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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 computationSun, 30 Nov 2014 14:17:31 +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/t1417357137z1sqbw65tzl350h.htm/, Retrieved Tue, 28 May 2024 16:26:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261455, Retrieved Tue, 28 May 2024 16:26:54 +0000
QR Codes:

Original text written by user:type: single
IsPrivate?No (this computation is public)
User-defined keywordsExponential Smoothing
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Workshop 9] [2014-11-30 14:17:31] [99d5c1073827aabbadf7ab1e7da1d584] [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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261455&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261455&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.99542857728993
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99542857728993 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261455&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]0.99542857728993[/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=261455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261455&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
alpha0.99542857728993
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2873127655362217765
31107897872131.504133542235765.495866458
415559641106819.21625795449144.783742055
516711591553910.76933549117248.230664508
614933081670623.00877562-177315.008775625
729577961494118.581857951463677.41814205
826386912951104.91181049-312413.911810489
913056692640119.17605139-1334450.17605139
1012804961311769.33584026-31273.3358402576
119219001280638.96363768-358738.96363768
12867888923539.94744536-55651.9474453601
13652586868142.408576411-215556.408576411
14913831653571.399461467260259.600538533
151108544912641.243351585195902.756648415
1615558271107648.44568929448178.554310708
1716992831553778.18637866145504.813621342
1815094581698617.83599059-189159.835990587
1932689751510322.729570081758652.27042992
2024250163260935.45707184-835919.457071841
2113127032428837.34118985-1116134.34118985
2213654981317805.321874847692.6781251961
239344531365279.97660811-430826.976608114
24775019936422.492224977-161403.492224977
25651142775756.843589842-124614.843589842
26843192651711.667125998191480.332874002
271146766842316.662457768304449.337542232
2816526011145374.23338429507226.766615706
2914659061650282.25203994-184376.252039938
3016527341466748.86178577185985.138214227
3129223341651883.783315431270450.21668457
3227028052916526.23502744-213721.235027435
3314589562703782.01010743-1244826.01010743
3414103631464646.62589269-54283.6258926904
3510192791410611.15340019-391332.153400191
369365741021067.94469323-84493.9446932341
37708917936960.257537634-228043.257537634
38885295709959.482126386175335.517873614
391099663884493.467231711215169.532768289
4015762201098679.36911139477540.630888612
4114878701574036.95991497-86166.9599149749
4214886351488263.90559741371.094402587041
4328825301488633.303570621393896.69642938
4426770262876157.90898645-199131.908986452
4514043982677936.31613104-1273538.31613104
4613443701410219.88198051-65849.8819805053
479368651344671.02764594-407806.027645941
48872705938729.253736084-66024.253736084
49628151873006.824772945-244855.824772945
50953712629270.33947806324441.66052194
511160384952228.840024997208155.159975003
5214006181159432.43477447241185.565225528
5316615111399515.43882979261995.561170213
5414953471660313.30754173-164966.307541729
5529187861496101.130724691422684.86927531
