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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 computationThu, 02 Apr 2015 10:18:30 +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/Apr/02/t1427966627kw8a595ybc4p16q.htm/, Retrieved Thu, 09 May 2024 10:19:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278542, Retrieved Thu, 09 May 2024 10:19:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-02 09:18:30] [8e46ac5a02f6c72569c3bd9e9d260f29] [Current]
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Dataseries X:
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577
23872
57276
56389
57657
62300
48929
51168
39636
33213
38127
43291
30600
21956
48033
46148
50736
48114
38390
44112
36287
30333
35908
40005
35263
26591
49709
47840
64781
57802
48154
54353
39737
37732
37163
43782
40649
29412
53597
53588
64172
53955
55509
48908
35331
38073
41776
42717
40736
49020
45099
44114
60487
48760
41281
48346
37025
31514
33977
42060
36036
22012
51048
45834
53712
53577
45022
43740
34898
30103
35137
39752
32348
25198




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278542&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278542&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278542&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.210234550872341
beta0
gamma0.309889472904834

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.210234550872341 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.309889472904834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278542&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]0.210234550872341[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.309889472904834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278542&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278542&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
alpha0.210234550872341
beta0
gamma0.309889472904834







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135612656979.9436431624-853.943643162391
144923149703.5062396504-472.506239650407
155972360006.2601573517-283.260157351673
164810348078.800140169424.1998598306236
174747247203.1038416106268.896158389412
185049750119.2678261461377.732173853896
194005935306.81290151154752.18709848847
203414934211.3528766021-62.3528766021336
213686036636.0018690393223.998130960703
224635643561.81007027662794.18992972338
233657737660.6280566492-1083.62805664924
242387223787.069720292184.9302797078562
255727658186.6885547883-910.688554788256
265638950991.67439992455397.32560007548
275765762574.7858640917-4917.7858640917
286230049748.23618066712551.763819333
294892951566.1536364618-2637.15363646182
305116853898.0020738527-2730.00207385272
313963639502.7981282019133.201871798083
323321336257.9573111944-3044.95731119444
333812738125.64134512781.35865487216506
344329145633.6717737161-2342.67177371612
353060037703.4867778406-7103.4867778406
362195622850.3391126966-894.33911269662
374803356800.4139339889-8767.41393398886
384614849497.4680240692-3349.4680240692
395073656717.1808922591-5981.18089225911
404811447942.5664003481171.433599651908
413839043440.3750536329-5050.37505363286
424411245242.1572437784-1130.15724377843
433628731884.03648751944402.96351248064
443033328759.02441690421573.97558309578
453590832343.32309910123564.67690089876
464000540026.8081345987-21.808134598723
473526331419.38700537723843.61299462284
482659120387.32473604916203.67526395094
494970953902.7910999904-4193.79109999037
504784048887.3668076497-1047.36680764969
516478155946.97548706878834.0245129313
525780251792.81991265046009.18008734959
