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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 14:17:06 +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/2016/Apr/25/t1461590244wb7e6mzx54j5ql0.htm/, Retrieved Sun, 05 May 2024 23:40:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294699, Retrieved Sun, 05 May 2024 23:40:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 13:17:06] [3cc5eb308fa11ebf92933824162ee6d9] [Current]
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Dataseries X:
7,4361
7,4324
7,4367
7,4368
7,4456
7,4564
7,4597
7,4537
7,4639
7,4593
7,4438
7,4415
7,4317
7,4343
7,4281
7,4281
7,4305
7,425
7,4309
7,4361
7,4495
7,4393
7,4367
7,4343
7,4433
7,4463
7,4588
7,4586
7,4621
7,4581
7,4604
7,4557
7,4524
7,45
7,4446
7,4557
7,4534
7,4599
7,4592
7,4512
7,4514
7,4471
7,4442
7,4424
7,4426
7,4416
7,4498
7,4547
7,455
7,4573
7,4506
7,4398
7,435
7,4349
7,4457
7,459
7,4589
7,4555
7,458
7,4593
7,4625
7,4628
7,4522
7,4423
7,4501
7,4623
7,4617
7,4605




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294699&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294699&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294699&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294699&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]0.999933893038648[/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=294699&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294699&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
27.43247.4361-0.00369999999999937
37.43677.432400244595760.00429975540424277
47.43687.436699715756240.000100284243764293
57.44567.436799993370510.00880000662948621
67.45647.44559941825830.010800581741699
77.45977.456399286006360.00330071399363874
87.45377.45969978179983-0.00599978179982674
97.46397.453700396627340.0101996033726559
107.45937.46389932573521-0.0045993257352146
117.44387.45930030404745-0.015500304047448
127.44157.443801024678-0.00230102467800108
137.43177.44150015211375-0.00980015211374852
147.43437.431700647858280.00259935214172291
157.42817.43429982816473-0.0061998281647293
167.42817.4281004098518-4.09851801386196e-07
177.43057.428100000027090.00239999997290674
187.4257.43049984134329-0.00549984134329495
197.43097.42500036357780.00589963642220148
207.43617.430899609992960.00520039000703676
217.44957.436099656218020.0134003437819814
227.43937.44949911414399-0.0101991141439903
237.43677.43930067423245-0.00260067423244514
247.43437.43670017192267-0.0024001719226705
257.44337.434300158668070.00899984133192699
267.44637.443299405047840.0030005949521632
277.45887.446299801639790.0125001983602147
287.45867.45879917364987-0.000199173649870765
297.46217.458600013166760.00349998683323616
307.45817.46209976862651-0.00399976862650675
317.46047.458100264412550.00229973558745034
327.45577.46039984797147-0.00469984797146772
337.45247.45570031069267-0.00330031069266834
347.457.45240021817351-0.00240021817351099
357.44467.45000015867113-0.00540015867112942
367.45577.444600356988080.011099643011919
377.45347.45569926623633-0.00229926623632881
