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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 06:59:44 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/28/t1338202949ilddwi9znfveujm.htm/, Retrieved Thu, 02 May 2024 01:59:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167782, Retrieved Thu, 02 May 2024 01:59:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Voorspelling bouw...] [2012-05-28 10:59:44] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1.974
2.037
2.259
2.550
2.549
2.738
2.228
2.533
2.475
2.260
2.158
2.253
2.670
2.449
2.620
2.205
2.589
2.706
2.352
2.478
2.316
2.295
2.110
1.944
2.202
2.036
2.434
2.297
2.354
2.650
2.555
2.477
2.268
2.510
2.015
1.994
2.271
2.289
2.333
2.795
2.332
2.799
2.294
2.415
2.473
2.236
1.970
2.318
2.108
2.064
2.519
2.298
2.187
2.746
2.364
2.512
2.224
2.209
2.186
2.303
2.381
2.432
2.913
2.392
2.532
2.709
2.387
2.609
2.399
2.184
1.839
2.056
2.151
2.155
2.463
2.155
2.679
2.367
2.052
2.547
2.466




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167782&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167782&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167782&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.111979586853965
beta0
gamma0.324308302608781

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.111979586853965 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.324308302608781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167782&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]0.111979586853965[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.324308302608781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167782&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167782&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
alpha0.111979586853965
beta0
gamma0.324308302608781







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132.672.644004273504270.0259957264957262
142.4492.424488982165950.0245110178340484
152.622.608599100431760.0114008995682364
162.2052.201491153070560.00350884692943687
172.5892.587874456915440.00112554308456048
182.7062.72132421271375-0.0153242127137529
192.3522.286931931653920.0650680683460774
202.4782.55450027834675-0.076500278346753
212.3162.45717419339866-0.141174193398656
222.2952.227147616829480.0678523831705169
232.112.14690274994603-0.0369027499460262
241.9442.23888577986868-0.29488577986868
252.2022.62796654816314-0.425966548163141
262.0362.35741312323475-0.32141312323475
272.4342.49901118477069-0.065011184770694
282.2972.081073792650470.215926207349529
292.3542.49055713137858-0.136557131378579
302.652.603851833639090.0461481663609118
312.5552.199495569581610.355504430418386
322.4772.458816253188050.0181837468119537
332.2682.35346725070687-0.0854672507068654
342.512.189876778524660.320123221475341
352.0152.1077124144383-0.0927124144382998
361.9942.11914875108154-0.125148751081543
372.2712.48948633761313-0.218486337613135
382.2892.272277051970320.0167229480296811
392.3332.52558125886148-0.192581258861478
402.7952.174266454352810.620733545647186
412.3322.52756743141206-0.195567431412065
