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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, 30 Mar 2015 13:05:05 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Mar/30/t14277171684zjib0i11fturan.htm/, Retrieved Sun, 19 May 2024 13:37:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278452, Retrieved Sun, 19 May 2024 13:37:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2015-03-30 12:05:05] [c5baef828b4732814d7f41355a0722be] [Current]
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Dataseries X:
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167
27297
28287
33474
28229
28785
25597
18130
20198
22849
23118
21925
20801
18785
20659
29367
23992
20645
22356
17902
15879
16963
21035
17988
10437
24470
22237
27053
26419
22311
20624
17336
15586
17733
19231
16102
11770




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278452&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278452&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278452&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.279498346635524
beta0
gamma0.584618639467818

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.279498346635524 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.584618639467818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278452&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]0.279498346635524[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.584618639467818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278452&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278452&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
alpha0.279498346635524
beta0
gamma0.584618639467818







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133112431525.9345619658-401.934561965827
142655126741.048333457-190.04833345702
153065130690.1339554913-39.1339554912629
162585925688.5248966505170.475103349534
172510024769.6262231955330.373776804499
182577825349.5022979337428.497702066255
192041818371.0538475482046.94615245196
201868818323.2923964933364.707603506708
212042419637.3063856951786.693614304866
222477622913.55643388511862.44356611494
231981419995.0184816658-181.018481665807
241273811961.9612656794776.038734320604
253156633636.7226069979-2070.72260699788
263011128474.6633199591636.33668004097
273001932997.7884911292-2978.78849112918
283193427262.84210440064671.15789559936
292582627669.2291408871-1843.22914088713
302683527682.9184257654-847.918425765391
312020521029.4345243713-824.434524371296
321778919470.5365930901-1681.53659309013
332052020390.3771098661129.622890133909
342251823936.1029692999-1418.10296929994
351557219239.913264617-3667.91326461704
361150910635.4051147292873.594885270759
372544731138.324138006-5691.32413800596
382409026525.7953893075-2435.79538930752
392778627966.7893718397-180.789371839739
402619526236.1795568085-41.1795568084817
412051622581.4944516979-2065.49445169786
422275922952.3044315512-193.304431551231
431902816491.67591755432536.3240824457
441697115511.0770443171459.92295568297
452003618071.84454735641964.15545264361
462248521478.38815608271006.61184391733
471873016512.24007318632217.75992681369
481453811465.73599138213072.26400861786
492756129817.912766974-2256.91276697404
502598527536.5858935182-1551.58589351815
513467030174.56566308414495.43433691595
523206629809.75890742942256.24109257061
532718625944.51979437151241.48020562853
542958628028.22516287061557.77483712941
552135923206.7909734129-1847.79097341294
562155320547.43891126631005.56108873369
571957323193.6051787332-3620.6051787332
