Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 22 Jul 2016 11:19:03 +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/2016/Jul/22/t1469182775s4my8wxboaesvyt.htm/, Retrieved Mon, 29 Apr 2024 05:16:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295928, Retrieved Mon, 29 Apr 2024 05:16:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-07-22 10:19:03] [b1d105767b629000b6b6bd83f6a3d689] [Current]
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Dataseries X:
14724
14404
14058
13427
19946
19631
14724
11462
11778
11778
12093
12760
13742
13427
11462
11778
20929
22893
17666
14724
15387
15707
17351
18964
19315
16022
16369
12093
24222
27800
19631
17004
18649
20613
23555
27164
27164
24853
23871
17982
27800
32391
28462
24222
24853
27164
30426
34355
31724
30111
30111
24853
32391
37297
33373
29129
30426
35653
37964
41222
38595
34355
33373
25520
30742
36315
30111
26502
30111
33689
35653
40906
38280
31724
32391
26186
31409
36000
30742
27164
30426
34355
33689
41542
40244
35017
35333
28462
32706
39262
34355
31409
36315
39262
36982
47431
44835
38946
37297
29764
34035
37964
33053
33053
38595
41542
39924
51355
48413
42871
40560
32391
35333
40560
36631
35653
40244
44168
39924
50057




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295928&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]1 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=295928&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295928&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.86027857545682
beta0.00780892603310416
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.86027857545682 \tabularnewline
beta & 0.00780892603310416 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295928&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]0.86027857545682[/C][/ROW]
[ROW][C]beta[/C][C]0.00780892603310416[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295928&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295928&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
alpha0.86027857545682
beta0.00780892603310416
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31405814084-26
41342713741.4580928923-314.458092892268
51994613148.64938569836797.35061430173
61963118719.6409358627911.359064137327
71472419233.1624351971-4509.16243519706
81146215053.2335360333-3591.23353603331
91177811638.8538280692139.146171930764
101177811434.574624542343.425375457971
111209311408.3395239848684.660476015151
121276011680.26111721711079.73888278287
131374212299.31372517521442.68627482476
141342713240.2939510606186.706048939426
151146213102.0355609795-1640.03556097948
161177811381.2529852039396.747014796052
172092911415.33610986499513.66389013508
182289319356.41888034353536.5811196565
191766622179.3036273591-4513.30362735908
201472418046.7252868878-3322.72528688777
211538714916.0544091984470.945590801641
221570715052.1610525874654.838947412649
231735115350.86632181542000.13367818461
241896416820.33642715892143.66357284106
251931518427.6830399264887.316960073604
261602218960.1824421874-2938.18244218738
271636916181.9483941593187.051605840687
281209316093.5428258982-4000.54282589816
292422212375.764431631511846.2355683685
302780022370.21123446955429.7887655305
311963126881.2028383021-7250.20283830209
321700420435.1635404613-3431.16354046134
331864917251.51188133911397.48811866086
342061318231.23391092642381.76608907364
352355520073.70954227583481.2904577242
362716422885.46922440914278.53077559095
372716426411.8202070099752.179792990097
382485326909.580022087-2056.58002208703
392387124977.2081449209-1106.20814492086
401798223854.9894900602-5872.98949006016
412780018592.55709728549207.44290271457
423239126365.35183718216025.64816281786
432846231441.396141982-2979.39614198196
442422228750.5786186961-4528.57861869614
452485324696.6102813597156.389718640257
462716424674.07043427462489.92956572541
473042626675.75190033593750.24809966406
483435529786.85201020624568.14798979385
493172433632.2620134532-1908.26201345315
503011131893.3358237-1782.33582370003
513011130250.7677692238-139.767769223847
522485330020.3268815883-5167.32688158834