422.7992.68687192054060.112128079459403
432.2942.37899631062758-0.0849963106275835
442.4152.49184411240668-0.0768441124066848
452.4732.346003230711840.126996769288155
462.2362.32301136231877-0.0870113623187723
471.972.07636271309668-0.106362713096683
482.3182.076929076729920.241070923270076
492.1082.46139527620332-0.353395276203321
502.0642.29681742835163-0.232817428351632
512.5192.461900187612020.0570998123879756
522.2982.37277304301364-0.0747730430136393
532.1872.41310300793557-0.226103007935567
542.7462.657602102271680.0883978977283224
552.3642.290298871618390.0737011283816122
562.5122.42326531812530.0887346818746972
572.2242.35467050468976-0.130670504689762
582.2092.24119244749588-0.0321924474958797
592.1861.995109355891660.190890644108344
602.3032.129020271956230.173979728043771
612.3812.334771883840360.0462281161596394
622.4322.24966920129250.182330798707501
632.9132.544734047396810.368265952603195
642.3922.45247277944104-0.0604727794410396
652.5322.450822203259030.0811777967409695
662.7092.82030434353269-0.111304343532691
672.3872.42640598063757-0.0394059806375746
682.6092.551036288850080.0579637111499225
692.3992.41580873013904-0.0168087301390392
702.1842.3434417987542-0.159441798754195
711.8392.14735561072842-0.308355610728421
722.0562.22049092225493-0.164490922254935
732.1512.351549238157-0.200549238156998
742.1552.27800906665074-0.12300906665074
752.4632.59242999067113-0.129429990671134
762.1552.32096344325143-0.165963443251429
772.6792.348294354504960.33070564549504
782.3672.69028512802864-0.323285128028637
792.0522.29335542603824-0.241355426038238
802.5472.423413249320220.123586750679782
812.4662.274000237176340.191999762823656

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.67 & 2.64400427350427 & 0.0259957264957262 \tabularnewline
14 & 2.449 & 2.42448898216595 & 0.0245110178340484 \tabularnewline
15 & 2.62 & 2.60859910043176 & 0.0114008995682364 \tabularnewline
16 & 2.205 & 2.20149115307056 & 0.00350884692943687 \tabularnewline
17 & 2.589 & 2.58787445691544 & 0.00112554308456048 \tabularnewline
18 & 2.706 & 2.72132421271375 & -0.0153242127137529 \tabularnewline
19 & 2.352 & 2.28693193165392 & 0.0650680683460774 \tabularnewline
20 & 2.478 & 2.55450027834675 & -0.076500278346753 \tabularnewline
21 & 2.316 & 2.45717419339866 & -0.141174193398656 \tabularnewline
22 & 2.295 & 2.22714761682948 & 0.0678523831705169 \tabularnewline
23 & 2.11 & 2.14690274994603 & -0.0369027499460262 \tabularnewline
24 & 1.944 & 2.23888577986868 & -0.29488577986868 \tabularnewline
25 & 2.202 & 2.62796654816314 & -0.425966548163141 \tabularnewline
26 & 2.036 & 2.35741312323475 & -0.32141312323475 \tabularnewline
27 & 2.434 & 2.49901118477069 & -0.065011184770694 \tabularnewline
28 & 2.297 & 2.08107379265047 & 0.215926207349529 \tabularnewline
29 & 2.354 & 2.49055713137858 & -0.136557131378579 \tabularnewline
30 & 2.65 & 2.60385183363909 & 0.0461481663609118 \tabularnewline
31 & 2.555 & 2.19949556958161 & 0.355504430418386 \tabularnewline
32 & 2.477 & 2.45881625318805 & 0.0181837468119537 \tabularnewline
33 & 2.268 & 2.35346725070687 & -0.0854672507068654 \tabularnewline