387.45997.45340015199750.00649984800249559
397.45927.4598995703148-0.000699570314798947
407.45127.45920004624647-0.00800004624646711
417.45147.451200528858750.000199471141251628
427.44717.45139998681357-0.00429998681356913
437.44427.44710028425906-0.00290028425906197
447.44247.44420019172898-0.00180019172897961
457.44267.442400119005210.000199880994793844
467.44167.44259998678647-0.000999986786474061
477.44987.441600066106090.00819993389391183
487.45477.449799457927290.00490054207271307
497.4557.454699676040050.000300323959945281
507.45737.45499998014650.00230001985350459
517.45067.45729984795268-0.00669984795267631
527.43987.45060044290659-0.0108004429065893
537.4357.43980071398446-0.00480071398446213
547.43497.43500031736061-0.000100317360614
557.44577.434900006631680.0107999933683249
567.4597.445699286045260.0133007139547434
577.45897.45899912073022-9.9120730216562e-05
587.45557.45890000655257-0.00340000655257011
597.4587.45550022476410.00249977523589884
607.45937.457999834747460.00130016525254462
617.46257.459299914050030.00320008594997478
627.46287.462499788452040.000300211547957119
637.45227.46279998015393-0.010599980153926
647.44237.45220070073248-0.00990070073247828
657.45017.442300654505240.00779934549475847
667.46237.450099484408970.0122005155910312
677.46177.46229919346099-0.000599193460987024
687.46057.46170003961086-0.00120003961085935

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 7.4324 & 7.4361 & -0.00369999999999937 \tabularnewline
3 & 7.4367 & 7.43240024459576 & 0.00429975540424277 \tabularnewline
4 & 7.4368 & 7.43669971575624 & 0.000100284243764293 \tabularnewline
5 & 7.4456 & 7.43679999337051 & 0.00880000662948621 \tabularnewline
6 & 7.4564 & 7.4455994182583 & 0.010800581741699 \tabularnewline
7 & 7.4597 & 7.45639928600636 & 0.00330071399363874 \tabularnewline
8 & 7.4537 & 7.45969978179983 & -0.00599978179982674 \tabularnewline
9 & 7.4639 & 7.45370039662734 & 0.0101996033726559 \tabularnewline
10 & 7.4593 & 7.46389932573521 & -0.0045993257352146 \tabularnewline
11 & 7.4438 & 7.45930030404745 & -0.015500304047448 \tabularnewline
12 & 7.4415 & 7.443801024678 & -0.00230102467800108 \tabularnewline
13 & 7.4317 & 7.44150015211375 & -0.00980015211374852 \tabularnewline
14 & 7.4343 & 7.43170064785828 & 0.00259935214172291 \tabularnewline
15 & 7.4281 & 7.43429982816473 & -0.0061998281647293 \tabularnewline
16 & 7.4281 & 7.4281004098518 & -4.09851801386196e-07 \tabularnewline
17 & 7.4305 & 7.42810000002709 & 0.00239999997290674 \tabularnewline
18 & 7.425 & 7.43049984134329 & -0.00549984134329495 \tabularnewline
19 & 7.4309 & 7.4250003635778 & 0.00589963642220148 \tabularnewline
20 & 7.4361 & 7.43089960999296 & 0.00520039000703676 \tabularnewline
21 & 7.4495 & 7.43609965621802 & 0.0134003437819814 \tabularnewline
22 & 7.4393 & 7.44949911414399 & -0.0101991141439903 \tabularnewline
23 & 7.4367 & 7.43930067423245 & -0.00260067423244514 \tabularnewline
24 & 7.4343 & 7.43670017192267 & -0.0024001719226705 \tabularnewline
25 & 7.4433 & 7.43430015866807 & 0.00899984133192699 \tabularnewline