533239125430.07126673836960.92873326166
543729731320.25660237485976.74339762524
553337336403.9192556588-3030.91925565875
562912933718.121447113-4589.12144711302
573042629661.0066394224764.993360577588
583565330215.06120332075437.93879667935
593796434825.68187691163138.31812308837
604122237479.07090927263742.92909072735
613859540677.7382463729-2082.73824637289
623435538850.7172588257-4495.71725882569
633337334917.6605617225-1544.66056172251
642552033512.9579154168-7992.95791541682
653074226507.22770112454234.77229887551
663631530049.20038921046265.79961078964
673011135380.5150728694-5269.51507286936
682650230752.8458518984-4250.84585189842
693011126972.95938490313138.04061509692
703368929570.65453362714118.34546637294
713565333039.35137767462613.6486223254
724090635231.14786823755674.85213176251
733828040094.5549684839-1814.55496848393
743172438502.795686219-6778.79568621897
753239132594.8675265204-203.867526520367
762618632341.8396459556-6155.83964595564
773140926927.10365110244481.89634889764
783600030693.89273927895306.10726072106
793074235205.3784585743-4463.37845857426
802716431282.4006054789-4118.40060547888
813042627628.53300363782797.46699636221
823435529943.03109895174411.96890104833
833368933676.089545964112.9104540358603
844154233624.81898934587917.18101065416
854024440426.6094956156-182.609495615638
863501740259.0970201308-5242.0970201308
873533335703.8001938028-370.800193802825
882846235336.6846811197-6874.68468111972
893270629328.23357414263377.76642585737
903926232162.43783455757099.56216544251
913435538246.1170381779-3891.11703817786
923140934848.6104457475-3439.61044574748
933631531816.41850836344498.58149163661
943926235643.50382618223618.49617381778
953698238737.7791214103-1755.77912141029
964743137196.885457679510234.1145423205
974483546039.3916992889-1204.39169928887
983894645033.5051611114-6087.50516111144
993729739785.8857729207-2488.88577292074
1002976437617.361579935-7853.36157993499
1013403530781.13606267843253.86393732156
1023796433522.07766627494441.92233372513
1033305337314.9206304723-4261.9206304723
1043305333591.4030174063-538.40301740633
1053859533067.53092053715527.46907946288
1064154237799.13134796963742.86865203043
1073992441020.6222987058-1096.6222987058
1085135540071.435922363111283.5640776369
1094841349848.4599565892-1435.45995658917
1104287148673.9369062492-5802.93690624922
1114056043703.1837373855-3143.18373738547
1123239140999.4437932851-8608.44379328506
1133533333536.22746447571796.77253552434
1144056035036.4662678815523.53373211897
1153663139779.8641653842-3148.86416538425
1163565337041.4303511419-1388.43035114188
1174024435808.13276151894435.86723848111
1184416839615.15310388454552.84689611549
1193992443553.3938900278-3629.39389002776
1205005740428.24649847819628.75350152194

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 14058 & 14084 & -26 \tabularnewline
4 & 13427 & 13741.4580928923 & -314.458092892268 \tabularnewline
5 & 19946 & 13148.6493856983 & 6797.35061430173 \tabularnewline
6 & 19631 & 18719.6409358627 & 911.359064137327 \tabularnewline
7 & 14724 & 19233.1624351971 & -4509.16243519706 \tabularnewline
8 & 11462 & 15053.2335360333 & -3591.23353603331 \tabularnewline
9 & 11778 & 11638.8538280692 & 139.146171930764 \tabularnewline
10 & 11778 & 11434.574624542 & 343.425375457971 \tabularnewline
11 & 12093 & 11408.3395239848 & 684.660476015151 \tabularnewline
12 & 12760 & 11680.2611172171 & 1079.73888278287 \tabularnewline
13 & 13742 & 12299.3137251752 & 1442.68627482476 \tabularnewline
14 & 13427 & 13240.2939510606 & 186.706048939426 \tabularnewline
15 & 11462 & 13102.0355609795 & -1640.03556097948 \tabularnewline
16 & 11778 & 11381.2529852039 & 396.747014796052 \tabularnewline
17 & 20929 & 11415.3361098649 & 9513.66389013508 \tabularnewline
18 & 22893 & 19356.4188803435 & 3536.5811196565 \tabularnewline
19 & 17666 & 22179.3036273591 & -4513.30362735908 \tabularnewline
20 & 14724 & 18046.7252868878 & -3322.72528688777 \tabularnewline
21 & 15387 & 14916.0544091984 & 470.945590801641 \tabularnewline
22 & 15707 & 15052.1610525874 & 654.838947412649 \tabularnewline
