573343 \tabularnewline
81 & 20246 & 20909.0922936955 & -663.092293695499 \tabularnewline
82 & 19584 & 20246.0438350166 & -662.04383501663 \tabularnewline
83 & 19213 & 19584.0437657062 & -371.043765706214 \tabularnewline
84 & 19947 & 19213.0245285759 & 733.975471424121 \tabularnewline
85 & 19506 & 19946.9514791119 & -440.951479111875 \tabularnewline
86 & 19584 & 19506.0291499624 & 77.9708500376109 \tabularnewline
87 & 19947 & 19583.994845584 & 363.005154415972 \tabularnewline
88 & 20246 & 19946.9760028323 & 299.023997167715 \tabularnewline
89 & 21714 & 20245.9802324322 & 1468.01976756782 \tabularnewline
90 & 21935 & 21713.902953674 & 221.097046326038 \tabularnewline
91 & 19584 & 21934.9853839461 & -2350.9853839461 \tabularnewline
92 & 18480 & 19584.1554164999 & -1104.15541649991 \tabularnewline
93 & 17375 & 18480.0729923594 & -1105.07299235944 \tabularnewline
94 & 16635 & 17375.0730530176 & -740.073053017597 \tabularnewline
95 & 16122 & 16635.0489239807 & -513.048923980714 \tabularnewline
96 & 16855 & 16122.0339161054 & 732.966083894609 \tabularnewline
97 & 16492 & 16854.9515458394 & -362.95154583942 \tabularnewline
98 & 17076 & 16492.0239936238 & 583.976006376186 \tabularnewline
99 & 17297 & 17075.9613951207 & 221.038604879283 \tabularnewline
100 & 17518 & 17296.9853878095 & 221.014612190509 \tabularnewline
101 & 18480 & 17517.9853893956 & 962.014610604427 \tabularnewline
102 & 19064 & 18479.9364041373 & 584.063595862684 \tabularnewline
103 & 16122 & 19063.9613893304 & -2941.96138933044 \tabularnewline
104 & 15388 & 16122.1944841279 & -734.194484127864 \tabularnewline
105 & 13543 & 15388.0485353664 & -1845.04853536639 \tabularnewline
106 & 12367 & 13543.1219705522 & -1176.12197055222 \tabularnewline
107 & 11997 & 12367.0777498497 & -370.077749849654 \tabularnewline
108 & 13030 & 11997.0244647155 & 1032.97553528449 \tabularnewline
109 & 12439 & 13029.9317131262 & -590.931713126212 \tabularnewline
110 & 13179 & 12439.0390646999 & 739.960935300078 \tabularnewline
111 & 13179 & 13178.951083431 & 0.0489165689523361 \tabularnewline
112 & 13251 & 13178.9999967663 & 72.0000032337266 \tabularnewline
113 & 14134 & 13250.9952402986 & 883.004759701433 \tabularnewline
114 & 14725 & 14133.9416272385 & 591.058372761523 \tabularnewline
115 & 11854 & 14724.960926927 & -2870.96092692699 \tabularnewline
116 & 10821 & 11854.189790503 & -1033.18979050304 \tabularnewline
117 & 9126 & 10821.0683010376 & -1695.06830103755 \tabularnewline
118 & 8022 & 9126.11205581466 & -1104.11205581466 \tabularnewline
119 & 7437 & 8022.072989493 & -585.072989493002 \tabularnewline
120 & 8905 & 7437.0386773975 & 1467.9613226025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235523&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]24442[/C][C]24514[/C][C]-72[/C][/ROW]
[ROW][C]3[/C][C]24364[/C][C]24442.0047597012[/C][C]-78.0047597012162[/C][/ROW]
[ROW][C]4[/C][C]24222[/C][C]24364.0051566576[/C][C]-142.005156657637[/C][/ROW]
