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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 computationFri, 28 Nov 2014 17:17:54 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/28/t1417195094gvd0m794kizfuq7.htm/, Retrieved Sun, 19 May 2024 15:24:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260992, Retrieved Sun, 19 May 2024 15:24:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 17:17:54] [b14d23c6a1d7f8e7693f95bb395763d5] [Current]
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Dataseries X:
6900
7045
8044
8196
8257
8623
8644
8648
8961
8961
9116
9313
9360
9429
9485
9580
9606
9679
9726
9898
10028
10082
10091
10228
10337
10372
10425
10573
10680
10685
10771
10783
10849
10865
10954
10962
11026
11080
11210
11222
11236
11329
11334
11394
11648
11677
11816
11839
11874
11911
11918
12164
12177
12347
12624
12627
12782
12794
13142
13149
13240
13270
13445
13579
13601
13878
13957
14360
14687
14771
14779
14825
15119
16244
18983
19940
20067
20993
21545
21709
22165
22205
23533
23882
59646




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=260992&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=260992&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260992&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
alpha0.999937166054276
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999937166054276 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260992&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]0.999937166054276[/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=260992&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260992&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
alpha0.999937166054276
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
270456900145
380447044.99088907787999.00911092213
481968043.93722831575152.062771684253
582578195.9904452960661.0095547039418
686238256.99616652895366.00383347105
786448622.9770025349921.0229974650065
886488643.998679042124.00132095788285
989618647.99974858122313.000251418784
1089618960.980332959190.0196670408076898
1191168960.99999876424155.000001235758
1293139115.99026073834197.009739261664
1393609312.9876211007447.0123788992623
1494299359.9970460267469.0029539732641
1594859428.9956642721456.0043357278646
1695809484.9964810266195.0035189733899
1796069579.9940305540426.005969445956
1896799605.9983659423373.0016340576731
1997269678.9954130192947.0045869807127
2098989725.99704651633172.002953483669
21100289897.98919237576130.010807624245
221008210027.99183090854.0081690920306
231009110081.99660645369.00339354636526
241022810090.9994342813137.000565718741
251033710227.9913917139109.008608286111
261037210336.99315055935.006849440977
271042510371.997800381553.0021996184769
281057310424.9966696627148.003330337335
291068010572.9907003668107.009299633224
301068510679.99327618355.00672381652475
311077110684.999685407886.0003145922128
321078310770.994596260912.0054037391001
331084910782.999245653166.0007543468855
341086510848.995852912216.004147087815
351095410864.998994396389.0010056037099
361096210953.99440771568.00559228435486
371102610961.99949697764.0005030229513
381108011025.995978595954.0040214041328
391121011079.9966067143130.00339328575
401122211209.991831373812.0081686261583
411123611221.999245479414.0007545206154
421132911235.999120277493.0008797226492
431133411328.99415638785.005843612229
441139411333.999685463160.0003145369064
451164811393.9962299435254.003770056508