534815447239.9391336124914.060866387561
545435351255.08593248843097.91406751156
553973740140.0278163775-403.027816377456
563773235312.2638149462419.73618505404
573716339561.5748354692-2398.57483546917
584378245113.621977333-1331.62197733303
594064937176.85588548643472.14411451358
602941226644.29965982752767.70034017247
615359756892.7294739598-3295.72947395984
625358852836.1646415935751.835358406548
636417262692.39947975551479.60052024454
645395556300.737459128-2345.73745912799
655550948744.38487036856764.61512963146
664890854523.9965468422-5615.99654684215
673533140720.1528340988-5389.1528340988
683807335534.97633715132538.02366284869
694177638629.92203930923146.07796069081
704271745608.7728126819-2891.77281268189
714073638519.68281797982216.31718202019
724902027550.702812744121469.2971872559
734509960246.8906354955-15147.8906354955
744411454689.1930364753-10575.1930364753
756048762342.2083921186-1855.20839211863
764876054313.2411052707-5553.24110527072
774128148312.2281092155-7031.22810921553
784834648161.4459922576184.554007742372
793702535632.59615014261392.4038498574
803151433813.234342805-2299.23434280499
813397736040.0364887836-2063.03648878361
824206040446.04783470881613.95216529116
833603635554.3708460164481.629153983566
842201228932.6737846914-6920.67378469139
855104846698.61830895854349.38169104151
864583446359.0430054056-525.043005405583
875371258259.0761699783-4547.0761699783
885357748759.12874825514817.87125174486
894502244576.7593631278445.240636872222
904374047763.7798013893-4023.77980138931
913489834645.8019598384252.198040161646
923010331683.2379695448-1580.23796954476
933513734119.00505763221017.99494236779
943975240072.6618613061-320.661861306071
953234834497.1374292502-2149.13742925021
962519825510.7227249008-312.722724900828

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 56126 & 56979.9436431624 & -853.943643162391 \tabularnewline
14 & 49231 & 49703.5062396504 & -472.506239650407 \tabularnewline
15 & 59723 & 60006.2601573517 & -283.260157351673 \tabularnewline
16 & 48103 & 48078.8001401694 & 24.1998598306236 \tabularnewline
17 & 47472 & 47203.1038416106 & 268.896158389412 \tabularnewline
18 & 50497 & 50119.2678261461 & 377.732173853896 \tabularnewline
19 & 40059 & 35306.8129015115 & 4752.18709848847 \tabularnewline
20 & 34149 & 34211.3528766021 & -62.3528766021336 \tabularnewline
21 & 36860 & 36636.0018690393 & 223.998130960703 \tabularnewline
22 & 46356 & 43561.8100702766 & 2794.18992972338 \tabularnewline
23 & 36577 & 37660.6280566492 & -1083.62805664924 \tabularnewline
24 & 23872 & 23787.0697202921 & 84.9302797078562 \tabularnewline
25 & 57276 & 58186.6885547883 & -910.688554788256 \tabularnewline
26 & 56389 & 50991.6743999245 & 5397.32560007548 \tabularnewline
27 & 57657 & 62574.7858640917 & -4917.7858640917 \tabularnewline
28 & 62300 & 49748.236180667 & 12551.763819333 \tabularnewline
29 & 48929 & 51566.1536364618 & -2637.15363646182 \tabularnewline
30 & 51168 & 53898.0020738527 & -2730.00207385272 \tabularnewline
31 & 39636 & 39502.7981282019 & 133.201871798083 \tabularnewline
32 & 33213 & 36257.9573111944 & -3044.95731119444 \tabularnewline
33 & 38127 & 38125.6413451278 & 1.35865487216506 \tabularnewline
34 & 43291 & 45633.6717737161 & -2342.67177371612 \tabularnewline
35 & 30600 & 37703.4867778406 & -7103.4867778406 \tabularnewline
36 & 21956 & 22850.3391126966 & -894.33911269662 \tabularnewline
37 & 48033 & 56800.4139339889 & -8767.41393398886 \tabularnewline
38 & 46148 & 49497.4680240692 & -3349.4680240692 \tabularnewline
