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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 computationMon, 26 May 2008 09:16:21 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t1211815027z7bs7eg4fbbmho5.htm/, Retrieved Tue, 14 May 2024 01:55:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13264, Retrieved Tue, 14 May 2024 01:55:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact220
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-26 15:16:21] [d8973bbb712c03ae516525a15d4e5e48] [Current]
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Dataseries X:
7840
8292
8534
8441
8602
8468
8832
9006
8749
8714
8193
8251
8192
9056
9407
9068
9431
9907
10044
10838
10871
11127
11303
11349
11493
12694
13227
12253
12234
12491
13248
14042
14392
14834
15542
15518
16197
17325
24016
23671
24998
25329
25904
26548
26752
26967
27034
27056
27476
28497
29085
28720
29067
29249
29672
29761
30066
30315
30571
30757
30742
31310
31381
31470
31226
31081
31061
31114
30828
30418
30195
29877
29192
29876
29409
28458
28340
28164
28438
28053




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13264&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13264&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13264&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.959966669295933
beta0.130110948060397
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.959966669295933 \tabularnewline
beta & 0.130110948060397 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13264&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]0.959966669295933[/C][/ROW]
[ROW][C]beta[/C][C]0.130110948060397[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13264&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13264&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
alpha0.959966669295933
beta0.130110948060397
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
385348744-210
484418968.17754302367-527.177543023674
586028822.02959557856-220.029595578560
684688943.25126551266-475.251265512663
788328760.1087230313171.8912769686904
890069111.18416143127-105.184161431267
987499279.13535064118-530.135350641178
1087148972.93250461495-258.932504614952
1181938894.73411878923-701.734118789234
1282518303.81282562604-52.8128256260425
1381928329.23790818928-137.237908189281
1490568256.47641242689799.52358757311
1594079182.8369634874224.163036512600
1690689584.86901316931-516.869013169315
1794319210.97693114353220.023068856473
1899079571.95804623956335.041953760441
191004410085.2009254041-41.2009254040859
201083810232.1170958797605.882904120328
211087111075.8882665190-204.888266518972
221112711115.755147116211.2448528838122
231130311364.5071250363-61.5071250363308
241134911535.7372554282-186.737255428176
251149311563.4267455855-70.426745585486
261269411693.97399488811000.02600511193
271322712977.0256274598249.974372540206
281225313571.2750349484-1318.27503494835
291223412495.4018650369-261.401865036885
301249112401.442050827089.5579491730277
311324812655.5779430222592.422056977832
321404213466.4414204106575.558579589439
331439214333.005039115358.9949608846910
341483414711.0534001296122.946599870389
351554215165.8495005589376.150499441057
361551815910.6949200358-392.694920035789
371619715868.4259139594328.574086040635
381732516559.5907307978765.409269202162
392401617765.70404474816250.29595525188