461167711647.984039940929.0159600591014
471181611676.9981768127139.00182318726
481183911815.99126596723.0087340330138
491187411838.998554270535.0014457295456
501191111873.997800721137.0021992789407
511191811910.99767500587.00232499418053
521216411917.9995600163246.000439983709
531217712163.984542821713.015457178295
541234712176.9991821875170.00081781253
551262412346.9893181778277.010681822161
561262712623.98259432593.01740567414708
571278212626.9998104045155.000189595505
581279412781.990260726512.0097392735006
591314212793.9992453807348.000754619306
601314913141.97813373957.02186626052753
611324013148.999558788491.000441211565
621327013239.994282083230.0057179167834
631344513269.9981146223175.001885377651
641357913444.989003941134.010996058967
651360113578.991579560322.0084204396517
661387813600.9986171241277.001382875897
671395713877.982594910179.0174050898568
681436013956.9950350247403.004964975342
691468714359.9746776079327.025322392095
701477114686.979451708684.0205482913589
711477914770.99472065748.00527934257116
721482514778.999496996746.000503003288
731511914824.9971096069294.002890393109
741624415118.98152663831125.01847336166
751898316243.92931065032739.07068934969
761994018982.827893381957.172106619029
772006719939.9398570998127.060142900198
782099320066.9920163099926.00798369012
792154520992.9418152646552.058184735386
802170921544.965312006164.034687994015
812216521708.9896930533456.010306946682
822220522164.971347073140.0286529268742
832353322204.99748484181328.0025151582
842388223532.916556362349.083443637959
855964623881.978065709835764.0219342902

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 7045 & 6900 & 145 \tabularnewline
3 & 8044 & 7044.99088907787 & 999.00911092213 \tabularnewline
4 & 8196 & 8043.93722831575 & 152.062771684253 \tabularnewline
5 & 8257 & 8195.99044529606 & 61.0095547039418 \tabularnewline
6 & 8623 & 8256.99616652895 & 366.00383347105 \tabularnewline
7 & 8644 & 8622.97700253499 & 21.0229974650065 \tabularnewline
8 & 8648 & 8643.99867904212 & 4.00132095788285 \tabularnewline
9 & 8961 & 8647.99974858122 & 313.000251418784 \tabularnewline
10 & 8961 & 8960.98033295919 & 0.0196670408076898 \tabularnewline
11 & 9116 & 8960.99999876424 & 155.000001235758 \tabularnewline
12 & 9313 & 9115.99026073834 & 197.009739261664 \tabularnewline
13 & 9360 & 9312.98762110074 & 47.0123788992623 \tabularnewline
14 & 9429 & 9359.99704602674 & 69.0029539732641 \tabularnewline
15 & 9485 & 9428.99566427214 & 56.0043357278646 \tabularnewline
16 & 9580 & 9484.99648102661 & 95.0035189733899 \tabularnewline
17 & 9606 & 9579.99403055404 & 26.005969445956 \tabularnewline
18 & 9679 & 9605.99836594233 & 73.0016340576731 \tabularnewline
19 & 9726 & 9678.99541301929 & 47.0045869807127 \tabularnewline
20 & 9898 & 9725.99704651633 & 172.002953483669 \tabularnewline
21 & 10028 & 9897.98919237576 & 130.010807624245 \tabularnewline
22 & 10082 & 10027.991830908 & 54.0081690920306 \tabularnewline
23 & 10091 & 10081.9966064536 & 9.00339354636526 \tabularnewline
24 & 10228 & 10090.9994342813 & 137.000565718741 \tabularnewline
25 & 10337 & 10227.9913917139 & 109.008608286111 \tabularnewline
26 & 10372 & 10336.993150559 & 35.006849440977 \tabularnewline
27 & 10425 & 10371.9978003815 & 53.0021996184769 \tabularnewline
28 & 10573 & 10424.9966696627 & 148.003330337335 \tabularnewline
29 & 10680 & 10572.9907003668 & 107.009299633224 \tabularnewline
30 & 10685 & 10679.9932761835 & 5.00672381652475 \tabularnewline