39 & 50736 & 56717.1808922591 & -5981.18089225911 \tabularnewline
40 & 48114 & 47942.5664003481 & 171.433599651908 \tabularnewline
41 & 38390 & 43440.3750536329 & -5050.37505363286 \tabularnewline
42 & 44112 & 45242.1572437784 & -1130.15724377843 \tabularnewline
43 & 36287 & 31884.0364875194 & 4402.96351248064 \tabularnewline
44 & 30333 & 28759.0244169042 & 1573.97558309578 \tabularnewline
45 & 35908 & 32343.3230991012 & 3564.67690089876 \tabularnewline
46 & 40005 & 40026.8081345987 & -21.808134598723 \tabularnewline
47 & 35263 & 31419.3870053772 & 3843.61299462284 \tabularnewline
48 & 26591 & 20387.3247360491 & 6203.67526395094 \tabularnewline
49 & 49709 & 53902.7910999904 & -4193.79109999037 \tabularnewline
50 & 47840 & 48887.3668076497 & -1047.36680764969 \tabularnewline
51 & 64781 & 55946.9754870687 & 8834.0245129313 \tabularnewline
52 & 57802 & 51792.8199126504 & 6009.18008734959 \tabularnewline
53 & 48154 & 47239.9391336124 & 914.060866387561 \tabularnewline
54 & 54353 & 51255.0859324884 & 3097.91406751156 \tabularnewline
55 & 39737 & 40140.0278163775 & -403.027816377456 \tabularnewline
56 & 37732 & 35312.263814946 & 2419.73618505404 \tabularnewline
57 & 37163 & 39561.5748354692 & -2398.57483546917 \tabularnewline
58 & 43782 & 45113.621977333 & -1331.62197733303 \tabularnewline
59 & 40649 & 37176.8558854864 & 3472.14411451358 \tabularnewline
60 & 29412 & 26644.2996598275 & 2767.70034017247 \tabularnewline
61 & 53597 & 56892.7294739598 & -3295.72947395984 \tabularnewline
62 & 53588 & 52836.1646415935 & 751.835358406548 \tabularnewline
63 & 64172 & 62692.3994797555 & 1479.60052024454 \tabularnewline
64 & 53955 & 56300.737459128 & -2345.73745912799 \tabularnewline
65 & 55509 & 48744.3848703685 & 6764.61512963146 \tabularnewline
66 & 48908 & 54523.9965468422 & -5615.99654684215 \tabularnewline
67 & 35331 & 40720.1528340988 & -5389.1528340988 \tabularnewline
68 & 38073 & 35534.9763371513 & 2538.02366284869 \tabularnewline
69 & 41776 & 38629.9220393092 & 3146.07796069081 \tabularnewline
70 & 42717 & 45608.7728126819 & -2891.77281268189 \tabularnewline
71 & 40736 & 38519.6828179798 & 2216.31718202019 \tabularnewline
72 & 49020 & 27550.7028127441 & 21469.2971872559 \tabularnewline
73 & 45099 & 60246.8906354955 & -15147.8906354955 \tabularnewline
74 & 44114 & 54689.1930364753 & -10575.1930364753 \tabularnewline
75 & 60487 & 62342.2083921186 & -1855.20839211863 \tabularnewline
76 & 48760 & 54313.2411052707 & -5553.24110527072 \tabularnewline
77 & 41281 & 48312.2281092155 & -7031.22810921553 \tabularnewline
78 & 48346 & 48161.4459922576 & 184.554007742372 \tabularnewline
79 & 37025 & 35632.5961501426 & 1392.4038498574 \tabularnewline
80 & 31514 & 33813.234342805 & -2299.23434280499 \tabularnewline
81 & 33977 & 36040.0364887836 & -2063.03648878361 \tabularnewline
82 & 42060 & 40446.0478347088 & 1613.95216529116 \tabularnewline
83 & 36036 & 35554.3708460164 & 481.629153983566 \tabularnewline
84 & 22012 & 28932.6737846914 & -6920.67378469139 \tabularnewline
85 & 51048 & 46698.6183089585 & 4349.38169104151 \tabularnewline
86 & 45834 & 46359.0430054056 & -525.043005405583 \tabularnewline
87 & 53712 & 58259.0761699783 & -4547.0761699783 \tabularnewline
88 & 53577 & 48759.1287482551 & 4817.87125174486 \tabularnewline
89 & 45022 & 44576.7593631278 & 445.240636872222 \tabularnewline
90 & 43740 & 47763.7798013893 & -4023.77980138931 \tabularnewline
91 & 34898 & 34645.8019598384 & 252.198040161646 \tabularnewline
92 & 30103 & 31683.2379695448 & -1580.23796954476 \tabularnewline
