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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 18 Dec 2012 12:44:20 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/18/t1355852682qsgotqe3aw94oej.htm/, Retrieved Sat, 20 Apr 2024 14:17:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201525, Retrieved Sat, 20 Apr 2024 14:17:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Exponential Smoothing] [Births] [2010-11-30 13:57:06] [b98453cac15ba1066b407e146608df68]
- R PD            [Exponential Smoothing] [exp. smoothing] [2012-12-18 17:44:20] [164264d60f8cebcb0f9613bc1a0dee58] [Current]
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Dataseries X:
655362
873127
1107897
1555964
1671159
1493308
2957796
2638691
1305669
1280496
921900
867888
652586
913831
1108544
1555827
1699283
1509458
3268975
2425016
1312703
1365498
934453
775019
651142
843192
1146766
1652601
1465906
1652734
2922334
2702805
1458956
1410363
1019279
936574
708917
885295
1099663
1576220
1487870
1488635
2882530
2677026
1404398
1344370
936865
872705
628151
953712
1160384
1400618
1661511
1495347
2918786
2775677
1407026
1370199
964526
850851
683118
847224
1073256
1514326
1503734
1507712
2865698
2788128
1391596
1366378
946295
859626




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201525&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201525&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201525&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.995428577289699
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.995428577289699 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201525&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]0.995428577289699[/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=201525&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201525&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
alpha0.995428577289699
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2873127655362217765
31107897872131.504133491235765.495866509
415559641106819.21625789449144.78374211
516711591553910.76933539117248.230664612
614933081670623.0087756-177315.008775597
729577961494118.581857991463677.41814201
826386912951104.91181015-312413.911810151
913056692640119.17605146-1334450.17605146
1012804961311769.33584057-31273.335840567
119219001280638.96363769-358738.963637688
12867888923539.947445443-55651.9474454432
13652586868142.408576425-215556.408576425
14913831653571.399461517260259.600538483
151108544912641.243351524195902.756648476
1615558271107648.44568925448178.554310753
1716992831553778.18637855145504.813621446
1815094581698617.83599055-189159.835990553
1932689751510322.729570121758652.27042988
2024250163260935.45707143-835919.457071434
2113127032428837.34119004-1116134.34119004
2213654981317805.3218750647692.678124937
239344531365279.9766081-430826.976608105
24775019936422.492225077-161403.492225077
25651142775756.84358988-124614.84358988
26843192651711.667126027191480.332873973
271146766842316.662457724304449.337542276
2816526011145374.23338422507226.766615777
2914659061650282.25203982-184376.25203982
3016527341466748.86178582185985.138214185
3129223341651883.783315391270450.21668461
