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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 Dec 2011 14:04:04 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/28/t1325099097zknvnw7kamn6v9i.htm/, Retrieved Fri, 03 May 2024 07:44:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160885, Retrieved Fri, 03 May 2024 07:44:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2011-12-28 19:04:04] [0e4b98151bf75fbee698897d61f4279d] [Current]
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Dataseries X:
192.89
194.76
194.76
194.76
194.76
194.76
194.76
194.76
194.76
194.76
194.76
194.76
194.76
194.76
199.15
199.15
199.15
199.15
199.15
199.15
199.15
199.15
199.15
199.15
199.15
200.4
200.4
200.4
200.4
200.4
200.4
200.4
200.4
200.4
200.4
200.4
200.4
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
204.15
212.25
212.25
212.25
212.25
212.25
212.25
212.25
212.25
212.25
212.25
212.25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160885&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160885&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.136823719451082
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.136823719451082 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160885&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.136823719451082[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160885&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
alpha1
beta0.136823719451082
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3194.76196.63-1.87
4194.76196.374139644626-1.61413964462648
5194.76196.153287054735-1.39328705473523
6194.76195.962652337643-1.20265233764331
7194.76195.7981009716-1.03810097160041
8194.76195.6560641355-0.896064135500268
9194.76195.533461307614-0.773461307614411
10194.76195.427633454655-0.667633454655117
11194.76195.336285362159-0.576285362159211
12194.76195.257435855443-0.497435855443371
13194.76195.189374831513-0.429374831513286
14194.76195.130626170027-0.370626170026952
15199.15195.0799157189184.07008428108205
16199.15200.026799788735-0.876799788734985
17199.15199.906832780426-0.75683278042635
18199.15199.803280104406-0.653280104405894
19199.15199.713895890678-0.563895890677713
20199.15199.636741557532-0.486741557531985
21199.15199.570143767219-0.420143767219059
22199.15199.512658134284-0.362658134283947
23199.15199.463037899462-0.313037899462046
24199.15199.420206889728-0.270206889728485
25199.15199.383236178055-0.233236178054511
26200.4199.3513239366631.04867606333744
27200.4200.744807696148-0.344807696147711
28200.4200.697629824665-0.297629824665421
29200.4200.656907005035-0.256907005035117
30200.4200.621756033053-0.221756033053168
31200.4200.5914145478-0.191414547800122
32200.4200.565224497413-0.16522449741305
33200.4200.542617867133-0.142617867132572
34200.4200.523104360091-0.123104360091304
35200.4200.506260763663-0.106260763662988
36200.4200.491721770747-0.0917217707468865
37200.4200.479172056919-0.0791720569186509
38204.15200.4683394416143.68166055838554
39204.15204.722077932969-0.572077932969108
40204.15204.643804102364-0.493804102364408
41204.15204.576239988399-0.426239988398692
42204.15204.517920247807-0.367920247807206
43204.15204.467580031041-0.317580031040848
44204.15204.42412754997-0.274127549970444
45204.15204.386620398979-0.236620398979483
46204.15204.354245115893-0.204245115893116
47204.15204.326299539457-0.176299539456892
48204.15204.302177580731-0.152177580730893
49204.15204.281356078118-0.131356078118216
50204.15204.263383450938-0.11338345093759