402367125017.8013116783-1346.80131167833
412499824808.7200079244189.279992075568
422532926097.8670395035-768.867039503471
432590426371.1916921549-467.191692154913
442654826875.7613654420-327.761365442024
452675227473.2413981464-721.241398146401
462696727602.9090962116-635.909096211599
472703427735.066531716-701.066531716024
482705627717.1102673361-661.11026733608
492747627654.9365757111-178.936575711083
502849728033.2839896417463.716010358283
512908529086.4756036924-1.47560369238272
522872029692.9144673101-972.914467310104
532906729245.2852690496-178.285269049597
542924929538.2053979704-289.205397970389
552967229688.5235173937-16.5235173936780
562976130098.5433302561-337.543330256056
573006630158.2349270049-92.2349270049199
583031530441.8940717223-126.894071722301
593057130676.4322473689-105.432247368852
603075730918.4043422091-161.404342209069
613074231086.4853384461-344.485338446073
623131031035.787713021274.212286978986
633138131613.2688970065-232.268897006503
643147031675.5341356798-205.534135679791
653122631737.7921938740-511.79219387404
663108131442.1287666297-361.128766629681
673106131245.991439975-184.991439974987
683111431195.8342432055-81.8342432054524
693082831234.4832421938-406.483242193804
703041830910.7093825127-492.709382512658
713019530442.6208293491-247.620829349089
722987730178.8807384717-301.880738471697
732919229825.3473830002-633.34738300023
742987629074.5106321134801.489367886625
752940929801.1771020037-392.177102003654
762845829332.9797741262-874.97977412615
772834028292.021097652247.9789023477751
782816428143.064656913720.9353430863339
792843827970.7621705184467.237829481634
802805328285.2542159061-232.254215906061

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8534 & 8744 & -210 \tabularnewline
4 & 8441 & 8968.17754302367 & -527.177543023674 \tabularnewline
5 & 8602 & 8822.02959557856 & -220.029595578560 \tabularnewline
6 & 8468 & 8943.25126551266 & -475.251265512663 \tabularnewline
7 & 8832 & 8760.10872303131 & 71.8912769686904 \tabularnewline
8 & 9006 & 9111.18416143127 & -105.184161431267 \tabularnewline
9 & 8749 & 9279.13535064118 & -530.135350641178 \tabularnewline
10 & 8714 & 8972.93250461495 & -258.932504614952 \tabularnewline
11 & 8193 & 8894.73411878923 & -701.734118789234 \tabularnewline
12 & 8251 & 8303.81282562604 & -52.8128256260425 \tabularnewline
13 & 8192 & 8329.23790818928 & -137.237908189281 \tabularnewline
14 & 9056 & 8256.47641242689 & 799.52358757311 \tabularnewline
15 & 9407 & 9182.8369634874 & 224.163036512600 \tabularnewline
16 & 9068 & 9584.86901316931 & -516.869013169315 \tabularnewline
17 & 9431 & 9210.97693114353 & 220.023068856473 \tabularnewline
18 & 9907 & 9571.95804623956 & 335.041953760441 \tabularnewline
19 & 10044 & 10085.2009254041 & -41.2009254040859 \tabularnewline
20 & 10838 & 10232.1170958797 & 605.882904120328 \tabularnewline
21 & 10871 & 11075.8882665190 & -204.888266518972 \tabularnewline
22 & 11127 & 11115.7551471162 & 11.2448528838122 \tabularnewline
23 & 11303 & 11364.5071250363 & -61.5071250363308 \tabularnewline
24 & 11349 & 11535.7372554282 & -186.737255428176 \tabularnewline
25 & 11493 & 11563.4267455855 & -70.426745585486 \tabularnewline
26 & 12694 & 11693.9739948881 & 1000.02600511193 \tabularnewline
27 & 13227 & 12977.0256274598 & 249.974372540206 \tabularnewline
