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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 17:21:49 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/30/t1417368130nz7jj6is7i1q0sr.htm/, Retrieved Sun, 19 May 2024 15:36:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261555, Retrieved Sun, 19 May 2024 15:36:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 17:21:49] [0837030ca90013de3b1661dab7c6b0da] [Current]
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Dataseries X:
1196
1141
6081
-3508
1782
-891
-2043
35
5042
-1837
406
-3621
1987
1627
6692
-3999
679
-215
-2820
799
9957
5154
1302
6287
1891
2191
7336
-2351
881
388
-1936
1120
4438
-3495
1012
-3704
2879
1907
6451
-2814
1613
-40
-3086
292
5283
-1671
3529
-3191
2090
3278
5686
-1817
2322
-705
-1980
646
6077
2632
2356
-1717
1733
2232
6167
-4668
1694
589
-4163
174
5421
-38
3158
-4322
1920
2527
7755
-2567
-388
-2084
-2024
-131
5615
187
2054
-7172




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261555&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261555&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261555&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0337193525205134
beta0.0578956054096416
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0337193525205134 \tabularnewline
beta & 0.0578956054096416 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261555&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]0.0337193525205134[/C][/ROW]
[ROW][C]beta[/C][C]0.0578956054096416[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261555&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261555&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
alpha0.0337193525205134
beta0.0578956054096416
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3608110864995
4-35081209.1794164693-4717.1794164693
51782995.661542812856786.338457187144
6-891969.253820208046-1860.25382020805
7-2043849.973127784834-2892.97312778483
835690.222140099229-655.222140099229
95042604.6475406331344437.35245936687
10-1837699.453869125652-2536.45386912565
11406554.156292469274-148.156292469274
12-3621489.101332664965-4110.10133266496
131987282.4284019926461704.57159800735
141627275.1501463033621351.84985369664
156692258.6174262077726433.38257379223
16-3999425.989963684343-4424.98996368434
17679218.586734061331460.413265938669
18-215176.81495799253-391.81495799253
19-2820105.541695939846-2925.54169593985
20799-56.8784404903823855.878440490382
219957-90.12069042797410047.120690428
225154206.1738095650394947.82619043496
231302340.182558515349961.817441484651
246287341.663335558525945.33666444148
251891522.791654151561368.20834584844
262191552.253188956561638.74681104344
277336594.0362709796726741.96372902033
28-2351821.058200537102-3172.0582005371
29881707.593230351423173.406769648577
30388707.273697939896-319.273697939896
31-1936689.718012305332-2625.71801230533
321120589.264584948937530.735415051063
334438596.2808263370743841.71917366293
34-3495722.441109386639-4217.44110938664
351012568.618427479961443.381572520039
36-3704572.821239158252-4276.82123915825
372879409.5126478808792469.48735211912
381907478.5061531632151428.49384683678
396451515.1867404829795935.81325951702
40-2814715.439128466429-3529.43912846643
411613589.6391552000151023.36084479998
42-40619.354456611359-659.354456611359
43-3086591.042494277448-3677.04249427745
44292453.797714286333-161.797714286333