26 & 7.4463 & 7.44329940504784 & 0.0030005949521632 \tabularnewline
27 & 7.4588 & 7.44629980163979 & 0.0125001983602147 \tabularnewline
28 & 7.4586 & 7.45879917364987 & -0.000199173649870765 \tabularnewline
29 & 7.4621 & 7.45860001316676 & 0.00349998683323616 \tabularnewline
30 & 7.4581 & 7.46209976862651 & -0.00399976862650675 \tabularnewline
31 & 7.4604 & 7.45810026441255 & 0.00229973558745034 \tabularnewline
32 & 7.4557 & 7.46039984797147 & -0.00469984797146772 \tabularnewline
33 & 7.4524 & 7.45570031069267 & -0.00330031069266834 \tabularnewline
34 & 7.45 & 7.45240021817351 & -0.00240021817351099 \tabularnewline
35 & 7.4446 & 7.45000015867113 & -0.00540015867112942 \tabularnewline
36 & 7.4557 & 7.44460035698808 & 0.011099643011919 \tabularnewline
37 & 7.4534 & 7.45569926623633 & -0.00229926623632881 \tabularnewline
38 & 7.4599 & 7.4534001519975 & 0.00649984800249559 \tabularnewline
39 & 7.4592 & 7.4598995703148 & -0.000699570314798947 \tabularnewline
40 & 7.4512 & 7.45920004624647 & -0.00800004624646711 \tabularnewline
41 & 7.4514 & 7.45120052885875 & 0.000199471141251628 \tabularnewline
42 & 7.4471 & 7.45139998681357 & -0.00429998681356913 \tabularnewline
43 & 7.4442 & 7.44710028425906 & -0.00290028425906197 \tabularnewline
44 & 7.4424 & 7.44420019172898 & -0.00180019172897961 \tabularnewline
45 & 7.4426 & 7.44240011900521 & 0.000199880994793844 \tabularnewline
46 & 7.4416 & 7.44259998678647 & -0.000999986786474061 \tabularnewline
47 & 7.4498 & 7.44160006610609 & 0.00819993389391183 \tabularnewline
48 & 7.4547 & 7.44979945792729 & 0.00490054207271307 \tabularnewline
49 & 7.455 & 7.45469967604005 & 0.000300323959945281 \tabularnewline
50 & 7.4573 & 7.4549999801465 & 0.00230001985350459 \tabularnewline
51 & 7.4506 & 7.45729984795268 & -0.00669984795267631 \tabularnewline
52 & 7.4398 & 7.45060044290659 & -0.0108004429065893 \tabularnewline
53 & 7.435 & 7.43980071398446 & -0.00480071398446213 \tabularnewline
54 & 7.4349 & 7.43500031736061 & -0.000100317360614 \tabularnewline
55 & 7.4457 & 7.43490000663168 & 0.0107999933683249 \tabularnewline
56 & 7.459 & 7.44569928604526 & 0.0133007139547434 \tabularnewline
57 & 7.4589 & 7.45899912073022 & -9.9120730216562e-05 \tabularnewline
58 & 7.4555 & 7.45890000655257 & -0.00340000655257011 \tabularnewline
59 & 7.458 & 7.4555002247641 & 0.00249977523589884 \tabularnewline
60 & 7.4593 & 7.45799983474746 & 0.00130016525254462 \tabularnewline
61 & 7.4625 & 7.45929991405003 & 0.00320008594997478 \tabularnewline
62 & 7.4628 & 7.46249978845204 & 0.000300211547957119 \tabularnewline
63 & 7.4522 & 7.46279998015393 & -0.010599980153926 \tabularnewline
64 & 7.4423 & 7.45220070073248 & -0.00990070073247828 \tabularnewline
65 & 7.4501 & 7.44230065450524 & 0.00779934549475847 \tabularnewline
66 & 7.4623 & 7.45009948440897 & 0.0122005155910312 \tabularnewline
67 & 7.4617 & 7.46229919346099 & -0.000599193460987024 \tabularnewline
68 & 7.4605 & 7.46170003961086 & -0.00120003961085935 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294699&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]7.4324[/C][C]7.4361[/C][C]-0.00369999999999937[/C][/ROW]