28 & 12253 & 13571.2750349484 & -1318.27503494835 \tabularnewline
29 & 12234 & 12495.4018650369 & -261.401865036885 \tabularnewline
30 & 12491 & 12401.4420508270 & 89.5579491730277 \tabularnewline
31 & 13248 & 12655.5779430222 & 592.422056977832 \tabularnewline
32 & 14042 & 13466.4414204106 & 575.558579589439 \tabularnewline
33 & 14392 & 14333.0050391153 & 58.9949608846910 \tabularnewline
34 & 14834 & 14711.0534001296 & 122.946599870389 \tabularnewline
35 & 15542 & 15165.8495005589 & 376.150499441057 \tabularnewline
36 & 15518 & 15910.6949200358 & -392.694920035789 \tabularnewline
37 & 16197 & 15868.4259139594 & 328.574086040635 \tabularnewline
38 & 17325 & 16559.5907307978 & 765.409269202162 \tabularnewline
39 & 24016 & 17765.7040447481 & 6250.29595525188 \tabularnewline
40 & 23671 & 25017.8013116783 & -1346.80131167833 \tabularnewline
41 & 24998 & 24808.7200079244 & 189.279992075568 \tabularnewline
42 & 25329 & 26097.8670395035 & -768.867039503471 \tabularnewline
43 & 25904 & 26371.1916921549 & -467.191692154913 \tabularnewline
44 & 26548 & 26875.7613654420 & -327.761365442024 \tabularnewline
45 & 26752 & 27473.2413981464 & -721.241398146401 \tabularnewline
46 & 26967 & 27602.9090962116 & -635.909096211599 \tabularnewline
47 & 27034 & 27735.066531716 & -701.066531716024 \tabularnewline
48 & 27056 & 27717.1102673361 & -661.11026733608 \tabularnewline
49 & 27476 & 27654.9365757111 & -178.936575711083 \tabularnewline
50 & 28497 & 28033.2839896417 & 463.716010358283 \tabularnewline
51 & 29085 & 29086.4756036924 & -1.47560369238272 \tabularnewline
52 & 28720 & 29692.9144673101 & -972.914467310104 \tabularnewline
53 & 29067 & 29245.2852690496 & -178.285269049597 \tabularnewline
54 & 29249 & 29538.2053979704 & -289.205397970389 \tabularnewline
55 & 29672 & 29688.5235173937 & -16.5235173936780 \tabularnewline
56 & 29761 & 30098.5433302561 & -337.543330256056 \tabularnewline
57 & 30066 & 30158.2349270049 & -92.2349270049199 \tabularnewline
58 & 30315 & 30441.8940717223 & -126.894071722301 \tabularnewline
59 & 30571 & 30676.4322473689 & -105.432247368852 \tabularnewline
60 & 30757 & 30918.4043422091 & -161.404342209069 \tabularnewline
61 & 30742 & 31086.4853384461 & -344.485338446073 \tabularnewline
62 & 31310 & 31035.787713021 & 274.212286978986 \tabularnewline
63 & 31381 & 31613.2688970065 & -232.268897006503 \tabularnewline
64 & 31470 & 31675.5341356798 & -205.534135679791 \tabularnewline
65 & 31226 & 31737.7921938740 & -511.79219387404 \tabularnewline
66 & 31081 & 31442.1287666297 & -361.128766629681 \tabularnewline
67 & 31061 & 31245.991439975 & -184.991439974987 \tabularnewline
68 & 31114 & 31195.8342432055 & -81.8342432054524 \tabularnewline
69 & 30828 & 31234.4832421938 & -406.483242193804 \tabularnewline
70 & 30418 & 30910.7093825127 & -492.709382512658 \tabularnewline
71 & 30195 & 30442.6208293491 & -247.620829349089 \tabularnewline
72 & 29877 & 30178.8807384717 & -301.880738471697 \tabularnewline
73 & 29192 & 29825.3473830002 & -633.34738300023 \tabularnewline
74 & 29876 & 29074.5106321134 & 801.489367886625 \tabularnewline
75 & 29409 & 29801.1771020037 & -392.177102003654 \tabularnewline
76 & 28458 & 29332.9797741262 & -874.97977412615 \tabularnewline
77 & 28340 & 28292.0210976522 & 47.9789023477751 \tabularnewline
78 & 28164 & 28143.0646569137 & 20.9353430863339 \tabularnewline