455283434.7688503531064848.23114964689
46-1671594.139643958765-2265.13964395877
473529509.2301692790853019.76983072091
48-3191608.41962190928-3799.41962190928
492090470.2531856503861619.74681434961
503278517.9796063251012760.0203936749
515686609.5434320293145076.45656797069
52-1817789.126256016856-2606.12625601686
532322704.5696757497511617.43032425025
54-705765.586239947703-1470.5862399477
55-1980719.60600314684-2699.60600314684
56646626.91383857143319.0861614285674
576077625.9314735368785451.06852646312
582632818.7536254226531813.24637457735
592356892.4505935561031463.5494064439
60-1717957.213150904397-2674.2131509044
611733877.232428795994855.767571204006
622232917.951002491881314.04899750812
636167976.6878186672175190.31218133278
64-46681176.26225912469-5844.26225912469
651694992.348811721675701.651188278325
665891030.52909250375-441.529092503752
67-41631029.30012028129-5192.30012028129
68174857.741804645441-683.741804645441
695421836.87435387094584.1256461291
70-381002.58512345948-1040.58512345948
713158976.6028550816712181.39714491833
72-43221063.52227121117-5385.52227121117
731920884.7764349374641035.22356506254
742527924.5549568156111602.44504318439
757755986.5881166158676768.41188338413
76-25671236.02764284703-3803.02764284703
77-3881121.58079362536-1509.58079362536
78-20841081.52048005974-3165.52048005974
79-2024979.443216003406-3003.44321600341
80-131876.96776351046-1007.96776351046
815615839.8106942314824775.18930576852
821871006.98007253332-819.98007253332
832054983.8831951495431070.11680485046
84-71721026.60824519006-8198.60824519006

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6081 & 1086 & 4995 \tabularnewline
4 & -3508 & 1209.1794164693 & -4717.1794164693 \tabularnewline
5 & 1782 & 995.661542812856 & 786.338457187144 \tabularnewline
6 & -891 & 969.253820208046 & -1860.25382020805 \tabularnewline
7 & -2043 & 849.973127784834 & -2892.97312778483 \tabularnewline
8 & 35 & 690.222140099229 & -655.222140099229 \tabularnewline
9 & 5042 & 604.647540633134 & 4437.35245936687 \tabularnewline
10 & -1837 & 699.453869125652 & -2536.45386912565 \tabularnewline
11 & 406 & 554.156292469274 & -148.156292469274 \tabularnewline
12 & -3621 & 489.101332664965 & -4110.10133266496 \tabularnewline
13 & 1987 & 282.428401992646 & 1704.57159800735 \tabularnewline
14 & 1627 & 275.150146303362 & 1351.84985369664 \tabularnewline
15 & 6692 & 258.617426207772 & 6433.38257379223 \tabularnewline
16 & -3999 & 425.989963684343 & -4424.98996368434 \tabularnewline
17 & 679 & 218.586734061331 & 460.413265938669 \tabularnewline
18 & -215 & 176.81495799253 & -391.81495799253 \tabularnewline
19 & -2820 & 105.541695939846 & -2925.54169593985 \tabularnewline
20 & 799 & -56.8784404903823 & 855.878440490382 \tabularnewline
21 & 9957 & -90.120690427974 & 10047.120690428 \tabularnewline
22 & 5154 & 206.173809565039 & 4947.82619043496 \tabularnewline
23 & 1302 & 340.182558515349 & 961.817441484651 \tabularnewline
24 & 6287 & 341.66333555852 & 5945.33666444148 \tabularnewline
25 & 1891 & 522.79165415156 & 1368.20834584844 \tabularnewline
26 & 2191 & 552.25318895656 & 1638.74681104344 \tabularnewline
27 & 7336 & 594.036270979672 & 6741.96372902033 \tabularnewline
28 & -2351 & 821.058200537102 & -3172.0582005371 \tabularnewline
29 & 881 & 707.593230351423 & 173.406769648577 \tabularnewline
30 & 388 & 707.273697939896 & -319.273697939896 \tabularnewline