23 & 17351 & 15350.8663218154 & 2000.13367818461 \tabularnewline
24 & 18964 & 16820.3364271589 & 2143.66357284106 \tabularnewline
25 & 19315 & 18427.6830399264 & 887.316960073604 \tabularnewline
26 & 16022 & 18960.1824421874 & -2938.18244218738 \tabularnewline
27 & 16369 & 16181.9483941593 & 187.051605840687 \tabularnewline
28 & 12093 & 16093.5428258982 & -4000.54282589816 \tabularnewline
29 & 24222 & 12375.7644316315 & 11846.2355683685 \tabularnewline
30 & 27800 & 22370.2112344695 & 5429.7887655305 \tabularnewline
31 & 19631 & 26881.2028383021 & -7250.20283830209 \tabularnewline
32 & 17004 & 20435.1635404613 & -3431.16354046134 \tabularnewline
33 & 18649 & 17251.5118813391 & 1397.48811866086 \tabularnewline
34 & 20613 & 18231.2339109264 & 2381.76608907364 \tabularnewline
35 & 23555 & 20073.7095422758 & 3481.2904577242 \tabularnewline
36 & 27164 & 22885.4692244091 & 4278.53077559095 \tabularnewline
37 & 27164 & 26411.8202070099 & 752.179792990097 \tabularnewline
38 & 24853 & 26909.580022087 & -2056.58002208703 \tabularnewline
39 & 23871 & 24977.2081449209 & -1106.20814492086 \tabularnewline
40 & 17982 & 23854.9894900602 & -5872.98949006016 \tabularnewline
41 & 27800 & 18592.5570972854 & 9207.44290271457 \tabularnewline
42 & 32391 & 26365.3518371821 & 6025.64816281786 \tabularnewline
43 & 28462 & 31441.396141982 & -2979.39614198196 \tabularnewline
44 & 24222 & 28750.5786186961 & -4528.57861869614 \tabularnewline
45 & 24853 & 24696.6102813597 & 156.389718640257 \tabularnewline
46 & 27164 & 24674.0704342746 & 2489.92956572541 \tabularnewline
47 & 30426 & 26675.7519003359 & 3750.24809966406 \tabularnewline
48 & 34355 & 29786.8520102062 & 4568.14798979385 \tabularnewline
49 & 31724 & 33632.2620134532 & -1908.26201345315 \tabularnewline
50 & 30111 & 31893.3358237 & -1782.33582370003 \tabularnewline
51 & 30111 & 30250.7677692238 & -139.767769223847 \tabularnewline
52 & 24853 & 30020.3268815883 & -5167.32688158834 \tabularnewline
53 & 32391 & 25430.0712667383 & 6960.92873326166 \tabularnewline
54 & 37297 & 31320.2566023748 & 5976.74339762524 \tabularnewline
55 & 33373 & 36403.9192556588 & -3030.91925565875 \tabularnewline
56 & 29129 & 33718.121447113 & -4589.12144711302 \tabularnewline
57 & 30426 & 29661.0066394224 & 764.993360577588 \tabularnewline
58 & 35653 & 30215.0612033207 & 5437.93879667935 \tabularnewline
59 & 37964 & 34825.6818769116 & 3138.31812308837 \tabularnewline
60 & 41222 & 37479.0709092726 & 3742.92909072735 \tabularnewline
61 & 38595 & 40677.7382463729 & -2082.73824637289 \tabularnewline
62 & 34355 & 38850.7172588257 & -4495.71725882569 \tabularnewline
63 & 33373 & 34917.6605617225 & -1544.66056172251 \tabularnewline
64 & 25520 & 33512.9579154168 & -7992.95791541682 \tabularnewline
65 & 30742 & 26507.2277011245 & 4234.77229887551 \tabularnewline
66 & 36315 & 30049.2003892104 & 6265.79961078964 \tabularnewline
67 & 30111 & 35380.5150728694 & -5269.51507286936 \tabularnewline
68 & 26502 & 30752.8458518984 & -4250.84585189842 \tabularnewline
69 & 30111 & 26972.9593849031 & 3138.04061509692 \tabularnewline
70 & 33689 & 29570.6545336271 & 4118.34546637294 \tabularnewline
71 & 35653 & 33039.3513776746 & 2613.6486223254 \tabularnewline
72 & 40906 & 35231.1478682375 & 5674.85213176251 \tabularnewline
73 & 38280 & 40094.5549684839 & -1814.55496848393 \tabularnewline
74 & 31724 & 38502.795686219 & -6778.79568621897 \tabularnewline
75 & 32391 & 32594.8675265204 & -203.867526520367 \tabularnewline
76 & 26186 & 32341.8396459556 & -6155.83964595564 \tabularnewline
77 & 31409 & 26927.1036511024 & 4481.89634889764 \tabularnewline
78 & 36000 & 30693.8927392789 & 5306.10726072106 \tabularnewline
79 & 30742 & 35205.3784585743 & -4463.37845857426 \tabularnewline
80 & 27164 & 31282.4006054789 & -4118.40060547888 \tabularnewline
81 & 30426 & 27628.5330036378 & 2797.46699636221 \tabularnewline
82 & 34355 & 29943.0310989517 & 4411.96890104833 \tabularnewline
83 & 33689 & 33676.0895459641 & 12.9104540358603 \tabularnewline
84 & 41542 & 33624.8189893458 & 7917.18101065416 \tabularnewline