79 & 28438 & 27970.7621705184 & 467.237829481634 \tabularnewline
80 & 28053 & 28285.2542159061 & -232.254215906061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13264&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]8534[/C][C]8744[/C][C]-210[/C][/ROW]
[ROW][C]4[/C][C]8441[/C][C]8968.17754302367[/C][C]-527.177543023674[/C][/ROW]
[ROW][C]5[/C][C]8602[/C][C]8822.02959557856[/C][C]-220.029595578560[/C][/ROW]
[ROW][C]6[/C][C]8468[/C][C]8943.25126551266[/C][C]-475.251265512663[/C][/ROW]
[ROW][C]7[/C][C]8832[/C][C]8760.10872303131[/C][C]71.8912769686904[/C][/ROW]
[ROW][C]8[/C][C]9006[/C][C]9111.18416143127[/C][C]-105.184161431267[/C][/ROW]
[ROW][C]9[/C][C]8749[/C][C]9279.13535064118[/C][C]-530.135350641178[/C][/ROW]
[ROW][C]10[/C][C]8714[/C][C]8972.93250461495[/C][C]-258.932504614952[/C][/ROW]
[ROW][C]11[/C][C]8193[/C][C]8894.73411878923[/C][C]-701.734118789234[/C][/ROW]
[ROW][C]12[/C][C]8251[/C][C]8303.81282562604[/C][C]-52.8128256260425[/C][/ROW]
[ROW][C]13[/C][C]8192[/C][C]8329.23790818928[/C][C]-137.237908189281[/C][/ROW]
[ROW][C]14[/C][C]9056[/C][C]8256.47641242689[/C][C]799.52358757311[/C][/ROW]
[ROW][C]15[/C][C]9407[/C][C]9182.8369634874[/C][C]224.163036512600[/C][/ROW]
[ROW][C]16[/C][C]9068[/C][C]9584.86901316931[/C][C]-516.869013169315[/C][/ROW]
[ROW][C]17[/C][C]9431[/C][C]9210.97693114353[/C][C]220.023068856473[/C][/ROW]
[ROW][C]18[/C][C]9907[/C][C]9571.95804623956[/C][C]335.041953760441[/C][/ROW]
[ROW][C]19[/C][C]10044[/C][C]10085.2009254041[/C][C]-41.2009254040859[/C][/ROW]
[ROW][C]20[/C][C]10838[/C][C]10232.1170958797[/C][C]605.882904120328[/C][/ROW]
[ROW][C]21[/C][C]10871[/C][C]11075.8882665190[/C][C]-204.888266518972[/C][/ROW]
[ROW][C]22[/C][C]11127[/C][C]11115.7551471162[/C][C]11.2448528838122[/C][/ROW]
[ROW][C]23[/C][C]11303[/C][C]11364.5071250363[/C][C]-61.5071250363308[/C][/ROW]
[ROW][C]24[/C][C]11349[/C][C]11535.7372554282[/C][C]-186.737255428176[/C][/ROW]
[ROW][C]25[/C][C]11493[/C][C]11563.4267455855[/C][C]-70.426745585486[/C][/ROW]
[ROW][C]26[/C][C]12694[/C][C]11693.9739948881[/C][C]1000.02600511193[/C][/ROW]
[ROW][C]27[/C][C]13227[/C][C]12977.0256274598[/C][C]249.974372540206[/C][/ROW]
[ROW][C]28[/C][C]12253[/C][C]13571.2750349484[/C][C]-1318.27503494835[/C][/ROW]
[ROW][C]29[/C][C]12234[/C][C]12495.4018650369[/C][C]-261.401865036885[/C][/ROW]
[ROW][C]30[/C][C]12491[/C][C]12401.4420508270[/C][C]89.5579491730277[/C][/ROW]
[ROW][C]31[/C][C]13248[/C][C]12655.5779430222[/C][C]592.422056977832[/C][/ROW]
[ROW][C]32[/C][C]14042[/C][C]13466.4414204106[/C][C]575.558579589439[/C][/ROW]
[ROW][C]33[/C][C]14392[/C][C]14333.0050391153[/C][C]58.9949608846910[/C][/ROW]
[ROW][C]34[/C][C]14834[/C][C]14711.0534001296[/C][C]122.946599870389[/C][/ROW]
[ROW][C]35[/C][C]15542[/C][C]15165.8495005589[/C][C]376.150499441057[/C][/ROW]
[ROW][C]36[/C][C]15518[/C][C]15910.6949200358[/C][C]-392.694920035789[/C][/ROW]
[ROW][C]37[/C][C]16197[/C][C]15868.4259139594[/C][C]328.574086040635[/C][/ROW]
[ROW][C]38[/C][C]17325[/C][C]16559.5907307978[/C][C]765.409269202162[/C][/ROW]
[ROW][C]39[/C][C]24016[/C][C]17765.7040447481[/C][C]6250.29595525188[/C][/ROW]
[ROW][C]40[/C][C]23671[/C][C]25017.8013116783[/C][C]-1346.80131167833[/C][/ROW]
[ROW][C]41[/C][C]24998[/C][C]24808.7200079244[/C][C]189.279992075568[/C][/ROW]
[ROW][C]42[/C][C]25329[/C][C]26097.8670395035[/C][C]-768.867039503471[/C][/ROW]