31 & -1936 & 689.718012305332 & -2625.71801230533 \tabularnewline
32 & 1120 & 589.264584948937 & 530.735415051063 \tabularnewline
33 & 4438 & 596.280826337074 & 3841.71917366293 \tabularnewline
34 & -3495 & 722.441109386639 & -4217.44110938664 \tabularnewline
35 & 1012 & 568.618427479961 & 443.381572520039 \tabularnewline
36 & -3704 & 572.821239158252 & -4276.82123915825 \tabularnewline
37 & 2879 & 409.512647880879 & 2469.48735211912 \tabularnewline
38 & 1907 & 478.506153163215 & 1428.49384683678 \tabularnewline
39 & 6451 & 515.186740482979 & 5935.81325951702 \tabularnewline
40 & -2814 & 715.439128466429 & -3529.43912846643 \tabularnewline
41 & 1613 & 589.639155200015 & 1023.36084479998 \tabularnewline
42 & -40 & 619.354456611359 & -659.354456611359 \tabularnewline
43 & -3086 & 591.042494277448 & -3677.04249427745 \tabularnewline
44 & 292 & 453.797714286333 & -161.797714286333 \tabularnewline
45 & 5283 & 434.768850353106 & 4848.23114964689 \tabularnewline
46 & -1671 & 594.139643958765 & -2265.13964395877 \tabularnewline
47 & 3529 & 509.230169279085 & 3019.76983072091 \tabularnewline
48 & -3191 & 608.41962190928 & -3799.41962190928 \tabularnewline
49 & 2090 & 470.253185650386 & 1619.74681434961 \tabularnewline
50 & 3278 & 517.979606325101 & 2760.0203936749 \tabularnewline
51 & 5686 & 609.543432029314 & 5076.45656797069 \tabularnewline
52 & -1817 & 789.126256016856 & -2606.12625601686 \tabularnewline
53 & 2322 & 704.569675749751 & 1617.43032425025 \tabularnewline
54 & -705 & 765.586239947703 & -1470.5862399477 \tabularnewline
55 & -1980 & 719.60600314684 & -2699.60600314684 \tabularnewline
56 & 646 & 626.913838571433 & 19.0861614285674 \tabularnewline
57 & 6077 & 625.931473536878 & 5451.06852646312 \tabularnewline
58 & 2632 & 818.753625422653 & 1813.24637457735 \tabularnewline
59 & 2356 & 892.450593556103 & 1463.5494064439 \tabularnewline
60 & -1717 & 957.213150904397 & -2674.2131509044 \tabularnewline
61 & 1733 & 877.232428795994 & 855.767571204006 \tabularnewline
62 & 2232 & 917.95100249188 & 1314.04899750812 \tabularnewline
63 & 6167 & 976.687818667217 & 5190.31218133278 \tabularnewline
64 & -4668 & 1176.26225912469 & -5844.26225912469 \tabularnewline
65 & 1694 & 992.348811721675 & 701.651188278325 \tabularnewline
66 & 589 & 1030.52909250375 & -441.529092503752 \tabularnewline
67 & -4163 & 1029.30012028129 & -5192.30012028129 \tabularnewline
68 & 174 & 857.741804645441 & -683.741804645441 \tabularnewline
69 & 5421 & 836.8743538709 & 4584.1256461291 \tabularnewline
70 & -38 & 1002.58512345948 & -1040.58512345948 \tabularnewline
71 & 3158 & 976.602855081671 & 2181.39714491833 \tabularnewline
72 & -4322 & 1063.52227121117 & -5385.52227121117 \tabularnewline
73 & 1920 & 884.776434937464 & 1035.22356506254 \tabularnewline
74 & 2527 & 924.554956815611 & 1602.44504318439 \tabularnewline
75 & 7755 & 986.588116615867 & 6768.41188338413 \tabularnewline
76 & -2567 & 1236.02764284703 & -3803.02764284703 \tabularnewline
77 & -388 & 1121.58079362536 & -1509.58079362536 \tabularnewline
78 & -2084 & 1081.52048005974 & -3165.52048005974 \tabularnewline
79 & -2024 & 979.443216003406 & -3003.44321600341 \tabularnewline
80 & -131 & 876.96776351046 & -1007.96776351046 \tabularnewline
81 & 5615 & 839.810694231482 & 4775.18930576852 \tabularnewline
82 & 187 & 1006.98007253332 & -819.98007253332 \tabularnewline
83 & 2054 & 983.883195149543 & 1070.11680485046 \tabularnewline