[ROW][C]5[/C][C]25689[/C][C]24222.0093875294[/C][C]1466.9906124706[/C][/ROW]
[ROW][C]6[/C][C]25618[/C][C]25688.9030217083[/C][C]-70.9030217082764[/C][/ROW]
[ROW][C]7[/C][C]24514[/C][C]25618.0046871833[/C][C]-1104.00468718331[/C][/ROW]
[ROW][C]8[/C][C]23780[/C][C]24514.0729823952[/C][C]-734.072982395188[/C][/ROW]
[ROW][C]9[/C][C]23851[/C][C]23780.0485273343[/C][C]70.9514726657253[/C][/ROW]
[ROW][C]10[/C][C]23851[/C][C]23850.9953096137[/C][C]0.00469038626397378[/C][/ROW]
[ROW][C]11[/C][C]23922[/C][C]23850.9999996899[/C][C]71.0000003100686[/C][/ROW]
[ROW][C]12[/C][C]24072[/C][C]23921.9953064057[/C][C]150.004693594277[/C][/ROW]
[ROW][C]13[/C][C]24514[/C][C]24071.9900836455[/C][C]442.00991635448[/C][/ROW]
[ROW][C]14[/C][C]24735[/C][C]24513.9707800675[/C][C]221.029219932458[/C][/ROW]
[ROW][C]15[/C][C]25105[/C][C]24734.9853884299[/C][C]370.014611570103[/C][/ROW]
[ROW][C]16[/C][C]25397[/C][C]25104.9755394584[/C][C]292.024460541626[/C][/ROW]
[ROW][C]17[/C][C]26722[/C][C]25396.9806951503[/C][C]1325.01930484973[/C][/ROW]
[ROW][C]18[/C][C]26573[/C][C]26721.912407[/C][C]-148.912407000025[/C][/ROW]
[ROW][C]19[/C][C]25468[/C][C]26573.0098441467[/C][C]-1105.00984414673[/C][/ROW]
[ROW][C]20[/C][C]23851[/C][C]25468.0730488431[/C][C]-1617.07304884306[/C][/ROW]
[ROW][C]21[/C][C]24143[/C][C]23851.1068997855[/C][C]291.89310021446[/C][/ROW]
[ROW][C]22[/C][C]24442[/C][C]24142.9807038341[/C][C]299.019296165898[/C][/ROW]
[ROW][C]23[/C][C]24364[/C][C]24441.9802327429[/C][C]-77.9802327429425[/C][/ROW]
[ROW][C]24[/C][C]24735[/C][C]24364.0051550362[/C][C]370.994844963767[/C][/ROW]
[ROW][C]25[/C][C]24442[/C][C]24734.9754746581[/C][C]-292.97547465812[/C][/ROW]
[ROW][C]26[/C][C]24955[/C][C]24442.0193677184[/C][C]512.980632281622[/C][/ROW]
[ROW][C]27[/C][C]25176[/C][C]24954.9660884092[/C][C]221.033911590832[/C][/ROW]
[ROW][C]28[/C][C]25247[/C][C]25175.9853881197[/C][C]71.0146118802513[/C][/ROW]
[ROW][C]29[/C][C]26872[/C][C]25246.9953054398[/C][C]1625.0046945602[/C][/ROW]
[ROW][C]30[/C][C]26573[/C][C]26871.8925758775[/C][C]-298.89257587746[/C][/ROW]
[ROW][C]31[/C][C]25468[/C][C]26573.01975888[/C][C]-1105.01975887996[/C][/ROW]
[ROW][C]32[/C][C]23851[/C][C]25468.0730494985[/C][C]-1617.07304949849[/C][/ROW]
[ROW][C]33[/C][C]24143[/C][C]23851.1068997856[/C][C]291.893100214416[/C][/ROW]
[ROW][C]34[/C][C]23922[/C][C]24142.9807038341[/C][C]-220.980703834102[/C][/ROW]
[ROW][C]35[/C][C]24293[/C][C]23922.0146083628[/C][C]370.985391637154[/C][/ROW]
[ROW][C]36[/C][C]25105[/C][C]24292.9754752831[/C][C]812.024524716948[/C][/ROW]
[ROW][C]37[/C][C]25027[/C][C]25104.9463195261[/C][C]-77.9463195261269[/C][/ROW]
[ROW][C]38[/C][C]24884[/C][C]25027.0051527943[/C][C]-143.005152794332[/C][/ROW]
[ROW][C]39[/C][C]25247[/C][C]24884.0094536361[/C][C]362.99054636389[/C][/ROW]
[ROW][C]40[/C][C]25468[/C][C]25246.976003798[/C][C]221.02399620202[/C][/ROW]
[ROW][C]41[/C][C]26722[/C][C]25467.9853887752[/C][C]1254.01461122477[/C][/ROW]
[ROW][C]42[/C][C]26793[/C][C]26721.9171009046[/C][C]71.0828990954396[/C][/ROW]