[ROW][C]3[/C][C]7.4367[/C][C]7.43240024459576[/C][C]0.00429975540424277[/C][/ROW]
[ROW][C]4[/C][C]7.4368[/C][C]7.43669971575624[/C][C]0.000100284243764293[/C][/ROW]
[ROW][C]5[/C][C]7.4456[/C][C]7.43679999337051[/C][C]0.00880000662948621[/C][/ROW]
[ROW][C]6[/C][C]7.4564[/C][C]7.4455994182583[/C][C]0.010800581741699[/C][/ROW]
[ROW][C]7[/C][C]7.4597[/C][C]7.45639928600636[/C][C]0.00330071399363874[/C][/ROW]
[ROW][C]8[/C][C]7.4537[/C][C]7.45969978179983[/C][C]-0.00599978179982674[/C][/ROW]
[ROW][C]9[/C][C]7.4639[/C][C]7.45370039662734[/C][C]0.0101996033726559[/C][/ROW]
[ROW][C]10[/C][C]7.4593[/C][C]7.46389932573521[/C][C]-0.0045993257352146[/C][/ROW]
[ROW][C]11[/C][C]7.4438[/C][C]7.45930030404745[/C][C]-0.015500304047448[/C][/ROW]
[ROW][C]12[/C][C]7.4415[/C][C]7.443801024678[/C][C]-0.00230102467800108[/C][/ROW]
[ROW][C]13[/C][C]7.4317[/C][C]7.44150015211375[/C][C]-0.00980015211374852[/C][/ROW]
[ROW][C]14[/C][C]7.4343[/C][C]7.43170064785828[/C][C]0.00259935214172291[/C][/ROW]
[ROW][C]15[/C][C]7.4281[/C][C]7.43429982816473[/C][C]-0.0061998281647293[/C][/ROW]
[ROW][C]16[/C][C]7.4281[/C][C]7.4281004098518[/C][C]-4.09851801386196e-07[/C][/ROW]
[ROW][C]17[/C][C]7.4305[/C][C]7.42810000002709[/C][C]0.00239999997290674[/C][/ROW]
[ROW][C]18[/C][C]7.425[/C][C]7.43049984134329[/C][C]-0.00549984134329495[/C][/ROW]
[ROW][C]19[/C][C]7.4309[/C][C]7.4250003635778[/C][C]0.00589963642220148[/C][/ROW]
[ROW][C]20[/C][C]7.4361[/C][C]7.43089960999296[/C][C]0.00520039000703676[/C][/ROW]
[ROW][C]21[/C][C]7.4495[/C][C]7.43609965621802[/C][C]0.0134003437819814[/C][/ROW]
[ROW][C]22[/C][C]7.4393[/C][C]7.44949911414399[/C][C]-0.0101991141439903[/C][/ROW]
[ROW][C]23[/C][C]7.4367[/C][C]7.43930067423245[/C][C]-0.00260067423244514[/C][/ROW]
[ROW][C]24[/C][C]7.4343[/C][C]7.43670017192267[/C][C]-0.0024001719226705[/C][/ROW]
[ROW][C]25[/C][C]7.4433[/C][C]7.43430015866807[/C][C]0.00899984133192699[/C][/ROW]
[ROW][C]26[/C][C]7.4463[/C][C]7.44329940504784[/C][C]0.0030005949521632[/C][/ROW]
[ROW][C]27[/C][C]7.4588[/C][C]7.44629980163979[/C][C]0.0125001983602147[/C][/ROW]
[ROW][C]28[/C][C]7.4586[/C][C]7.45879917364987[/C][C]-0.000199173649870765[/C][/ROW]
[ROW][C]29[/C][C]7.4621[/C][C]7.45860001316676[/C][C]0.00349998683323616[/C][/ROW]
[ROW][C]30[/C][C]7.4581[/C][C]7.46209976862651[/C][C]-0.00399976862650675[/C][/ROW]
[ROW][C]31[/C][C]7.4604[/C][C]7.45810026441255[/C][C]0.00229973558745034[/C][/ROW]
[ROW][C]32[/C][C]7.4557[/C][C]7.46039984797147[/C][C]-0.00469984797146772[/C][/ROW]
[ROW][C]33[/C][C]7.4524[/C][C]7.45570031069267[/C][C]-0.00330031069266834[/C][/ROW]
[ROW][C]34[/C][C]7.45[/C][C]7.45240021817351[/C][C]-0.00240021817351099[/C][/ROW]
[ROW][C]35[/C][C]7.4446[/C][C]7.45000015867113[/C][C]-0.00540015867112942[/C][/ROW]
[ROW][C]36[/C][C]7.4557[/C][C]7.44460035698808[/C][C]0.011099643011919[/C][/ROW]
[ROW][C]37[/C][C]7.4534[/C][C]7.45569926623633[/C][C]-0.00229926623632881[/C][/ROW]
[ROW][C]38[/C][C]7.4599[/C][C]7.4534001519975[/C][C]0.00649984800249559[/C][/ROW]
[ROW][C]39[/C][C]7.4592[/C][C]7.4598995703148[/C][C]-0.000699570314798947[/C][/ROW]