84 & -7172 & 1026.60824519006 & -8198.60824519006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261555&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]6081[/C][C]1086[/C][C]4995[/C][/ROW]
[ROW][C]4[/C][C]-3508[/C][C]1209.1794164693[/C][C]-4717.1794164693[/C][/ROW]
[ROW][C]5[/C][C]1782[/C][C]995.661542812856[/C][C]786.338457187144[/C][/ROW]
[ROW][C]6[/C][C]-891[/C][C]969.253820208046[/C][C]-1860.25382020805[/C][/ROW]
[ROW][C]7[/C][C]-2043[/C][C]849.973127784834[/C][C]-2892.97312778483[/C][/ROW]
[ROW][C]8[/C][C]35[/C][C]690.222140099229[/C][C]-655.222140099229[/C][/ROW]
[ROW][C]9[/C][C]5042[/C][C]604.647540633134[/C][C]4437.35245936687[/C][/ROW]
[ROW][C]10[/C][C]-1837[/C][C]699.453869125652[/C][C]-2536.45386912565[/C][/ROW]
[ROW][C]11[/C][C]406[/C][C]554.156292469274[/C][C]-148.156292469274[/C][/ROW]
[ROW][C]12[/C][C]-3621[/C][C]489.101332664965[/C][C]-4110.10133266496[/C][/ROW]
[ROW][C]13[/C][C]1987[/C][C]282.428401992646[/C][C]1704.57159800735[/C][/ROW]
[ROW][C]14[/C][C]1627[/C][C]275.150146303362[/C][C]1351.84985369664[/C][/ROW]
[ROW][C]15[/C][C]6692[/C][C]258.617426207772[/C][C]6433.38257379223[/C][/ROW]
[ROW][C]16[/C][C]-3999[/C][C]425.989963684343[/C][C]-4424.98996368434[/C][/ROW]
[ROW][C]17[/C][C]679[/C][C]218.586734061331[/C][C]460.413265938669[/C][/ROW]
[ROW][C]18[/C][C]-215[/C][C]176.81495799253[/C][C]-391.81495799253[/C][/ROW]
[ROW][C]19[/C][C]-2820[/C][C]105.541695939846[/C][C]-2925.54169593985[/C][/ROW]
[ROW][C]20[/C][C]799[/C][C]-56.8784404903823[/C][C]855.878440490382[/C][/ROW]
[ROW][C]21[/C][C]9957[/C][C]-90.120690427974[/C][C]10047.120690428[/C][/ROW]
[ROW][C]22[/C][C]5154[/C][C]206.173809565039[/C][C]4947.82619043496[/C][/ROW]
[ROW][C]23[/C][C]1302[/C][C]340.182558515349[/C][C]961.817441484651[/C][/ROW]
[ROW][C]24[/C][C]6287[/C][C]341.66333555852[/C][C]5945.33666444148[/C][/ROW]
[ROW][C]25[/C][C]1891[/C][C]522.79165415156[/C][C]1368.20834584844[/C][/ROW]
[ROW][C]26[/C][C]2191[/C][C]552.25318895656[/C][C]1638.74681104344[/C][/ROW]
[ROW][C]27[/C][C]7336[/C][C]594.036270979672[/C][C]6741.96372902033[/C][/ROW]
[ROW][C]28[/C][C]-2351[/C][C]821.058200537102[/C][C]-3172.0582005371[/C][/ROW]
[ROW][C]29[/C][C]881[/C][C]707.593230351423[/C][C]173.406769648577[/C][/ROW]
[ROW][C]30[/C][C]388[/C][C]707.273697939896[/C][C]-319.273697939896[/C][/ROW]
[ROW][C]31[/C][C]-1936[/C][C]689.718012305332[/C][C]-2625.71801230533[/C][/ROW]
[ROW][C]32[/C][C]1120[/C][C]589.264584948937[/C][C]530.735415051063[/C][/ROW]
[ROW][C]33[/C][C]4438[/C][C]596.280826337074[/C][C]3841.71917366293[/C][/ROW]
[ROW][C]34[/C][C]-3495[/C][C]722.441109386639[/C][C]-4217.44110938664[/C][/ROW]
[ROW][C]35[/C][C]1012[/C][C]568.618427479961[/C][C]443.381572520039[/C][/ROW]
[ROW][C]36[/C][C]-3704[/C][C]572.821239158252[/C][C]-4276.82123915825[/C][/ROW]
[ROW][C]37[/C][C]2879[/C][C]409.512647880879[/C][C]2469.48735211912[/C][/ROW]
[ROW][C]38[/C][C]1907[/C][C]478.506153163215[/C][C]1428.49384683678[/C][/ROW]
[ROW][C]39[/C][C]6451[/C][C]515.186740482979[/C][C]5935.81325951702[/C][/ROW]
[ROW][C]40[/C][C]-2814[/C][C]715.439128466429[/C][C]-3529.43912846643[/C][/ROW]
[ROW][C]41[/C][C]1613[/C][C]589.639155200015[/C][C]1023.36084479998[/C][/ROW]
[ROW][C]42[/C][C]-40[/C][C]619.354456611359[/C][C]-659.354456611359[/C][/ROW]
[ROW][C]43[/C][C]-3086[/C][C]591.042494277448[/C][C]-3677.04249427745[/C][/ROW]
[ROW][C]44[/C][C]292[/C][C]453.797714286333[/C][C]-161.797714286333[/C][/ROW]