[ROW][C]43[/C][C]25904[/C][C]26371.1916921549[/C][C]-467.191692154913[/C][/ROW]
[ROW][C]44[/C][C]26548[/C][C]26875.7613654420[/C][C]-327.761365442024[/C][/ROW]
[ROW][C]45[/C][C]26752[/C][C]27473.2413981464[/C][C]-721.241398146401[/C][/ROW]
[ROW][C]46[/C][C]26967[/C][C]27602.9090962116[/C][C]-635.909096211599[/C][/ROW]
[ROW][C]47[/C][C]27034[/C][C]27735.066531716[/C][C]-701.066531716024[/C][/ROW]
[ROW][C]48[/C][C]27056[/C][C]27717.1102673361[/C][C]-661.11026733608[/C][/ROW]
[ROW][C]49[/C][C]27476[/C][C]27654.9365757111[/C][C]-178.936575711083[/C][/ROW]
[ROW][C]50[/C][C]28497[/C][C]28033.2839896417[/C][C]463.716010358283[/C][/ROW]
[ROW][C]51[/C][C]29085[/C][C]29086.4756036924[/C][C]-1.47560369238272[/C][/ROW]
[ROW][C]52[/C][C]28720[/C][C]29692.9144673101[/C][C]-972.914467310104[/C][/ROW]
[ROW][C]53[/C][C]29067[/C][C]29245.2852690496[/C][C]-178.285269049597[/C][/ROW]
[ROW][C]54[/C][C]29249[/C][C]29538.2053979704[/C][C]-289.205397970389[/C][/ROW]
[ROW][C]55[/C][C]29672[/C][C]29688.5235173937[/C][C]-16.5235173936780[/C][/ROW]
[ROW][C]56[/C][C]29761[/C][C]30098.5433302561[/C][C]-337.543330256056[/C][/ROW]
[ROW][C]57[/C][C]30066[/C][C]30158.2349270049[/C][C]-92.2349270049199[/C][/ROW]
[ROW][C]58[/C][C]30315[/C][C]30441.8940717223[/C][C]-126.894071722301[/C][/ROW]
[ROW][C]59[/C][C]30571[/C][C]30676.4322473689[/C][C]-105.432247368852[/C][/ROW]
[ROW][C]60[/C][C]30757[/C][C]30918.4043422091[/C][C]-161.404342209069[/C][/ROW]
[ROW][C]61[/C][C]30742[/C][C]31086.4853384461[/C][C]-344.485338446073[/C][/ROW]
[ROW][C]62[/C][C]31310[/C][C]31035.787713021[/C][C]274.212286978986[/C][/ROW]
[ROW][C]63[/C][C]31381[/C][C]31613.2688970065[/C][C]-232.268897006503[/C][/ROW]
[ROW][C]64[/C][C]31470[/C][C]31675.5341356798[/C][C]-205.534135679791[/C][/ROW]
[ROW][C]65[/C][C]31226[/C][C]31737.7921938740[/C][C]-511.79219387404[/C][/ROW]
[ROW][C]66[/C][C]31081[/C][C]31442.1287666297[/C][C]-361.128766629681[/C][/ROW]
[ROW][C]67[/C][C]31061[/C][C]31245.991439975[/C][C]-184.991439974987[/C][/ROW]
[ROW][C]68[/C][C]31114[/C][C]31195.8342432055[/C][C]-81.8342432054524[/C][/ROW]
[ROW][C]69[/C][C]30828[/C][C]31234.4832421938[/C][C]-406.483242193804[/C][/ROW]
[ROW][C]70[/C][C]30418[/C][C]30910.7093825127[/C][C]-492.709382512658[/C][/ROW]
[ROW][C]71[/C][C]30195[/C][C]30442.6208293491[/C][C]-247.620829349089[/C][/ROW]
[ROW][C]72[/C][C]29877[/C][C]30178.8807384717[/C][C]-301.880738471697[/C][/ROW]
[ROW][C]73[/C][C]29192[/C][C]29825.3473830002[/C][C]-633.34738300023[/C][/ROW]
[ROW][C]74[/C][C]29876[/C][C]29074.5106321134[/C][C]801.489367886625[/C][/ROW]
[ROW][C]75[/C][C]29409[/C][C]29801.1771020037[/C][C]-392.177102003654[/C][/ROW]
[ROW][C]76[/C][C]28458[/C][C]29332.9797741262[/C][C]-874.97977412615[/C][/ROW]
[ROW][C]77[/C][C]28340[/C][C]28292.0210976522[/C][C]47.9789023477751[/C][/ROW]
[ROW][C]78[/C][C]28164[/C][C]28143.0646569137[/C][C]20.9353430863339[/C][/ROW]
[ROW][C]79[/C][C]28438[/C][C]27970.7621705184[/C][C]467.237829481634[/C][/ROW]
[ROW][C]80[/C][C]28053[/C][C]28285.2542159061[/C][C]-232.254215906061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13264&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13264&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
385348744-210
484418968.17754302367-527.177543023674
586028822.02959557856-220.029595578560
