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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, 06 Dec 2011 15:04:42 -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/2011/Dec/06/t1323201970tgnc6zajrib4ik2.htm/, Retrieved Mon, 29 Apr 2024 05:16:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151866, Retrieved Mon, 29 Apr 2024 05:16:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2011-12-03 17:51:28] [63b27a8f1021b1dec8e8fd0dfee8bfd3]
- R P     [Exponential Smoothing] [] [2011-12-06 20:04:42] [888e326c8b932e070d5e53fa2c51e0f3] [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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151866&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151866&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151866&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0306414050313823
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0306414050313823 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151866&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0306414050313823[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151866&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151866&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
alpha1
beta0.0306414050313823
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31107897109089217005
415559641326183.05709256229780.942907441
516711591781290.86803268-110131.868032678
614933081893111.27285743-399803.272857426
729577961703009.738840931254786.26115907
826386913205946.15289692-567255.152896919
913056692869459.65800087-1563790.65800087
1012804961488520.91506477-208024.915064769
119219001456973.73938565-535073.739385651
128678881081982.32821548-214094.328215479
136525861021410.17718971-368824.177189707
14913831794806.88619107119024.11380893
1511085441059698.9522707948845.0477292088
1615558271255908.63316204299918.366837961
1716992831712381.55331667-13098.5533166716
1815094581855436.19523917-345978.19523917
1932689751655009.937226821613965.06277318
2024250163463981.09442175-1038965.09442175
2113127032588186.74415011-1275483.74415011
2213654981436791.13013466-71293.130134661
239344531487401.60845825-552948.60845825
247750191039413.48618494-264394.486184941
25651142871878.067645684-220736.067645684
26843192741237.404391918101954.595608082
271146766936411.436450756210354.563549244
2816526011246430.99583267406170.004167332
2914659061764711.61544196-298805.615441958
3016527341568860.7915535583873.2084464508
3129223341758258.784504841164075.21549516
3227028053063527.68466982-360722.684669819
3314589562832945.63478484-1373989.63478484
3414103631546995.66187648-136632.661876481
3510192791494216.04514341-474937.045143407
369365741088579.30677876-152005.30677876
377089171001216.65060683-292299.650606833
38885295764603.178622057120691.821377943
391099663944679.345604874154983.654395126
4015762201163796.26253244412423.737467561
4114878701652990.50531674-165120.505316739
4214886351559580.98103434-70945.9810343422
4328825301558172.096494121324357.90350588
4426770262992647.28342196-315621.283421956
4514043982777472.2038401-1373074.2038401
4613443701462771.28102209-118401.281022092
479368651399115.29941406-462250.29941406
48872705977446.300763836-104741.300763836
49628151910076.880143617-281925.880143617
50953712656884.275061308296827.724938692
511160384991540.493605698168843.506394302
5214006181203386.09587204197231.904127956
5316615111449663.55853154211847.44146846
5414953471717047.86179044-221700.861790437
5529187861544090.635888511374695.36411149
5627756773009652.23333501-233975.233335014