[ROW][C]45[/C][C]5283[/C][C]434.768850353106[/C][C]4848.23114964689[/C][/ROW]
[ROW][C]46[/C][C]-1671[/C][C]594.139643958765[/C][C]-2265.13964395877[/C][/ROW]
[ROW][C]47[/C][C]3529[/C][C]509.230169279085[/C][C]3019.76983072091[/C][/ROW]
[ROW][C]48[/C][C]-3191[/C][C]608.41962190928[/C][C]-3799.41962190928[/C][/ROW]
[ROW][C]49[/C][C]2090[/C][C]470.253185650386[/C][C]1619.74681434961[/C][/ROW]
[ROW][C]50[/C][C]3278[/C][C]517.979606325101[/C][C]2760.0203936749[/C][/ROW]
[ROW][C]51[/C][C]5686[/C][C]609.543432029314[/C][C]5076.45656797069[/C][/ROW]
[ROW][C]52[/C][C]-1817[/C][C]789.126256016856[/C][C]-2606.12625601686[/C][/ROW]
[ROW][C]53[/C][C]2322[/C][C]704.569675749751[/C][C]1617.43032425025[/C][/ROW]
[ROW][C]54[/C][C]-705[/C][C]765.586239947703[/C][C]-1470.5862399477[/C][/ROW]
[ROW][C]55[/C][C]-1980[/C][C]719.60600314684[/C][C]-2699.60600314684[/C][/ROW]
[ROW][C]56[/C][C]646[/C][C]626.913838571433[/C][C]19.0861614285674[/C][/ROW]
[ROW][C]57[/C][C]6077[/C][C]625.931473536878[/C][C]5451.06852646312[/C][/ROW]
[ROW][C]58[/C][C]2632[/C][C]818.753625422653[/C][C]1813.24637457735[/C][/ROW]
[ROW][C]59[/C][C]2356[/C][C]892.450593556103[/C][C]1463.5494064439[/C][/ROW]
[ROW][C]60[/C][C]-1717[/C][C]957.213150904397[/C][C]-2674.2131509044[/C][/ROW]
[ROW][C]61[/C][C]1733[/C][C]877.232428795994[/C][C]855.767571204006[/C][/ROW]
[ROW][C]62[/C][C]2232[/C][C]917.95100249188[/C][C]1314.04899750812[/C][/ROW]
[ROW][C]63[/C][C]6167[/C][C]976.687818667217[/C][C]5190.31218133278[/C][/ROW]
[ROW][C]64[/C][C]-4668[/C][C]1176.26225912469[/C][C]-5844.26225912469[/C][/ROW]
[ROW][C]65[/C][C]1694[/C][C]992.348811721675[/C][C]701.651188278325[/C][/ROW]
[ROW][C]66[/C][C]589[/C][C]1030.52909250375[/C][C]-441.529092503752[/C][/ROW]
[ROW][C]67[/C][C]-4163[/C][C]1029.30012028129[/C][C]-5192.30012028129[/C][/ROW]
[ROW][C]68[/C][C]174[/C][C]857.741804645441[/C][C]-683.741804645441[/C][/ROW]
[ROW][C]69[/C][C]5421[/C][C]836.8743538709[/C][C]4584.1256461291[/C][/ROW]
[ROW][C]70[/C][C]-38[/C][C]1002.58512345948[/C][C]-1040.58512345948[/C][/ROW]
[ROW][C]71[/C][C]3158[/C][C]976.602855081671[/C][C]2181.39714491833[/C][/ROW]
[ROW][C]72[/C][C]-4322[/C][C]1063.52227121117[/C][C]-5385.52227121117[/C][/ROW]
[ROW][C]73[/C][C]1920[/C][C]884.776434937464[/C][C]1035.22356506254[/C][/ROW]
[ROW][C]74[/C][C]2527[/C][C]924.554956815611[/C][C]1602.44504318439[/C][/ROW]
[ROW][C]75[/C][C]7755[/C][C]986.588116615867[/C][C]6768.41188338413[/C][/ROW]
[ROW][C]76[/C][C]-2567[/C][C]1236.02764284703[/C][C]-3803.02764284703[/C][/ROW]
[ROW][C]77[/C][C]-388[/C][C]1121.58079362536[/C][C]-1509.58079362536[/C][/ROW]
[ROW][C]78[/C][C]-2084[/C][C]1081.52048005974[/C][C]-3165.52048005974[/C][/ROW]
[ROW][C]79[/C][C]-2024[/C][C]979.443216003406[/C][C]-3003.44321600341[/C][/ROW]
[ROW][C]80[/C][C]-131[/C][C]876.96776351046[/C][C]-1007.96776351046[/C][/ROW]
[ROW][C]81[/C][C]5615[/C][C]839.810694231482[/C][C]4775.18930576852[/C][/ROW]
[ROW][C]82[/C][C]187[/C][C]1006.98007253332[/C][C]-819.98007253332[/C][/ROW]
[ROW][C]83[/C][C]2054[/C][C]983.883195149543[/C][C]1070.11680485046[/C][/ROW]
[ROW][C]84[/C][C]-7172[/C][C]1026.60824519006[/C][C]-8198.60824519006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261555&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261555&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
3608110864995
4-35081209.1794164693-4717.1794164693
51782995.661542812856786.338457187144