93 & 35137 & 34119.0050576322 & 1017.99494236779 \tabularnewline
94 & 39752 & 40072.6618613061 & -320.661861306071 \tabularnewline
95 & 32348 & 34497.1374292502 & -2149.13742925021 \tabularnewline
96 & 25198 & 25510.7227249008 & -312.722724900828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278542&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]56126[/C][C]56979.9436431624[/C][C]-853.943643162391[/C][/ROW]
[ROW][C]14[/C][C]49231[/C][C]49703.5062396504[/C][C]-472.506239650407[/C][/ROW]
[ROW][C]15[/C][C]59723[/C][C]60006.2601573517[/C][C]-283.260157351673[/C][/ROW]
[ROW][C]16[/C][C]48103[/C][C]48078.8001401694[/C][C]24.1998598306236[/C][/ROW]
[ROW][C]17[/C][C]47472[/C][C]47203.1038416106[/C][C]268.896158389412[/C][/ROW]
[ROW][C]18[/C][C]50497[/C][C]50119.2678261461[/C][C]377.732173853896[/C][/ROW]
[ROW][C]19[/C][C]40059[/C][C]35306.8129015115[/C][C]4752.18709848847[/C][/ROW]
[ROW][C]20[/C][C]34149[/C][C]34211.3528766021[/C][C]-62.3528766021336[/C][/ROW]
[ROW][C]21[/C][C]36860[/C][C]36636.0018690393[/C][C]223.998130960703[/C][/ROW]
[ROW][C]22[/C][C]46356[/C][C]43561.8100702766[/C][C]2794.18992972338[/C][/ROW]
[ROW][C]23[/C][C]36577[/C][C]37660.6280566492[/C][C]-1083.62805664924[/C][/ROW]
[ROW][C]24[/C][C]23872[/C][C]23787.0697202921[/C][C]84.9302797078562[/C][/ROW]
[ROW][C]25[/C][C]57276[/C][C]58186.6885547883[/C][C]-910.688554788256[/C][/ROW]
[ROW][C]26[/C][C]56389[/C][C]50991.6743999245[/C][C]5397.32560007548[/C][/ROW]
[ROW][C]27[/C][C]57657[/C][C]62574.7858640917[/C][C]-4917.7858640917[/C][/ROW]
[ROW][C]28[/C][C]62300[/C][C]49748.236180667[/C][C]12551.763819333[/C][/ROW]
[ROW][C]29[/C][C]48929[/C][C]51566.1536364618[/C][C]-2637.15363646182[/C][/ROW]
[ROW][C]30[/C][C]51168[/C][C]53898.0020738527[/C][C]-2730.00207385272[/C][/ROW]
[ROW][C]31[/C][C]39636[/C][C]39502.7981282019[/C][C]133.201871798083[/C][/ROW]
[ROW][C]32[/C][C]33213[/C][C]36257.9573111944[/C][C]-3044.95731119444[/C][/ROW]
[ROW][C]33[/C][C]38127[/C][C]38125.6413451278[/C][C]1.35865487216506[/C][/ROW]
[ROW][C]34[/C][C]43291[/C][C]45633.6717737161[/C][C]-2342.67177371612[/C][/ROW]
[ROW][C]35[/C][C]30600[/C][C]37703.4867778406[/C][C]-7103.4867778406[/C][/ROW]
[ROW][C]36[/C][C]21956[/C][C]22850.3391126966[/C][C]-894.33911269662[/C][/ROW]
[ROW][C]37[/C][C]48033[/C][C]56800.4139339889[/C][C]-8767.41393398886[/C][/ROW]
[ROW][C]38[/C][C]46148[/C][C]49497.4680240692[/C][C]-3349.4680240692[/C][/ROW]
[ROW][C]39[/C][C]50736[/C][C]56717.1808922591[/C][C]-5981.18089225911[/C][/ROW]
[ROW][C]40[/C][C]48114[/C][C]47942.5664003481[/C][C]171.433599651908[/C][/ROW]
[ROW][C]41[/C][C]38390[/C][C]43440.3750536329[/C][C]-5050.37505363286[/C][/ROW]
[ROW][C]42[/C][C]44112[/C][C]45242.1572437784[/C][C]-1130.15724377843[/C][/ROW]
[ROW][C]43[/C][C]36287[/C][C]31884.0364875194[/C][C]4402.96351248064[/C][/ROW]
[ROW][C]44[/C][C]30333[/C][C]28759.0244169042[/C][C]1573.97558309578[/C][/ROW]
[ROW][C]45[/C][C]35908[/C][C]32343.3230991012[/C][C]3564.67690089876[/C][/ROW]
[ROW][C]46[/C][C]40005[/C][C]40026.8081345987[/C][C]-21.808134598723[/C][/ROW]
[ROW][C]47[/C][C]35263[/C][C]31419.3870053772[/C][C]3843.61299462284[/C][/ROW]
[ROW][C]48[/C][C]26591[/C][C]20387.3247360491[/C][C]6203.67526395094[/C][/ROW]
[ROW][C]49[/C][C]49709[/C][C]53902.7910999904[/C][C]-4193.79109999037[/C][/ROW]
[ROW][C]50[/C][C]47840[/C][C]48887.3668076497[/C][C]-1047.36680764969[/C][/ROW]
[ROW][C]51[/C][C]64781[/C][C]55946.9754870687[/C][C]8834.0245129313[/C][/ROW]
[ROW][C]52[/C][C]57802[/C][C]51792.8199126504[/C][C]6009.18008734959[/C][/ROW]
[ROW][C]53[/C][C]48154[/C][C]47239.9391336124[/C][C]914.060866387561[/C][/ROW]