34 & 2.51 & 2.18987677852466 & 0.320123221475341 \tabularnewline
35 & 2.015 & 2.1077124144383 & -0.0927124144382998 \tabularnewline
36 & 1.994 & 2.11914875108154 & -0.125148751081543 \tabularnewline
37 & 2.271 & 2.48948633761313 & -0.218486337613135 \tabularnewline
38 & 2.289 & 2.27227705197032 & 0.0167229480296811 \tabularnewline
39 & 2.333 & 2.52558125886148 & -0.192581258861478 \tabularnewline
40 & 2.795 & 2.17426645435281 & 0.620733545647186 \tabularnewline
41 & 2.332 & 2.52756743141206 & -0.195567431412065 \tabularnewline
42 & 2.799 & 2.6868719205406 & 0.112128079459403 \tabularnewline
43 & 2.294 & 2.37899631062758 & -0.0849963106275835 \tabularnewline
44 & 2.415 & 2.49184411240668 & -0.0768441124066848 \tabularnewline
45 & 2.473 & 2.34600323071184 & 0.126996769288155 \tabularnewline
46 & 2.236 & 2.32301136231877 & -0.0870113623187723 \tabularnewline
47 & 1.97 & 2.07636271309668 & -0.106362713096683 \tabularnewline
48 & 2.318 & 2.07692907672992 & 0.241070923270076 \tabularnewline
49 & 2.108 & 2.46139527620332 & -0.353395276203321 \tabularnewline
50 & 2.064 & 2.29681742835163 & -0.232817428351632 \tabularnewline
51 & 2.519 & 2.46190018761202 & 0.0570998123879756 \tabularnewline
52 & 2.298 & 2.37277304301364 & -0.0747730430136393 \tabularnewline
53 & 2.187 & 2.41310300793557 & -0.226103007935567 \tabularnewline
54 & 2.746 & 2.65760210227168 & 0.0883978977283224 \tabularnewline
55 & 2.364 & 2.29029887161839 & 0.0737011283816122 \tabularnewline
56 & 2.512 & 2.4232653181253 & 0.0887346818746972 \tabularnewline
57 & 2.224 & 2.35467050468976 & -0.130670504689762 \tabularnewline
58 & 2.209 & 2.24119244749588 & -0.0321924474958797 \tabularnewline
59 & 2.186 & 1.99510935589166 & 0.190890644108344 \tabularnewline
60 & 2.303 & 2.12902027195623 & 0.173979728043771 \tabularnewline
61 & 2.381 & 2.33477188384036 & 0.0462281161596394 \tabularnewline
62 & 2.432 & 2.2496692012925 & 0.182330798707501 \tabularnewline
63 & 2.913 & 2.54473404739681 & 0.368265952603195 \tabularnewline
64 & 2.392 & 2.45247277944104 & -0.0604727794410396 \tabularnewline
65 & 2.532 & 2.45082220325903 & 0.0811777967409695 \tabularnewline
66 & 2.709 & 2.82030434353269 & -0.111304343532691 \tabularnewline
67 & 2.387 & 2.42640598063757 & -0.0394059806375746 \tabularnewline
68 & 2.609 & 2.55103628885008 & 0.0579637111499225 \tabularnewline
69 & 2.399 & 2.41580873013904 & -0.0168087301390392 \tabularnewline
70 & 2.184 & 2.3434417987542 & -0.159441798754195 \tabularnewline
71 & 1.839 & 2.14735561072842 & -0.308355610728421 \tabularnewline
72 & 2.056 & 2.22049092225493 & -0.164490922254935 \tabularnewline
73 & 2.151 & 2.351549238157 & -0.200549238156998 \tabularnewline
74 & 2.155 & 2.27800906665074 & -0.12300906665074 \tabularnewline
75 & 2.463 & 2.59242999067113 & -0.129429990671134 \tabularnewline
76 & 2.155 & 2.32096344325143 & -0.165963443251429 \tabularnewline
77 & 2.679 & 2.34829435450496 & 0.33070564549504 \tabularnewline
78 & 2.367 & 2.69028512802864 & -0.323285128028637 \tabularnewline
79 & 2.052 & 2.29335542603824 & -0.241355426038238 \tabularnewline
80 & 2.547 & 2.42341324932022 & 0.123586750679782 \tabularnewline