6-891969.253820208046-1860.25382020805
7-2043849.973127784834-2892.97312778483
835690.222140099229-655.222140099229
95042604.6475406331344437.35245936687
10-1837699.453869125652-2536.45386912565
11406554.156292469274-148.156292469274
12-3621489.101332664965-4110.10133266496
131987282.4284019926461704.57159800735
141627275.1501463033621351.84985369664
156692258.6174262077726433.38257379223
16-3999425.989963684343-4424.98996368434
17679218.586734061331460.413265938669
18-215176.81495799253-391.81495799253
19-2820105.541695939846-2925.54169593985
20799-56.8784404903823855.878440490382
219957-90.12069042797410047.120690428
225154206.1738095650394947.82619043496
231302340.182558515349961.817441484651
246287341.663335558525945.33666444148
251891522.791654151561368.20834584844
262191552.253188956561638.74681104344
277336594.0362709796726741.96372902033
28-2351821.058200537102-3172.0582005371
29881707.593230351423173.406769648577
30388707.273697939896-319.273697939896
31-1936689.718012305332-2625.71801230533
321120589.264584948937530.735415051063
334438596.2808263370743841.71917366293
34-3495722.441109386639-4217.44110938664
351012568.618427479961443.381572520039
36-3704572.821239158252-4276.82123915825
372879409.5126478808792469.48735211912
381907478.5061531632151428.49384683678
396451515.1867404829795935.81325951702
40-2814715.439128466429-3529.43912846643
411613589.6391552000151023.36084479998
42-40619.354456611359-659.354456611359
43-3086591.042494277448-3677.04249427745
44292453.797714286333-161.797714286333
455283434.7688503531064848.23114964689
46-1671594.139643958765-2265.13964395877
473529509.2301692790853019.76983072091
48-3191608.41962190928-3799.41962190928
492090470.2531856503861619.74681434961
503278517.9796063251012760.0203936749
515686609.5434320293145076.45656797069
52-1817789.126256016856-2606.12625601686
532322704.5696757497511617.43032425025
54-705765.586239947703-1470.5862399477
55-1980719.60600314684-2699.60600314684
56646626.91383857143319.0861614285674
576077625.9314735368785451.06852646312
582632818.7536254226531813.24637457735
592356892.4505935561031463.5494064439
60-1717957.213150904397-2674.2131509044
611733877.232428795994855.767571204006
622232917.951002491881314.04899750812
636167976.6878186672175190.31218133278
64-46681176.26225912469-5844.26225912469
651694992.348811721675701.651188278325
665891030.52909250375-441.529092503752
67-41631029.30012028129-5192.30012028129
68174857.741804645441-683.741804645441
695421836.87435387094584.1256461291
70-381002.58512345948-1040.58512345948
713158976.6028550816712181.39714491833
72-43221063.52227121117-5385.52227121117
731920884.7764349374641035.22356506254
742527924.5549568156111602.44504318439
757755986.5881166158676768.41188338413
76-25671236.02764284703-3803.02764284703
77-3881121.58079362536-1509.58079362536
78-20841081.52048005974-3165.52048005974
79-2024979.443216003406-3003.44321600341
80-131876.96776351046-1007.96776351046
815615839.8106942314824775.18930576852
821871006.98007253332-819.98007253332
832054983.8831951495431070.11680485046
84-71721026.60824519006-8198.60824519006







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85740.792545748322-6138.086189793397619.67128129003
86731.428607903734-6151.825284694687614.68250050215
87722.064670059146-6166.053097857357610.18243797564
88712.700732214558-6180.794755310927606.19621974003