3227028052916526.23502714-213721.235027141
3314589562703782.01010748-1244826.01010748
3414103631464646.62589298-54283.6258929789
3510192791410611.1534002-391332.153400205
369365741021067.94469332-84493.9446933247
37708917936960.257537654-228043.257537654
38885295709959.482126439175335.517873561
391099663884493.46723167215169.53276833
4015762201098679.36911134477540.630888662
4114878701574036.95991486-86166.959914864
4214886351488263.90559743371.094402567483
4328825301488633.303570621393896.69642938
4426770262876157.90898613-199131.908986129
4514043982677936.31613108-1273538.31613108
4613443701410219.8819808-65849.8819808003
479368651344671.02764596-407806.027645958
48872705938729.253736178-66024.2537361784
49628151873006.82477296-244855.82477296
50953712629270.339478117324441.660521883
511160384952228.840024923208155.159975077
5214006181159432.43477442241185.565225577
5316615111399515.43882973261995.561170269
5414953471660313.30754167-164966.307541668
5529187861496101.130724731422684.86927527
5627756772912282.30607899-136605.306078993
5714070262776301.48059856-1369275.48059856
5813701991413285.53702867-43086.5370286666
599645261370395.96677388-405869.966773881
60850851966381.403183539-115530.403183539
61683118851379.138308843-168261.138308843
62847224683887.192788926163336.807211074
631073256846477.318410087226778.681589913
6415143261072219.29878477442106.701215232
6515037341512304.94338569-8570.94338568836
6615077121503773.181405243938.81859475793
6728656981507693.993995221358004.00600478
6827881282859489.98964627-71361.9896462699
6913915962788454.22582012-1396858.22582012
7013663781397981.62941658-31603.629416585
719462951366522.47354924-420227.473549243
72859626948216.037416075-88590.0374160755

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 873127 & 655362 & 217765 \tabularnewline
3 & 1107897 & 872131.504133491 & 235765.495866509 \tabularnewline
4 & 1555964 & 1106819.21625789 & 449144.78374211 \tabularnewline
5 & 1671159 & 1553910.76933539 & 117248.230664612 \tabularnewline
6 & 1493308 & 1670623.0087756 & -177315.008775597 \tabularnewline
7 & 2957796 & 1494118.58185799 & 1463677.41814201 \tabularnewline
8 & 2638691 & 2951104.91181015 & -312413.911810151 \tabularnewline
9 & 1305669 & 2640119.17605146 & -1334450.17605146 \tabularnewline
10 & 1280496 & 1311769.33584057 & -31273.335840567 \tabularnewline
11 & 921900 & 1280638.96363769 & -358738.963637688 \tabularnewline
12 & 867888 & 923539.947445443 & -55651.9474454432 \tabularnewline
13 & 652586 & 868142.408576425 & -215556.408576425 \tabularnewline
14 & 913831 & 653571.399461517 & 260259.600538483 \tabularnewline
15 & 1108544 & 912641.243351524 & 195902.756648476 \tabularnewline
16 & 1555827 & 1107648.44568925 & 448178.554310753 \tabularnewline
17 & 1699283 & 1553778.18637855 & 145504.813621446 \tabularnewline
18 & 1509458 & 1698617.83599055 & -189159.835990553 \tabularnewline
19 & 3268975 & 1510322.72957012 & 1758652.27042988 \tabularnewline
20 & 2425016 & 3260935.45707143 & -835919.457071434 \tabularnewline
21 & 1312703 & 2428837.34119004 & -1116134.34119004 \tabularnewline
22 & 1365498 & 1317805.32187506 & 47692.678124937 \tabularnewline