81 & 2.466 & 2.27400023717634 & 0.191999762823656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167782&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]2.67[/C][C]2.64400427350427[/C][C]0.0259957264957262[/C][/ROW]
[ROW][C]14[/C][C]2.449[/C][C]2.42448898216595[/C][C]0.0245110178340484[/C][/ROW]
[ROW][C]15[/C][C]2.62[/C][C]2.60859910043176[/C][C]0.0114008995682364[/C][/ROW]
[ROW][C]16[/C][C]2.205[/C][C]2.20149115307056[/C][C]0.00350884692943687[/C][/ROW]
[ROW][C]17[/C][C]2.589[/C][C]2.58787445691544[/C][C]0.00112554308456048[/C][/ROW]
[ROW][C]18[/C][C]2.706[/C][C]2.72132421271375[/C][C]-0.0153242127137529[/C][/ROW]
[ROW][C]19[/C][C]2.352[/C][C]2.28693193165392[/C][C]0.0650680683460774[/C][/ROW]
[ROW][C]20[/C][C]2.478[/C][C]2.55450027834675[/C][C]-0.076500278346753[/C][/ROW]
[ROW][C]21[/C][C]2.316[/C][C]2.45717419339866[/C][C]-0.141174193398656[/C][/ROW]
[ROW][C]22[/C][C]2.295[/C][C]2.22714761682948[/C][C]0.0678523831705169[/C][/ROW]
[ROW][C]23[/C][C]2.11[/C][C]2.14690274994603[/C][C]-0.0369027499460262[/C][/ROW]
[ROW][C]24[/C][C]1.944[/C][C]2.23888577986868[/C][C]-0.29488577986868[/C][/ROW]
[ROW][C]25[/C][C]2.202[/C][C]2.62796654816314[/C][C]-0.425966548163141[/C][/ROW]
[ROW][C]26[/C][C]2.036[/C][C]2.35741312323475[/C][C]-0.32141312323475[/C][/ROW]
[ROW][C]27[/C][C]2.434[/C][C]2.49901118477069[/C][C]-0.065011184770694[/C][/ROW]
[ROW][C]28[/C][C]2.297[/C][C]2.08107379265047[/C][C]0.215926207349529[/C][/ROW]
[ROW][C]29[/C][C]2.354[/C][C]2.49055713137858[/C][C]-0.136557131378579[/C][/ROW]
[ROW][C]30[/C][C]2.65[/C][C]2.60385183363909[/C][C]0.0461481663609118[/C][/ROW]
[ROW][C]31[/C][C]2.555[/C][C]2.19949556958161[/C][C]0.355504430418386[/C][/ROW]
[ROW][C]32[/C][C]2.477[/C][C]2.45881625318805[/C][C]0.0181837468119537[/C][/ROW]
[ROW][C]33[/C][C]2.268[/C][C]2.35346725070687[/C][C]-0.0854672507068654[/C][/ROW]
[ROW][C]34[/C][C]2.51[/C][C]2.18987677852466[/C][C]0.320123221475341[/C][/ROW]
[ROW][C]35[/C][C]2.015[/C][C]2.1077124144383[/C][C]-0.0927124144382998[/C][/ROW]
[ROW][C]36[/C][C]1.994[/C][C]2.11914875108154[/C][C]-0.125148751081543[/C][/ROW]
[ROW][C]37[/C][C]2.271[/C][C]2.48948633761313[/C][C]-0.218486337613135[/C][/ROW]
[ROW][C]38[/C][C]2.289[/C][C]2.27227705197032[/C][C]0.0167229480296811[/C][/ROW]
[ROW][C]39[/C][C]2.333[/C][C]2.52558125886148[/C][C]-0.192581258861478[/C][/ROW]
[ROW][C]40[/C][C]2.795[/C][C]2.17426645435281[/C][C]0.620733545647186[/C][/ROW]
[ROW][C]41[/C][C]2.332[/C][C]2.52756743141206[/C][C]-0.195567431412065[/C][/ROW]
[ROW][C]42[/C][C]2.799[/C][C]2.6868719205406[/C][C]0.112128079459403[/C][/ROW]
[ROW][C]43[/C][C]2.294[/C][C]2.37899631062758[/C][C]-0.0849963106275835[/C][/ROW]
[ROW][C]44[/C][C]2.415[/C][C]2.49184411240668[/C][C]-0.0768441124066848[/C][/ROW]
[ROW][C]45[/C][C]2.473[/C][C]2.34600323071184[/C][C]0.126996769288155[/C][/ROW]
[ROW][C]46[/C][C]2.236[/C][C]2.32301136231877[/C][C]-0.0870113623187723[/C][/ROW]
[ROW][C]47[/C][C]1.97[/C][C]2.07636271309668[/C][C]-0.106362713096683[/C][/ROW]
[ROW][C]48[/C][C]2.318[/C][C]2.07692907672992[/C][C]0.241070923270076[/C][/ROW]