85 & 40244 & 40426.6094956156 & -182.609495615638 \tabularnewline
86 & 35017 & 40259.0970201308 & -5242.0970201308 \tabularnewline
87 & 35333 & 35703.8001938028 & -370.800193802825 \tabularnewline
88 & 28462 & 35336.6846811197 & -6874.68468111972 \tabularnewline
89 & 32706 & 29328.2335741426 & 3377.76642585737 \tabularnewline
90 & 39262 & 32162.4378345575 & 7099.56216544251 \tabularnewline
91 & 34355 & 38246.1170381779 & -3891.11703817786 \tabularnewline
92 & 31409 & 34848.6104457475 & -3439.61044574748 \tabularnewline
93 & 36315 & 31816.4185083634 & 4498.58149163661 \tabularnewline
94 & 39262 & 35643.5038261822 & 3618.49617381778 \tabularnewline
95 & 36982 & 38737.7791214103 & -1755.77912141029 \tabularnewline
96 & 47431 & 37196.8854576795 & 10234.1145423205 \tabularnewline
97 & 44835 & 46039.3916992889 & -1204.39169928887 \tabularnewline
98 & 38946 & 45033.5051611114 & -6087.50516111144 \tabularnewline
99 & 37297 & 39785.8857729207 & -2488.88577292074 \tabularnewline
100 & 29764 & 37617.361579935 & -7853.36157993499 \tabularnewline
101 & 34035 & 30781.1360626784 & 3253.86393732156 \tabularnewline
102 & 37964 & 33522.0776662749 & 4441.92233372513 \tabularnewline
103 & 33053 & 37314.9206304723 & -4261.9206304723 \tabularnewline
104 & 33053 & 33591.4030174063 & -538.40301740633 \tabularnewline
105 & 38595 & 33067.5309205371 & 5527.46907946288 \tabularnewline
106 & 41542 & 37799.1313479696 & 3742.86865203043 \tabularnewline
107 & 39924 & 41020.6222987058 & -1096.6222987058 \tabularnewline
108 & 51355 & 40071.4359223631 & 11283.5640776369 \tabularnewline
109 & 48413 & 49848.4599565892 & -1435.45995658917 \tabularnewline
110 & 42871 & 48673.9369062492 & -5802.93690624922 \tabularnewline
111 & 40560 & 43703.1837373855 & -3143.18373738547 \tabularnewline
112 & 32391 & 40999.4437932851 & -8608.44379328506 \tabularnewline
113 & 35333 & 33536.2274644757 & 1796.77253552434 \tabularnewline
114 & 40560 & 35036.466267881 & 5523.53373211897 \tabularnewline
115 & 36631 & 39779.8641653842 & -3148.86416538425 \tabularnewline
116 & 35653 & 37041.4303511419 & -1388.43035114188 \tabularnewline
117 & 40244 & 35808.1327615189 & 4435.86723848111 \tabularnewline
118 & 44168 & 39615.1531038845 & 4552.84689611549 \tabularnewline
119 & 39924 & 43553.3938900278 & -3629.39389002776 \tabularnewline
120 & 50057 & 40428.2464984781 & 9628.75350152194 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295928&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]3[/C][C]14058[/C][C]14084[/C][C]-26[/C][/ROW]
[ROW][C]4[/C][C]13427[/C][C]13741.4580928923[/C][C]-314.458092892268[/C][/ROW]
[ROW][C]5[/C][C]19946[/C][C]13148.6493856983[/C][C]6797.35061430173[/C][/ROW]
[ROW][C]6[/C][C]19631[/C][C]18719.6409358627[/C][C]911.359064137327[/C][/ROW]
[ROW][C]7[/C][C]14724[/C][C]19233.1624351971[/C][C]-4509.16243519706[/C][/ROW]
[ROW][C]8[/C][C]11462[/C][C]15053.2335360333[/C][C]-3591.23353603331[/C][/ROW]
[ROW][C]9[/C][C]11778[/C][C]11638.8538280692[/C][C]139.146171930764[/C][/ROW]
[ROW][C]10[/C][C]11778[/C][C]11434.574624542[/C][C]343.425375457971[/C][/ROW]
[ROW][C]11[/C][C]12093[/C][C]11408.3395239848[/C][C]684.660476015151[/C][/ROW]
[ROW][C]12[/C][C]12760[/C][C]11680.2611172171[/C][C]1079.73888278287[/C][/ROW]
[ROW][C]13[/C][C]13742[/C][C]12299.3137251752[/C][C]1442.68627482476[/C][/ROW]
[ROW][C]14[/C][C]13427[/C][C]13240.2939510606[/C][C]186.706048939426[/C][/ROW]
[ROW][C]15[/C][C]11462[/C][C]13102.0355609795[/C][C]-1640.03556097948[/C][/ROW]
[ROW][C]16[/C][C]11778[/C][C]11381.2529852039[/C][C]396.747014796052[/C][/ROW]
[ROW][C]17[/C][C]20929[/C][C]11415.3361098649[/C][C]9513.66389013508[/C][/ROW]
[ROW][C]18[/C][C]22893[/C][C]19356.4188803435[/C][C]3536.5811196565[/C][/ROW]
[ROW][C]19[/C][C]17666[/C][C]22179.3036273591[/C][C]-4513.30362735908[/C][/ROW]
[ROW][C]20[/C][C]14724[/C][C]18046.7252868878[/C][C]-3322.72528688777[/C][/ROW]
[ROW][C]21[/C][C]15387[/C][C]14916.0544091984[/C][C]470.945590801641[/C][/ROW]
[ROW][C]22[/C][C]15707[/C][C]15052.1610525874[/C][C]654.838947412649[/C][/ROW]
[ROW][C]23[/C][C]17351[/C][C]15350.8663218154[/C][C]2000.13367818461[/C][/ROW]