23 & 934453 & 1365279.9766081 & -430826.976608105 \tabularnewline
24 & 775019 & 936422.492225077 & -161403.492225077 \tabularnewline
25 & 651142 & 775756.84358988 & -124614.84358988 \tabularnewline
26 & 843192 & 651711.667126027 & 191480.332873973 \tabularnewline
27 & 1146766 & 842316.662457724 & 304449.337542276 \tabularnewline
28 & 1652601 & 1145374.23338422 & 507226.766615777 \tabularnewline
29 & 1465906 & 1650282.25203982 & -184376.25203982 \tabularnewline
30 & 1652734 & 1466748.86178582 & 185985.138214185 \tabularnewline
31 & 2922334 & 1651883.78331539 & 1270450.21668461 \tabularnewline
32 & 2702805 & 2916526.23502714 & -213721.235027141 \tabularnewline
33 & 1458956 & 2703782.01010748 & -1244826.01010748 \tabularnewline
34 & 1410363 & 1464646.62589298 & -54283.6258929789 \tabularnewline
35 & 1019279 & 1410611.1534002 & -391332.153400205 \tabularnewline
36 & 936574 & 1021067.94469332 & -84493.9446933247 \tabularnewline
37 & 708917 & 936960.257537654 & -228043.257537654 \tabularnewline
38 & 885295 & 709959.482126439 & 175335.517873561 \tabularnewline
39 & 1099663 & 884493.46723167 & 215169.53276833 \tabularnewline
40 & 1576220 & 1098679.36911134 & 477540.630888662 \tabularnewline
41 & 1487870 & 1574036.95991486 & -86166.959914864 \tabularnewline
42 & 1488635 & 1488263.90559743 & 371.094402567483 \tabularnewline
43 & 2882530 & 1488633.30357062 & 1393896.69642938 \tabularnewline
44 & 2677026 & 2876157.90898613 & -199131.908986129 \tabularnewline
45 & 1404398 & 2677936.31613108 & -1273538.31613108 \tabularnewline
46 & 1344370 & 1410219.8819808 & -65849.8819808003 \tabularnewline
47 & 936865 & 1344671.02764596 & -407806.027645958 \tabularnewline
48 & 872705 & 938729.253736178 & -66024.2537361784 \tabularnewline
49 & 628151 & 873006.82477296 & -244855.82477296 \tabularnewline
50 & 953712 & 629270.339478117 & 324441.660521883 \tabularnewline
51 & 1160384 & 952228.840024923 & 208155.159975077 \tabularnewline
52 & 1400618 & 1159432.43477442 & 241185.565225577 \tabularnewline
53 & 1661511 & 1399515.43882973 & 261995.561170269 \tabularnewline
54 & 1495347 & 1660313.30754167 & -164966.307541668 \tabularnewline
55 & 2918786 & 1496101.13072473 & 1422684.86927527 \tabularnewline
56 & 2775677 & 2912282.30607899 & -136605.306078993 \tabularnewline
57 & 1407026 & 2776301.48059856 & -1369275.48059856 \tabularnewline
58 & 1370199 & 1413285.53702867 & -43086.5370286666 \tabularnewline
59 & 964526 & 1370395.96677388 & -405869.966773881 \tabularnewline
60 & 850851 & 966381.403183539 & -115530.403183539 \tabularnewline
61 & 683118 & 851379.138308843 & -168261.138308843 \tabularnewline
62 & 847224 & 683887.192788926 & 163336.807211074 \tabularnewline
63 & 1073256 & 846477.318410087 & 226778.681589913 \tabularnewline
64 & 1514326 & 1072219.29878477 & 442106.701215232 \tabularnewline
65 & 1503734 & 1512304.94338569 & -8570.94338568836 \tabularnewline
66 & 1507712 & 1503773.18140524 & 3938.81859475793 \tabularnewline
67 & 2865698 & 1507693.99399522 & 1358004.00600478 \tabularnewline
68 & 2788128 & 2859489.98964627 & -71361.9896462699 \tabularnewline
69 & 1391596 & 2788454.22582012 & -1396858.22582012 \tabularnewline
70 & 1366378 & 1397981.62941658 & -31603.629416585 \tabularnewline