[ROW][C]49[/C][C]2.108[/C][C]2.46139527620332[/C][C]-0.353395276203321[/C][/ROW]
[ROW][C]50[/C][C]2.064[/C][C]2.29681742835163[/C][C]-0.232817428351632[/C][/ROW]
[ROW][C]51[/C][C]2.519[/C][C]2.46190018761202[/C][C]0.0570998123879756[/C][/ROW]
[ROW][C]52[/C][C]2.298[/C][C]2.37277304301364[/C][C]-0.0747730430136393[/C][/ROW]
[ROW][C]53[/C][C]2.187[/C][C]2.41310300793557[/C][C]-0.226103007935567[/C][/ROW]
[ROW][C]54[/C][C]2.746[/C][C]2.65760210227168[/C][C]0.0883978977283224[/C][/ROW]
[ROW][C]55[/C][C]2.364[/C][C]2.29029887161839[/C][C]0.0737011283816122[/C][/ROW]
[ROW][C]56[/C][C]2.512[/C][C]2.4232653181253[/C][C]0.0887346818746972[/C][/ROW]
[ROW][C]57[/C][C]2.224[/C][C]2.35467050468976[/C][C]-0.130670504689762[/C][/ROW]
[ROW][C]58[/C][C]2.209[/C][C]2.24119244749588[/C][C]-0.0321924474958797[/C][/ROW]
[ROW][C]59[/C][C]2.186[/C][C]1.99510935589166[/C][C]0.190890644108344[/C][/ROW]
[ROW][C]60[/C][C]2.303[/C][C]2.12902027195623[/C][C]0.173979728043771[/C][/ROW]
[ROW][C]61[/C][C]2.381[/C][C]2.33477188384036[/C][C]0.0462281161596394[/C][/ROW]
[ROW][C]62[/C][C]2.432[/C][C]2.2496692012925[/C][C]0.182330798707501[/C][/ROW]
[ROW][C]63[/C][C]2.913[/C][C]2.54473404739681[/C][C]0.368265952603195[/C][/ROW]
[ROW][C]64[/C][C]2.392[/C][C]2.45247277944104[/C][C]-0.0604727794410396[/C][/ROW]
[ROW][C]65[/C][C]2.532[/C][C]2.45082220325903[/C][C]0.0811777967409695[/C][/ROW]
[ROW][C]66[/C][C]2.709[/C][C]2.82030434353269[/C][C]-0.111304343532691[/C][/ROW]
[ROW][C]67[/C][C]2.387[/C][C]2.42640598063757[/C][C]-0.0394059806375746[/C][/ROW]
[ROW][C]68[/C][C]2.609[/C][C]2.55103628885008[/C][C]0.0579637111499225[/C][/ROW]
[ROW][C]69[/C][C]2.399[/C][C]2.41580873013904[/C][C]-0.0168087301390392[/C][/ROW]
[ROW][C]70[/C][C]2.184[/C][C]2.3434417987542[/C][C]-0.159441798754195[/C][/ROW]
[ROW][C]71[/C][C]1.839[/C][C]2.14735561072842[/C][C]-0.308355610728421[/C][/ROW]
[ROW][C]72[/C][C]2.056[/C][C]2.22049092225493[/C][C]-0.164490922254935[/C][/ROW]
[ROW][C]73[/C][C]2.151[/C][C]2.351549238157[/C][C]-0.200549238156998[/C][/ROW]
[ROW][C]74[/C][C]2.155[/C][C]2.27800906665074[/C][C]-0.12300906665074[/C][/ROW]
[ROW][C]75[/C][C]2.463[/C][C]2.59242999067113[/C][C]-0.129429990671134[/C][/ROW]
[ROW][C]76[/C][C]2.155[/C][C]2.32096344325143[/C][C]-0.165963443251429[/C][/ROW]
[ROW][C]77[/C][C]2.679[/C][C]2.34829435450496[/C][C]0.33070564549504[/C][/ROW]
[ROW][C]78[/C][C]2.367[/C][C]2.69028512802864[/C][C]-0.323285128028637[/C][/ROW]
[ROW][C]79[/C][C]2.052[/C][C]2.29335542603824[/C][C]-0.241355426038238[/C][/ROW]
[ROW][C]80[/C][C]2.547[/C][C]2.42341324932022[/C][C]0.123586750679782[/C][/ROW]
[ROW][C]81[/C][C]2.466[/C][C]2.27400023717634[/C][C]0.191999762823656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167782&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167782&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
132.672.644004273504270.0259957264957262
142.4492.424488982165950.0245110178340484
152.622.608599100431760.0114008995682364
162.2052.201491153070560.00350884692943687
172.5892.587874456915440.00112554308456048
182.7062.72132421271375-0.0153242127137529
192.3522.286931931653920.0650680683460774