[ROW][C]43[/C][C]25468[/C][C]26792.9953009255[/C][C]-1324.99530092554[/C][/ROW]
[ROW][C]44[/C][C]23559[/C][C]25468.0875914132[/C][C]-1909.08759141315[/C][/ROW]
[ROW][C]45[/C][C]23409[/C][C]23559.1262039796[/C][C]-150.126203979624[/C][/ROW]
[ROW][C]46[/C][C]23851[/C][C]23409.0099243872[/C][C]441.990075612834[/C][/ROW]
[ROW][C]47[/C][C]23481[/C][C]23850.9707813792[/C][C]-369.970781379154[/C][/ROW]
[ROW][C]48[/C][C]24663[/C][C]23481.0244576441[/C][C]1181.97554235585[/C][/ROW]
[ROW][C]49[/C][C]24663[/C][C]24662.9218631885[/C][C]0.0781368114949146[/C][/ROW]
[ROW][C]50[/C][C]24222[/C][C]24662.9999948346[/C][C]-440.999994834616[/C][/ROW]
[ROW][C]51[/C][C]24806[/C][C]24222.0291531696[/C][C]583.970846830383[/C][/ROW]
[ROW][C]52[/C][C]25176[/C][C]24805.9613954618[/C][C]370.038604538204[/C][/ROW]
[ROW][C]53[/C][C]26430[/C][C]25175.9755378723[/C][C]1254.02446212773[/C][/ROW]
[ROW][C]54[/C][C]26793[/C][C]26429.9171002533[/C][C]363.082899746652[/C][/ROW]
[ROW][C]55[/C][C]25247[/C][C]26792.9759976928[/C][C]-1545.97599769278[/C][/ROW]
[ROW][C]56[/C][C]23409[/C][C]25247.1021997755[/C][C]-1838.10219977553[/C][/ROW]
[ROW][C]57[/C][C]23409[/C][C]23409.1215113511[/C][C]-0.121511351080699[/C][/ROW]
[ROW][C]58[/C][C]22818[/C][C]23409.0000080327[/C][C]-591.000008032748[/C][/ROW]
[ROW][C]59[/C][C]22376[/C][C]22818.0390692147[/C][C]-442.03906921469[/C][/ROW]
[ROW][C]60[/C][C]23338[/C][C]22376.0292218597[/C][C]961.970778140338[/C][/ROW]
[ROW][C]61[/C][C]22968[/C][C]23337.9364070349[/C][C]-369.936407034947[/C][/ROW]
[ROW][C]62[/C][C]22084[/C][C]22968.0244553718[/C][C]-884.02445537176[/C][/ROW]
[ROW][C]63[/C][C]22676[/C][C]22084.0584401705[/C][C]591.941559829495[/C][/ROW]
[ROW][C]64[/C][C]23189[/C][C]22675.9608685422[/C][C]513.039131457819[/C][/ROW]
[ROW][C]65[/C][C]24735[/C][C]23188.966084542[/C][C]1546.03391545804[/C][/ROW]
[ROW][C]66[/C][C]25326[/C][C]24734.8977963957[/C][C]591.1022036043[/C][/ROW]
[ROW][C]67[/C][C]23702[/C][C]25325.9609240295[/C][C]-1623.96092402947[/C][/ROW]
[ROW][C]68[/C][C]22526[/C][C]23702.107355122[/C][C]-1176.10735512204[/C][/ROW]
[ROW][C]69[/C][C]22526[/C][C]22526.0777488835[/C][C]-0.0777488834719406[/C][/ROW]
[ROW][C]70[/C][C]22084[/C][C]22526.0000051397[/C][C]-442.000005139744[/C][/ROW]
[ROW][C]71[/C][C]21792[/C][C]22084.0292192773[/C][C]-292.029219277258[/C][/ROW]
[ROW][C]72[/C][C]22376[/C][C]21792.0193051643[/C][C]583.980694835689[/C][/ROW]
[ROW][C]73[/C][C]21643[/C][C]22375.9613948108[/C][C]-732.961394810776[/C][/ROW]
[ROW][C]74[/C][C]21493[/C][C]21643.0484538506[/C][C]-150.048453850603[/C][/ROW]
[ROW][C]75[/C][C]21864[/C][C]21493.0099192473[/C][C]370.990080752661[/C][/ROW]
[ROW][C]76[/C][C]22376[/C][C]21863.9754749731[/C][C]512.024525026929[/C][/ROW]
[ROW][C]77[/C][C]23922[/C][C]22375.9661516145[/C][C]1546.03384838549[/C][/ROW]
[ROW][C]78[/C][C]24222[/C][C]23921.8977964001[/C][C]300.102203599865[/C][/ROW]
[ROW][C]79[/C][C]22305[/C][C]24221.9801611552[/C][C]-1916.98016115522[/C][/ROW]
[ROW][C]80[/C][C]20909[/C][C]22305.1267257334[/C][C]-1396.12672573343[/C][/ROW]