51204.15204.247869905456-0.0978699054560934
52204.15204.234478980969-0.0844789809692656
53204.15204.222920252578-0.0729202525776316
54204.15204.212943032397-0.062943032396646
55204.15204.204330932591-0.0543309325906023
56204.15204.196897172312-0.0468971723122991
57204.15204.190480526765-0.0404805267648101
58204.15204.184941830528-0.0349418305275151
59204.15204.18016095931-0.030160959310308
60204.15204.176034224675-0.026034224675243
61204.15204.172472125222-0.0224721252221514
62212.25204.1693974054658.0806025945347
63212.25213.375015507856-1.12501550785561
64212.25213.221086701631-0.971086701630639
65212.25213.088219007204-0.83821900720406
66212.25212.973530764924-0.723530764923794
67212.25212.87453459453-0.624534594529649
68212.25212.78908344838-0.539083448380211
69212.25212.715324045878-0.465324045878333
70212.25212.651656679171-0.401656679171225
71212.25212.596700518385-0.346700518384637
72212.25212.549263663924-0.299263663923654

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 194.76 & 196.63 & -1.87 \tabularnewline
4 & 194.76 & 196.374139644626 & -1.61413964462648 \tabularnewline
5 & 194.76 & 196.153287054735 & -1.39328705473523 \tabularnewline
6 & 194.76 & 195.962652337643 & -1.20265233764331 \tabularnewline
7 & 194.76 & 195.7981009716 & -1.03810097160041 \tabularnewline
8 & 194.76 & 195.6560641355 & -0.896064135500268 \tabularnewline
9 & 194.76 & 195.533461307614 & -0.773461307614411 \tabularnewline
10 & 194.76 & 195.427633454655 & -0.667633454655117 \tabularnewline
11 & 194.76 & 195.336285362159 & -0.576285362159211 \tabularnewline
12 & 194.76 & 195.257435855443 & -0.497435855443371 \tabularnewline
13 & 194.76 & 195.189374831513 & -0.429374831513286 \tabularnewline
14 & 194.76 & 195.130626170027 & -0.370626170026952 \tabularnewline
15 & 199.15 & 195.079915718918 & 4.07008428108205 \tabularnewline
16 & 199.15 & 200.026799788735 & -0.876799788734985 \tabularnewline
17 & 199.15 & 199.906832780426 & -0.75683278042635 \tabularnewline
18 & 199.15 & 199.803280104406 & -0.653280104405894 \tabularnewline
19 & 199.15 & 199.713895890678 & -0.563895890677713 \tabularnewline
20 & 199.15 & 199.636741557532 & -0.486741557531985 \tabularnewline
21 & 199.15 & 199.570143767219 & -0.420143767219059 \tabularnewline
22 & 199.15 & 199.512658134284 & -0.362658134283947 \tabularnewline
23 & 199.15 & 199.463037899462 & -0.313037899462046 \tabularnewline
24 & 199.15 & 199.420206889728 & -0.270206889728485 \tabularnewline
25 & 199.15 & 199.383236178055 & -0.233236178054511 \tabularnewline
26 & 200.4 & 199.351323936663 & 1.04867606333744 \tabularnewline
27 & 200.4 & 200.744807696148 & -0.344807696147711 \tabularnewline
28 & 200.4 & 200.697629824665 & -0.297629824665421 \tabularnewline
29 & 200.4 & 200.656907005035 & -0.256907005035117 \tabularnewline
30 & 200.4 & 200.621756033053 & -0.221756033053168 \tabularnewline
31 & 200.4 & 200.5914145478 & -0.191414547800122 \tabularnewline
32 & 200.4 & 200.565224497413 & -0.16522449741305 \tabularnewline
33 & 200.4 & 200.542617867133 & -0.142617867132572 \tabularnewline
34 & 200.4 & 200.523104360091 & -0.123104360091304 \tabularnewline
35 & 200.4 & 200.506260763663 & -0.106260763662988 \tabularnewline
36 & 200.4 & 200.491721770747 & -0.0917217707468865 \tabularnewline
37 & 200.4 & 200.479172056919 & -0.0791720569186509 \tabularnewline
38 & 204.15 & 200.468339441614 & 3.68166055838554 \tabularnewline
39 & 204.15 & 204.722077932969 & -0.572077932969108 \tabularnewline
40 & 204.15 & 204.643804102364 & -0.493804102364408 \tabularnewline