5714070262859373.90344308-1452347.90344308
5813701991446220.9230872-76021.9230872048
599645261407064.50455063-442538.504550625
60850851987831.502990707-136980.502990707
61683118869959.227917166-186841.227917166
62847224696501.150175996150722.849824004
631073256865225.510064937208030.489935063
6415143261097631.85656591416694.143434086
6515037341551469.95058908-47735.9505890831
6615077121539415.25399252-31703.2539925249
6728656981542421.821746131323276.17825387
6827881282940954.86309238-152826.863092384
6913915962858702.03328069-1467106.03328069
7013663781417215.84309096-50837.8430909561
719462951390440.10014988-444145.100149884
72859626956747.870243488-97121.8702434878

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1107897 & 1090892 & 17005 \tabularnewline
4 & 1555964 & 1326183.05709256 & 229780.942907441 \tabularnewline
5 & 1671159 & 1781290.86803268 & -110131.868032678 \tabularnewline
6 & 1493308 & 1893111.27285743 & -399803.272857426 \tabularnewline
7 & 2957796 & 1703009.73884093 & 1254786.26115907 \tabularnewline
8 & 2638691 & 3205946.15289692 & -567255.152896919 \tabularnewline
9 & 1305669 & 2869459.65800087 & -1563790.65800087 \tabularnewline
10 & 1280496 & 1488520.91506477 & -208024.915064769 \tabularnewline
11 & 921900 & 1456973.73938565 & -535073.739385651 \tabularnewline
12 & 867888 & 1081982.32821548 & -214094.328215479 \tabularnewline
13 & 652586 & 1021410.17718971 & -368824.177189707 \tabularnewline
14 & 913831 & 794806.88619107 & 119024.11380893 \tabularnewline
15 & 1108544 & 1059698.95227079 & 48845.0477292088 \tabularnewline
16 & 1555827 & 1255908.63316204 & 299918.366837961 \tabularnewline
17 & 1699283 & 1712381.55331667 & -13098.5533166716 \tabularnewline
18 & 1509458 & 1855436.19523917 & -345978.19523917 \tabularnewline
19 & 3268975 & 1655009.93722682 & 1613965.06277318 \tabularnewline
20 & 2425016 & 3463981.09442175 & -1038965.09442175 \tabularnewline
21 & 1312703 & 2588186.74415011 & -1275483.74415011 \tabularnewline
22 & 1365498 & 1436791.13013466 & -71293.130134661 \tabularnewline
23 & 934453 & 1487401.60845825 & -552948.60845825 \tabularnewline
24 & 775019 & 1039413.48618494 & -264394.486184941 \tabularnewline
25 & 651142 & 871878.067645684 & -220736.067645684 \tabularnewline
26 & 843192 & 741237.404391918 & 101954.595608082 \tabularnewline
27 & 1146766 & 936411.436450756 & 210354.563549244 \tabularnewline
28 & 1652601 & 1246430.99583267 & 406170.004167332 \tabularnewline
29 & 1465906 & 1764711.61544196 & -298805.615441958 \tabularnewline
30 & 1652734 & 1568860.79155355 & 83873.2084464508 \tabularnewline
31 & 2922334 & 1758258.78450484 & 1164075.21549516 \tabularnewline
32 & 2702805 & 3063527.68466982 & -360722.684669819 \tabularnewline
33 & 1458956 & 2832945.63478484 & -1373989.63478484 \tabularnewline
34 & 1410363 & 1546995.66187648 & -136632.661876481 \tabularnewline
35 & 1019279 & 1494216.04514341 & -474937.045143407 \tabularnewline
36 & 936574 & 1088579.30677876 & -152005.30677876 \tabularnewline
37 & 708917 & 1001216.65060683 & -292299.650606833 \tabularnewline
38 & 885295 & 764603.178622057 & 120691.821377943 \tabularnewline
39 & 1099663 & 944679.345604874 & 154983.654395126 \tabularnewline
40 & 1576220 & 1163796.26253244 & 412423.737467561 \tabularnewline
41 & 1487870 & 1652990.50531674 & -165120.505316739 \tabularnewline
42 & 1488635 & 1559580.98103434 & -70945.9810343422 \tabularnewline
43 & 2882530 & 1558172.09649412 & 1324357.90350588 \tabularnewline
44 & 2677026 & 2992647.28342196 & -315621.283421956 \tabularnewline
45 & 1404398 & 2777472.2038401 & -1373074.2038401 \tabularnewline