[ROW][C]81[/C][C]20246[/C][C]20909.0922936955[/C][C]-663.092293695499[/C][/ROW]
[ROW][C]82[/C][C]19584[/C][C]20246.0438350166[/C][C]-662.04383501663[/C][/ROW]
[ROW][C]83[/C][C]19213[/C][C]19584.0437657062[/C][C]-371.043765706214[/C][/ROW]
[ROW][C]84[/C][C]19947[/C][C]19213.0245285759[/C][C]733.975471424121[/C][/ROW]
[ROW][C]85[/C][C]19506[/C][C]19946.9514791119[/C][C]-440.951479111875[/C][/ROW]
[ROW][C]86[/C][C]19584[/C][C]19506.0291499624[/C][C]77.9708500376109[/C][/ROW]
[ROW][C]87[/C][C]19947[/C][C]19583.994845584[/C][C]363.005154415972[/C][/ROW]
[ROW][C]88[/C][C]20246[/C][C]19946.9760028323[/C][C]299.023997167715[/C][/ROW]
[ROW][C]89[/C][C]21714[/C][C]20245.9802324322[/C][C]1468.01976756782[/C][/ROW]
[ROW][C]90[/C][C]21935[/C][C]21713.902953674[/C][C]221.097046326038[/C][/ROW]
[ROW][C]91[/C][C]19584[/C][C]21934.9853839461[/C][C]-2350.9853839461[/C][/ROW]
[ROW][C]92[/C][C]18480[/C][C]19584.1554164999[/C][C]-1104.15541649991[/C][/ROW]
[ROW][C]93[/C][C]17375[/C][C]18480.0729923594[/C][C]-1105.07299235944[/C][/ROW]
[ROW][C]94[/C][C]16635[/C][C]17375.0730530176[/C][C]-740.073053017597[/C][/ROW]
[ROW][C]95[/C][C]16122[/C][C]16635.0489239807[/C][C]-513.048923980714[/C][/ROW]
[ROW][C]96[/C][C]16855[/C][C]16122.0339161054[/C][C]732.966083894609[/C][/ROW]
[ROW][C]97[/C][C]16492[/C][C]16854.9515458394[/C][C]-362.95154583942[/C][/ROW]
[ROW][C]98[/C][C]17076[/C][C]16492.0239936238[/C][C]583.976006376186[/C][/ROW]
[ROW][C]99[/C][C]17297[/C][C]17075.9613951207[/C][C]221.038604879283[/C][/ROW]
[ROW][C]100[/C][C]17518[/C][C]17296.9853878095[/C][C]221.014612190509[/C][/ROW]
[ROW][C]101[/C][C]18480[/C][C]17517.9853893956[/C][C]962.014610604427[/C][/ROW]
[ROW][C]102[/C][C]19064[/C][C]18479.9364041373[/C][C]584.063595862684[/C][/ROW]
[ROW][C]103[/C][C]16122[/C][C]19063.9613893304[/C][C]-2941.96138933044[/C][/ROW]
[ROW][C]104[/C][C]15388[/C][C]16122.1944841279[/C][C]-734.194484127864[/C][/ROW]
[ROW][C]105[/C][C]13543[/C][C]15388.0485353664[/C][C]-1845.04853536639[/C][/ROW]
[ROW][C]106[/C][C]12367[/C][C]13543.1219705522[/C][C]-1176.12197055222[/C][/ROW]
[ROW][C]107[/C][C]11997[/C][C]12367.0777498497[/C][C]-370.077749849654[/C][/ROW]
[ROW][C]108[/C][C]13030[/C][C]11997.0244647155[/C][C]1032.97553528449[/C][/ROW]
[ROW][C]109[/C][C]12439[/C][C]13029.9317131262[/C][C]-590.931713126212[/C][/ROW]
[ROW][C]110[/C][C]13179[/C][C]12439.0390646999[/C][C]739.960935300078[/C][/ROW]
[ROW][C]111[/C][C]13179[/C][C]13178.951083431[/C][C]0.0489165689523361[/C][/ROW]
[ROW][C]112[/C][C]13251[/C][C]13178.9999967663[/C][C]72.0000032337266[/C][/ROW]
[ROW][C]113[/C][C]14134[/C][C]13250.9952402986[/C][C]883.004759701433[/C][/ROW]
[ROW][C]114[/C][C]14725[/C][C]14133.9416272385[/C][C]591.058372761523[/C][/ROW]
[ROW][C]115[/C][C]11854[/C][C]14724.960926927[/C][C]-2870.96092692699[/C][/ROW]
[ROW][C]116[/C][C]10821[/C][C]11854.189790503[/C][C]-1033.18979050304[/C][/ROW]
[ROW][C]117[/C][C]9126[/C][C]10821.0683010376[/C][C]-1695.06830103755[/C][/ROW]