684688943.25126551266-475.251265512663
788328760.1087230313171.8912769686904
890069111.18416143127-105.184161431267
987499279.13535064118-530.135350641178
1087148972.93250461495-258.932504614952
1181938894.73411878923-701.734118789234
1282518303.81282562604-52.8128256260425
1381928329.23790818928-137.237908189281
1490568256.47641242689799.52358757311
1594079182.8369634874224.163036512600
1690689584.86901316931-516.869013169315
1794319210.97693114353220.023068856473
1899079571.95804623956335.041953760441
191004410085.2009254041-41.2009254040859
201083810232.1170958797605.882904120328
211087111075.8882665190-204.888266518972
221112711115.755147116211.2448528838122
231130311364.5071250363-61.5071250363308
241134911535.7372554282-186.737255428176
251149311563.4267455855-70.426745585486
261269411693.97399488811000.02600511193
271322712977.0256274598249.974372540206
281225313571.2750349484-1318.27503494835
291223412495.4018650369-261.401865036885
301249112401.442050827089.5579491730277
311324812655.5779430222592.422056977832
321404213466.4414204106575.558579589439
331439214333.005039115358.9949608846910
341483414711.0534001296122.946599870389
351554215165.8495005589376.150499441057
361551815910.6949200358-392.694920035789
371619715868.4259139594328.574086040635
381732516559.5907307978765.409269202162
392401617765.70404474816250.29595525188
402367125017.8013116783-1346.80131167833
412499824808.7200079244189.279992075568
422532926097.8670395035-768.867039503471
432590426371.1916921549-467.191692154913
442654826875.7613654420-327.761365442024
452675227473.2413981464-721.241398146401
462696727602.9090962116-635.909096211599
472703427735.066531716-701.066531716024
482705627717.1102673361-661.11026733608
492747627654.9365757111-178.936575711083
502849728033.2839896417463.716010358283
512908529086.4756036924-1.47560369238272
522872029692.9144673101-972.914467310104
532906729245.2852690496-178.285269049597
542924929538.2053979704-289.205397970389
552967229688.5235173937-16.5235173936780
562976130098.5433302561-337.543330256056
573006630158.2349270049-92.2349270049199
583031530441.8940717223-126.894071722301
593057130676.4322473689-105.432247368852
603075730918.4043422091-161.404342209069
613074231086.4853384461-344.485338446073
623131031035.787713021274.212286978986
633138131613.2688970065-232.268897006503
643147031675.5341356798-205.534135679791
653122631737.7921938740-511.79219387404
663108131442.1287666297-361.128766629681
673106131245.991439975-184.991439974987
683111431195.8342432055-81.8342432054524
693082831234.4832421938-406.483242193804
703041830910.7093825127-492.709382512658
713019530442.6208293491-247.620829349089
722987730178.8807384717-301.880738471697
732919229825.3473830002-633.34738300023
742987629074.5106321134801.489367886625
752940929801.1771020037-392.177102003654
762845829332.9797741262-874.97977412615
772834028292.021097652247.9789023477751
782816428143.064656913720.9353430863339
792843827970.7621705184467.237829481634
802805328285.2542159061-232.254215906061







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8127899.248155924726227.856067021729570.6402448277
8227736.198402016625270.149909225830202.2468948074
8327573.148648108524384.122767490430762.1745287266
8427410.098894200423518.288761785431301.9090266155
8527247.049140292322653.852303241231840.2459773435