[ROW][C]54[/C][C]54353[/C][C]51255.0859324884[/C][C]3097.91406751156[/C][/ROW]
[ROW][C]55[/C][C]39737[/C][C]40140.0278163775[/C][C]-403.027816377456[/C][/ROW]
[ROW][C]56[/C][C]37732[/C][C]35312.263814946[/C][C]2419.73618505404[/C][/ROW]
[ROW][C]57[/C][C]37163[/C][C]39561.5748354692[/C][C]-2398.57483546917[/C][/ROW]
[ROW][C]58[/C][C]43782[/C][C]45113.621977333[/C][C]-1331.62197733303[/C][/ROW]
[ROW][C]59[/C][C]40649[/C][C]37176.8558854864[/C][C]3472.14411451358[/C][/ROW]
[ROW][C]60[/C][C]29412[/C][C]26644.2996598275[/C][C]2767.70034017247[/C][/ROW]
[ROW][C]61[/C][C]53597[/C][C]56892.7294739598[/C][C]-3295.72947395984[/C][/ROW]
[ROW][C]62[/C][C]53588[/C][C]52836.1646415935[/C][C]751.835358406548[/C][/ROW]
[ROW][C]63[/C][C]64172[/C][C]62692.3994797555[/C][C]1479.60052024454[/C][/ROW]
[ROW][C]64[/C][C]53955[/C][C]56300.737459128[/C][C]-2345.73745912799[/C][/ROW]
[ROW][C]65[/C][C]55509[/C][C]48744.3848703685[/C][C]6764.61512963146[/C][/ROW]
[ROW][C]66[/C][C]48908[/C][C]54523.9965468422[/C][C]-5615.99654684215[/C][/ROW]
[ROW][C]67[/C][C]35331[/C][C]40720.1528340988[/C][C]-5389.1528340988[/C][/ROW]
[ROW][C]68[/C][C]38073[/C][C]35534.9763371513[/C][C]2538.02366284869[/C][/ROW]
[ROW][C]69[/C][C]41776[/C][C]38629.9220393092[/C][C]3146.07796069081[/C][/ROW]
[ROW][C]70[/C][C]42717[/C][C]45608.7728126819[/C][C]-2891.77281268189[/C][/ROW]
[ROW][C]71[/C][C]40736[/C][C]38519.6828179798[/C][C]2216.31718202019[/C][/ROW]
[ROW][C]72[/C][C]49020[/C][C]27550.7028127441[/C][C]21469.2971872559[/C][/ROW]
[ROW][C]73[/C][C]45099[/C][C]60246.8906354955[/C][C]-15147.8906354955[/C][/ROW]
[ROW][C]74[/C][C]44114[/C][C]54689.1930364753[/C][C]-10575.1930364753[/C][/ROW]
[ROW][C]75[/C][C]60487[/C][C]62342.2083921186[/C][C]-1855.20839211863[/C][/ROW]
[ROW][C]76[/C][C]48760[/C][C]54313.2411052707[/C][C]-5553.24110527072[/C][/ROW]
[ROW][C]77[/C][C]41281[/C][C]48312.2281092155[/C][C]-7031.22810921553[/C][/ROW]
[ROW][C]78[/C][C]48346[/C][C]48161.4459922576[/C][C]184.554007742372[/C][/ROW]
[ROW][C]79[/C][C]37025[/C][C]35632.5961501426[/C][C]1392.4038498574[/C][/ROW]
[ROW][C]80[/C][C]31514[/C][C]33813.234342805[/C][C]-2299.23434280499[/C][/ROW]
[ROW][C]81[/C][C]33977[/C][C]36040.0364887836[/C][C]-2063.03648878361[/C][/ROW]
[ROW][C]82[/C][C]42060[/C][C]40446.0478347088[/C][C]1613.95216529116[/C][/ROW]
[ROW][C]83[/C][C]36036[/C][C]35554.3708460164[/C][C]481.629153983566[/C][/ROW]
[ROW][C]84[/C][C]22012[/C][C]28932.6737846914[/C][C]-6920.67378469139[/C][/ROW]
[ROW][C]85[/C][C]51048[/C][C]46698.6183089585[/C][C]4349.38169104151[/C][/ROW]
[ROW][C]86[/C][C]45834[/C][C]46359.0430054056[/C][C]-525.043005405583[/C][/ROW]
[ROW][C]87[/C][C]53712[/C][C]58259.0761699783[/C][C]-4547.0761699783[/C][/ROW]
[ROW][C]88[/C][C]53577[/C][C]48759.1287482551[/C][C]4817.87125174486[/C][/ROW]
[ROW][C]89[/C][C]45022[/C][C]44576.7593631278[/C][C]445.240636872222[/C][/ROW]
[ROW][C]90[/C][C]43740[/C][C]47763.7798013893[/C][C]-4023.77980138931[/C][/ROW]
[ROW][C]91[/C][C]34898[/C][C]34645.8019598384[/C][C]252.198040161646[/C][/ROW]
[ROW][C]92[/C][C]30103[/C][C]31683.2379695448[/C][C]-1580.23796954476[/C][/ROW]
[ROW][C]93[/C][C]35137[/C][C]34119.0050576322[/C][C]1017.99494236779[/C][/ROW]
[ROW][C]94[/C][C]39752[/C][C]40072.6618613061[/C][C]-320.661861306071[/C][/ROW]
[ROW][C]95[/C][C]32348[/C][C]34497.1374292502[/C][C]-2149.13742925021[/C][/ROW]
[ROW][C]96[/C][C]25198[/C][C]25510.7227249008[/C][C]-312.722724900828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278542&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278542&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