[ROW][C]40[/C][C]7.4512[/C][C]7.45920004624647[/C][C]-0.00800004624646711[/C][/ROW]
[ROW][C]41[/C][C]7.4514[/C][C]7.45120052885875[/C][C]0.000199471141251628[/C][/ROW]
[ROW][C]42[/C][C]7.4471[/C][C]7.45139998681357[/C][C]-0.00429998681356913[/C][/ROW]
[ROW][C]43[/C][C]7.4442[/C][C]7.44710028425906[/C][C]-0.00290028425906197[/C][/ROW]
[ROW][C]44[/C][C]7.4424[/C][C]7.44420019172898[/C][C]-0.00180019172897961[/C][/ROW]
[ROW][C]45[/C][C]7.4426[/C][C]7.44240011900521[/C][C]0.000199880994793844[/C][/ROW]
[ROW][C]46[/C][C]7.4416[/C][C]7.44259998678647[/C][C]-0.000999986786474061[/C][/ROW]
[ROW][C]47[/C][C]7.4498[/C][C]7.44160006610609[/C][C]0.00819993389391183[/C][/ROW]
[ROW][C]48[/C][C]7.4547[/C][C]7.44979945792729[/C][C]0.00490054207271307[/C][/ROW]
[ROW][C]49[/C][C]7.455[/C][C]7.45469967604005[/C][C]0.000300323959945281[/C][/ROW]
[ROW][C]50[/C][C]7.4573[/C][C]7.4549999801465[/C][C]0.00230001985350459[/C][/ROW]
[ROW][C]51[/C][C]7.4506[/C][C]7.45729984795268[/C][C]-0.00669984795267631[/C][/ROW]
[ROW][C]52[/C][C]7.4398[/C][C]7.45060044290659[/C][C]-0.0108004429065893[/C][/ROW]
[ROW][C]53[/C][C]7.435[/C][C]7.43980071398446[/C][C]-0.00480071398446213[/C][/ROW]
[ROW][C]54[/C][C]7.4349[/C][C]7.43500031736061[/C][C]-0.000100317360614[/C][/ROW]
[ROW][C]55[/C][C]7.4457[/C][C]7.43490000663168[/C][C]0.0107999933683249[/C][/ROW]
[ROW][C]56[/C][C]7.459[/C][C]7.44569928604526[/C][C]0.0133007139547434[/C][/ROW]
[ROW][C]57[/C][C]7.4589[/C][C]7.45899912073022[/C][C]-9.9120730216562e-05[/C][/ROW]
[ROW][C]58[/C][C]7.4555[/C][C]7.45890000655257[/C][C]-0.00340000655257011[/C][/ROW]
[ROW][C]59[/C][C]7.458[/C][C]7.4555002247641[/C][C]0.00249977523589884[/C][/ROW]
[ROW][C]60[/C][C]7.4593[/C][C]7.45799983474746[/C][C]0.00130016525254462[/C][/ROW]
[ROW][C]61[/C][C]7.4625[/C][C]7.45929991405003[/C][C]0.00320008594997478[/C][/ROW]
[ROW][C]62[/C][C]7.4628[/C][C]7.46249978845204[/C][C]0.000300211547957119[/C][/ROW]
[ROW][C]63[/C][C]7.4522[/C][C]7.46279998015393[/C][C]-0.010599980153926[/C][/ROW]
[ROW][C]64[/C][C]7.4423[/C][C]7.45220070073248[/C][C]-0.00990070073247828[/C][/ROW]
[ROW][C]65[/C][C]7.4501[/C][C]7.44230065450524[/C][C]0.00779934549475847[/C][/ROW]
[ROW][C]66[/C][C]7.4623[/C][C]7.45009948440897[/C][C]0.0122005155910312[/C][/ROW]
[ROW][C]67[/C][C]7.4617[/C][C]7.46229919346099[/C][C]-0.000599193460987024[/C][/ROW]
[ROW][C]68[/C][C]7.4605[/C][C]7.46170003961086[/C][C]-0.00120003961085935[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294699&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294699&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
27.43247.4361-0.00369999999999937
37.43677.432400244595760.00429975540424277
47.43687.436699715756240.000100284243764293
57.44567.436799993370510.00880000662948621
67.45647.44559941825830.010800581741699
77.45977.456399286006360.00330071399363874
87.45377.45969978179983-0.00599978179982674
97.46397.453700396627340.0101996033726559
107.45937.46389932573521-0.0045993257352146
117.44387.45930030404745-0.015500304047448
127.44157.443801024678-0.00230102467800108