89703.33679436997-6196.075193590437602.74878233037
90693.972856525382-6211.919141473037599.86485452379
91684.608918680793-6228.35110115547597.56893851699
92675.244980836205-6245.395328933997595.8852906064
93665.881042991617-6263.075815454317594.83790143754
94656.517105147029-6281.416265599537594.45047589359
95647.153167302441-6300.440078092457594.74641269733
96637.789229457853-6320.170324888377595.74878380407

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 740.792545748322 & -6138.08618979339 & 7619.67128129003 \tabularnewline
86 & 731.428607903734 & -6151.82528469468 & 7614.68250050215 \tabularnewline
87 & 722.064670059146 & -6166.05309785735 & 7610.18243797564 \tabularnewline
88 & 712.700732214558 & -6180.79475531092 & 7606.19621974003 \tabularnewline
89 & 703.33679436997 & -6196.07519359043 & 7602.74878233037 \tabularnewline
90 & 693.972856525382 & -6211.91914147303 & 7599.86485452379 \tabularnewline
91 & 684.608918680793 & -6228.3511011554 & 7597.56893851699 \tabularnewline
92 & 675.244980836205 & -6245.39532893399 & 7595.8852906064 \tabularnewline
93 & 665.881042991617 & -6263.07581545431 & 7594.83790143754 \tabularnewline
94 & 656.517105147029 & -6281.41626559953 & 7594.45047589359 \tabularnewline
95 & 647.153167302441 & -6300.44007809245 & 7594.74641269733 \tabularnewline
96 & 637.789229457853 & -6320.17032488837 & 7595.74878380407 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261555&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]85[/C][C]740.792545748322[/C][C]-6138.08618979339[/C][C]7619.67128129003[/C][/ROW]
[ROW][C]86[/C][C]731.428607903734[/C][C]-6151.82528469468[/C][C]7614.68250050215[/C][/ROW]
[ROW][C]87[/C][C]722.064670059146[/C][C]-6166.05309785735[/C][C]7610.18243797564[/C][/ROW]
[ROW][C]88[/C][C]712.700732214558[/C][C]-6180.79475531092[/C][C]7606.19621974003[/C][/ROW]
[ROW][C]89[/C][C]703.33679436997[/C][C]-6196.07519359043[/C][C]7602.74878233037[/C][/ROW]
[ROW][C]90[/C][C]693.972856525382[/C][C]-6211.91914147303[/C][C]7599.86485452379[/C][/ROW]
[ROW][C]91[/C][C]684.608918680793[/C][C]-6228.3511011554[/C][C]7597.56893851699[/C][/ROW]
[ROW][C]92[/C][C]675.244980836205[/C][C]-6245.39532893399[/C][C]7595.8852906064[/C][/ROW]
[ROW][C]93[/C][C]665.881042991617[/C][C]-6263.07581545431[/C][C]7594.83790143754[/C][/ROW]
[ROW][C]94[/C][C]656.517105147029[/C][C]-6281.41626559953[/C][C]7594.45047589359[/C][/ROW]
[ROW][C]95[/C][C]647.153167302441[/C][C]-6300.44007809245[/C][C]7594.74641269733[/C][/ROW]
[ROW][C]96[/C][C]637.789229457853[/C][C]-6320.17032488837[/C][C]7595.74878380407[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261555&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261555&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
85740.792545748322-6138.086189793397619.67128129003
86731.428607903734-6151.825284694687614.68250050215
87722.064670059146-6166.053097857357610.18243797564
88712.700732214558-6180.794755310927606.19621974003
89703.33679436997-6196.075193590437602.74878233037
90693.972856525382-6211.919141473037599.86485452379
91684.608918680793-6228.35110115547597.56893851699
92675.244980836205-6245.395328933997595.8852906064
93665.881042991617-6263.075815454317594.83790143754
94656.517105147029-6281.416265599537594.45047589359
95647.153167302441-6300.440078092457594.74641269733
96637.789229457853-6320.170324888377595.74878380407



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