46 & 1344370 & 1462771.28102209 & -118401.281022092 \tabularnewline
47 & 936865 & 1399115.29941406 & -462250.29941406 \tabularnewline
48 & 872705 & 977446.300763836 & -104741.300763836 \tabularnewline
49 & 628151 & 910076.880143617 & -281925.880143617 \tabularnewline
50 & 953712 & 656884.275061308 & 296827.724938692 \tabularnewline
51 & 1160384 & 991540.493605698 & 168843.506394302 \tabularnewline
52 & 1400618 & 1203386.09587204 & 197231.904127956 \tabularnewline
53 & 1661511 & 1449663.55853154 & 211847.44146846 \tabularnewline
54 & 1495347 & 1717047.86179044 & -221700.861790437 \tabularnewline
55 & 2918786 & 1544090.63588851 & 1374695.36411149 \tabularnewline
56 & 2775677 & 3009652.23333501 & -233975.233335014 \tabularnewline
57 & 1407026 & 2859373.90344308 & -1452347.90344308 \tabularnewline
58 & 1370199 & 1446220.9230872 & -76021.9230872048 \tabularnewline
59 & 964526 & 1407064.50455063 & -442538.504550625 \tabularnewline
60 & 850851 & 987831.502990707 & -136980.502990707 \tabularnewline
61 & 683118 & 869959.227917166 & -186841.227917166 \tabularnewline
62 & 847224 & 696501.150175996 & 150722.849824004 \tabularnewline
63 & 1073256 & 865225.510064937 & 208030.489935063 \tabularnewline
64 & 1514326 & 1097631.85656591 & 416694.143434086 \tabularnewline
65 & 1503734 & 1551469.95058908 & -47735.9505890831 \tabularnewline
66 & 1507712 & 1539415.25399252 & -31703.2539925249 \tabularnewline
67 & 2865698 & 1542421.82174613 & 1323276.17825387 \tabularnewline
68 & 2788128 & 2940954.86309238 & -152826.863092384 \tabularnewline
69 & 1391596 & 2858702.03328069 & -1467106.03328069 \tabularnewline
70 & 1366378 & 1417215.84309096 & -50837.8430909561 \tabularnewline
71 & 946295 & 1390440.10014988 & -444145.100149884 \tabularnewline
72 & 859626 & 956747.870243488 & -97121.8702434878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151866&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]1107897[/C][C]1090892[/C][C]17005[/C][/ROW]
[ROW][C]4[/C][C]1555964[/C][C]1326183.05709256[/C][C]229780.942907441[/C][/ROW]
[ROW][C]5[/C][C]1671159[/C][C]1781290.86803268[/C][C]-110131.868032678[/C][/ROW]
[ROW][C]6[/C][C]1493308[/C][C]1893111.27285743[/C][C]-399803.272857426[/C][/ROW]
[ROW][C]7[/C][C]2957796[/C][C]1703009.73884093[/C][C]1254786.26115907[/C][/ROW]
[ROW][C]8[/C][C]2638691[/C][C]3205946.15289692[/C][C]-567255.152896919[/C][/ROW]
[ROW][C]9[/C][C]1305669[/C][C]2869459.65800087[/C][C]-1563790.65800087[/C][/ROW]
[ROW][C]10[/C][C]1280496[/C][C]1488520.91506477[/C][C]-208024.915064769[/C][/ROW]
[ROW][C]11[/C][C]921900[/C][C]1456973.73938565[/C][C]-535073.739385651[/C][/ROW]
[ROW][C]12[/C][C]867888[/C][C]1081982.32821548[/C][C]-214094.328215479[/C][/ROW]
[ROW][C]13[/C][C]652586[/C][C]1021410.17718971[/C][C]-368824.177189707[/C][/ROW]
[ROW][C]14[/C][C]913831[/C][C]794806.88619107[/C][C]119024.11380893[/C][/ROW]
[ROW][C]15[/C][C]1108544[/C][C]1059698.95227079[/C][C]48845.0477292088[/C][/ROW]
[ROW][C]16[/C][C]1555827[/C][C]1255908.63316204[/C][C]299918.366837961[/C][/ROW]
[ROW][C]17[/C][C]1699283[/C][C]1712381.55331667[/C][C]-13098.5533166716[/C][/ROW]
[ROW][C]18[/C][C]1509458[/C][C]1855436.19523917[/C][C]-345978.19523917[/C][/ROW]
[ROW][C]19[/C][C]3268975[/C][C]1655009.93722682[/C][C]1613965.06277318[/C][/ROW]
[ROW][C]20[/C][C]2425016[/C][C]3463981.09442175[/C][C]-1038965.09442175[/C][/ROW]
[ROW][C]21[/C][C]1312703[/C][C]2588186.74415011[/C][C]-1275483.74415011[/C][/ROW]
[ROW][C]22[/C][C]1365498[/C][C]1436791.13013466[/C][C]-71293.130134661[/C][/ROW]
[ROW][C]23[/C][C]934453[/C][C]1487401.60845825[/C][C]-552948.60845825[/C][/ROW]