137.43177.44150015211375-0.00980015211374852
147.43437.431700647858280.00259935214172291
157.42817.43429982816473-0.0061998281647293
167.42817.4281004098518-4.09851801386196e-07
177.43057.428100000027090.00239999997290674
187.4257.43049984134329-0.00549984134329495
197.43097.42500036357780.00589963642220148
207.43617.430899609992960.00520039000703676
217.44957.436099656218020.0134003437819814
227.43937.44949911414399-0.0101991141439903
237.43677.43930067423245-0.00260067423244514
247.43437.43670017192267-0.0024001719226705
257.44337.434300158668070.00899984133192699
267.44637.443299405047840.0030005949521632
277.45887.446299801639790.0125001983602147
287.45867.45879917364987-0.000199173649870765
297.46217.458600013166760.00349998683323616
307.45817.46209976862651-0.00399976862650675
317.46047.458100264412550.00229973558745034
327.45577.46039984797147-0.00469984797146772
337.45247.45570031069267-0.00330031069266834
347.457.45240021817351-0.00240021817351099
357.44467.45000015867113-0.00540015867112942
367.45577.444600356988080.011099643011919
377.45347.45569926623633-0.00229926623632881
387.45997.45340015199750.00649984800249559
397.45927.4598995703148-0.000699570314798947
407.45127.45920004624647-0.00800004624646711
417.45147.451200528858750.000199471141251628
427.44717.45139998681357-0.00429998681356913
437.44427.44710028425906-0.00290028425906197
447.44247.44420019172898-0.00180019172897961
457.44267.442400119005210.000199880994793844
467.44167.44259998678647-0.000999986786474061
477.44987.441600066106090.00819993389391183
487.45477.449799457927290.00490054207271307
497.4557.454699676040050.000300323959945281
507.45737.45499998014650.00230001985350459
517.45067.45729984795268-0.00669984795267631
527.43987.45060044290659-0.0108004429065893
537.4357.43980071398446-0.00480071398446213
547.43497.43500031736061-0.000100317360614
557.44577.434900006631680.0107999933683249
567.4597.445699286045260.0133007139547434
577.45897.45899912073022-9.9120730216562e-05
587.45557.45890000655257-0.00340000655257011
597.4587.45550022476410.00249977523589884
607.45937.457999834747460.00130016525254462
617.46257.459299914050030.00320008594997478
627.46287.462499788452040.000300211547957119
637.45227.46279998015393-0.010599980153926
647.44237.45220070073248-0.00990070073247828
657.45017.442300654505240.00779934549475847
667.46237.450099484408970.0122005155910312
677.46177.46229919346099-0.000599193460987024
687.46057.46170003961086-0.00120003961085935







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
697.460500079330977.447709238964687.47329091969726
707.460500079330977.442411697304687.47858846135727
717.460500079330977.438346670307037.48265348835492
727.460500079330977.434919666933297.48608049172865
737.460500079330977.431900403362737.48909975529922
747.460500079330977.42917077304217.49182938561984
757.460500079330977.426660614211167.49433954445078
767.460500079330977.424324212145127.49667594651682
777.460500079330977.422129813060057.49887034560189
787.460500079330977.420054297094087.50094586156787