31 & 10771 & 10684.9996854078 & 86.0003145922128 \tabularnewline
32 & 10783 & 10770.9945962609 & 12.0054037391001 \tabularnewline
33 & 10849 & 10782.9992456531 & 66.0007543468855 \tabularnewline
34 & 10865 & 10848.9958529122 & 16.004147087815 \tabularnewline
35 & 10954 & 10864.9989943963 & 89.0010056037099 \tabularnewline
36 & 10962 & 10953.9944077156 & 8.00559228435486 \tabularnewline
37 & 11026 & 10961.999496977 & 64.0005030229513 \tabularnewline
38 & 11080 & 11025.9959785959 & 54.0040214041328 \tabularnewline
39 & 11210 & 11079.9966067143 & 130.00339328575 \tabularnewline
40 & 11222 & 11209.9918313738 & 12.0081686261583 \tabularnewline
41 & 11236 & 11221.9992454794 & 14.0007545206154 \tabularnewline
42 & 11329 & 11235.9991202774 & 93.0008797226492 \tabularnewline
43 & 11334 & 11328.9941563878 & 5.005843612229 \tabularnewline
44 & 11394 & 11333.9996854631 & 60.0003145369064 \tabularnewline
45 & 11648 & 11393.9962299435 & 254.003770056508 \tabularnewline
46 & 11677 & 11647.9840399409 & 29.0159600591014 \tabularnewline
47 & 11816 & 11676.9981768127 & 139.00182318726 \tabularnewline
48 & 11839 & 11815.991265967 & 23.0087340330138 \tabularnewline
49 & 11874 & 11838.9985542705 & 35.0014457295456 \tabularnewline
50 & 11911 & 11873.9978007211 & 37.0021992789407 \tabularnewline
51 & 11918 & 11910.9976750058 & 7.00232499418053 \tabularnewline
52 & 12164 & 11917.9995600163 & 246.000439983709 \tabularnewline
53 & 12177 & 12163.9845428217 & 13.015457178295 \tabularnewline
54 & 12347 & 12176.9991821875 & 170.00081781253 \tabularnewline
55 & 12624 & 12346.9893181778 & 277.010681822161 \tabularnewline
56 & 12627 & 12623.9825943259 & 3.01740567414708 \tabularnewline
57 & 12782 & 12626.9998104045 & 155.000189595505 \tabularnewline
58 & 12794 & 12781.9902607265 & 12.0097392735006 \tabularnewline
59 & 13142 & 12793.9992453807 & 348.000754619306 \tabularnewline
60 & 13149 & 13141.9781337395 & 7.02186626052753 \tabularnewline
61 & 13240 & 13148.9995587884 & 91.000441211565 \tabularnewline
62 & 13270 & 13239.9942820832 & 30.0057179167834 \tabularnewline
63 & 13445 & 13269.9981146223 & 175.001885377651 \tabularnewline
64 & 13579 & 13444.989003941 & 134.010996058967 \tabularnewline
65 & 13601 & 13578.9915795603 & 22.0084204396517 \tabularnewline
66 & 13878 & 13600.9986171241 & 277.001382875897 \tabularnewline
67 & 13957 & 13877.9825949101 & 79.0174050898568 \tabularnewline
68 & 14360 & 13956.9950350247 & 403.004964975342 \tabularnewline
69 & 14687 & 14359.9746776079 & 327.025322392095 \tabularnewline
70 & 14771 & 14686.9794517086 & 84.0205482913589 \tabularnewline
71 & 14779 & 14770.9947206574 & 8.00527934257116 \tabularnewline
72 & 14825 & 14778.9994969967 & 46.000503003288 \tabularnewline
73 & 15119 & 14824.9971096069 & 294.002890393109 \tabularnewline
74 & 16244 & 15118.9815266383 & 1125.01847336166 \tabularnewline
75 & 18983 & 16243.9293106503 & 2739.07068934969 \tabularnewline
76 & 19940 & 18982.827893381 & 957.172106619029 \tabularnewline
77 & 20067 & 19939.9398570998 & 127.060142900198 \tabularnewline
78 & 20993 & 20066.9920163099 & 926.00798369012 \tabularnewline
79 & 21545 & 20992.9418152646 & 552.058184735386 \tabularnewline
80 & 21709 & 21544.965312006 & 164.034687994015 \tabularnewline
81 & 22165 & 21708.9896930533 & 456.010306946682 \tabularnewline
82 & 22205 & 22164.9713470731 & 40.0286529268742 \tabularnewline
83 & 23533 & 22204.9974848418 & 1328.0025151582 \tabularnewline