5627756772912282.30607932-136605.306079322
5714070262776301.48059853-1369275.48059853
5813701991413285.53702835-43086.5370283497
599645261370395.96677387-405869.96677387
60850851966381.403183445-115530.403183445
61683118851379.138308816-168261.138308816
62847224683887.192788887163336.807211113
631073256846477.318410125226778.681589875
6415143261072219.29878482442106.70121518
6515037341512304.94338579-8570.94338579103
6615077121503773.181405243938.81859475933
6728656981507693.993995231358004.00600477
6827881282859489.98964658-71361.9896465843
6913915962788454.22582011-1396858.22582011
7013663781397981.62941626-31603.6294162616
719462951366522.47354923-420227.473549234
72859626948216.037415978-88590.0374159781

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 873127 & 655362 & 217765 \tabularnewline
3 & 1107897 & 872131.504133542 & 235765.495866458 \tabularnewline
4 & 1555964 & 1106819.21625795 & 449144.783742055 \tabularnewline
5 & 1671159 & 1553910.76933549 & 117248.230664508 \tabularnewline
6 & 1493308 & 1670623.00877562 & -177315.008775625 \tabularnewline
7 & 2957796 & 1494118.58185795 & 1463677.41814205 \tabularnewline
8 & 2638691 & 2951104.91181049 & -312413.911810489 \tabularnewline
9 & 1305669 & 2640119.17605139 & -1334450.17605139 \tabularnewline
10 & 1280496 & 1311769.33584026 & -31273.3358402576 \tabularnewline
11 & 921900 & 1280638.96363768 & -358738.96363768 \tabularnewline
12 & 867888 & 923539.94744536 & -55651.9474453601 \tabularnewline
13 & 652586 & 868142.408576411 & -215556.408576411 \tabularnewline
14 & 913831 & 653571.399461467 & 260259.600538533 \tabularnewline
15 & 1108544 & 912641.243351585 & 195902.756648415 \tabularnewline
16 & 1555827 & 1107648.44568929 & 448178.554310708 \tabularnewline
17 & 1699283 & 1553778.18637866 & 145504.813621342 \tabularnewline
18 & 1509458 & 1698617.83599059 & -189159.835990587 \tabularnewline
19 & 3268975 & 1510322.72957008 & 1758652.27042992 \tabularnewline
20 & 2425016 & 3260935.45707184 & -835919.457071841 \tabularnewline
21 & 1312703 & 2428837.34118985 & -1116134.34118985 \tabularnewline
22 & 1365498 & 1317805.3218748 & 47692.6781251961 \tabularnewline
23 & 934453 & 1365279.97660811 & -430826.976608114 \tabularnewline
24 & 775019 & 936422.492224977 & -161403.492224977 \tabularnewline
25 & 651142 & 775756.843589842 & -124614.843589842 \tabularnewline
26 & 843192 & 651711.667125998 & 191480.332874002 \tabularnewline
27 & 1146766 & 842316.662457768 & 304449.337542232 \tabularnewline
28 & 1652601 & 1145374.23338429 & 507226.766615706 \tabularnewline
29 & 1465906 & 1650282.25203994 & -184376.252039938 \tabularnewline
30 & 1652734 & 1466748.86178577 & 185985.138214227 \tabularnewline
31 & 2922334 & 1651883.78331543 & 1270450.21668457 \tabularnewline
32 & 2702805 & 2916526.23502744 & -213721.235027435 \tabularnewline
33 & 1458956 & 2703782.01010743 & -1244826.01010743 \tabularnewline
34 & 1410363 & 1464646.62589269 & -54283.6258926904 \tabularnewline
35 & 1019279 & 1410611.15340019 & -391332.153400191 \tabularnewline
36 & 936574 & 1021067.94469323 & -84493.9446932341 \tabularnewline
37 & 708917 & 936960.257537634 & -228043.257537634 \tabularnewline
38 & 885295 & 709959.482126386 & 175335.517873614 \tabularnewline
39 & 1099663 & 884493.467231711 & 215169.532768289 \tabularnewline
40 & 1576220 & 1098679.36911139 & 477540.630888612 \tabularnewline
41 & 1487870 & 1574036.95991497 & -86166.9599149749 \tabularnewline
42 & 1488635 & 1488263.90559741 & 371.094402587041 \tabularnewline
43 & 2882530 & 1488633.30357062 & 1393896.69642938 \tabularnewline
44 & 2677026 & 2876157.90898645 & -199131.908986452 \tabularnewline