582425624635.8821540932-379.882154093193
592238019792.3695076662587.63049233396
601616715209.1767327352957.823267264763
612729730725.6219231638-3428.62192316385
622828728413.9011439348-126.901143934756
633347433997.1959235959-523.195923595893
642822931286.5002485519-3057.50024855194
652878525508.64295832283276.35704167715
662559728294.3222504396-2697.32225043964
671813020849.1074692697-2719.10746926971
682019819148.10912290641049.89087709363
692284919858.03776876492990.96223123507
702311824513.2900314672-1395.29003146722
712192520635.94437040711289.05562959288
722080115003.29679375425797.70320624577
731878530024.8277004323-11239.8277004323
742065926920.6343434804-6261.63434348043
752936730622.3545663695-1255.35456636952
762399226639.5253973485-2647.52539734852
772064523644.1945106871-2999.1945106871
782235622159.6421160075196.357883992536
791790215514.02980662862387.97019337135
801587916828.0237930161-949.023793016142
811696317796.8746387773-833.874638777335
822103519535.51986031581499.4801396842
831798817597.9542558178390.045744182244
841043713613.1615570068-3176.16155700684
852447018949.98554232995520.01445767007
862223722627.0484743053-390.048474305342
872705330078.6058809065-3025.60588090651
882641925014.58601385741404.41398614256
892231123003.6358800912-692.635880091155
902062423509.7892228038-2885.78922280379
911733616925.8699727927410.130027207339
921558616281.45664624-695.456646239971
931773317369.6820669175363.317933082501
941923120425.7932907407-1194.79329074066
951610217267.8682073242-1165.86820732422
961177011346.0469413312423.953058668798

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 31124 & 31525.9345619658 & -401.934561965827 \tabularnewline
14 & 26551 & 26741.048333457 & -190.04833345702 \tabularnewline
15 & 30651 & 30690.1339554913 & -39.1339554912629 \tabularnewline
16 & 25859 & 25688.5248966505 & 170.475103349534 \tabularnewline
17 & 25100 & 24769.6262231955 & 330.373776804499 \tabularnewline
18 & 25778 & 25349.5022979337 & 428.497702066255 \tabularnewline
19 & 20418 & 18371.053847548 & 2046.94615245196 \tabularnewline
20 & 18688 & 18323.2923964933 & 364.707603506708 \tabularnewline
21 & 20424 & 19637.3063856951 & 786.693614304866 \tabularnewline
22 & 24776 & 22913.5564338851 & 1862.44356611494 \tabularnewline
23 & 19814 & 19995.0184816658 & -181.018481665807 \tabularnewline
24 & 12738 & 11961.9612656794 & 776.038734320604 \tabularnewline
25 & 31566 & 33636.7226069979 & -2070.72260699788 \tabularnewline
26 & 30111 & 28474.663319959 & 1636.33668004097 \tabularnewline
27 & 30019 & 32997.7884911292 & -2978.78849112918 \tabularnewline
28 & 31934 & 27262.8421044006 & 4671.15789559936 \tabularnewline
29 & 25826 & 27669.2291408871 & -1843.22914088713 \tabularnewline
30 & 26835 & 27682.9184257654 & -847.918425765391 \tabularnewline
31 & 20205 & 21029.4345243713 & -824.434524371296 \tabularnewline
32 & 17789 & 19470.5365930901 & -1681.53659309013 \tabularnewline
33 & 20520 & 20390.3771098661 & 129.622890133909 \tabularnewline
34 & 22518 & 23936.1029692999 & -1418.10296929994 \tabularnewline
35 & 15572 & 19239.913264617 & -3667.91326461704 \tabularnewline
36 & 11509 & 10635.4051147292 & 873.594885270759 \tabularnewline
37 & 25447 & 31138.324138006 & -5691.32413800596 \tabularnewline
38 & 24090 & 26525.7953893075 & -2435.79538930752 \tabularnewline
39 & 27786 & 27966.7893718397 & -180.789371839739 \tabularnewline
40 & 26195 & 26236.1795568085 & -41.1795568084817 \tabularnewline
41 & 20516 & 22581.4944516979 & -2065.49445169786 \tabularnewline