84 & 23882 & 23532.916556362 & 349.083443637959 \tabularnewline
85 & 59646 & 23881.9780657098 & 35764.0219342902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260992&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]7045[/C][C]6900[/C][C]145[/C][/ROW]
[ROW][C]3[/C][C]8044[/C][C]7044.99088907787[/C][C]999.00911092213[/C][/ROW]
[ROW][C]4[/C][C]8196[/C][C]8043.93722831575[/C][C]152.062771684253[/C][/ROW]
[ROW][C]5[/C][C]8257[/C][C]8195.99044529606[/C][C]61.0095547039418[/C][/ROW]
[ROW][C]6[/C][C]8623[/C][C]8256.99616652895[/C][C]366.00383347105[/C][/ROW]
[ROW][C]7[/C][C]8644[/C][C]8622.97700253499[/C][C]21.0229974650065[/C][/ROW]
[ROW][C]8[/C][C]8648[/C][C]8643.99867904212[/C][C]4.00132095788285[/C][/ROW]
[ROW][C]9[/C][C]8961[/C][C]8647.99974858122[/C][C]313.000251418784[/C][/ROW]
[ROW][C]10[/C][C]8961[/C][C]8960.98033295919[/C][C]0.0196670408076898[/C][/ROW]
[ROW][C]11[/C][C]9116[/C][C]8960.99999876424[/C][C]155.000001235758[/C][/ROW]
[ROW][C]12[/C][C]9313[/C][C]9115.99026073834[/C][C]197.009739261664[/C][/ROW]
[ROW][C]13[/C][C]9360[/C][C]9312.98762110074[/C][C]47.0123788992623[/C][/ROW]
[ROW][C]14[/C][C]9429[/C][C]9359.99704602674[/C][C]69.0029539732641[/C][/ROW]
[ROW][C]15[/C][C]9485[/C][C]9428.99566427214[/C][C]56.0043357278646[/C][/ROW]
[ROW][C]16[/C][C]9580[/C][C]9484.99648102661[/C][C]95.0035189733899[/C][/ROW]
[ROW][C]17[/C][C]9606[/C][C]9579.99403055404[/C][C]26.005969445956[/C][/ROW]
[ROW][C]18[/C][C]9679[/C][C]9605.99836594233[/C][C]73.0016340576731[/C][/ROW]
[ROW][C]19[/C][C]9726[/C][C]9678.99541301929[/C][C]47.0045869807127[/C][/ROW]
[ROW][C]20[/C][C]9898[/C][C]9725.99704651633[/C][C]172.002953483669[/C][/ROW]
[ROW][C]21[/C][C]10028[/C][C]9897.98919237576[/C][C]130.010807624245[/C][/ROW]
[ROW][C]22[/C][C]10082[/C][C]10027.991830908[/C][C]54.0081690920306[/C][/ROW]
[ROW][C]23[/C][C]10091[/C][C]10081.9966064536[/C][C]9.00339354636526[/C][/ROW]
[ROW][C]24[/C][C]10228[/C][C]10090.9994342813[/C][C]137.000565718741[/C][/ROW]
[ROW][C]25[/C][C]10337[/C][C]10227.9913917139[/C][C]109.008608286111[/C][/ROW]
[ROW][C]26[/C][C]10372[/C][C]10336.993150559[/C][C]35.006849440977[/C][/ROW]
[ROW][C]27[/C][C]10425[/C][C]10371.9978003815[/C][C]53.0021996184769[/C][/ROW]
[ROW][C]28[/C][C]10573[/C][C]10424.9966696627[/C][C]148.003330337335[/C][/ROW]
[ROW][C]29[/C][C]10680[/C][C]10572.9907003668[/C][C]107.009299633224[/C][/ROW]
[ROW][C]30[/C][C]10685[/C][C]10679.9932761835[/C][C]5.00672381652475[/C][/ROW]
[ROW][C]31[/C][C]10771[/C][C]10684.9996854078[/C][C]86.0003145922128[/C][/ROW]
[ROW][C]32[/C][C]10783[/C][C]10770.9945962609[/C][C]12.0054037391001[/C][/ROW]
[ROW][C]33[/C][C]10849[/C][C]10782.9992456531[/C][C]66.0007543468855[/C][/ROW]
[ROW][C]34[/C][C]10865[/C][C]10848.9958529122[/C][C]16.004147087815[/C][/ROW]
[ROW][C]35[/C][C]10954[/C][C]10864.9989943963[/C][C]89.0010056037099[/C][/ROW]
[ROW][C]36[/C][C]10962[/C][C]10953.9944077156[/C][C]8.00559228435486[/C][/ROW]
[ROW][C]37[/C][C]11026[/C][C]10961.999496977[/C][C]64.0005030229513[/C][/ROW]
[ROW][C]38[/C][C]11080[/C][C]11025.9959785959[/C][C]54.0040214041328[/C][/ROW]
[ROW][C]39[/C][C]11210[/C][C]11079.9966067143[/C][C]130.00339328575[/C][/ROW]
[ROW][C]40[/C][C]11222[/C][C]11209.9918313738[/C][C]12.0081686261583[/C][/ROW]
[ROW][C]41[/C][C]11236[/C][C]11221.9992454794[/C][C]14.0007545206154[/C][/ROW]
[ROW][C]42[/C][C]11329[/C][C]11235.9991202774[/C][C]93.0008797226492[/C][/ROW]
[ROW][C]43[/C][C]11334[/C][C]11328.9941563878[/C][C]5.005843612229[/C][/ROW]