45 & 1404398 & 2677936.31613104 & -1273538.31613104 \tabularnewline
46 & 1344370 & 1410219.88198051 & -65849.8819805053 \tabularnewline
47 & 936865 & 1344671.02764594 & -407806.027645941 \tabularnewline
48 & 872705 & 938729.253736084 & -66024.253736084 \tabularnewline
49 & 628151 & 873006.824772945 & -244855.824772945 \tabularnewline
50 & 953712 & 629270.33947806 & 324441.66052194 \tabularnewline
51 & 1160384 & 952228.840024997 & 208155.159975003 \tabularnewline
52 & 1400618 & 1159432.43477447 & 241185.565225528 \tabularnewline
53 & 1661511 & 1399515.43882979 & 261995.561170213 \tabularnewline
54 & 1495347 & 1660313.30754173 & -164966.307541729 \tabularnewline
55 & 2918786 & 1496101.13072469 & 1422684.86927531 \tabularnewline
56 & 2775677 & 2912282.30607932 & -136605.306079322 \tabularnewline
57 & 1407026 & 2776301.48059853 & -1369275.48059853 \tabularnewline
58 & 1370199 & 1413285.53702835 & -43086.5370283497 \tabularnewline
59 & 964526 & 1370395.96677387 & -405869.96677387 \tabularnewline
60 & 850851 & 966381.403183445 & -115530.403183445 \tabularnewline
61 & 683118 & 851379.138308816 & -168261.138308816 \tabularnewline
62 & 847224 & 683887.192788887 & 163336.807211113 \tabularnewline
63 & 1073256 & 846477.318410125 & 226778.681589875 \tabularnewline
64 & 1514326 & 1072219.29878482 & 442106.70121518 \tabularnewline
65 & 1503734 & 1512304.94338579 & -8570.94338579103 \tabularnewline
66 & 1507712 & 1503773.18140524 & 3938.81859475933 \tabularnewline
67 & 2865698 & 1507693.99399523 & 1358004.00600477 \tabularnewline
68 & 2788128 & 2859489.98964658 & -71361.9896465843 \tabularnewline
69 & 1391596 & 2788454.22582011 & -1396858.22582011 \tabularnewline
70 & 1366378 & 1397981.62941626 & -31603.6294162616 \tabularnewline
71 & 946295 & 1366522.47354923 & -420227.473549234 \tabularnewline
72 & 859626 & 948216.037415978 & -88590.0374159781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261455&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]872131.504133542[/C][C]235765.495866458[/C][/ROW]
[ROW][C]4[/C][C]1555964[/C][C]1106819.21625795[/C][C]449144.783742055[/C][/ROW]
[ROW][C]5[/C][C]1671159[/C][C]1553910.76933549[/C][C]117248.230664508[/C][/ROW]
[ROW][C]6[/C][C]1493308[/C][C]1670623.00877562[/C][C]-177315.008775625[/C][/ROW]
[ROW][C]7[/C][C]2957796[/C][C]1494118.58185795[/C][C]1463677.41814205[/C][/ROW]
[ROW][C]8[/C][C]2638691[/C][C]2951104.91181049[/C][C]-312413.911810489[/C][/ROW]
[ROW][C]9[/C][C]1305669[/C][C]2640119.17605139[/C][C]-1334450.17605139[/C][/ROW]
[ROW][C]10[/C][C]1280496[/C][C]1311769.33584026[/C][C]-31273.3358402576[/C][/ROW]
[ROW][C]11[/C][C]921900[/C][C]1280638.96363768[/C][C]-358738.96363768[/C][/ROW]
[ROW][C]12[/C][C]867888[/C][C]923539.94744536[/C][C]-55651.9474453601[/C][/ROW]
[ROW][C]13[/C][C]652586[/C][C]868142.408576411[/C][C]-215556.408576411[/C][/ROW]
[ROW][C]14[/C][C]913831[/C][C]653571.399461467[/C][C]260259.600538533[/C][/ROW]
[ROW][C]15[/C][C]1108544[/C][C]912641.243351585[/C][C]195902.756648415[/C][/ROW]
[ROW][C]16[/C][C]1555827[/C][C]1107648.44568929[/C][C]448178.554310708[/C][/ROW]
[ROW][C]17[/C][C]1699283[/C][C]1553778.18637866[/C][C]145504.813621342[/C][/ROW]
[ROW][C]18[/C][C]1509458[/C][C]1698617.83599059[/C][C]-189159.835990587[/C][/ROW]
[ROW][C]19[/C][C]3268975[/C][C]1510322.72957008[/C][C]1758652.27042992[/C][/ROW]
[ROW][C]20[/C][C]2425016[/C][C]3260935.45707184[/C][C]-835919.457071841[/C][/ROW]
[ROW][C]21[/C][C]1312703[/C][C]2428837.34118985[/C][C]-1116134.34118985[/C][/ROW]
[ROW][C]22[/C][C]1365498[/C][C]1317805.3218748[/C][C]47692.6781251961[/C][/ROW]