[ROW][C]24[/C][C]18964[/C][C]16820.3364271589[/C][C]2143.66357284106[/C][/ROW]
[ROW][C]25[/C][C]19315[/C][C]18427.6830399264[/C][C]887.316960073604[/C][/ROW]
[ROW][C]26[/C][C]16022[/C][C]18960.1824421874[/C][C]-2938.18244218738[/C][/ROW]
[ROW][C]27[/C][C]16369[/C][C]16181.9483941593[/C][C]187.051605840687[/C][/ROW]
[ROW][C]28[/C][C]12093[/C][C]16093.5428258982[/C][C]-4000.54282589816[/C][/ROW]
[ROW][C]29[/C][C]24222[/C][C]12375.7644316315[/C][C]11846.2355683685[/C][/ROW]
[ROW][C]30[/C][C]27800[/C][C]22370.2112344695[/C][C]5429.7887655305[/C][/ROW]
[ROW][C]31[/C][C]19631[/C][C]26881.2028383021[/C][C]-7250.20283830209[/C][/ROW]
[ROW][C]32[/C][C]17004[/C][C]20435.1635404613[/C][C]-3431.16354046134[/C][/ROW]
[ROW][C]33[/C][C]18649[/C][C]17251.5118813391[/C][C]1397.48811866086[/C][/ROW]
[ROW][C]34[/C][C]20613[/C][C]18231.2339109264[/C][C]2381.76608907364[/C][/ROW]
[ROW][C]35[/C][C]23555[/C][C]20073.7095422758[/C][C]3481.2904577242[/C][/ROW]
[ROW][C]36[/C][C]27164[/C][C]22885.4692244091[/C][C]4278.53077559095[/C][/ROW]
[ROW][C]37[/C][C]27164[/C][C]26411.8202070099[/C][C]752.179792990097[/C][/ROW]
[ROW][C]38[/C][C]24853[/C][C]26909.580022087[/C][C]-2056.58002208703[/C][/ROW]
[ROW][C]39[/C][C]23871[/C][C]24977.2081449209[/C][C]-1106.20814492086[/C][/ROW]
[ROW][C]40[/C][C]17982[/C][C]23854.9894900602[/C][C]-5872.98949006016[/C][/ROW]
[ROW][C]41[/C][C]27800[/C][C]18592.5570972854[/C][C]9207.44290271457[/C][/ROW]
[ROW][C]42[/C][C]32391[/C][C]26365.3518371821[/C][C]6025.64816281786[/C][/ROW]
[ROW][C]43[/C][C]28462[/C][C]31441.396141982[/C][C]-2979.39614198196[/C][/ROW]
[ROW][C]44[/C][C]24222[/C][C]28750.5786186961[/C][C]-4528.57861869614[/C][/ROW]
[ROW][C]45[/C][C]24853[/C][C]24696.6102813597[/C][C]156.389718640257[/C][/ROW]
[ROW][C]46[/C][C]27164[/C][C]24674.0704342746[/C][C]2489.92956572541[/C][/ROW]
[ROW][C]47[/C][C]30426[/C][C]26675.7519003359[/C][C]3750.24809966406[/C][/ROW]
[ROW][C]48[/C][C]34355[/C][C]29786.8520102062[/C][C]4568.14798979385[/C][/ROW]
[ROW][C]49[/C][C]31724[/C][C]33632.2620134532[/C][C]-1908.26201345315[/C][/ROW]
[ROW][C]50[/C][C]30111[/C][C]31893.3358237[/C][C]-1782.33582370003[/C][/ROW]
[ROW][C]51[/C][C]30111[/C][C]30250.7677692238[/C][C]-139.767769223847[/C][/ROW]
[ROW][C]52[/C][C]24853[/C][C]30020.3268815883[/C][C]-5167.32688158834[/C][/ROW]
[ROW][C]53[/C][C]32391[/C][C]25430.0712667383[/C][C]6960.92873326166[/C][/ROW]
[ROW][C]54[/C][C]37297[/C][C]31320.2566023748[/C][C]5976.74339762524[/C][/ROW]
[ROW][C]55[/C][C]33373[/C][C]36403.9192556588[/C][C]-3030.91925565875[/C][/ROW]
[ROW][C]56[/C][C]29129[/C][C]33718.121447113[/C][C]-4589.12144711302[/C][/ROW]
[ROW][C]57[/C][C]30426[/C][C]29661.0066394224[/C][C]764.993360577588[/C][/ROW]
[ROW][C]58[/C][C]35653[/C][C]30215.0612033207[/C][C]5437.93879667935[/C][/ROW]
[ROW][C]59[/C][C]37964[/C][C]34825.6818769116[/C][C]3138.31812308837[/C][/ROW]
[ROW][C]60[/C][C]41222[/C][C]37479.0709092726[/C][C]3742.92909072735[/C][/ROW]
[ROW][C]61[/C][C]38595[/C][C]40677.7382463729[/C][C]-2082.73824637289[/C][/ROW]
[ROW][C]62[/C][C]34355[/C][C]38850.7172588257[/C][C]-4495.71725882569[/C][/ROW]
[ROW][C]63[/C][C]33373[/C][C]34917.6605617225[/C][C]-1544.66056172251[/C][/ROW]
[ROW][C]64[/C][C]25520[/C][C]33512.9579154168[/C][C]-7992.95791541682[/C][/ROW]
[ROW][C]65[/C][C]30742[/C][C]26507.2277011245[/C][C]4234.77229887551[/C][/ROW]
[ROW][C]66[/C][C]36315[/C][C]30049.2003892104[/C][C]6265.79961078964[/C][/ROW]
[ROW][C]67[/C][C]30111[/C][C]35380.5150728694[/C][C]-5269.51507286936[/C][/ROW]
[ROW][C]68[/C][C]26502[/C][C]30752.8458518984[/C][C]-4250.84585189842[/C][/ROW]
[ROW][C]69[/C][C]30111[/C][C]26972.9593849031[/C][C]3138.04061509692[/C][/ROW]
[ROW][C]70[/C][C]33689[/C][C]29570.6545336271[/C][C]4118.34546637294[/C][/ROW]
[ROW][C]71[/C][C]35653[/C][C]33039.3513776746[/C][C]2613.6486223254[/C][/ROW]
[ROW][C]72[/C][C]40906[/C][C]35231.1478682375[/C][C]5674.85213176251[/C][/ROW]
[ROW][C]73[/C][C]38280[/C][C]40094.5549684839[/C][C]-1814.55496848393[/C][/ROW]
[ROW][C]74[/C][C]31724[/C][C]38502.795686219[/C][C]-6778.79568621897[/C][/ROW]