[ROW][C]24[/C][C]775019[/C][C]1039413.48618494[/C][C]-264394.486184941[/C][/ROW]
[ROW][C]25[/C][C]651142[/C][C]871878.067645684[/C][C]-220736.067645684[/C][/ROW]
[ROW][C]26[/C][C]843192[/C][C]741237.404391918[/C][C]101954.595608082[/C][/ROW]
[ROW][C]27[/C][C]1146766[/C][C]936411.436450756[/C][C]210354.563549244[/C][/ROW]
[ROW][C]28[/C][C]1652601[/C][C]1246430.99583267[/C][C]406170.004167332[/C][/ROW]
[ROW][C]29[/C][C]1465906[/C][C]1764711.61544196[/C][C]-298805.615441958[/C][/ROW]
[ROW][C]30[/C][C]1652734[/C][C]1568860.79155355[/C][C]83873.2084464508[/C][/ROW]
[ROW][C]31[/C][C]2922334[/C][C]1758258.78450484[/C][C]1164075.21549516[/C][/ROW]
[ROW][C]32[/C][C]2702805[/C][C]3063527.68466982[/C][C]-360722.684669819[/C][/ROW]
[ROW][C]33[/C][C]1458956[/C][C]2832945.63478484[/C][C]-1373989.63478484[/C][/ROW]
[ROW][C]34[/C][C]1410363[/C][C]1546995.66187648[/C][C]-136632.661876481[/C][/ROW]
[ROW][C]35[/C][C]1019279[/C][C]1494216.04514341[/C][C]-474937.045143407[/C][/ROW]
[ROW][C]36[/C][C]936574[/C][C]1088579.30677876[/C][C]-152005.30677876[/C][/ROW]
[ROW][C]37[/C][C]708917[/C][C]1001216.65060683[/C][C]-292299.650606833[/C][/ROW]
[ROW][C]38[/C][C]885295[/C][C]764603.178622057[/C][C]120691.821377943[/C][/ROW]
[ROW][C]39[/C][C]1099663[/C][C]944679.345604874[/C][C]154983.654395126[/C][/ROW]
[ROW][C]40[/C][C]1576220[/C][C]1163796.26253244[/C][C]412423.737467561[/C][/ROW]
[ROW][C]41[/C][C]1487870[/C][C]1652990.50531674[/C][C]-165120.505316739[/C][/ROW]
[ROW][C]42[/C][C]1488635[/C][C]1559580.98103434[/C][C]-70945.9810343422[/C][/ROW]
[ROW][C]43[/C][C]2882530[/C][C]1558172.09649412[/C][C]1324357.90350588[/C][/ROW]
[ROW][C]44[/C][C]2677026[/C][C]2992647.28342196[/C][C]-315621.283421956[/C][/ROW]
[ROW][C]45[/C][C]1404398[/C][C]2777472.2038401[/C][C]-1373074.2038401[/C][/ROW]
[ROW][C]46[/C][C]1344370[/C][C]1462771.28102209[/C][C]-118401.281022092[/C][/ROW]
[ROW][C]47[/C][C]936865[/C][C]1399115.29941406[/C][C]-462250.29941406[/C][/ROW]
[ROW][C]48[/C][C]872705[/C][C]977446.300763836[/C][C]-104741.300763836[/C][/ROW]
[ROW][C]49[/C][C]628151[/C][C]910076.880143617[/C][C]-281925.880143617[/C][/ROW]
[ROW][C]50[/C][C]953712[/C][C]656884.275061308[/C][C]296827.724938692[/C][/ROW]
[ROW][C]51[/C][C]1160384[/C][C]991540.493605698[/C][C]168843.506394302[/C][/ROW]
[ROW][C]52[/C][C]1400618[/C][C]1203386.09587204[/C][C]197231.904127956[/C][/ROW]
[ROW][C]53[/C][C]1661511[/C][C]1449663.55853154[/C][C]211847.44146846[/C][/ROW]
[ROW][C]54[/C][C]1495347[/C][C]1717047.86179044[/C][C]-221700.861790437[/C][/ROW]
[ROW][C]55[/C][C]2918786[/C][C]1544090.63588851[/C][C]1374695.36411149[/C][/ROW]
[ROW][C]56[/C][C]2775677[/C][C]3009652.23333501[/C][C]-233975.233335014[/C][/ROW]
[ROW][C]57[/C][C]1407026[/C][C]2859373.90344308[/C][C]-1452347.90344308[/C][/ROW]
[ROW][C]58[/C][C]1370199[/C][C]1446220.9230872[/C][C]-76021.9230872048[/C][/ROW]
[ROW][C]59[/C][C]964526[/C][C]1407064.50455063[/C][C]-442538.504550625[/C][/ROW]
[ROW][C]60[/C][C]850851[/C][C]987831.502990707[/C][C]-136980.502990707[/C][/ROW]
[ROW][C]61[/C][C]683118[/C][C]869959.227917166[/C][C]-186841.227917166[/C][/ROW]
[ROW][C]62[/C][C]847224[/C][C]696501.150175996[/C][C]150722.849824004[/C][/ROW]
[ROW][C]63[/C][C]1073256[/C][C]865225.510064937[/C][C]208030.489935063[/C][/ROW]
[ROW][C]64[/C][C]1514326[/C][C]1097631.85656591[/C][C]416694.143434086[/C][/ROW]
[ROW][C]65[/C][C]1503734[/C][C]1551469.95058908[/C][C]-47735.9505890831[/C][/ROW]
[ROW][C]66[/C][C]1507712[/C][C]1539415.25399252[/C][C]-31703.2539925249[/C][/ROW]
[ROW][C]67[/C][C]2865698[/C][C]1542421.82174613[/C][C]1323276.17825387[/C][/ROW]