[ROW][C]23[/C][C]934453[/C][C]1365279.97660811[/C][C]-430826.976608114[/C][/ROW]
[ROW][C]24[/C][C]775019[/C][C]936422.492224977[/C][C]-161403.492224977[/C][/ROW]
[ROW][C]25[/C][C]651142[/C][C]775756.843589842[/C][C]-124614.843589842[/C][/ROW]
[ROW][C]26[/C][C]843192[/C][C]651711.667125998[/C][C]191480.332874002[/C][/ROW]
[ROW][C]27[/C][C]1146766[/C][C]842316.662457768[/C][C]304449.337542232[/C][/ROW]
[ROW][C]28[/C][C]1652601[/C][C]1145374.23338429[/C][C]507226.766615706[/C][/ROW]
[ROW][C]29[/C][C]1465906[/C][C]1650282.25203994[/C][C]-184376.252039938[/C][/ROW]
[ROW][C]30[/C][C]1652734[/C][C]1466748.86178577[/C][C]185985.138214227[/C][/ROW]
[ROW][C]31[/C][C]2922334[/C][C]1651883.78331543[/C][C]1270450.21668457[/C][/ROW]
[ROW][C]32[/C][C]2702805[/C][C]2916526.23502744[/C][C]-213721.235027435[/C][/ROW]
[ROW][C]33[/C][C]1458956[/C][C]2703782.01010743[/C][C]-1244826.01010743[/C][/ROW]
[ROW][C]34[/C][C]1410363[/C][C]1464646.62589269[/C][C]-54283.6258926904[/C][/ROW]
[ROW][C]35[/C][C]1019279[/C][C]1410611.15340019[/C][C]-391332.153400191[/C][/ROW]
[ROW][C]36[/C][C]936574[/C][C]1021067.94469323[/C][C]-84493.9446932341[/C][/ROW]
[ROW][C]37[/C][C]708917[/C][C]936960.257537634[/C][C]-228043.257537634[/C][/ROW]
[ROW][C]38[/C][C]885295[/C][C]709959.482126386[/C][C]175335.517873614[/C][/ROW]
[ROW][C]39[/C][C]1099663[/C][C]884493.467231711[/C][C]215169.532768289[/C][/ROW]
[ROW][C]40[/C][C]1576220[/C][C]1098679.36911139[/C][C]477540.630888612[/C][/ROW]
[ROW][C]41[/C][C]1487870[/C][C]1574036.95991497[/C][C]-86166.9599149749[/C][/ROW]
[ROW][C]42[/C][C]1488635[/C][C]1488263.90559741[/C][C]371.094402587041[/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]2876157.90898645[/C][C]-199131.908986452[/C][/ROW]
[ROW][C]45[/C][C]1404398[/C][C]2677936.31613104[/C][C]-1273538.31613104[/C][/ROW]
[ROW][C]46[/C][C]1344370[/C][C]1410219.88198051[/C][C]-65849.8819805053[/C][/ROW]
[ROW][C]47[/C][C]936865[/C][C]1344671.02764594[/C][C]-407806.027645941[/C][/ROW]
[ROW][C]48[/C][C]872705[/C][C]938729.253736084[/C][C]-66024.253736084[/C][/ROW]
[ROW][C]49[/C][C]628151[/C][C]873006.824772945[/C][C]-244855.824772945[/C][/ROW]
[ROW][C]50[/C][C]953712[/C][C]629270.33947806[/C][C]324441.66052194[/C][/ROW]
[ROW][C]51[/C][C]1160384[/C][C]952228.840024997[/C][C]208155.159975003[/C][/ROW]
[ROW][C]52[/C][C]1400618[/C][C]1159432.43477447[/C][C]241185.565225528[/C][/ROW]
[ROW][C]53[/C][C]1661511[/C][C]1399515.43882979[/C][C]261995.561170213[/C][/ROW]
[ROW][C]54[/C][C]1495347[/C][C]1660313.30754173[/C][C]-164966.307541729[/C][/ROW]
[ROW][C]55[/C][C]2918786[/C][C]1496101.13072469[/C][C]1422684.86927531[/C][/ROW]
[ROW][C]56[/C][C]2775677[/C][C]2912282.30607932[/C][C]-136605.306079322[/C][/ROW]
[ROW][C]57[/C][C]1407026[/C][C]2776301.48059853[/C][C]-1369275.48059853[/C][/ROW]
[ROW][C]58[/C][C]1370199[/C][C]1413285.53702835[/C][C]-43086.5370283497[/C][/ROW]
[ROW][C]59[/C][C]964526[/C][C]1370395.96677387[/C][C]-405869.96677387[/C][/ROW]
[ROW][C]60[/C][C]850851[/C][C]966381.403183445[/C][C]-115530.403183445[/C][/ROW]
[ROW][C]61[/C][C]683118[/C][C]851379.138308816[/C][C]-168261.138308816[/C][/ROW]
[ROW][C]62[/C][C]847224[/C][C]683887.192788887[/C][C]163336.807211113[/C][/ROW]
[ROW][C]63[/C][C]1073256[/C][C]846477.318410125[/C][C]226778.681589875[/C][/ROW]
[ROW][C]64[/C][C]1514326[/C][C]1072219.29878482[/C][C]442106.70121518[/C][/ROW]
[ROW][C]65[/C][C]1503734[/C][C]1512304.94338579[/C][C]-8570.94338579103[/C][/ROW]
[ROW][C]66[/C][C]1507712[/C][C]1503773.18140524[/C][C]3938.81859475933[/C][/ROW]
[ROW][C]67[/C][C]2865698[/C][C]1507693.99399523[/C][C]1358004.00600477[/C][/ROW]