42 & 22759 & 22952.3044315512 & -193.304431551231 \tabularnewline
43 & 19028 & 16491.6759175543 & 2536.3240824457 \tabularnewline
44 & 16971 & 15511.077044317 & 1459.92295568297 \tabularnewline
45 & 20036 & 18071.8445473564 & 1964.15545264361 \tabularnewline
46 & 22485 & 21478.3881560827 & 1006.61184391733 \tabularnewline
47 & 18730 & 16512.2400731863 & 2217.75992681369 \tabularnewline
48 & 14538 & 11465.7359913821 & 3072.26400861786 \tabularnewline
49 & 27561 & 29817.912766974 & -2256.91276697404 \tabularnewline
50 & 25985 & 27536.5858935182 & -1551.58589351815 \tabularnewline
51 & 34670 & 30174.5656630841 & 4495.43433691595 \tabularnewline
52 & 32066 & 29809.7589074294 & 2256.24109257061 \tabularnewline
53 & 27186 & 25944.5197943715 & 1241.48020562853 \tabularnewline
54 & 29586 & 28028.2251628706 & 1557.77483712941 \tabularnewline
55 & 21359 & 23206.7909734129 & -1847.79097341294 \tabularnewline
56 & 21553 & 20547.4389112663 & 1005.56108873369 \tabularnewline
57 & 19573 & 23193.6051787332 & -3620.6051787332 \tabularnewline
58 & 24256 & 24635.8821540932 & -379.882154093193 \tabularnewline
59 & 22380 & 19792.369507666 & 2587.63049233396 \tabularnewline
60 & 16167 & 15209.1767327352 & 957.823267264763 \tabularnewline
61 & 27297 & 30725.6219231638 & -3428.62192316385 \tabularnewline
62 & 28287 & 28413.9011439348 & -126.901143934756 \tabularnewline
63 & 33474 & 33997.1959235959 & -523.195923595893 \tabularnewline
64 & 28229 & 31286.5002485519 & -3057.50024855194 \tabularnewline
65 & 28785 & 25508.6429583228 & 3276.35704167715 \tabularnewline
66 & 25597 & 28294.3222504396 & -2697.32225043964 \tabularnewline
67 & 18130 & 20849.1074692697 & -2719.10746926971 \tabularnewline
68 & 20198 & 19148.1091229064 & 1049.89087709363 \tabularnewline
69 & 22849 & 19858.0377687649 & 2990.96223123507 \tabularnewline
70 & 23118 & 24513.2900314672 & -1395.29003146722 \tabularnewline
71 & 21925 & 20635.9443704071 & 1289.05562959288 \tabularnewline
72 & 20801 & 15003.2967937542 & 5797.70320624577 \tabularnewline
73 & 18785 & 30024.8277004323 & -11239.8277004323 \tabularnewline
74 & 20659 & 26920.6343434804 & -6261.63434348043 \tabularnewline
75 & 29367 & 30622.3545663695 & -1255.35456636952 \tabularnewline
76 & 23992 & 26639.5253973485 & -2647.52539734852 \tabularnewline
77 & 20645 & 23644.1945106871 & -2999.1945106871 \tabularnewline
78 & 22356 & 22159.6421160075 & 196.357883992536 \tabularnewline
79 & 17902 & 15514.0298066286 & 2387.97019337135 \tabularnewline
80 & 15879 & 16828.0237930161 & -949.023793016142 \tabularnewline
81 & 16963 & 17796.8746387773 & -833.874638777335 \tabularnewline
82 & 21035 & 19535.5198603158 & 1499.4801396842 \tabularnewline
83 & 17988 & 17597.9542558178 & 390.045744182244 \tabularnewline
84 & 10437 & 13613.1615570068 & -3176.16155700684 \tabularnewline
85 & 24470 & 18949.9855423299 & 5520.01445767007 \tabularnewline
86 & 22237 & 22627.0484743053 & -390.048474305342 \tabularnewline
87 & 27053 & 30078.6058809065 & -3025.60588090651 \tabularnewline
88 & 26419 & 25014.5860138574 & 1404.41398614256 \tabularnewline
89 & 22311 & 23003.6358800912 & -692.635880091155 \tabularnewline
90 & 20624 & 23509.7892228038 & -2885.78922280379 \tabularnewline
91 & 17336 & 16925.8699727927 & 410.130027207339 \tabularnewline
92 & 15586 & 16281.45664624 & -695.456646239971 \tabularnewline
93 & 17733 & 17369.6820669175 & 363.317933082501 \tabularnewline
94 & 19231 & 20425.7932907407 & -1194.79329074066 \tabularnewline