[ROW][C]118[/C][C]8022[/C][C]9126.11205581466[/C][C]-1104.11205581466[/C][/ROW]
[ROW][C]119[/C][C]7437[/C][C]8022.072989493[/C][C]-585.072989493002[/C][/ROW]
[ROW][C]120[/C][C]8905[/C][C]7437.0386773975[/C][C]1467.9613226025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235523&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235523&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22444224514-72
32436424442.0047597012-78.0047597012162
42422224364.0051566576-142.005156657637
52568924222.00938752941466.9906124706
62561825688.9030217083-70.9030217082764
72451425618.0046871833-1104.00468718331
82378024514.0729823952-734.072982395188
92385123780.048527334370.9514726657253
102385123850.99530961370.00469038626397378
112392223850.999999689971.0000003100686
122407223921.9953064057150.004693594277
132451424071.9900836455442.00991635448
142473524513.9707800675221.029219932458
152510524734.9853884299370.014611570103
162539725104.9755394584292.024460541626
172672225396.98069515031325.01930484973
182657326721.912407-148.912407000025
192546826573.0098441467-1105.00984414673
202385125468.0730488431-1617.07304884306
212414323851.1068997855291.89310021446
222444224142.9807038341299.019296165898
232436424441.9802327429-77.9802327429425
242473524364.0051550362370.994844963767
252444224734.9754746581-292.97547465812
262495524442.0193677184512.980632281622
272517624954.9660884092221.033911590832
282524725175.985388119771.0146118802513
292687225246.99530543981625.0046945602
302657326871.8925758775-298.89257587746
312546826573.01975888-1105.01975887996
322385125468.0730494985-1617.07304949849
332414323851.1068997856291.893100214416
342392224142.9807038341-220.980703834102
352429323922.0146083628370.985391637154
362510524292.9754752831812.024524716948
372502725104.9463195261-77.9463195261269
382488425027.0051527943-143.005152794332
392524724884.0094536361362.99054636389
402546825246.976003798221.02399620202
412672225467.98538877521254.01461122477
422679326721.917100904671.0828990954396
432546826792.9953009255-1324.99530092554
442355925468.0875914132-1909.08759141315
452340923559.1262039796-150.126203979624
462385123409.0099243872441.990075612834
472348123850.9707813792-369.970781379154
482466323481.02445764411181.97554235585
492466324662.92186318850.0781368114949146
502422224662.9999948346-440.999994834616
512480624222.0291531696583.970846830383
522517624805.9613954618370.038604538204
532643025175.97553787231254.02446212773
542679326429.9171002533363.082899746652
552524726792.9759976928-1545.97599769278
562340925247.1021997755-1838.10219977553
572340923409.1215113511-0.121511351080699
582281823409.0000080327-591.000008032748
592237622818.0390692147-442.03906921469
602333822376.0292218597961.970778140338
612296823337.9364070349-369.936407034947
622208422968.0244553718-884.02445537176
632267622084.0584401705591.941559829495
642318922675.9608685422513.039131457819
652473523188.9660845421546.03391545804
662532624734.8977963957591.1022036043