[ROW][C]68[/C][C]2788128[/C][C]2859489.98964658[/C][C]-71361.9896465843[/C][/ROW]
[ROW][C]69[/C][C]1391596[/C][C]2788454.22582011[/C][C]-1396858.22582011[/C][/ROW]
[ROW][C]70[/C][C]1366378[/C][C]1397981.62941626[/C][C]-31603.6294162616[/C][/ROW]
[ROW][C]71[/C][C]946295[/C][C]1366522.47354923[/C][C]-420227.473549234[/C][/ROW]
[ROW][C]72[/C][C]859626[/C][C]948216.037415978[/C][C]-88590.0374159781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261455&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261455&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
31107897872131.504133542235765.495866458
415559641106819.21625795449144.783742055
516711591553910.76933549117248.230664508
614933081670623.00877562-177315.008775625
729577961494118.581857951463677.41814205
826386912951104.91181049-312413.911810489
913056692640119.17605139-1334450.17605139
1012804961311769.33584026-31273.3358402576
119219001280638.96363768-358738.96363768
12867888923539.94744536-55651.9474453601
13652586868142.408576411-215556.408576411
14913831653571.399461467260259.600538533
151108544912641.243351585195902.756648415
1615558271107648.44568929448178.554310708
1716992831553778.18637866145504.813621342
1815094581698617.83599059-189159.835990587
1932689751510322.729570081758652.27042992
2024250163260935.45707184-835919.457071841
2113127032428837.34118985-1116134.34118985
2213654981317805.321874847692.6781251961
239344531365279.97660811-430826.976608114
24775019936422.492224977-161403.492224977
25651142775756.843589842-124614.843589842
26843192651711.667125998191480.332874002
271146766842316.662457768304449.337542232
2816526011145374.23338429507226.766615706
2914659061650282.25203994-184376.252039938
3016527341466748.86178577185985.138214227
3129223341651883.783315431270450.21668457
3227028052916526.23502744-213721.235027435
3314589562703782.01010743-1244826.01010743
3414103631464646.62589269-54283.6258926904
3510192791410611.15340019-391332.153400191
369365741021067.94469323-84493.9446932341
37708917936960.257537634-228043.257537634
38885295709959.482126386175335.517873614
391099663884493.467231711215169.532768289
4015762201098679.36911139477540.630888612
4114878701574036.95991497-86166.9599149749
4214886351488263.90559741371.094402587041
4328825301488633.303570621393896.69642938
4426770262876157.90898645-199131.908986452
4514043982677936.31613104-1273538.31613104
4613443701410219.88198051-65849.8819805053
479368651344671.02764594-407806.027645941
48872705938729.253736084-66024.253736084
49628151873006.824772945-244855.824772945
50953712629270.33947806324441.66052194
511160384952228.840024997208155.159975003
5214006181159432.43477447241185.565225528
5316615111399515.43882979261995.561170213
5414953471660313.30754173-164966.307541729
5529187861496101.130724691422684.86927531
5627756772912282.30607932-136605.306079322
5714070262776301.48059853-1369275.48059853
5813701991413285.53702835-43086.5370283497
599645261370395.96677387-405869.96677387
60850851966381.403183445-115530.403183445
61683118851379.138308816-168261.138308816
62847224683887.192788887163336.807211113
631073256846477.318410125226778.681589875
6415143261072219.29878482442106.70121518
6515037341512304.94338579-8570.94338579103
6615077121503773.181405243938.81859475933
6728656981507693.993995231358004.00600477
6827881282859489.98964658-71361.9896465843
6913915962788454.22582011-1396858.22582011
7013663781397981.62941626-31603.6294162616
719462951366522.47354923-420227.473549234
72859626948216.037415978-88590.0374159781







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73860030.982508929-354961.9588761252075023.92389398