135612656979.9436431624-853.943643162391
144923149703.5062396504-472.506239650407
155972360006.2601573517-283.260157351673
164810348078.800140169424.1998598306236
174747247203.1038416106268.896158389412
185049750119.2678261461377.732173853896
194005935306.81290151154752.18709848847
203414934211.3528766021-62.3528766021336
213686036636.0018690393223.998130960703
224635643561.81007027662794.18992972338
233657737660.6280566492-1083.62805664924
242387223787.069720292184.9302797078562
255727658186.6885547883-910.688554788256
265638950991.67439992455397.32560007548
275765762574.7858640917-4917.7858640917
286230049748.23618066712551.763819333
294892951566.1536364618-2637.15363646182
305116853898.0020738527-2730.00207385272
313963639502.7981282019133.201871798083
323321336257.9573111944-3044.95731119444
333812738125.64134512781.35865487216506
344329145633.6717737161-2342.67177371612
353060037703.4867778406-7103.4867778406
362195622850.3391126966-894.33911269662
374803356800.4139339889-8767.41393398886
384614849497.4680240692-3349.4680240692
395073656717.1808922591-5981.18089225911
404811447942.5664003481171.433599651908
413839043440.3750536329-5050.37505363286
424411245242.1572437784-1130.15724377843
433628731884.03648751944402.96351248064
443033328759.02441690421573.97558309578
453590832343.32309910123564.67690089876
464000540026.8081345987-21.808134598723
473526331419.38700537723843.61299462284
482659120387.32473604916203.67526395094
494970953902.7910999904-4193.79109999037
504784048887.3668076497-1047.36680764969
516478155946.97548706878834.0245129313
525780251792.81991265046009.18008734959
534815447239.9391336124914.060866387561
545435351255.08593248843097.91406751156
553973740140.0278163775-403.027816377456
563773235312.2638149462419.73618505404
573716339561.5748354692-2398.57483546917
584378245113.621977333-1331.62197733303
594064937176.85588548643472.14411451358
602941226644.29965982752767.70034017247
615359756892.7294739598-3295.72947395984
625358852836.1646415935751.835358406548
636417262692.39947975551479.60052024454
645395556300.737459128-2345.73745912799
655550948744.38487036856764.61512963146
664890854523.9965468422-5615.99654684215
673533140720.1528340988-5389.1528340988
683807335534.97633715132538.02366284869
694177638629.92203930923146.07796069081
704271745608.7728126819-2891.77281268189
714073638519.68281797982216.31718202019
724902027550.702812744121469.2971872559
734509960246.8906354955-15147.8906354955
744411454689.1930364753-10575.1930364753
756048762342.2083921186-1855.20839211863
764876054313.2411052707-5553.24110527072
774128148312.2281092155-7031.22810921553
784834648161.4459922576184.554007742372
793702535632.59615014261392.4038498574
803151433813.234342805-2299.23434280499
813397736040.0364887836-2063.03648878361
824206040446.04783470881613.95216529116
833603635554.3708460164481.629153983566
842201228932.6737846914-6920.67378469139
855104846698.61830895854349.38169104151
864583446359.0430054056-525.043005405583
875371258259.0761699783-4547.0761699783
885357748759.12874825514817.87125174486
894502244576.7593631278445.240636872222
904374047763.7798013893-4023.77980138931
913489834645.8019598384252.198040161646
923010331683.2379695448-1580.23796954476
933513734119.00505763221017.99494236779
943975240072.6618613061-320.661861306071
953234834497.1374292502-2149.13742925021
962519825510.7227249008-312.722724900828







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9747424.120235437137980.120648817656868.1198220567