71 & 946295 & 1366522.47354924 & -420227.473549243 \tabularnewline
72 & 859626 & 948216.037416075 & -88590.0374160755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201525&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]873127[/C][C]655362[/C][C]217765[/C][/ROW]
[ROW][C]3[/C][C]1107897[/C][C]872131.504133491[/C][C]235765.495866509[/C][/ROW]
[ROW][C]4[/C][C]1555964[/C][C]1106819.21625789[/C][C]449144.78374211[/C][/ROW]
[ROW][C]5[/C][C]1671159[/C][C]1553910.76933539[/C][C]117248.230664612[/C][/ROW]
[ROW][C]6[/C][C]1493308[/C][C]1670623.0087756[/C][C]-177315.008775597[/C][/ROW]
[ROW][C]7[/C][C]2957796[/C][C]1494118.58185799[/C][C]1463677.41814201[/C][/ROW]
[ROW][C]8[/C][C]2638691[/C][C]2951104.91181015[/C][C]-312413.911810151[/C][/ROW]
[ROW][C]9[/C][C]1305669[/C][C]2640119.17605146[/C][C]-1334450.17605146[/C][/ROW]
[ROW][C]10[/C][C]1280496[/C][C]1311769.33584057[/C][C]-31273.335840567[/C][/ROW]
[ROW][C]11[/C][C]921900[/C][C]1280638.96363769[/C][C]-358738.963637688[/C][/ROW]
[ROW][C]12[/C][C]867888[/C][C]923539.947445443[/C][C]-55651.9474454432[/C][/ROW]
[ROW][C]13[/C][C]652586[/C][C]868142.408576425[/C][C]-215556.408576425[/C][/ROW]
[ROW][C]14[/C][C]913831[/C][C]653571.399461517[/C][C]260259.600538483[/C][/ROW]
[ROW][C]15[/C][C]1108544[/C][C]912641.243351524[/C][C]195902.756648476[/C][/ROW]
[ROW][C]16[/C][C]1555827[/C][C]1107648.44568925[/C][C]448178.554310753[/C][/ROW]
[ROW][C]17[/C][C]1699283[/C][C]1553778.18637855[/C][C]145504.813621446[/C][/ROW]
[ROW][C]18[/C][C]1509458[/C][C]1698617.83599055[/C][C]-189159.835990553[/C][/ROW]
[ROW][C]19[/C][C]3268975[/C][C]1510322.72957012[/C][C]1758652.27042988[/C][/ROW]
[ROW][C]20[/C][C]2425016[/C][C]3260935.45707143[/C][C]-835919.457071434[/C][/ROW]
[ROW][C]21[/C][C]1312703[/C][C]2428837.34119004[/C][C]-1116134.34119004[/C][/ROW]
[ROW][C]22[/C][C]1365498[/C][C]1317805.32187506[/C][C]47692.678124937[/C][/ROW]
[ROW][C]23[/C][C]934453[/C][C]1365279.9766081[/C][C]-430826.976608105[/C][/ROW]
[ROW][C]24[/C][C]775019[/C][C]936422.492225077[/C][C]-161403.492225077[/C][/ROW]
[ROW][C]25[/C][C]651142[/C][C]775756.84358988[/C][C]-124614.84358988[/C][/ROW]
[ROW][C]26[/C][C]843192[/C][C]651711.667126027[/C][C]191480.332873973[/C][/ROW]
[ROW][C]27[/C][C]1146766[/C][C]842316.662457724[/C][C]304449.337542276[/C][/ROW]
[ROW][C]28[/C][C]1652601[/C][C]1145374.23338422[/C][C]507226.766615777[/C][/ROW]
[ROW][C]29[/C][C]1465906[/C][C]1650282.25203982[/C][C]-184376.25203982[/C][/ROW]
[ROW][C]30[/C][C]1652734[/C][C]1466748.86178582[/C][C]185985.138214185[/C][/ROW]
[ROW][C]31[/C][C]2922334[/C][C]1651883.78331539[/C][C]1270450.21668461[/C][/ROW]
[ROW][C]32[/C][C]2702805[/C][C]2916526.23502714[/C][C]-213721.235027141[/C][/ROW]
[ROW][C]33[/C][C]1458956[/C][C]2703782.01010748[/C][C]-1244826.01010748[/C][/ROW]
[ROW][C]34[/C][C]1410363[/C][C]1464646.62589298[/C][C]-54283.6258929789[/C][/ROW]
[ROW][C]35[/C][C]1019279[/C][C]1410611.1534002[/C][C]-391332.153400205[/C][/ROW]
[ROW][C]36[/C][C]936574[/C][C]1021067.94469332[/C][C]-84493.9446933247[/C][/ROW]
[ROW][C]37[/C][C]708917[/C][C]936960.257537654[/C][C]-228043.257537654[/C][/ROW]
[ROW][C]38[/C][C]885295[/C][C]709959.482126439[/C][C]175335.517873561[/C][/ROW]