672370225325.9609240295-1623.96092402947
682252623702.107355122-1176.10735512204
692252622526.0777488835-0.0777488834719406
702208422526.0000051397-442.000005139744
712179222084.0292192773-292.029219277258
722237621792.0193051643583.980694835689
732164322375.9613948108-732.961394810776
742149321643.0484538506-150.048453850603
752186421493.0099192473370.990080752661
762237621863.9754749731512.024525026929
772392222375.96615161451546.03384838549
782422223921.8977964001300.102203599865
792230524221.9801611552-1916.98016115522
802090922305.1267257334-1396.12672573343
812024620909.0922936955-663.092293695499
821958420246.0438350166-662.04383501663
831921319584.0437657062-371.043765706214
841994719213.0245285759733.975471424121
851950619946.9514791119-440.951479111875
861958419506.029149962477.9708500376109
871994719583.994845584363.005154415972
882024619946.9760028323299.023997167715
892171420245.98023243221468.01976756782
902193521713.902953674221.097046326038
911958421934.9853839461-2350.9853839461
921848019584.1554164999-1104.15541649991
931737518480.0729923594-1105.07299235944
941663517375.0730530176-740.073053017597
951612216635.0489239807-513.048923980714
961685516122.0339161054732.966083894609
971649216854.9515458394-362.95154583942
981707616492.0239936238583.976006376186
991729717075.9613951207221.038604879283
1001751817296.9853878095221.014612190509
1011848017517.9853893956962.014610604427
1021906418479.9364041373584.063595862684
1031612219063.9613893304-2941.96138933044
1041538816122.1944841279-734.194484127864
1051354315388.0485353664-1845.04853536639
1061236713543.1219705522-1176.12197055222
1071199712367.0777498497-370.077749849654
1081303011997.02446471551032.97553528449
1091243913029.9317131262-590.931713126212
1101317912439.0390646999739.960935300078
1111317913178.9510834310.0489165689523361
1121325113178.999996766372.0000032337266
1131413413250.9952402986883.004759701433
1141472514133.9416272385591.058372761523
1151185414724.960926927-2870.96092692699
1161082111854.189790503-1033.18979050304
117912610821.0683010376-1695.06830103755
11880229126.11205581466-1104.11205581466
11974378022.072989493-585.072989493002
12089057437.03867739751467.9613226025







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1218904.902957537587089.7418029938210720.0641120813
1228904.902957537586337.9622826151611471.84363246
1238904.902957537585761.0901704623612048.7157446128
1248904.902957537585274.7606391450712535.0452759301
1258904.902957537584846.2938776444912963.5120374307
1268904.902957537584458.9292649706613350.8766501045
1278904.902957537584102.710074426413707.0958406488
1288904.902957537583771.148882963114038.6570321121
1298904.902957537583459.7394788331414350.066436242
1308904.902957537583165.2008989440214644.6050161311
1318904.902957537582885.0562706999814924.7496443752
1328904.902957537582617.3813039258715192.4246111493

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 8904.90295753758 & 7089.74180299382 & 10720.0641120813 \tabularnewline