[ROW][C]68[/C][C]2788128[/C][C]2940954.86309238[/C][C]-152826.863092384[/C][/ROW]
[ROW][C]69[/C][C]1391596[/C][C]2858702.03328069[/C][C]-1467106.03328069[/C][/ROW]
[ROW][C]70[/C][C]1366378[/C][C]1417215.84309096[/C][C]-50837.8430909561[/C][/ROW]
[ROW][C]71[/C][C]946295[/C][C]1390440.10014988[/C][C]-444145.100149884[/C][/ROW]
[ROW][C]72[/C][C]859626[/C][C]956747.870243488[/C][C]-97121.8702434878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151866&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151866&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
31107897109089217005
415559641326183.05709256229780.942907441
516711591781290.86803268-110131.868032678
614933081893111.27285743-399803.272857426
729577961703009.738840931254786.26115907
826386913205946.15289692-567255.152896919
913056692869459.65800087-1563790.65800087
1012804961488520.91506477-208024.915064769
119219001456973.73938565-535073.739385651
128678881081982.32821548-214094.328215479
136525861021410.17718971-368824.177189707
14913831794806.88619107119024.11380893
1511085441059698.9522707948845.0477292088
1615558271255908.63316204299918.366837961
1716992831712381.55331667-13098.5533166716
1815094581855436.19523917-345978.19523917
1932689751655009.937226821613965.06277318
2024250163463981.09442175-1038965.09442175
2113127032588186.74415011-1275483.74415011
2213654981436791.13013466-71293.130134661
239344531487401.60845825-552948.60845825
247750191039413.48618494-264394.486184941
25651142871878.067645684-220736.067645684
26843192741237.404391918101954.595608082
271146766936411.436450756210354.563549244
2816526011246430.99583267406170.004167332
2914659061764711.61544196-298805.615441958
3016527341568860.7915535583873.2084464508
3129223341758258.784504841164075.21549516
3227028053063527.68466982-360722.684669819
3314589562832945.63478484-1373989.63478484
3414103631546995.66187648-136632.661876481
3510192791494216.04514341-474937.045143407
369365741088579.30677876-152005.30677876
377089171001216.65060683-292299.650606833
38885295764603.178622057120691.821377943
391099663944679.345604874154983.654395126
4015762201163796.26253244412423.737467561
4114878701652990.50531674-165120.505316739
4214886351559580.98103434-70945.9810343422
4328825301558172.096494121324357.90350588
4426770262992647.28342196-315621.283421956
4514043982777472.2038401-1373074.2038401
4613443701462771.28102209-118401.281022092
479368651399115.29941406-462250.29941406
48872705977446.300763836-104741.300763836
49628151910076.880143617-281925.880143617
50953712656884.275061308296827.724938692
511160384991540.493605698168843.506394302
5214006181203386.09587204197231.904127956
5316615111449663.55853154211847.44146846
5414953471717047.86179044-221700.861790437
5529187861544090.635888511374695.36411149
5627756773009652.23333501-233975.233335014
5714070262859373.90344308-1452347.90344308
5813701991446220.9230872-76021.9230872048
599645261407064.50455063-442538.504550625
60850851987831.502990707-136980.502990707
61683118869959.227917166-186841.227917166
62847224696501.150175996150722.849824004
631073256865225.510064937208030.489935063
6415143261097631.85656591416694.143434086
6515037341551469.95058908-47735.9505890831
6615077121539415.25399252-31703.2539925249
6728656981542421.821746131323276.17825387
6827881282940954.86309238-152826.863092384
6913915962858702.03328069-1467106.03328069
7013663781417215.84309096-50837.8430909561
719462951390440.10014988-444145.100149884
72859626956747.870243488-97121.8702434878







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73867102.919679952-373606.085776582107811.92513648