[ROW][C]44[/C][C]11394[/C][C]11333.9996854631[/C][C]60.0003145369064[/C][/ROW]
[ROW][C]45[/C][C]11648[/C][C]11393.9962299435[/C][C]254.003770056508[/C][/ROW]
[ROW][C]46[/C][C]11677[/C][C]11647.9840399409[/C][C]29.0159600591014[/C][/ROW]
[ROW][C]47[/C][C]11816[/C][C]11676.9981768127[/C][C]139.00182318726[/C][/ROW]
[ROW][C]48[/C][C]11839[/C][C]11815.991265967[/C][C]23.0087340330138[/C][/ROW]
[ROW][C]49[/C][C]11874[/C][C]11838.9985542705[/C][C]35.0014457295456[/C][/ROW]
[ROW][C]50[/C][C]11911[/C][C]11873.9978007211[/C][C]37.0021992789407[/C][/ROW]
[ROW][C]51[/C][C]11918[/C][C]11910.9976750058[/C][C]7.00232499418053[/C][/ROW]
[ROW][C]52[/C][C]12164[/C][C]11917.9995600163[/C][C]246.000439983709[/C][/ROW]
[ROW][C]53[/C][C]12177[/C][C]12163.9845428217[/C][C]13.015457178295[/C][/ROW]
[ROW][C]54[/C][C]12347[/C][C]12176.9991821875[/C][C]170.00081781253[/C][/ROW]
[ROW][C]55[/C][C]12624[/C][C]12346.9893181778[/C][C]277.010681822161[/C][/ROW]
[ROW][C]56[/C][C]12627[/C][C]12623.9825943259[/C][C]3.01740567414708[/C][/ROW]
[ROW][C]57[/C][C]12782[/C][C]12626.9998104045[/C][C]155.000189595505[/C][/ROW]
[ROW][C]58[/C][C]12794[/C][C]12781.9902607265[/C][C]12.0097392735006[/C][/ROW]
[ROW][C]59[/C][C]13142[/C][C]12793.9992453807[/C][C]348.000754619306[/C][/ROW]
[ROW][C]60[/C][C]13149[/C][C]13141.9781337395[/C][C]7.02186626052753[/C][/ROW]
[ROW][C]61[/C][C]13240[/C][C]13148.9995587884[/C][C]91.000441211565[/C][/ROW]
[ROW][C]62[/C][C]13270[/C][C]13239.9942820832[/C][C]30.0057179167834[/C][/ROW]
[ROW][C]63[/C][C]13445[/C][C]13269.9981146223[/C][C]175.001885377651[/C][/ROW]
[ROW][C]64[/C][C]13579[/C][C]13444.989003941[/C][C]134.010996058967[/C][/ROW]
[ROW][C]65[/C][C]13601[/C][C]13578.9915795603[/C][C]22.0084204396517[/C][/ROW]
[ROW][C]66[/C][C]13878[/C][C]13600.9986171241[/C][C]277.001382875897[/C][/ROW]
[ROW][C]67[/C][C]13957[/C][C]13877.9825949101[/C][C]79.0174050898568[/C][/ROW]
[ROW][C]68[/C][C]14360[/C][C]13956.9950350247[/C][C]403.004964975342[/C][/ROW]
[ROW][C]69[/C][C]14687[/C][C]14359.9746776079[/C][C]327.025322392095[/C][/ROW]
[ROW][C]70[/C][C]14771[/C][C]14686.9794517086[/C][C]84.0205482913589[/C][/ROW]
[ROW][C]71[/C][C]14779[/C][C]14770.9947206574[/C][C]8.00527934257116[/C][/ROW]
[ROW][C]72[/C][C]14825[/C][C]14778.9994969967[/C][C]46.000503003288[/C][/ROW]
[ROW][C]73[/C][C]15119[/C][C]14824.9971096069[/C][C]294.002890393109[/C][/ROW]
[ROW][C]74[/C][C]16244[/C][C]15118.9815266383[/C][C]1125.01847336166[/C][/ROW]
[ROW][C]75[/C][C]18983[/C][C]16243.9293106503[/C][C]2739.07068934969[/C][/ROW]
[ROW][C]76[/C][C]19940[/C][C]18982.827893381[/C][C]957.172106619029[/C][/ROW]
[ROW][C]77[/C][C]20067[/C][C]19939.9398570998[/C][C]127.060142900198[/C][/ROW]
[ROW][C]78[/C][C]20993[/C][C]20066.9920163099[/C][C]926.00798369012[/C][/ROW]
[ROW][C]79[/C][C]21545[/C][C]20992.9418152646[/C][C]552.058184735386[/C][/ROW]
[ROW][C]80[/C][C]21709[/C][C]21544.965312006[/C][C]164.034687994015[/C][/ROW]
[ROW][C]81[/C][C]22165[/C][C]21708.9896930533[/C][C]456.010306946682[/C][/ROW]
[ROW][C]82[/C][C]22205[/C][C]22164.9713470731[/C][C]40.0286529268742[/C][/ROW]
[ROW][C]83[/C][C]23533[/C][C]22204.9974848418[/C][C]1328.0025151582[/C][/ROW]
[ROW][C]84[/C][C]23882[/C][C]23532.916556362[/C][C]349.083443637959[/C][/ROW]
[ROW][C]85[/C][C]59646[/C][C]23881.9780657098[/C][C]35764.0219342902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260992&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260992&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
270456900145