[ROW][C]75[/C][C]32391[/C][C]32594.8675265204[/C][C]-203.867526520367[/C][/ROW]
[ROW][C]76[/C][C]26186[/C][C]32341.8396459556[/C][C]-6155.83964595564[/C][/ROW]
[ROW][C]77[/C][C]31409[/C][C]26927.1036511024[/C][C]4481.89634889764[/C][/ROW]
[ROW][C]78[/C][C]36000[/C][C]30693.8927392789[/C][C]5306.10726072106[/C][/ROW]
[ROW][C]79[/C][C]30742[/C][C]35205.3784585743[/C][C]-4463.37845857426[/C][/ROW]
[ROW][C]80[/C][C]27164[/C][C]31282.4006054789[/C][C]-4118.40060547888[/C][/ROW]
[ROW][C]81[/C][C]30426[/C][C]27628.5330036378[/C][C]2797.46699636221[/C][/ROW]
[ROW][C]82[/C][C]34355[/C][C]29943.0310989517[/C][C]4411.96890104833[/C][/ROW]
[ROW][C]83[/C][C]33689[/C][C]33676.0895459641[/C][C]12.9104540358603[/C][/ROW]
[ROW][C]84[/C][C]41542[/C][C]33624.8189893458[/C][C]7917.18101065416[/C][/ROW]
[ROW][C]85[/C][C]40244[/C][C]40426.6094956156[/C][C]-182.609495615638[/C][/ROW]
[ROW][C]86[/C][C]35017[/C][C]40259.0970201308[/C][C]-5242.0970201308[/C][/ROW]
[ROW][C]87[/C][C]35333[/C][C]35703.8001938028[/C][C]-370.800193802825[/C][/ROW]
[ROW][C]88[/C][C]28462[/C][C]35336.6846811197[/C][C]-6874.68468111972[/C][/ROW]
[ROW][C]89[/C][C]32706[/C][C]29328.2335741426[/C][C]3377.76642585737[/C][/ROW]
[ROW][C]90[/C][C]39262[/C][C]32162.4378345575[/C][C]7099.56216544251[/C][/ROW]
[ROW][C]91[/C][C]34355[/C][C]38246.1170381779[/C][C]-3891.11703817786[/C][/ROW]
[ROW][C]92[/C][C]31409[/C][C]34848.6104457475[/C][C]-3439.61044574748[/C][/ROW]
[ROW][C]93[/C][C]36315[/C][C]31816.4185083634[/C][C]4498.58149163661[/C][/ROW]
[ROW][C]94[/C][C]39262[/C][C]35643.5038261822[/C][C]3618.49617381778[/C][/ROW]
[ROW][C]95[/C][C]36982[/C][C]38737.7791214103[/C][C]-1755.77912141029[/C][/ROW]
[ROW][C]96[/C][C]47431[/C][C]37196.8854576795[/C][C]10234.1145423205[/C][/ROW]
[ROW][C]97[/C][C]44835[/C][C]46039.3916992889[/C][C]-1204.39169928887[/C][/ROW]
[ROW][C]98[/C][C]38946[/C][C]45033.5051611114[/C][C]-6087.50516111144[/C][/ROW]
[ROW][C]99[/C][C]37297[/C][C]39785.8857729207[/C][C]-2488.88577292074[/C][/ROW]
[ROW][C]100[/C][C]29764[/C][C]37617.361579935[/C][C]-7853.36157993499[/C][/ROW]
[ROW][C]101[/C][C]34035[/C][C]30781.1360626784[/C][C]3253.86393732156[/C][/ROW]
[ROW][C]102[/C][C]37964[/C][C]33522.0776662749[/C][C]4441.92233372513[/C][/ROW]
[ROW][C]103[/C][C]33053[/C][C]37314.9206304723[/C][C]-4261.9206304723[/C][/ROW]
[ROW][C]104[/C][C]33053[/C][C]33591.4030174063[/C][C]-538.40301740633[/C][/ROW]
[ROW][C]105[/C][C]38595[/C][C]33067.5309205371[/C][C]5527.46907946288[/C][/ROW]
[ROW][C]106[/C][C]41542[/C][C]37799.1313479696[/C][C]3742.86865203043[/C][/ROW]
[ROW][C]107[/C][C]39924[/C][C]41020.6222987058[/C][C]-1096.6222987058[/C][/ROW]
[ROW][C]108[/C][C]51355[/C][C]40071.4359223631[/C][C]11283.5640776369[/C][/ROW]
[ROW][C]109[/C][C]48413[/C][C]49848.4599565892[/C][C]-1435.45995658917[/C][/ROW]
[ROW][C]110[/C][C]42871[/C][C]48673.9369062492[/C][C]-5802.93690624922[/C][/ROW]
[ROW][C]111[/C][C]40560[/C][C]43703.1837373855[/C][C]-3143.18373738547[/C][/ROW]
[ROW][C]112[/C][C]32391[/C][C]40999.4437932851[/C][C]-8608.44379328506[/C][/ROW]
[ROW][C]113[/C][C]35333[/C][C]33536.2274644757[/C][C]1796.77253552434[/C][/ROW]
[ROW][C]114[/C][C]40560[/C][C]35036.466267881[/C][C]5523.53373211897[/C][/ROW]
[ROW][C]115[/C][C]36631[/C][C]39779.8641653842[/C][C]-3148.86416538425[/C][/ROW]
[ROW][C]116[/C][C]35653[/C][C]37041.4303511419[/C][C]-1388.43035114188[/C][/ROW]
[ROW][C]117[/C][C]40244[/C][C]35808.1327615189[/C][C]4435.86723848111[/C][/ROW]
[ROW][C]118[/C][C]44168[/C][C]39615.1531038845[/C][C]4552.84689611549[/C][/ROW]
[ROW][C]119[/C][C]39924[/C][C]43553.3938900278[/C][C]-3629.39389002776[/C][/ROW]
[ROW][C]120[/C][C]50057[/C][C]40428.2464984781[/C][C]9628.75350152194[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295928&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295928&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
31405814084-26
41342713741.4580928923-314.458092892268
51994613148.64938569836797.35061430173
61963118719.6409358627911.359064137327
71472419233.1624351971-4509.16243519706
81146215053.2335360333-3591.23353603331
91177811638.8538280692139.146171930764