74874579.839359903-907132.5967576812656292.27547749
75882056.759039855-1333414.229525923097527.74760563
76889533.678719807-1707327.295513093486394.6529527
77897010.598399759-2049769.92528353843791.12208302
78904487.51807971-2371285.352826224180260.38898564
79911964.437759662-2678034.845707954501963.72122727
80919441.357439614-2973966.778134454812849.49301367
81926918.277119565-3261777.780261965115614.33450109
82934395.196799517-3543397.641530195412188.03512923
83941872.116479469-3820257.620367855704001.85332679
84949349.03615942-4093449.595416195992147.66773503

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 867102.919679952 & -373606.08577658 & 2107811.92513648 \tabularnewline
74 & 874579.839359903 & -907132.596757681 & 2656292.27547749 \tabularnewline
75 & 882056.759039855 & -1333414.22952592 & 3097527.74760563 \tabularnewline
76 & 889533.678719807 & -1707327.29551309 & 3486394.6529527 \tabularnewline
77 & 897010.598399759 & -2049769.9252835 & 3843791.12208302 \tabularnewline
78 & 904487.51807971 & -2371285.35282622 & 4180260.38898564 \tabularnewline
79 & 911964.437759662 & -2678034.84570795 & 4501963.72122727 \tabularnewline
80 & 919441.357439614 & -2973966.77813445 & 4812849.49301367 \tabularnewline
81 & 926918.277119565 & -3261777.78026196 & 5115614.33450109 \tabularnewline
82 & 934395.196799517 & -3543397.64153019 & 5412188.03512923 \tabularnewline
83 & 941872.116479469 & -3820257.62036785 & 5704001.85332679 \tabularnewline
84 & 949349.03615942 & -4093449.59541619 & 5992147.66773503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151866&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]867102.919679952[/C][C]-373606.08577658[/C][C]2107811.92513648[/C][/ROW]
[ROW][C]74[/C][C]874579.839359903[/C][C]-907132.596757681[/C][C]2656292.27547749[/C][/ROW]
[ROW][C]75[/C][C]882056.759039855[/C][C]-1333414.22952592[/C][C]3097527.74760563[/C][/ROW]
[ROW][C]76[/C][C]889533.678719807[/C][C]-1707327.29551309[/C][C]3486394.6529527[/C][/ROW]
[ROW][C]77[/C][C]897010.598399759[/C][C]-2049769.9252835[/C][C]3843791.12208302[/C][/ROW]
[ROW][C]78[/C][C]904487.51807971[/C][C]-2371285.35282622[/C][C]4180260.38898564[/C][/ROW]
[ROW][C]79[/C][C]911964.437759662[/C][C]-2678034.84570795[/C][C]4501963.72122727[/C][/ROW]
[ROW][C]80[/C][C]919441.357439614[/C][C]-2973966.77813445[/C][C]4812849.49301367[/C][/ROW]
[ROW][C]81[/C][C]926918.277119565[/C][C]-3261777.78026196[/C][C]5115614.33450109[/C][/ROW]
[ROW][C]82[/C][C]934395.196799517[/C][C]-3543397.64153019[/C][C]5412188.03512923[/C][/ROW]
[ROW][C]83[/C][C]941872.116479469[/C][C]-3820257.62036785[/C][C]5704001.85332679[/C][/ROW]
[ROW][C]84[/C][C]949349.03615942[/C][C]-4093449.59541619[/C][C]5992147.66773503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151866&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151866&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
73867102.919679952-373606.085776582107811.92513648
74874579.839359903-907132.5967576812656292.27547749
75882056.759039855-1333414.229525923097527.74760563
76889533.678719807-1707327.295513093486394.6529527
77897010.598399759-2049769.92528353843791.12208302
78904487.51807971-2371285.352826224180260.38898564
79911964.437759662-2678034.845707954501963.72122727
80919441.357439614-2973966.778134454812849.49301367
81926918.277119565-3261777.780261965115614.33450109
82934395.196799517-3543397.641530195412188.03512923
83941872.116479469-3820257.620367855704001.85332679
84949349.03615942-4093449.595416195992147.66773503



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')