41 & 204.15 & 204.576239988399 & -0.426239988398692 \tabularnewline
42 & 204.15 & 204.517920247807 & -0.367920247807206 \tabularnewline
43 & 204.15 & 204.467580031041 & -0.317580031040848 \tabularnewline
44 & 204.15 & 204.42412754997 & -0.274127549970444 \tabularnewline
45 & 204.15 & 204.386620398979 & -0.236620398979483 \tabularnewline
46 & 204.15 & 204.354245115893 & -0.204245115893116 \tabularnewline
47 & 204.15 & 204.326299539457 & -0.176299539456892 \tabularnewline
48 & 204.15 & 204.302177580731 & -0.152177580730893 \tabularnewline
49 & 204.15 & 204.281356078118 & -0.131356078118216 \tabularnewline
50 & 204.15 & 204.263383450938 & -0.11338345093759 \tabularnewline
51 & 204.15 & 204.247869905456 & -0.0978699054560934 \tabularnewline
52 & 204.15 & 204.234478980969 & -0.0844789809692656 \tabularnewline
53 & 204.15 & 204.222920252578 & -0.0729202525776316 \tabularnewline
54 & 204.15 & 204.212943032397 & -0.062943032396646 \tabularnewline
55 & 204.15 & 204.204330932591 & -0.0543309325906023 \tabularnewline
56 & 204.15 & 204.196897172312 & -0.0468971723122991 \tabularnewline
57 & 204.15 & 204.190480526765 & -0.0404805267648101 \tabularnewline
58 & 204.15 & 204.184941830528 & -0.0349418305275151 \tabularnewline
59 & 204.15 & 204.18016095931 & -0.030160959310308 \tabularnewline
60 & 204.15 & 204.176034224675 & -0.026034224675243 \tabularnewline
61 & 204.15 & 204.172472125222 & -0.0224721252221514 \tabularnewline
62 & 212.25 & 204.169397405465 & 8.0806025945347 \tabularnewline
63 & 212.25 & 213.375015507856 & -1.12501550785561 \tabularnewline
64 & 212.25 & 213.221086701631 & -0.971086701630639 \tabularnewline
65 & 212.25 & 213.088219007204 & -0.83821900720406 \tabularnewline
66 & 212.25 & 212.973530764924 & -0.723530764923794 \tabularnewline
67 & 212.25 & 212.87453459453 & -0.624534594529649 \tabularnewline
68 & 212.25 & 212.78908344838 & -0.539083448380211 \tabularnewline
69 & 212.25 & 212.715324045878 & -0.465324045878333 \tabularnewline
70 & 212.25 & 212.651656679171 & -0.401656679171225 \tabularnewline
71 & 212.25 & 212.596700518385 & -0.346700518384637 \tabularnewline
72 & 212.25 & 212.549263663924 & -0.299263663923654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160885&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]3[/C][C]194.76[/C][C]196.63[/C][C]-1.87[/C][/ROW]
[ROW][C]4[/C][C]194.76[/C][C]196.374139644626[/C][C]-1.61413964462648[/C][/ROW]
[ROW][C]5[/C][C]194.76[/C][C]196.153287054735[/C][C]-1.39328705473523[/C][/ROW]
[ROW][C]6[/C][C]194.76[/C][C]195.962652337643[/C][C]-1.20265233764331[/C][/ROW]
[ROW][C]7[/C][C]194.76[/C][C]195.7981009716[/C][C]-1.03810097160041[/C][/ROW]
[ROW][C]8[/C][C]194.76[/C][C]195.6560641355[/C][C]-0.896064135500268[/C][/ROW]
[ROW][C]9[/C][C]194.76[/C][C]195.533461307614[/C][C]-0.773461307614411[/C][/ROW]
[ROW][C]10[/C][C]194.76[/C][C]195.427633454655[/C][C]-0.667633454655117[/C][/ROW]
[ROW][C]11[/C][C]194.76[/C][C]195.336285362159[/C][C]-0.576285362159211[/C][/ROW]
[ROW][C]12[/C][C]194.76[/C][C]195.257435855443[/C][C]-0.497435855443371[/C][/ROW]
[ROW][C]13[/C][C]194.76[/C][C]195.189374831513[/C][C]-0.429374831513286[/C][/ROW]
[ROW][C]14[/C][C]194.76[/C][C]195.130626170027[/C][C]-0.370626170026952[/C][/ROW]
[ROW][C]15[/C][C]199.15[/C][C]195.079915718918[/C][C]4.07008428108205[/C][/ROW]
[ROW][C]16[/C][C]199.15[/C][C]200.026799788735[/C][C]-0.876799788734985[/C][/ROW]
[ROW][C]17[/C][C]199.15[/C][C]199.906832780426[/C][C]-0.75683278042635[/C][/ROW]
[ROW][C]18[/C][C]199.15[/C][C]199.803280104406[/C][C]-0.653280104405894[/C][/ROW]