[ROW][C]39[/C][C]1099663[/C][C]884493.46723167[/C][C]215169.53276833[/C][/ROW]
[ROW][C]40[/C][C]1576220[/C][C]1098679.36911134[/C][C]477540.630888662[/C][/ROW]
[ROW][C]41[/C][C]1487870[/C][C]1574036.95991486[/C][C]-86166.959914864[/C][/ROW]
[ROW][C]42[/C][C]1488635[/C][C]1488263.90559743[/C][C]371.094402567483[/C][/ROW]
[ROW][C]43[/C][C]2882530[/C][C]1488633.30357062[/C][C]1393896.69642938[/C][/ROW]
[ROW][C]44[/C][C]2677026[/C][C]2876157.90898613[/C][C]-199131.908986129[/C][/ROW]
[ROW][C]45[/C][C]1404398[/C][C]2677936.31613108[/C][C]-1273538.31613108[/C][/ROW]
[ROW][C]46[/C][C]1344370[/C][C]1410219.8819808[/C][C]-65849.8819808003[/C][/ROW]
[ROW][C]47[/C][C]936865[/C][C]1344671.02764596[/C][C]-407806.027645958[/C][/ROW]
[ROW][C]48[/C][C]872705[/C][C]938729.253736178[/C][C]-66024.2537361784[/C][/ROW]
[ROW][C]49[/C][C]628151[/C][C]873006.82477296[/C][C]-244855.82477296[/C][/ROW]
[ROW][C]50[/C][C]953712[/C][C]629270.339478117[/C][C]324441.660521883[/C][/ROW]
[ROW][C]51[/C][C]1160384[/C][C]952228.840024923[/C][C]208155.159975077[/C][/ROW]
[ROW][C]52[/C][C]1400618[/C][C]1159432.43477442[/C][C]241185.565225577[/C][/ROW]
[ROW][C]53[/C][C]1661511[/C][C]1399515.43882973[/C][C]261995.561170269[/C][/ROW]
[ROW][C]54[/C][C]1495347[/C][C]1660313.30754167[/C][C]-164966.307541668[/C][/ROW]
[ROW][C]55[/C][C]2918786[/C][C]1496101.13072473[/C][C]1422684.86927527[/C][/ROW]
[ROW][C]56[/C][C]2775677[/C][C]2912282.30607899[/C][C]-136605.306078993[/C][/ROW]
[ROW][C]57[/C][C]1407026[/C][C]2776301.48059856[/C][C]-1369275.48059856[/C][/ROW]
[ROW][C]58[/C][C]1370199[/C][C]1413285.53702867[/C][C]-43086.5370286666[/C][/ROW]
[ROW][C]59[/C][C]964526[/C][C]1370395.96677388[/C][C]-405869.966773881[/C][/ROW]
[ROW][C]60[/C][C]850851[/C][C]966381.403183539[/C][C]-115530.403183539[/C][/ROW]
[ROW][C]61[/C][C]683118[/C][C]851379.138308843[/C][C]-168261.138308843[/C][/ROW]
[ROW][C]62[/C][C]847224[/C][C]683887.192788926[/C][C]163336.807211074[/C][/ROW]
[ROW][C]63[/C][C]1073256[/C][C]846477.318410087[/C][C]226778.681589913[/C][/ROW]
[ROW][C]64[/C][C]1514326[/C][C]1072219.29878477[/C][C]442106.701215232[/C][/ROW]
[ROW][C]65[/C][C]1503734[/C][C]1512304.94338569[/C][C]-8570.94338568836[/C][/ROW]
[ROW][C]66[/C][C]1507712[/C][C]1503773.18140524[/C][C]3938.81859475793[/C][/ROW]
[ROW][C]67[/C][C]2865698[/C][C]1507693.99399522[/C][C]1358004.00600478[/C][/ROW]
[ROW][C]68[/C][C]2788128[/C][C]2859489.98964627[/C][C]-71361.9896462699[/C][/ROW]
[ROW][C]69[/C][C]1391596[/C][C]2788454.22582012[/C][C]-1396858.22582012[/C][/ROW]
[ROW][C]70[/C][C]1366378[/C][C]1397981.62941658[/C][C]-31603.629416585[/C][/ROW]
[ROW][C]71[/C][C]946295[/C][C]1366522.47354924[/C][C]-420227.473549243[/C][/ROW]
[ROW][C]72[/C][C]859626[/C][C]948216.037416075[/C][C]-88590.0374160755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201525&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201525&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
2873127655362217765
31107897872131.504133491235765.495866509
415559641106819.21625789449144.78374211
516711591553910.76933539117248.230664612
614933081670623.0087756-177315.008775597
729577961494118.581857991463677.41814201