380447044.99088907787999.00911092213
481968043.93722831575152.062771684253
582578195.9904452960661.0095547039418
686238256.99616652895366.00383347105
786448622.9770025349921.0229974650065
886488643.998679042124.00132095788285
989618647.99974858122313.000251418784
1089618960.980332959190.0196670408076898
1191168960.99999876424155.000001235758
1293139115.99026073834197.009739261664
1393609312.9876211007447.0123788992623
1494299359.9970460267469.0029539732641
1594859428.9956642721456.0043357278646
1695809484.9964810266195.0035189733899
1796069579.9940305540426.005969445956
1896799605.9983659423373.0016340576731
1997269678.9954130192947.0045869807127
2098989725.99704651633172.002953483669
21100289897.98919237576130.010807624245
221008210027.99183090854.0081690920306
231009110081.99660645369.00339354636526
241022810090.9994342813137.000565718741
251033710227.9913917139109.008608286111
261037210336.99315055935.006849440977
271042510371.997800381553.0021996184769
281057310424.9966696627148.003330337335
291068010572.9907003668107.009299633224
301068510679.99327618355.00672381652475
311077110684.999685407886.0003145922128
321078310770.994596260912.0054037391001
331084910782.999245653166.0007543468855
341086510848.995852912216.004147087815
351095410864.998994396389.0010056037099
361096210953.99440771568.00559228435486
371102610961.99949697764.0005030229513
381108011025.995978595954.0040214041328
391121011079.9966067143130.00339328575
401122211209.991831373812.0081686261583
411123611221.999245479414.0007545206154
421132911235.999120277493.0008797226492
431133411328.99415638785.005843612229
441139411333.999685463160.0003145369064
451164811393.9962299435254.003770056508
461167711647.984039940929.0159600591014
471181611676.9981768127139.00182318726
481183911815.99126596723.0087340330138
491187411838.998554270535.0014457295456
501191111873.997800721137.0021992789407
511191811910.99767500587.00232499418053
521216411917.9995600163246.000439983709
531217712163.984542821713.015457178295
541234712176.9991821875170.00081781253
551262412346.9893181778277.010681822161
561262712623.98259432593.01740567414708
571278212626.9998104045155.000189595505
581279412781.990260726512.0097392735006
591314212793.9992453807348.000754619306
601314913141.97813373957.02186626052753
611324013148.999558788491.000441211565
621327013239.994282083230.0057179167834
631344513269.9981146223175.001885377651
641357913444.989003941134.010996058967
651360113578.991579560322.0084204396517
661387813600.9986171241277.001382875897
671395713877.982594910179.0174050898568
681436013956.9950350247403.004964975342
691468714359.9746776079327.025322392095
701477114686.979451708684.0205482913589
711477914770.99472065748.00527934257116
721482514778.999496996746.000503003288
731511914824.9971096069294.002890393109
741624415118.98152663831125.01847336166
751898316243.92931065032739.07068934969
761994018982.827893381957.172106619029
772006719939.9398570998127.060142900198
782099320066.9920163099926.00798369012
792154520992.9418152646552.058184735386
802170921544.965312006164.034687994015
812216521708.9896930533456.010306946682
822220522164.971347073140.0286529268742
832353322204.99748484181328.0025151582
842388223532.916556362349.083443637959
855964623881.978065709835764.0219342902







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8659643.752805386952003.083902288567284.4217084853
8759643.752805386948838.554688971170448.9509218027