95 & 16102 & 17267.8682073242 & -1165.86820732422 \tabularnewline
96 & 11770 & 11346.0469413312 & 423.953058668798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278452&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]13[/C][C]31124[/C][C]31525.9345619658[/C][C]-401.934561965827[/C][/ROW]
[ROW][C]14[/C][C]26551[/C][C]26741.048333457[/C][C]-190.04833345702[/C][/ROW]
[ROW][C]15[/C][C]30651[/C][C]30690.1339554913[/C][C]-39.1339554912629[/C][/ROW]
[ROW][C]16[/C][C]25859[/C][C]25688.5248966505[/C][C]170.475103349534[/C][/ROW]
[ROW][C]17[/C][C]25100[/C][C]24769.6262231955[/C][C]330.373776804499[/C][/ROW]
[ROW][C]18[/C][C]25778[/C][C]25349.5022979337[/C][C]428.497702066255[/C][/ROW]
[ROW][C]19[/C][C]20418[/C][C]18371.053847548[/C][C]2046.94615245196[/C][/ROW]
[ROW][C]20[/C][C]18688[/C][C]18323.2923964933[/C][C]364.707603506708[/C][/ROW]
[ROW][C]21[/C][C]20424[/C][C]19637.3063856951[/C][C]786.693614304866[/C][/ROW]
[ROW][C]22[/C][C]24776[/C][C]22913.5564338851[/C][C]1862.44356611494[/C][/ROW]
[ROW][C]23[/C][C]19814[/C][C]19995.0184816658[/C][C]-181.018481665807[/C][/ROW]
[ROW][C]24[/C][C]12738[/C][C]11961.9612656794[/C][C]776.038734320604[/C][/ROW]
[ROW][C]25[/C][C]31566[/C][C]33636.7226069979[/C][C]-2070.72260699788[/C][/ROW]
[ROW][C]26[/C][C]30111[/C][C]28474.663319959[/C][C]1636.33668004097[/C][/ROW]
[ROW][C]27[/C][C]30019[/C][C]32997.7884911292[/C][C]-2978.78849112918[/C][/ROW]
[ROW][C]28[/C][C]31934[/C][C]27262.8421044006[/C][C]4671.15789559936[/C][/ROW]
[ROW][C]29[/C][C]25826[/C][C]27669.2291408871[/C][C]-1843.22914088713[/C][/ROW]
[ROW][C]30[/C][C]26835[/C][C]27682.9184257654[/C][C]-847.918425765391[/C][/ROW]
[ROW][C]31[/C][C]20205[/C][C]21029.4345243713[/C][C]-824.434524371296[/C][/ROW]
[ROW][C]32[/C][C]17789[/C][C]19470.5365930901[/C][C]-1681.53659309013[/C][/ROW]
[ROW][C]33[/C][C]20520[/C][C]20390.3771098661[/C][C]129.622890133909[/C][/ROW]
[ROW][C]34[/C][C]22518[/C][C]23936.1029692999[/C][C]-1418.10296929994[/C][/ROW]
[ROW][C]35[/C][C]15572[/C][C]19239.913264617[/C][C]-3667.91326461704[/C][/ROW]
[ROW][C]36[/C][C]11509[/C][C]10635.4051147292[/C][C]873.594885270759[/C][/ROW]
[ROW][C]37[/C][C]25447[/C][C]31138.324138006[/C][C]-5691.32413800596[/C][/ROW]
[ROW][C]38[/C][C]24090[/C][C]26525.7953893075[/C][C]-2435.79538930752[/C][/ROW]
[ROW][C]39[/C][C]27786[/C][C]27966.7893718397[/C][C]-180.789371839739[/C][/ROW]
[ROW][C]40[/C][C]26195[/C][C]26236.1795568085[/C][C]-41.1795568084817[/C][/ROW]
[ROW][C]41[/C][C]20516[/C][C]22581.4944516979[/C][C]-2065.49445169786[/C][/ROW]
[ROW][C]42[/C][C]22759[/C][C]22952.3044315512[/C][C]-193.304431551231[/C][/ROW]
[ROW][C]43[/C][C]19028[/C][C]16491.6759175543[/C][C]2536.3240824457[/C][/ROW]
[ROW][C]44[/C][C]16971[/C][C]15511.077044317[/C][C]1459.92295568297[/C][/ROW]
[ROW][C]45[/C][C]20036[/C][C]18071.8445473564[/C][C]1964.15545264361[/C][/ROW]
[ROW][C]46[/C][C]22485[/C][C]21478.3881560827[/C][C]1006.61184391733[/C][/ROW]
[ROW][C]47[/C][C]18730[/C][C]16512.2400731863[/C][C]2217.75992681369[/C][/ROW]
[ROW][C]48[/C][C]14538[/C][C]11465.7359913821[/C][C]3072.26400861786[/C][/ROW]
[ROW][C]49[/C][C]27561[/C][C]29817.912766974[/C][C]-2256.91276697404[/C][/ROW]
[ROW][C]50[/C][C]25985[/C][C]27536.5858935182[/C][C]-1551.58589351815[/C][/ROW]
[ROW][C]51[/C][C]34670[/C][C]30174.5656630841[/C][C]4495.43433691595[/C][/ROW]
[ROW][C]52[/C][C]32066[/C][C]29809.7589074294[/C][C]2256.24109257061[/C][/ROW]
[ROW][C]53[/C][C]27186[/C][C]25944.5197943715[/C][C]1241.48020562853[/C][/ROW]
[ROW][C]54[/C][C]29586[/C][C]28028.2251628706[/C][C]1557.77483712941[/C][/ROW]