[ROW][C]19[/C][C]199.15[/C][C]199.713895890678[/C][C]-0.563895890677713[/C][/ROW]
[ROW][C]20[/C][C]199.15[/C][C]199.636741557532[/C][C]-0.486741557531985[/C][/ROW]
[ROW][C]21[/C][C]199.15[/C][C]199.570143767219[/C][C]-0.420143767219059[/C][/ROW]
[ROW][C]22[/C][C]199.15[/C][C]199.512658134284[/C][C]-0.362658134283947[/C][/ROW]
[ROW][C]23[/C][C]199.15[/C][C]199.463037899462[/C][C]-0.313037899462046[/C][/ROW]
[ROW][C]24[/C][C]199.15[/C][C]199.420206889728[/C][C]-0.270206889728485[/C][/ROW]
[ROW][C]25[/C][C]199.15[/C][C]199.383236178055[/C][C]-0.233236178054511[/C][/ROW]
[ROW][C]26[/C][C]200.4[/C][C]199.351323936663[/C][C]1.04867606333744[/C][/ROW]
[ROW][C]27[/C][C]200.4[/C][C]200.744807696148[/C][C]-0.344807696147711[/C][/ROW]
[ROW][C]28[/C][C]200.4[/C][C]200.697629824665[/C][C]-0.297629824665421[/C][/ROW]
[ROW][C]29[/C][C]200.4[/C][C]200.656907005035[/C][C]-0.256907005035117[/C][/ROW]
[ROW][C]30[/C][C]200.4[/C][C]200.621756033053[/C][C]-0.221756033053168[/C][/ROW]
[ROW][C]31[/C][C]200.4[/C][C]200.5914145478[/C][C]-0.191414547800122[/C][/ROW]
[ROW][C]32[/C][C]200.4[/C][C]200.565224497413[/C][C]-0.16522449741305[/C][/ROW]
[ROW][C]33[/C][C]200.4[/C][C]200.542617867133[/C][C]-0.142617867132572[/C][/ROW]
[ROW][C]34[/C][C]200.4[/C][C]200.523104360091[/C][C]-0.123104360091304[/C][/ROW]
[ROW][C]35[/C][C]200.4[/C][C]200.506260763663[/C][C]-0.106260763662988[/C][/ROW]
[ROW][C]36[/C][C]200.4[/C][C]200.491721770747[/C][C]-0.0917217707468865[/C][/ROW]
[ROW][C]37[/C][C]200.4[/C][C]200.479172056919[/C][C]-0.0791720569186509[/C][/ROW]
[ROW][C]38[/C][C]204.15[/C][C]200.468339441614[/C][C]3.68166055838554[/C][/ROW]
[ROW][C]39[/C][C]204.15[/C][C]204.722077932969[/C][C]-0.572077932969108[/C][/ROW]
[ROW][C]40[/C][C]204.15[/C][C]204.643804102364[/C][C]-0.493804102364408[/C][/ROW]
[ROW][C]41[/C][C]204.15[/C][C]204.576239988399[/C][C]-0.426239988398692[/C][/ROW]
[ROW][C]42[/C][C]204.15[/C][C]204.517920247807[/C][C]-0.367920247807206[/C][/ROW]
[ROW][C]43[/C][C]204.15[/C][C]204.467580031041[/C][C]-0.317580031040848[/C][/ROW]
[ROW][C]44[/C][C]204.15[/C][C]204.42412754997[/C][C]-0.274127549970444[/C][/ROW]
[ROW][C]45[/C][C]204.15[/C][C]204.386620398979[/C][C]-0.236620398979483[/C][/ROW]
[ROW][C]46[/C][C]204.15[/C][C]204.354245115893[/C][C]-0.204245115893116[/C][/ROW]
[ROW][C]47[/C][C]204.15[/C][C]204.326299539457[/C][C]-0.176299539456892[/C][/ROW]
[ROW][C]48[/C][C]204.15[/C][C]204.302177580731[/C][C]-0.152177580730893[/C][/ROW]
[ROW][C]49[/C][C]204.15[/C][C]204.281356078118[/C][C]-0.131356078118216[/C][/ROW]
[ROW][C]50[/C][C]204.15[/C][C]204.263383450938[/C][C]-0.11338345093759[/C][/ROW]
[ROW][C]51[/C][C]204.15[/C][C]204.247869905456[/C][C]-0.0978699054560934[/C][/ROW]
[ROW][C]52[/C][C]204.15[/C][C]204.234478980969[/C][C]-0.0844789809692656[/C][/ROW]
[ROW][C]53[/C][C]204.15[/C][C]204.222920252578[/C][C]-0.0729202525776316[/C][/ROW]
[ROW][C]54[/C][C]204.15[/C][C]204.212943032397[/C][C]-0.062943032396646[/C][/ROW]
[ROW][C]55[/C][C]204.15[/C][C]204.204330932591[/C][C]-0.0543309325906023[/C][/ROW]
[ROW][C]56[/C][C]204.15[/C][C]204.196897172312[/C][C]-0.0468971723122991[/C][/ROW]
[ROW][C]57[/C][C]204.15[/C][C]204.190480526765[/C][C]-0.0404805267648101[/C][/ROW]
[ROW][C]58[/C][C]204.15[/C][C]204.184941830528[/C][C]-0.0349418305275151[/C][/ROW]
[ROW][C]59[/C][C]204.15[/C][C]204.18016095931[/C][C]-0.030160959310308[/C][/ROW]
[ROW][C]60[/C][C]204.15[/C][C]204.176034224675[/C][C]-0.026034224675243[/C][/ROW]
[ROW][C]61[/C][C]204.15[/C][C]204.172472125222[/C][C]-0.0224721252221514[/C][/ROW]