202.4782.55450027834675-0.076500278346753
212.3162.45717419339866-0.141174193398656
222.2952.227147616829480.0678523831705169
232.112.14690274994603-0.0369027499460262
241.9442.23888577986868-0.29488577986868
252.2022.62796654816314-0.425966548163141
262.0362.35741312323475-0.32141312323475
272.4342.49901118477069-0.065011184770694
282.2972.081073792650470.215926207349529
292.3542.49055713137858-0.136557131378579
302.652.603851833639090.0461481663609118
312.5552.199495569581610.355504430418386
322.4772.458816253188050.0181837468119537
332.2682.35346725070687-0.0854672507068654
342.512.189876778524660.320123221475341
352.0152.1077124144383-0.0927124144382998
361.9942.11914875108154-0.125148751081543
372.2712.48948633761313-0.218486337613135
382.2892.272277051970320.0167229480296811
392.3332.52558125886148-0.192581258861478
402.7952.174266454352810.620733545647186
412.3322.52756743141206-0.195567431412065
422.7992.68687192054060.112128079459403
432.2942.37899631062758-0.0849963106275835
442.4152.49184411240668-0.0768441124066848
452.4732.346003230711840.126996769288155
462.2362.32301136231877-0.0870113623187723
471.972.07636271309668-0.106362713096683
482.3182.076929076729920.241070923270076
492.1082.46139527620332-0.353395276203321
502.0642.29681742835163-0.232817428351632
512.5192.461900187612020.0570998123879756
522.2982.37277304301364-0.0747730430136393
532.1872.41310300793557-0.226103007935567
542.7462.657602102271680.0883978977283224
552.3642.290298871618390.0737011283816122
562.5122.42326531812530.0887346818746972
572.2242.35467050468976-0.130670504689762
582.2092.24119244749588-0.0321924474958797
592.1861.995109355891660.190890644108344
602.3032.129020271956230.173979728043771
612.3812.334771883840360.0462281161596394
622.4322.24966920129250.182330798707501
632.9132.544734047396810.368265952603195
642.3922.45247277944104-0.0604727794410396
652.5322.450822203259030.0811777967409695
662.7092.82030434353269-0.111304343532691
672.3872.42640598063757-0.0394059806375746
682.6092.551036288850080.0579637111499225
692.3992.41580873013904-0.0168087301390392
702.1842.3434417987542-0.159441798754195
711.8392.14735561072842-0.308355610728421
722.0562.22049092225493-0.164490922254935
732.1512.351549238157-0.200549238156998
742.1552.27800906665074-0.12300906665074
752.4632.59242999067113-0.129429990671134
762.1552.32096344325143-0.165963443251429
772.6792.348294354504960.33070564549504
782.3672.69028512802864-0.323285128028637
792.0522.29335542603824-0.241355426038238
802.5472.423413249320220.123586750679782
812.4662.274000237176340.191999762823656







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
822.183938355832291.811912651497542.55596406016704
831.962820349516511.588469416987922.33717128204509
842.111917130819371.735255324042692.48857893759605
852.25101055155731.872051961888812.62996914122578
862.222258780419321.841017244535862.60350031630279
872.548605031629492.165094139108782.93211592415021
882.281110644663281.895343745252132.66687754407443
892.47006299305732.0820532036442.85807278247059
902.586677117246612.196437328552792.97691690594043