[ROW][C]55[/C][C]21359[/C][C]23206.7909734129[/C][C]-1847.79097341294[/C][/ROW]
[ROW][C]56[/C][C]21553[/C][C]20547.4389112663[/C][C]1005.56108873369[/C][/ROW]
[ROW][C]57[/C][C]19573[/C][C]23193.6051787332[/C][C]-3620.6051787332[/C][/ROW]
[ROW][C]58[/C][C]24256[/C][C]24635.8821540932[/C][C]-379.882154093193[/C][/ROW]
[ROW][C]59[/C][C]22380[/C][C]19792.369507666[/C][C]2587.63049233396[/C][/ROW]
[ROW][C]60[/C][C]16167[/C][C]15209.1767327352[/C][C]957.823267264763[/C][/ROW]
[ROW][C]61[/C][C]27297[/C][C]30725.6219231638[/C][C]-3428.62192316385[/C][/ROW]
[ROW][C]62[/C][C]28287[/C][C]28413.9011439348[/C][C]-126.901143934756[/C][/ROW]
[ROW][C]63[/C][C]33474[/C][C]33997.1959235959[/C][C]-523.195923595893[/C][/ROW]
[ROW][C]64[/C][C]28229[/C][C]31286.5002485519[/C][C]-3057.50024855194[/C][/ROW]
[ROW][C]65[/C][C]28785[/C][C]25508.6429583228[/C][C]3276.35704167715[/C][/ROW]
[ROW][C]66[/C][C]25597[/C][C]28294.3222504396[/C][C]-2697.32225043964[/C][/ROW]
[ROW][C]67[/C][C]18130[/C][C]20849.1074692697[/C][C]-2719.10746926971[/C][/ROW]
[ROW][C]68[/C][C]20198[/C][C]19148.1091229064[/C][C]1049.89087709363[/C][/ROW]
[ROW][C]69[/C][C]22849[/C][C]19858.0377687649[/C][C]2990.96223123507[/C][/ROW]
[ROW][C]70[/C][C]23118[/C][C]24513.2900314672[/C][C]-1395.29003146722[/C][/ROW]
[ROW][C]71[/C][C]21925[/C][C]20635.9443704071[/C][C]1289.05562959288[/C][/ROW]
[ROW][C]72[/C][C]20801[/C][C]15003.2967937542[/C][C]5797.70320624577[/C][/ROW]
[ROW][C]73[/C][C]18785[/C][C]30024.8277004323[/C][C]-11239.8277004323[/C][/ROW]
[ROW][C]74[/C][C]20659[/C][C]26920.6343434804[/C][C]-6261.63434348043[/C][/ROW]
[ROW][C]75[/C][C]29367[/C][C]30622.3545663695[/C][C]-1255.35456636952[/C][/ROW]
[ROW][C]76[/C][C]23992[/C][C]26639.5253973485[/C][C]-2647.52539734852[/C][/ROW]
[ROW][C]77[/C][C]20645[/C][C]23644.1945106871[/C][C]-2999.1945106871[/C][/ROW]
[ROW][C]78[/C][C]22356[/C][C]22159.6421160075[/C][C]196.357883992536[/C][/ROW]
[ROW][C]79[/C][C]17902[/C][C]15514.0298066286[/C][C]2387.97019337135[/C][/ROW]
[ROW][C]80[/C][C]15879[/C][C]16828.0237930161[/C][C]-949.023793016142[/C][/ROW]
[ROW][C]81[/C][C]16963[/C][C]17796.8746387773[/C][C]-833.874638777335[/C][/ROW]
[ROW][C]82[/C][C]21035[/C][C]19535.5198603158[/C][C]1499.4801396842[/C][/ROW]
[ROW][C]83[/C][C]17988[/C][C]17597.9542558178[/C][C]390.045744182244[/C][/ROW]
[ROW][C]84[/C][C]10437[/C][C]13613.1615570068[/C][C]-3176.16155700684[/C][/ROW]
[ROW][C]85[/C][C]24470[/C][C]18949.9855423299[/C][C]5520.01445767007[/C][/ROW]
[ROW][C]86[/C][C]22237[/C][C]22627.0484743053[/C][C]-390.048474305342[/C][/ROW]
[ROW][C]87[/C][C]27053[/C][C]30078.6058809065[/C][C]-3025.60588090651[/C][/ROW]
[ROW][C]88[/C][C]26419[/C][C]25014.5860138574[/C][C]1404.41398614256[/C][/ROW]
[ROW][C]89[/C][C]22311[/C][C]23003.6358800912[/C][C]-692.635880091155[/C][/ROW]
[ROW][C]90[/C][C]20624[/C][C]23509.7892228038[/C][C]-2885.78922280379[/C][/ROW]
[ROW][C]91[/C][C]17336[/C][C]16925.8699727927[/C][C]410.130027207339[/C][/ROW]
[ROW][C]92[/C][C]15586[/C][C]16281.45664624[/C][C]-695.456646239971[/C][/ROW]
[ROW][C]93[/C][C]17733[/C][C]17369.6820669175[/C][C]363.317933082501[/C][/ROW]
[ROW][C]94[/C][C]19231[/C][C]20425.7932907407[/C][C]-1194.79329074066[/C][/ROW]
[ROW][C]95[/C][C]16102[/C][C]17267.8682073242[/C][C]-1165.86820732422[/C][/ROW]
[ROW][C]96[/C][C]11770[/C][C]11346.0469413312[/C][C]423.953058668798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278452&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278452&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