[ROW][C]62[/C][C]212.25[/C][C]204.169397405465[/C][C]8.0806025945347[/C][/ROW]
[ROW][C]63[/C][C]212.25[/C][C]213.375015507856[/C][C]-1.12501550785561[/C][/ROW]
[ROW][C]64[/C][C]212.25[/C][C]213.221086701631[/C][C]-0.971086701630639[/C][/ROW]
[ROW][C]65[/C][C]212.25[/C][C]213.088219007204[/C][C]-0.83821900720406[/C][/ROW]
[ROW][C]66[/C][C]212.25[/C][C]212.973530764924[/C][C]-0.723530764923794[/C][/ROW]
[ROW][C]67[/C][C]212.25[/C][C]212.87453459453[/C][C]-0.624534594529649[/C][/ROW]
[ROW][C]68[/C][C]212.25[/C][C]212.78908344838[/C][C]-0.539083448380211[/C][/ROW]
[ROW][C]69[/C][C]212.25[/C][C]212.715324045878[/C][C]-0.465324045878333[/C][/ROW]
[ROW][C]70[/C][C]212.25[/C][C]212.651656679171[/C][C]-0.401656679171225[/C][/ROW]
[ROW][C]71[/C][C]212.25[/C][C]212.596700518385[/C][C]-0.346700518384637[/C][/ROW]
[ROW][C]72[/C][C]212.25[/C][C]212.549263663924[/C][C]-0.299263663923654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160885&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160885&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
3194.76196.63-1.87
4194.76196.374139644626-1.61413964462648
5194.76196.153287054735-1.39328705473523
6194.76195.962652337643-1.20265233764331
7194.76195.7981009716-1.03810097160041
8194.76195.6560641355-0.896064135500268
9194.76195.533461307614-0.773461307614411
10194.76195.427633454655-0.667633454655117
11194.76195.336285362159-0.576285362159211
12194.76195.257435855443-0.497435855443371
13194.76195.189374831513-0.429374831513286
14194.76195.130626170027-0.370626170026952
15199.15195.0799157189184.07008428108205
16199.15200.026799788735-0.876799788734985
17199.15199.906832780426-0.75683278042635
18199.15199.803280104406-0.653280104405894
19199.15199.713895890678-0.563895890677713
20199.15199.636741557532-0.486741557531985
21199.15199.570143767219-0.420143767219059
22199.15199.512658134284-0.362658134283947
23199.15199.463037899462-0.313037899462046
24199.15199.420206889728-0.270206889728485
25199.15199.383236178055-0.233236178054511
26200.4199.3513239366631.04867606333744
27200.4200.744807696148-0.344807696147711
28200.4200.697629824665-0.297629824665421
29200.4200.656907005035-0.256907005035117
30200.4200.621756033053-0.221756033053168
31200.4200.5914145478-0.191414547800122
32200.4200.565224497413-0.16522449741305
33200.4200.542617867133-0.142617867132572
34200.4200.523104360091-0.123104360091304
35200.4200.506260763663-0.106260763662988
36200.4200.491721770747-0.0917217707468865
37200.4200.479172056919-0.0791720569186509
38204.15200.4683394416143.68166055838554
39204.15204.722077932969-0.572077932969108
40204.15204.643804102364-0.493804102364408
41204.15204.576239988399-0.426239988398692
42204.15204.517920247807-0.367920247807206
43204.15204.467580031041-0.317580031040848
44204.15204.42412754997-0.274127549970444
45204.15204.386620398979-0.236620398979483
46204.15204.354245115893-0.204245115893116
47204.15204.326299539457-0.176299539456892
48204.15204.302177580731-0.152177580730893
49204.15204.281356078118-0.131356078118216
50204.15204.263383450938-0.11338345093759
51204.15204.247869905456-0.0978699054560934
52204.15204.234478980969-0.0844789809692656
53204.15204.222920252578-0.0729202525776316
54204.15204.212943032397-0.062943032396646
55204.15204.204330932591-0.0543309325906023
56204.15204.196897172312-0.0468971723122991
57204.15204.190480526765-0.0404805267648101
58204.15204.184941830528-0.0349418305275151
59204.15204.18016095931-0.030160959310308
60204.15204.176034224675-0.026034224675243