101177811434.574624542343.425375457971
111209311408.3395239848684.660476015151
121276011680.26111721711079.73888278287
131374212299.31372517521442.68627482476
141342713240.2939510606186.706048939426
151146213102.0355609795-1640.03556097948
161177811381.2529852039396.747014796052
172092911415.33610986499513.66389013508
182289319356.41888034353536.5811196565
191766622179.3036273591-4513.30362735908
201472418046.7252868878-3322.72528688777
211538714916.0544091984470.945590801641
221570715052.1610525874654.838947412649
231735115350.86632181542000.13367818461
241896416820.33642715892143.66357284106
251931518427.6830399264887.316960073604
261602218960.1824421874-2938.18244218738
271636916181.9483941593187.051605840687
281209316093.5428258982-4000.54282589816
292422212375.764431631511846.2355683685
302780022370.21123446955429.7887655305
311963126881.2028383021-7250.20283830209
321700420435.1635404613-3431.16354046134
331864917251.51188133911397.48811866086
342061318231.23391092642381.76608907364
352355520073.70954227583481.2904577242
362716422885.46922440914278.53077559095
372716426411.8202070099752.179792990097
382485326909.580022087-2056.58002208703
392387124977.2081449209-1106.20814492086
401798223854.9894900602-5872.98949006016
412780018592.55709728549207.44290271457
423239126365.35183718216025.64816281786
432846231441.396141982-2979.39614198196
442422228750.5786186961-4528.57861869614
452485324696.6102813597156.389718640257
462716424674.07043427462489.92956572541
473042626675.75190033593750.24809966406
483435529786.85201020624568.14798979385
493172433632.2620134532-1908.26201345315
503011131893.3358237-1782.33582370003
513011130250.7677692238-139.767769223847
522485330020.3268815883-5167.32688158834
533239125430.07126673836960.92873326166
543729731320.25660237485976.74339762524
553337336403.9192556588-3030.91925565875
562912933718.121447113-4589.12144711302
573042629661.0066394224764.993360577588
583565330215.06120332075437.93879667935
593796434825.68187691163138.31812308837
604122237479.07090927263742.92909072735
613859540677.7382463729-2082.73824637289
623435538850.7172588257-4495.71725882569
633337334917.6605617225-1544.66056172251
642552033512.9579154168-7992.95791541682
653074226507.22770112454234.77229887551
663631530049.20038921046265.79961078964
673011135380.5150728694-5269.51507286936
682650230752.8458518984-4250.84585189842
693011126972.95938490313138.04061509692
703368929570.65453362714118.34546637294
713565333039.35137767462613.6486223254
724090635231.14786823755674.85213176251
733828040094.5549684839-1814.55496848393
743172438502.795686219-6778.79568621897
753239132594.8675265204-203.867526520367
762618632341.8396459556-6155.83964595564
773140926927.10365110244481.89634889764
783600030693.89273927895306.10726072106
793074235205.3784585743-4463.37845857426
802716431282.4006054789-4118.40060547888
813042627628.53300363782797.46699636221
823435529943.03109895174411.96890104833
833368933676.089545964112.9104540358603
844154233624.81898934587917.18101065416
854024440426.6094956156-182.609495615638
863501740259.0970201308-5242.0970201308
873533335703.8001938028-370.800193802825
882846235336.6846811197-6874.68468111972
893270629328.23357414263377.76642585737
903926232162.43783455757099.56216544251
913435538246.1170381779-3891.11703817786
923140934848.6104457475-3439.61044574748
933631531816.41850836344498.58149163661
943926235643.50382618223618.49617381778
953698238737.7791214103-1755.77912141029
964743137196.885457679510234.1145423205
974483546039.3916992889-1204.39169928887
983894645033.5051611114-6087.50516111144
993729739785.8857729207-2488.88577292074
1002976437617.361579935-7853.36157993499
1013403530781.13606267843253.86393732156
1023796433522.07766627494441.92233372513
1033305337314.9206304723-4261.9206304723
1043305333591.4030174063-538.40301740633
1053859533067.53092053715527.46907946288
1064154237799.13134796963742.86865203043
1073992441020.6222987058-1096.6222987058
1085135540071.435922363111283.5640776369
1094841349848.4599565892-1435.45995658917
1104287148673.9369062492-5802.93690624922