797.460500079330977.418080210545147.50291994811681
807.460500079330977.416193993576757.5048061650852

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
69 & 7.46050007933097 & 7.44770923896468 & 7.47329091969726 \tabularnewline
70 & 7.46050007933097 & 7.44241169730468 & 7.47858846135727 \tabularnewline
71 & 7.46050007933097 & 7.43834667030703 & 7.48265348835492 \tabularnewline
72 & 7.46050007933097 & 7.43491966693329 & 7.48608049172865 \tabularnewline
73 & 7.46050007933097 & 7.43190040336273 & 7.48909975529922 \tabularnewline
74 & 7.46050007933097 & 7.4291707730421 & 7.49182938561984 \tabularnewline
75 & 7.46050007933097 & 7.42666061421116 & 7.49433954445078 \tabularnewline
76 & 7.46050007933097 & 7.42432421214512 & 7.49667594651682 \tabularnewline
77 & 7.46050007933097 & 7.42212981306005 & 7.49887034560189 \tabularnewline
78 & 7.46050007933097 & 7.42005429709408 & 7.50094586156787 \tabularnewline
79 & 7.46050007933097 & 7.41808021054514 & 7.50291994811681 \tabularnewline
80 & 7.46050007933097 & 7.41619399357675 & 7.5048061650852 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294699&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]69[/C][C]7.46050007933097[/C][C]7.44770923896468[/C][C]7.47329091969726[/C][/ROW]
[ROW][C]70[/C][C]7.46050007933097[/C][C]7.44241169730468[/C][C]7.47858846135727[/C][/ROW]
[ROW][C]71[/C][C]7.46050007933097[/C][C]7.43834667030703[/C][C]7.48265348835492[/C][/ROW]
[ROW][C]72[/C][C]7.46050007933097[/C][C]7.43491966693329[/C][C]7.48608049172865[/C][/ROW]
[ROW][C]73[/C][C]7.46050007933097[/C][C]7.43190040336273[/C][C]7.48909975529922[/C][/ROW]
[ROW][C]74[/C][C]7.46050007933097[/C][C]7.4291707730421[/C][C]7.49182938561984[/C][/ROW]
[ROW][C]75[/C][C]7.46050007933097[/C][C]7.42666061421116[/C][C]7.49433954445078[/C][/ROW]
[ROW][C]76[/C][C]7.46050007933097[/C][C]7.42432421214512[/C][C]7.49667594651682[/C][/ROW]
[ROW][C]77[/C][C]7.46050007933097[/C][C]7.42212981306005[/C][C]7.49887034560189[/C][/ROW]
[ROW][C]78[/C][C]7.46050007933097[/C][C]7.42005429709408[/C][C]7.50094586156787[/C][/ROW]
[ROW][C]79[/C][C]7.46050007933097[/C][C]7.41808021054514[/C][C]7.50291994811681[/C][/ROW]
[ROW][C]80[/C][C]7.46050007933097[/C][C]7.41619399357675[/C][C]7.5048061650852[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294699&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294699&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
697.460500079330977.447709238964687.47329091969726
707.460500079330977.442411697304687.47858846135727
717.460500079330977.438346670307037.48265348835492
727.460500079330977.434919666933297.48608049172865
737.460500079330977.431900403362737.48909975529922
747.460500079330977.42917077304217.49182938561984
757.460500079330977.426660614211167.49433954445078
767.460500079330977.424324212145127.49667594651682
777.460500079330977.422129813060057.49887034560189
787.460500079330977.420054297094087.50094586156787
797.460500079330977.418080210545147.50291994811681
807.460500079330977.416193993576757.5048061650852



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')