74860030.982508929-854305.5669248462574367.53194271
75860030.982508929-1237989.932981072958051.89799893
76860030.982508929-1561628.307924493281690.27294235
77860030.982508929-1846844.64744743566906.61246526
78860030.982508929-2104748.542710523824810.50772838
79860030.982508929-2341946.467484984062008.43250284
80860030.982508929-2562745.894148164282807.85916602
81860030.982508929-2770140.295060154490202.260078
82860030.982508929-2966310.019231054686371.98424891
83860030.982508929-3152901.538566594872963.50358444
84860030.982508929-3331194.300843725051256.26586158

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 860030.982508929 & -354961.958876125 & 2075023.92389398 \tabularnewline
74 & 860030.982508929 & -854305.566924846 & 2574367.53194271 \tabularnewline
75 & 860030.982508929 & -1237989.93298107 & 2958051.89799893 \tabularnewline
76 & 860030.982508929 & -1561628.30792449 & 3281690.27294235 \tabularnewline
77 & 860030.982508929 & -1846844.6474474 & 3566906.61246526 \tabularnewline
78 & 860030.982508929 & -2104748.54271052 & 3824810.50772838 \tabularnewline
79 & 860030.982508929 & -2341946.46748498 & 4062008.43250284 \tabularnewline
80 & 860030.982508929 & -2562745.89414816 & 4282807.85916602 \tabularnewline
81 & 860030.982508929 & -2770140.29506015 & 4490202.260078 \tabularnewline
82 & 860030.982508929 & -2966310.01923105 & 4686371.98424891 \tabularnewline
83 & 860030.982508929 & -3152901.53856659 & 4872963.50358444 \tabularnewline
84 & 860030.982508929 & -3331194.30084372 & 5051256.26586158 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261455&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]860030.982508929[/C][C]-354961.958876125[/C][C]2075023.92389398[/C][/ROW]
[ROW][C]74[/C][C]860030.982508929[/C][C]-854305.566924846[/C][C]2574367.53194271[/C][/ROW]
[ROW][C]75[/C][C]860030.982508929[/C][C]-1237989.93298107[/C][C]2958051.89799893[/C][/ROW]
[ROW][C]76[/C][C]860030.982508929[/C][C]-1561628.30792449[/C][C]3281690.27294235[/C][/ROW]
[ROW][C]77[/C][C]860030.982508929[/C][C]-1846844.6474474[/C][C]3566906.61246526[/C][/ROW]
[ROW][C]78[/C][C]860030.982508929[/C][C]-2104748.54271052[/C][C]3824810.50772838[/C][/ROW]
[ROW][C]79[/C][C]860030.982508929[/C][C]-2341946.46748498[/C][C]4062008.43250284[/C][/ROW]
[ROW][C]80[/C][C]860030.982508929[/C][C]-2562745.89414816[/C][C]4282807.85916602[/C][/ROW]
[ROW][C]81[/C][C]860030.982508929[/C][C]-2770140.29506015[/C][C]4490202.260078[/C][/ROW]
[ROW][C]82[/C][C]860030.982508929[/C][C]-2966310.01923105[/C][C]4686371.98424891[/C][/ROW]
[ROW][C]83[/C][C]860030.982508929[/C][C]-3152901.53856659[/C][C]4872963.50358444[/C][/ROW]
[ROW][C]84[/C][C]860030.982508929[/C][C]-3331194.30084372[/C][C]5051256.26586158[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261455&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261455&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
73860030.982508929-354961.9588761252075023.92389398
74860030.982508929-854305.5669248462574367.53194271
75860030.982508929-1237989.932981072958051.89799893
76860030.982508929-1561628.307924493281690.27294235
77860030.982508929-1846844.64744743566906.61246526
78860030.982508929-2104748.542710523824810.50772838
79860030.982508929-2341946.467484984062008.43250284
80860030.982508929-2562745.894148164282807.85916602
81860030.982508929-2770140.295060154490202.260078
82860030.982508929-2966310.019231054686371.98424891
83860030.982508929-3152901.538566594872963.50358444
84860030.982508929-3331194.300843725051256.26586158



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')