8859643.752805386946410.280419681972877.2251910919
8959643.752805386944363.135133596474924.3704771775
9059643.752805386942559.556556231476727.9490545424
9159643.752805386940928.992680611678358.5129301622
9259643.752805386939429.531782154379857.9738286195
9359643.752805386938033.865794476481253.6398162975
9459643.752805386936723.026340622782564.4792701511
9559643.752805386935483.202589782183804.3030209917
9659643.752805386934303.968438329284983.5371724446
9759643.752805386933177.223814655986110.2817961179

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 59643.7528053869 & 52003.0839022885 & 67284.4217084853 \tabularnewline
87 & 59643.7528053869 & 48838.5546889711 & 70448.9509218027 \tabularnewline
88 & 59643.7528053869 & 46410.2804196819 & 72877.2251910919 \tabularnewline
89 & 59643.7528053869 & 44363.1351335964 & 74924.3704771775 \tabularnewline
90 & 59643.7528053869 & 42559.5565562314 & 76727.9490545424 \tabularnewline
91 & 59643.7528053869 & 40928.9926806116 & 78358.5129301622 \tabularnewline
92 & 59643.7528053869 & 39429.5317821543 & 79857.9738286195 \tabularnewline
93 & 59643.7528053869 & 38033.8657944764 & 81253.6398162975 \tabularnewline
94 & 59643.7528053869 & 36723.0263406227 & 82564.4792701511 \tabularnewline
95 & 59643.7528053869 & 35483.2025897821 & 83804.3030209917 \tabularnewline
96 & 59643.7528053869 & 34303.9684383292 & 84983.5371724446 \tabularnewline
97 & 59643.7528053869 & 33177.2238146559 & 86110.2817961179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260992&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]86[/C][C]59643.7528053869[/C][C]52003.0839022885[/C][C]67284.4217084853[/C][/ROW]
[ROW][C]87[/C][C]59643.7528053869[/C][C]48838.5546889711[/C][C]70448.9509218027[/C][/ROW]
[ROW][C]88[/C][C]59643.7528053869[/C][C]46410.2804196819[/C][C]72877.2251910919[/C][/ROW]
[ROW][C]89[/C][C]59643.7528053869[/C][C]44363.1351335964[/C][C]74924.3704771775[/C][/ROW]
[ROW][C]90[/C][C]59643.7528053869[/C][C]42559.5565562314[/C][C]76727.9490545424[/C][/ROW]
[ROW][C]91[/C][C]59643.7528053869[/C][C]40928.9926806116[/C][C]78358.5129301622[/C][/ROW]
[ROW][C]92[/C][C]59643.7528053869[/C][C]39429.5317821543[/C][C]79857.9738286195[/C][/ROW]
[ROW][C]93[/C][C]59643.7528053869[/C][C]38033.8657944764[/C][C]81253.6398162975[/C][/ROW]
[ROW][C]94[/C][C]59643.7528053869[/C][C]36723.0263406227[/C][C]82564.4792701511[/C][/ROW]
[ROW][C]95[/C][C]59643.7528053869[/C][C]35483.2025897821[/C][C]83804.3030209917[/C][/ROW]
[ROW][C]96[/C][C]59643.7528053869[/C][C]34303.9684383292[/C][C]84983.5371724446[/C][/ROW]
[ROW][C]97[/C][C]59643.7528053869[/C][C]33177.2238146559[/C][C]86110.2817961179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260992&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260992&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
8659643.752805386952003.083902288567284.4217084853
8759643.752805386948838.554688971170448.9509218027
8859643.752805386946410.280419681972877.2251910919
8959643.752805386944363.135133596474924.3704771775
9059643.752805386942559.556556231476727.9490545424
9159643.752805386940928.992680611678358.5129301622
9259643.752805386939429.531782154379857.9738286195
9359643.752805386938033.865794476481253.6398162975
9459643.752805386936723.026340622782564.4792701511
9559643.752805386935483.202589782183804.3030209917
9659643.752805386934303.968438329284983.5371724446
9759643.752805386933177.223814655986110.2817961179



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')