1114056043703.1837373855-3143.18373738547
1123239140999.4437932851-8608.44379328506
1133533333536.22746447571796.77253552434
1144056035036.4662678815523.53373211897
1153663139779.8641653842-3148.86416538425
1163565337041.4303511419-1388.43035114188
1174024435808.13276151894435.86723848111
1184416839615.15310388454552.84689611549
1193992443553.3938900278-3629.39389002776
1205005740428.24649847819628.75350152194







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12148773.483796818839893.225425347257653.7421682904
12248835.310749445437082.186288776960588.435210114
12348897.13770207234813.990164969762980.2852391744
12448958.964654698632851.095882755865066.8334266414
12549020.791607325231089.583399467566951.999815183
12649082.618559951829473.015388327168692.2217315766
12749144.445512578427966.733634808370322.1573903486
12849206.27246520526547.671956350571864.8729740596
12949268.099417831625199.577564315273336.6212713481
13049329.926370458223910.498766823674749.3539740929
13149391.753323084822671.349860410576112.1567857592
13249453.580275711521475.0376673777432.122884053

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 48773.4837968188 & 39893.2254253472 & 57653.7421682904 \tabularnewline
122 & 48835.3107494454 & 37082.1862887769 & 60588.435210114 \tabularnewline
123 & 48897.137702072 & 34813.9901649697 & 62980.2852391744 \tabularnewline
124 & 48958.9646546986 & 32851.0958827558 & 65066.8334266414 \tabularnewline
125 & 49020.7916073252 & 31089.5833994675 & 66951.999815183 \tabularnewline
126 & 49082.6185599518 & 29473.0153883271 & 68692.2217315766 \tabularnewline
127 & 49144.4455125784 & 27966.7336348083 & 70322.1573903486 \tabularnewline
128 & 49206.272465205 & 26547.6719563505 & 71864.8729740596 \tabularnewline
129 & 49268.0994178316 & 25199.5775643152 & 73336.6212713481 \tabularnewline
130 & 49329.9263704582 & 23910.4987668236 & 74749.3539740929 \tabularnewline
131 & 49391.7533230848 & 22671.3498604105 & 76112.1567857592 \tabularnewline
132 & 49453.5802757115 & 21475.03766737 & 77432.122884053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295928&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]48773.4837968188[/C][C]39893.2254253472[/C][C]57653.7421682904[/C][/ROW]
[ROW][C]122[/C][C]48835.3107494454[/C][C]37082.1862887769[/C][C]60588.435210114[/C][/ROW]
[ROW][C]123[/C][C]48897.137702072[/C][C]34813.9901649697[/C][C]62980.2852391744[/C][/ROW]
[ROW][C]124[/C][C]48958.9646546986[/C][C]32851.0958827558[/C][C]65066.8334266414[/C][/ROW]
[ROW][C]125[/C][C]49020.7916073252[/C][C]31089.5833994675[/C][C]66951.999815183[/C][/ROW]
[ROW][C]126[/C][C]49082.6185599518[/C][C]29473.0153883271[/C][C]68692.2217315766[/C][/ROW]
[ROW][C]127[/C][C]49144.4455125784[/C][C]27966.7336348083[/C][C]70322.1573903486[/C][/ROW]
[ROW][C]128[/C][C]49206.272465205[/C][C]26547.6719563505[/C][C]71864.8729740596[/C][/ROW]
[ROW][C]129[/C][C]49268.0994178316[/C][C]25199.5775643152[/C][C]73336.6212713481[/C][/ROW]
[ROW][C]130[/C][C]49329.9263704582[/C][C]23910.4987668236[/C][C]74749.3539740929[/C][/ROW]
[ROW][C]131[/C][C]49391.7533230848[/C][C]22671.3498604105[/C][C]76112.1567857592[/C][/ROW]
[ROW][C]132[/C][C]49453.5802757115[/C][C]21475.03766737[/C][C]77432.122884053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295928&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295928&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
12148773.483796818839893.225425347257653.7421682904
12248835.310749445437082.186288776960588.435210114
12348897.13770207234813.990164969762980.2852391744
12448958.964654698632851.095882755865066.8334266414
12549020.791607325231089.583399467566951.999815183
12649082.618559951829473.015388327168692.2217315766
12749144.445512578427966.733634808370322.1573903486
12849206.27246520526547.671956350571864.8729740596
12949268.099417831625199.577564315273336.6212713481
13049329.926370458223910.498766823674749.3539740929
13149391.753323084822671.349860410576112.1567857592
13249453.580275711521475.0376673777432.122884053



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')