826386912951104.91181015-312413.911810151
913056692640119.17605146-1334450.17605146
1012804961311769.33584057-31273.335840567
119219001280638.96363769-358738.963637688
12867888923539.947445443-55651.9474454432
13652586868142.408576425-215556.408576425
14913831653571.399461517260259.600538483
151108544912641.243351524195902.756648476
1615558271107648.44568925448178.554310753
1716992831553778.18637855145504.813621446
1815094581698617.83599055-189159.835990553
1932689751510322.729570121758652.27042988
2024250163260935.45707143-835919.457071434
2113127032428837.34119004-1116134.34119004
2213654981317805.3218750647692.678124937
239344531365279.9766081-430826.976608105
24775019936422.492225077-161403.492225077
25651142775756.84358988-124614.84358988
26843192651711.667126027191480.332873973
271146766842316.662457724304449.337542276
2816526011145374.23338422507226.766615777
2914659061650282.25203982-184376.25203982
3016527341466748.86178582185985.138214185
3129223341651883.783315391270450.21668461
3227028052916526.23502714-213721.235027141
3314589562703782.01010748-1244826.01010748
3414103631464646.62589298-54283.6258929789
3510192791410611.1534002-391332.153400205
369365741021067.94469332-84493.9446933247
37708917936960.257537654-228043.257537654
38885295709959.482126439175335.517873561
391099663884493.46723167215169.53276833
4015762201098679.36911134477540.630888662
4114878701574036.95991486-86166.959914864
4214886351488263.90559743371.094402567483
4328825301488633.303570621393896.69642938
4426770262876157.90898613-199131.908986129
4514043982677936.31613108-1273538.31613108
4613443701410219.8819808-65849.8819808003
479368651344671.02764596-407806.027645958
48872705938729.253736178-66024.2537361784
49628151873006.82477296-244855.82477296
50953712629270.339478117324441.660521883
511160384952228.840024923208155.159975077
5214006181159432.43477442241185.565225577
5316615111399515.43882973261995.561170269
5414953471660313.30754167-164966.307541668
5529187861496101.130724731422684.86927527
5627756772912282.30607899-136605.306078993
5714070262776301.48059856-1369275.48059856
5813701991413285.53702867-43086.5370286666
599645261370395.96677388-405869.966773881
60850851966381.403183539-115530.403183539
61683118851379.138308843-168261.138308843
62847224683887.192788926163336.807211074
631073256846477.318410087226778.681589913
6415143261072219.29878477442106.701215232
6515037341512304.94338569-8570.94338568836
6615077121503773.181405243938.81859475793
6728656981507693.993995221358004.00600478
6827881282859489.98964627-71361.9896462699
6913915962788454.22582012-1396858.22582012
7013663781397981.62941658-31603.629416585
719462951366522.47354924-420227.473549243
72859626948216.037416075-88590.0374160755







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73860030.98250895-354961.9588761042075023.923894
74860030.98250895-854305.5669246272574367.53194253
75860030.98250895-1237989.932980732958051.89799863
76860030.98250895-1561628.307924053281690.27294195
77860030.98250895-1846844.647446883566906.61246478
78860030.98250895-2104748.542709933824810.50772783
79860030.98250895-2341946.467484324062008.43250222
80860030.98250895-2562745.894147454282807.85916535