912.249543881252181.857086764258412.64200099824594
922.511729156158852.117067168277692.90639114404001
932.368179377803941.971324768812732.76503398679515

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
82 & 2.18393835583229 & 1.81191265149754 & 2.55596406016704 \tabularnewline
83 & 1.96282034951651 & 1.58846941698792 & 2.33717128204509 \tabularnewline
84 & 2.11191713081937 & 1.73525532404269 & 2.48857893759605 \tabularnewline
85 & 2.2510105515573 & 1.87205196188881 & 2.62996914122578 \tabularnewline
86 & 2.22225878041932 & 1.84101724453586 & 2.60350031630279 \tabularnewline
87 & 2.54860503162949 & 2.16509413910878 & 2.93211592415021 \tabularnewline
88 & 2.28111064466328 & 1.89534374525213 & 2.66687754407443 \tabularnewline
89 & 2.4700629930573 & 2.082053203644 & 2.85807278247059 \tabularnewline
90 & 2.58667711724661 & 2.19643732855279 & 2.97691690594043 \tabularnewline
91 & 2.24954388125218 & 1.85708676425841 & 2.64200099824594 \tabularnewline
92 & 2.51172915615885 & 2.11706716827769 & 2.90639114404001 \tabularnewline
93 & 2.36817937780394 & 1.97132476881273 & 2.76503398679515 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167782&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]82[/C][C]2.18393835583229[/C][C]1.81191265149754[/C][C]2.55596406016704[/C][/ROW]
[ROW][C]83[/C][C]1.96282034951651[/C][C]1.58846941698792[/C][C]2.33717128204509[/C][/ROW]
[ROW][C]84[/C][C]2.11191713081937[/C][C]1.73525532404269[/C][C]2.48857893759605[/C][/ROW]
[ROW][C]85[/C][C]2.2510105515573[/C][C]1.87205196188881[/C][C]2.62996914122578[/C][/ROW]
[ROW][C]86[/C][C]2.22225878041932[/C][C]1.84101724453586[/C][C]2.60350031630279[/C][/ROW]
[ROW][C]87[/C][C]2.54860503162949[/C][C]2.16509413910878[/C][C]2.93211592415021[/C][/ROW]
[ROW][C]88[/C][C]2.28111064466328[/C][C]1.89534374525213[/C][C]2.66687754407443[/C][/ROW]
[ROW][C]89[/C][C]2.4700629930573[/C][C]2.082053203644[/C][C]2.85807278247059[/C][/ROW]
[ROW][C]90[/C][C]2.58667711724661[/C][C]2.19643732855279[/C][C]2.97691690594043[/C][/ROW]
[ROW][C]91[/C][C]2.24954388125218[/C][C]1.85708676425841[/C][C]2.64200099824594[/C][/ROW]
[ROW][C]92[/C][C]2.51172915615885[/C][C]2.11706716827769[/C][C]2.90639114404001[/C][/ROW]
[ROW][C]93[/C][C]2.36817937780394[/C][C]1.97132476881273[/C][C]2.76503398679515[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167782&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167782&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
822.183938355832291.811912651497542.55596406016704
831.962820349516511.588469416987922.33717128204509
842.111917130819371.735255324042692.48857893759605
852.25101055155731.872051961888812.62996914122578
862.222258780419321.841017244535862.60350031630279
872.548605031629492.165094139108782.93211592415021
882.281110644663281.895343745252132.66687754407443
892.47006299305732.0820532036442.85807278247059
902.586677117246612.196437328552792.97691690594043
912.249543881252181.857086764258412.64200099824594
922.511729156158852.117067168277692.90639114404001
932.368179377803941.971324768812732.76503398679515



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')