133112431525.9345619658-401.934561965827
142655126741.048333457-190.04833345702
153065130690.1339554913-39.1339554912629
162585925688.5248966505170.475103349534
172510024769.6262231955330.373776804499
182577825349.5022979337428.497702066255
192041818371.0538475482046.94615245196
201868818323.2923964933364.707603506708
212042419637.3063856951786.693614304866
222477622913.55643388511862.44356611494
231981419995.0184816658-181.018481665807
241273811961.9612656794776.038734320604
253156633636.7226069979-2070.72260699788
263011128474.6633199591636.33668004097
273001932997.7884911292-2978.78849112918
283193427262.84210440064671.15789559936
292582627669.2291408871-1843.22914088713
302683527682.9184257654-847.918425765391
312020521029.4345243713-824.434524371296
321778919470.5365930901-1681.53659309013
332052020390.3771098661129.622890133909
342251823936.1029692999-1418.10296929994
351557219239.913264617-3667.91326461704
361150910635.4051147292873.594885270759
372544731138.324138006-5691.32413800596
382409026525.7953893075-2435.79538930752
392778627966.7893718397-180.789371839739
402619526236.1795568085-41.1795568084817
412051622581.4944516979-2065.49445169786
422275922952.3044315512-193.304431551231
431902816491.67591755432536.3240824457
441697115511.0770443171459.92295568297
452003618071.84454735641964.15545264361
462248521478.38815608271006.61184391733
471873016512.24007318632217.75992681369
481453811465.73599138213072.26400861786
492756129817.912766974-2256.91276697404
502598527536.5858935182-1551.58589351815
513467030174.56566308414495.43433691595
523206629809.75890742942256.24109257061
532718625944.51979437151241.48020562853
542958628028.22516287061557.77483712941
552135923206.7909734129-1847.79097341294
562155320547.43891126631005.56108873369
571957323193.6051787332-3620.6051787332
582425624635.8821540932-379.882154093193
592238019792.3695076662587.63049233396
601616715209.1767327352957.823267264763
612729730725.6219231638-3428.62192316385
622828728413.9011439348-126.901143934756
633347433997.1959235959-523.195923595893
642822931286.5002485519-3057.50024855194
652878525508.64295832283276.35704167715
662559728294.3222504396-2697.32225043964
671813020849.1074692697-2719.10746926971
682019819148.10912290641049.89087709363
692284919858.03776876492990.96223123507
702311824513.2900314672-1395.29003146722
712192520635.94437040711289.05562959288
722080115003.29679375425797.70320624577
731878530024.8277004323-11239.8277004323
742065926920.6343434804-6261.63434348043
752936730622.3545663695-1255.35456636952
762399226639.5253973485-2647.52539734852
772064523644.1945106871-2999.1945106871
782235622159.6421160075196.357883992536
791790215514.02980662862387.97019337135
801587916828.0237930161-949.023793016142
811696317796.8746387773-833.874638777335
822103519535.51986031581499.4801396842
831798817597.9542558178390.045744182244
841043713613.1615570068-3176.16155700684
852447018949.98554232995520.01445767007
862223722627.0484743053-390.048474305342
872705330078.6058809065-3025.60588090651
882641925014.58601385741404.41398614256
892231123003.6358800912-692.635880091155
902062423509.7892228038-2885.78922280379
911733616925.8699727927410.130027207339
921558616281.45664624-695.456646239971
931773317369.6820669175363.317933082501
941923120425.7932907407-1194.79329074066
951610217267.8682073242-1165.86820732422
961177011346.0469413312423.953058668798







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9721352.088933342516311.372944831726392.8049218532