81860030.98250895-2770140.295059384490202.26007728
82860030.98250895-2966310.019230234686371.98424813
83860030.98250895-3152901.538565724872963.50358362
84860030.98250895-3331194.30084285051256.26586071

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 860030.98250895 & -354961.958876104 & 2075023.923894 \tabularnewline
74 & 860030.98250895 & -854305.566924627 & 2574367.53194253 \tabularnewline
75 & 860030.98250895 & -1237989.93298073 & 2958051.89799863 \tabularnewline
76 & 860030.98250895 & -1561628.30792405 & 3281690.27294195 \tabularnewline
77 & 860030.98250895 & -1846844.64744688 & 3566906.61246478 \tabularnewline
78 & 860030.98250895 & -2104748.54270993 & 3824810.50772783 \tabularnewline
79 & 860030.98250895 & -2341946.46748432 & 4062008.43250222 \tabularnewline
80 & 860030.98250895 & -2562745.89414745 & 4282807.85916535 \tabularnewline
81 & 860030.98250895 & -2770140.29505938 & 4490202.26007728 \tabularnewline
82 & 860030.98250895 & -2966310.01923023 & 4686371.98424813 \tabularnewline
83 & 860030.98250895 & -3152901.53856572 & 4872963.50358362 \tabularnewline
84 & 860030.98250895 & -3331194.3008428 & 5051256.26586071 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201525&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]73[/C][C]860030.98250895[/C][C]-354961.958876104[/C][C]2075023.923894[/C][/ROW]
[ROW][C]74[/C][C]860030.98250895[/C][C]-854305.566924627[/C][C]2574367.53194253[/C][/ROW]
[ROW][C]75[/C][C]860030.98250895[/C][C]-1237989.93298073[/C][C]2958051.89799863[/C][/ROW]
[ROW][C]76[/C][C]860030.98250895[/C][C]-1561628.30792405[/C][C]3281690.27294195[/C][/ROW]
[ROW][C]77[/C][C]860030.98250895[/C][C]-1846844.64744688[/C][C]3566906.61246478[/C][/ROW]
[ROW][C]78[/C][C]860030.98250895[/C][C]-2104748.54270993[/C][C]3824810.50772783[/C][/ROW]
[ROW][C]79[/C][C]860030.98250895[/C][C]-2341946.46748432[/C][C]4062008.43250222[/C][/ROW]
[ROW][C]80[/C][C]860030.98250895[/C][C]-2562745.89414745[/C][C]4282807.85916535[/C][/ROW]
[ROW][C]81[/C][C]860030.98250895[/C][C]-2770140.29505938[/C][C]4490202.26007728[/C][/ROW]
[ROW][C]82[/C][C]860030.98250895[/C][C]-2966310.01923023[/C][C]4686371.98424813[/C][/ROW]
[ROW][C]83[/C][C]860030.98250895[/C][C]-3152901.53856572[/C][C]4872963.50358362[/C][/ROW]
[ROW][C]84[/C][C]860030.98250895[/C][C]-3331194.3008428[/C][C]5051256.26586071[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201525&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201525&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
73860030.98250895-354961.9588761042075023.923894
74860030.98250895-854305.5669246272574367.53194253
75860030.98250895-1237989.932980732958051.89799863
76860030.98250895-1561628.307924053281690.27294195
77860030.98250895-1846844.647446883566906.61246478
78860030.98250895-2104748.542709933824810.50772783
79860030.98250895-2341946.467484324062008.43250222
80860030.98250895-2562745.894147454282807.85916535
81860030.98250895-2770140.295059384490202.26007728
82860030.98250895-2966310.019230234686371.98424813
83860030.98250895-3152901.538565724872963.50358362
84860030.98250895-3331194.30084285051256.26586071



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')