8627083.999386384221782.031714360132385.9670584084
8726920.949632476120898.196106289132943.7031586632
8826757.899878568119999.740690854533516.0590662816
8926594.850124660019085.157068377634104.5431809424
9026431.800370751918153.573234882334710.0275066215
9126268.750616843817204.505383872435332.9958498152
9226105.700862935716237.715096462435973.686629409

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 27899.2481559247 & 26227.8560670217 & 29570.6402448277 \tabularnewline
82 & 27736.1984020166 & 25270.1499092258 & 30202.2468948074 \tabularnewline
83 & 27573.1486481085 & 24384.1227674904 & 30762.1745287266 \tabularnewline
84 & 27410.0988942004 & 23518.2887617854 & 31301.9090266155 \tabularnewline
85 & 27247.0491402923 & 22653.8523032412 & 31840.2459773435 \tabularnewline
86 & 27083.9993863842 & 21782.0317143601 & 32385.9670584084 \tabularnewline
87 & 26920.9496324761 & 20898.1961062891 & 32943.7031586632 \tabularnewline
88 & 26757.8998785681 & 19999.7406908545 & 33516.0590662816 \tabularnewline
89 & 26594.8501246600 & 19085.1570683776 & 34104.5431809424 \tabularnewline
90 & 26431.8003707519 & 18153.5732348823 & 34710.0275066215 \tabularnewline
91 & 26268.7506168438 & 17204.5053838724 & 35332.9958498152 \tabularnewline
92 & 26105.7008629357 & 16237.7150964624 & 35973.686629409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13264&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]81[/C][C]27899.2481559247[/C][C]26227.8560670217[/C][C]29570.6402448277[/C][/ROW]
[ROW][C]82[/C][C]27736.1984020166[/C][C]25270.1499092258[/C][C]30202.2468948074[/C][/ROW]
[ROW][C]83[/C][C]27573.1486481085[/C][C]24384.1227674904[/C][C]30762.1745287266[/C][/ROW]
[ROW][C]84[/C][C]27410.0988942004[/C][C]23518.2887617854[/C][C]31301.9090266155[/C][/ROW]
[ROW][C]85[/C][C]27247.0491402923[/C][C]22653.8523032412[/C][C]31840.2459773435[/C][/ROW]
[ROW][C]86[/C][C]27083.9993863842[/C][C]21782.0317143601[/C][C]32385.9670584084[/C][/ROW]
[ROW][C]87[/C][C]26920.9496324761[/C][C]20898.1961062891[/C][C]32943.7031586632[/C][/ROW]
[ROW][C]88[/C][C]26757.8998785681[/C][C]19999.7406908545[/C][C]33516.0590662816[/C][/ROW]
[ROW][C]89[/C][C]26594.8501246600[/C][C]19085.1570683776[/C][C]34104.5431809424[/C][/ROW]
[ROW][C]90[/C][C]26431.8003707519[/C][C]18153.5732348823[/C][C]34710.0275066215[/C][/ROW]
[ROW][C]91[/C][C]26268.7506168438[/C][C]17204.5053838724[/C][C]35332.9958498152[/C][/ROW]
[ROW][C]92[/C][C]26105.7008629357[/C][C]16237.7150964624[/C][C]35973.686629409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13264&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13264&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
8127899.248155924726227.856067021729570.6402448277
8227736.198402016625270.149909225830202.2468948074
8327573.148648108524384.122767490430762.1745287266
8427410.098894200423518.288761785431301.9090266155
8527247.049140292322653.852303241231840.2459773435
8627083.999386384221782.031714360132385.9670584084
8726920.949632476120898.196106289132943.7031586632
8826757.899878568119999.740690854533516.0590662816
8926594.850124660019085.157068377634104.5431809424
9026431.800370751918153.573234882334710.0275066215
9126268.750616843817204.505383872435332.9958498152
9226105.700862935716237.715096462435973.686629409



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')