9820996.887947593915762.98525625526230.7906389328
9927447.317202974922027.108988525732867.525417424
10025094.956370298819494.637022836630695.275717761
10121808.15823863216033.342527361527582.9739499025
10221584.104972793915639.91316862827528.2967769599
10317195.061848974811086.188310400723303.9353875489
10415970.32408064919701.0932174675322239.5549438307
10517698.904132110911273.316585322224124.4916788995
10619997.163015907413418.934148877726575.3918829371
10717185.36446775210457.956740209423912.7721952946
10812259.06387915115385.7142999301619132.4134583721

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 21352.0889333425 & 16311.3729448317 & 26392.8049218532 \tabularnewline
98 & 20996.8879475939 & 15762.985256255 & 26230.7906389328 \tabularnewline
99 & 27447.3172029749 & 22027.1089885257 & 32867.525417424 \tabularnewline
100 & 25094.9563702988 & 19494.6370228366 & 30695.275717761 \tabularnewline
101 & 21808.158238632 & 16033.3425273615 & 27582.9739499025 \tabularnewline
102 & 21584.1049727939 & 15639.913168628 & 27528.2967769599 \tabularnewline
103 & 17195.0618489748 & 11086.1883104007 & 23303.9353875489 \tabularnewline
104 & 15970.3240806491 & 9701.09321746753 & 22239.5549438307 \tabularnewline
105 & 17698.9041321109 & 11273.3165853222 & 24124.4916788995 \tabularnewline
106 & 19997.1630159074 & 13418.9341488777 & 26575.3918829371 \tabularnewline
107 & 17185.364467752 & 10457.9567402094 & 23912.7721952946 \tabularnewline
108 & 12259.0638791511 & 5385.71429993016 & 19132.4134583721 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278452&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]97[/C][C]21352.0889333425[/C][C]16311.3729448317[/C][C]26392.8049218532[/C][/ROW]
[ROW][C]98[/C][C]20996.8879475939[/C][C]15762.985256255[/C][C]26230.7906389328[/C][/ROW]
[ROW][C]99[/C][C]27447.3172029749[/C][C]22027.1089885257[/C][C]32867.525417424[/C][/ROW]
[ROW][C]100[/C][C]25094.9563702988[/C][C]19494.6370228366[/C][C]30695.275717761[/C][/ROW]
[ROW][C]101[/C][C]21808.158238632[/C][C]16033.3425273615[/C][C]27582.9739499025[/C][/ROW]
[ROW][C]102[/C][C]21584.1049727939[/C][C]15639.913168628[/C][C]27528.2967769599[/C][/ROW]
[ROW][C]103[/C][C]17195.0618489748[/C][C]11086.1883104007[/C][C]23303.9353875489[/C][/ROW]
[ROW][C]104[/C][C]15970.3240806491[/C][C]9701.09321746753[/C][C]22239.5549438307[/C][/ROW]
[ROW][C]105[/C][C]17698.9041321109[/C][C]11273.3165853222[/C][C]24124.4916788995[/C][/ROW]
[ROW][C]106[/C][C]19997.1630159074[/C][C]13418.9341488777[/C][C]26575.3918829371[/C][/ROW]
[ROW][C]107[/C][C]17185.364467752[/C][C]10457.9567402094[/C][C]23912.7721952946[/C][/ROW]
[ROW][C]108[/C][C]12259.0638791511[/C][C]5385.71429993016[/C][C]19132.4134583721[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278452&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278452&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
9721352.088933342516311.372944831726392.8049218532
9820996.887947593915762.98525625526230.7906389328
9927447.317202974922027.108988525732867.525417424
10025094.956370298819494.637022836630695.275717761
10121808.15823863216033.342527361527582.9739499025
10221584.104972793915639.91316862827528.2967769599
10317195.061848974811086.188310400723303.9353875489
10415970.32408064919701.0932174675322239.5549438307
10517698.904132110911273.316585322224124.4916788995
10619997.163015907413418.934148877726575.3918829371
10717185.36446775210457.956740209423912.7721952946
10812259.06387915115385.7142999301619132.4134583721



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