9844977.187931387135326.739247782454627.6366149917
9956003.250884725546150.678053342765855.8237161082
10049751.233199653439700.600234485659801.8661648212
10143485.823204542633240.958412690453730.6879963949
10245485.490621013535050.008542731355920.9726992957
10334259.953130407123637.273722227444882.6325385868
10430795.898011686819989.263502655841602.5325207179
10534199.77723918323212.267010992345187.2874673738
10639611.793468901928446.337248155250777.2496896487
10733656.182131029122315.571732103144996.7925299551
10825571.034501325514057.934318358137084.1346842929

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 47424.1202354371 & 37980.1206488176 & 56868.1198220567 \tabularnewline
98 & 44977.1879313871 & 35326.7392477824 & 54627.6366149917 \tabularnewline
99 & 56003.2508847255 & 46150.6780533427 & 65855.8237161082 \tabularnewline
100 & 49751.2331996534 & 39700.6002344856 & 59801.8661648212 \tabularnewline
101 & 43485.8232045426 & 33240.9584126904 & 53730.6879963949 \tabularnewline
102 & 45485.4906210135 & 35050.0085427313 & 55920.9726992957 \tabularnewline
103 & 34259.9531304071 & 23637.2737222274 & 44882.6325385868 \tabularnewline
104 & 30795.8980116868 & 19989.2635026558 & 41602.5325207179 \tabularnewline
105 & 34199.777239183 & 23212.2670109923 & 45187.2874673738 \tabularnewline
106 & 39611.7934689019 & 28446.3372481552 & 50777.2496896487 \tabularnewline
107 & 33656.1821310291 & 22315.5717321031 & 44996.7925299551 \tabularnewline
108 & 25571.0345013255 & 14057.9343183581 & 37084.1346842929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278542&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]47424.1202354371[/C][C]37980.1206488176[/C][C]56868.1198220567[/C][/ROW]
[ROW][C]98[/C][C]44977.1879313871[/C][C]35326.7392477824[/C][C]54627.6366149917[/C][/ROW]
[ROW][C]99[/C][C]56003.2508847255[/C][C]46150.6780533427[/C][C]65855.8237161082[/C][/ROW]
[ROW][C]100[/C][C]49751.2331996534[/C][C]39700.6002344856[/C][C]59801.8661648212[/C][/ROW]
[ROW][C]101[/C][C]43485.8232045426[/C][C]33240.9584126904[/C][C]53730.6879963949[/C][/ROW]
[ROW][C]102[/C][C]45485.4906210135[/C][C]35050.0085427313[/C][C]55920.9726992957[/C][/ROW]
[ROW][C]103[/C][C]34259.9531304071[/C][C]23637.2737222274[/C][C]44882.6325385868[/C][/ROW]
[ROW][C]104[/C][C]30795.8980116868[/C][C]19989.2635026558[/C][C]41602.5325207179[/C][/ROW]
[ROW][C]105[/C][C]34199.777239183[/C][C]23212.2670109923[/C][C]45187.2874673738[/C][/ROW]
[ROW][C]106[/C][C]39611.7934689019[/C][C]28446.3372481552[/C][C]50777.2496896487[/C][/ROW]
[ROW][C]107[/C][C]33656.1821310291[/C][C]22315.5717321031[/C][C]44996.7925299551[/C][/ROW]
[ROW][C]108[/C][C]25571.0345013255[/C][C]14057.9343183581[/C][C]37084.1346842929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278542&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278542&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
9747424.120235437137980.120648817656868.1198220567
9844977.187931387135326.739247782454627.6366149917
9956003.250884725546150.678053342765855.8237161082
10049751.233199653439700.600234485659801.8661648212
10143485.823204542633240.958412690453730.6879963949
10245485.490621013535050.008542731355920.9726992957
10334259.953130407123637.273722227444882.6325385868
10430795.898011686819989.263502655841602.5325207179
10534199.77723918323212.267010992345187.2874673738
10639611.793468901928446.337248155250777.2496896487
10733656.182131029122315.571732103144996.7925299551
10825571.034501325514057.934318358137084.1346842929



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')