122 & 8904.90295753758 & 6337.96228261516 & 11471.84363246 \tabularnewline
123 & 8904.90295753758 & 5761.09017046236 & 12048.7157446128 \tabularnewline
124 & 8904.90295753758 & 5274.76063914507 & 12535.0452759301 \tabularnewline
125 & 8904.90295753758 & 4846.29387764449 & 12963.5120374307 \tabularnewline
126 & 8904.90295753758 & 4458.92926497066 & 13350.8766501045 \tabularnewline
127 & 8904.90295753758 & 4102.7100744264 & 13707.0958406488 \tabularnewline
128 & 8904.90295753758 & 3771.1488829631 & 14038.6570321121 \tabularnewline
129 & 8904.90295753758 & 3459.73947883314 & 14350.066436242 \tabularnewline
130 & 8904.90295753758 & 3165.20089894402 & 14644.6050161311 \tabularnewline
131 & 8904.90295753758 & 2885.05627069998 & 14924.7496443752 \tabularnewline
132 & 8904.90295753758 & 2617.38130392587 & 15192.4246111493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235523&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]8904.90295753758[/C][C]7089.74180299382[/C][C]10720.0641120813[/C][/ROW]
[ROW][C]122[/C][C]8904.90295753758[/C][C]6337.96228261516[/C][C]11471.84363246[/C][/ROW]
[ROW][C]123[/C][C]8904.90295753758[/C][C]5761.09017046236[/C][C]12048.7157446128[/C][/ROW]
[ROW][C]124[/C][C]8904.90295753758[/C][C]5274.76063914507[/C][C]12535.0452759301[/C][/ROW]
[ROW][C]125[/C][C]8904.90295753758[/C][C]4846.29387764449[/C][C]12963.5120374307[/C][/ROW]
[ROW][C]126[/C][C]8904.90295753758[/C][C]4458.92926497066[/C][C]13350.8766501045[/C][/ROW]
[ROW][C]127[/C][C]8904.90295753758[/C][C]4102.7100744264[/C][C]13707.0958406488[/C][/ROW]
[ROW][C]128[/C][C]8904.90295753758[/C][C]3771.1488829631[/C][C]14038.6570321121[/C][/ROW]
[ROW][C]129[/C][C]8904.90295753758[/C][C]3459.73947883314[/C][C]14350.066436242[/C][/ROW]
[ROW][C]130[/C][C]8904.90295753758[/C][C]3165.20089894402[/C][C]14644.6050161311[/C][/ROW]
[ROW][C]131[/C][C]8904.90295753758[/C][C]2885.05627069998[/C][C]14924.7496443752[/C][/ROW]
[ROW][C]132[/C][C]8904.90295753758[/C][C]2617.38130392587[/C][C]15192.4246111493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235523&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235523&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1218904.902957537587089.7418029938210720.0641120813
1228904.902957537586337.9622826151611471.84363246
1238904.902957537585761.0901704623612048.7157446128
1248904.902957537585274.7606391450712535.0452759301
1258904.902957537584846.2938776444912963.5120374307
1268904.902957537584458.9292649706613350.8766501045
1278904.902957537584102.710074426413707.0958406488
1288904.902957537583771.148882963114038.6570321121
1298904.902957537583459.7394788331414350.066436242
1308904.902957537583165.2008989440214644.6050161311
1318904.902957537582885.0562706999814924.7496443752
1328904.902957537582617.3813039258715192.4246111493



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
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,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')