61204.15204.172472125222-0.0224721252221514
62212.25204.1693974054658.0806025945347
63212.25213.375015507856-1.12501550785561
64212.25213.221086701631-0.971086701630639
65212.25213.088219007204-0.83821900720406
66212.25212.973530764924-0.723530764923794
67212.25212.87453459453-0.624534594529649
68212.25212.78908344838-0.539083448380211
69212.25212.715324045878-0.465324045878333
70212.25212.651656679171-0.401656679171225
71212.25212.596700518385-0.346700518384637
72212.25212.549263663924-0.299263663923654







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73212.508317296329209.954582256898215.06205233576
74212.766634592658208.90013454282216.633134642496
75213.024951888987207.972333084726218.077570693248
76213.283269185316207.078179184457219.488359186176
77213.541586481645206.18519097311220.89798199018
78213.799903777974205.278555733874222.321251822075
79214.058221074303204.350606970896223.765835177711
80214.316538370632203.397109402789225.235967338476
81214.574855666961202.415660729474226.734050604448
82214.833172963291201.404910750978228.261435175603
83215.09149025962200.364144288332229.818836230907
84215.349807555949199.293043302096231.406571809801

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 212.508317296329 & 209.954582256898 & 215.06205233576 \tabularnewline
74 & 212.766634592658 & 208.90013454282 & 216.633134642496 \tabularnewline
75 & 213.024951888987 & 207.972333084726 & 218.077570693248 \tabularnewline
76 & 213.283269185316 & 207.078179184457 & 219.488359186176 \tabularnewline
77 & 213.541586481645 & 206.18519097311 & 220.89798199018 \tabularnewline
78 & 213.799903777974 & 205.278555733874 & 222.321251822075 \tabularnewline
79 & 214.058221074303 & 204.350606970896 & 223.765835177711 \tabularnewline
80 & 214.316538370632 & 203.397109402789 & 225.235967338476 \tabularnewline
81 & 214.574855666961 & 202.415660729474 & 226.734050604448 \tabularnewline
82 & 214.833172963291 & 201.404910750978 & 228.261435175603 \tabularnewline
83 & 215.09149025962 & 200.364144288332 & 229.818836230907 \tabularnewline
84 & 215.349807555949 & 199.293043302096 & 231.406571809801 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160885&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]73[/C][C]212.508317296329[/C][C]209.954582256898[/C][C]215.06205233576[/C][/ROW]
[ROW][C]74[/C][C]212.766634592658[/C][C]208.90013454282[/C][C]216.633134642496[/C][/ROW]
[ROW][C]75[/C][C]213.024951888987[/C][C]207.972333084726[/C][C]218.077570693248[/C][/ROW]
[ROW][C]76[/C][C]213.283269185316[/C][C]207.078179184457[/C][C]219.488359186176[/C][/ROW]
[ROW][C]77[/C][C]213.541586481645[/C][C]206.18519097311[/C][C]220.89798199018[/C][/ROW]
[ROW][C]78[/C][C]213.799903777974[/C][C]205.278555733874[/C][C]222.321251822075[/C][/ROW]
[ROW][C]79[/C][C]214.058221074303[/C][C]204.350606970896[/C][C]223.765835177711[/C][/ROW]
[ROW][C]80[/C][C]214.316538370632[/C][C]203.397109402789[/C][C]225.235967338476[/C][/ROW]
[ROW][C]81[/C][C]214.574855666961[/C][C]202.415660729474[/C][C]226.734050604448[/C][/ROW]
[ROW][C]82[/C][C]214.833172963291[/C][C]201.404910750978[/C][C]228.261435175603[/C][/ROW]
[ROW][C]83[/C][C]215.09149025962[/C][C]200.364144288332[/C][C]229.818836230907[/C][/ROW]
[ROW][C]84[/C][C]215.349807555949[/C][C]199.293043302096[/C][C]231.406571809801[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160885&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160885&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
73212.508317296329209.954582256898215.06205233576
74212.766634592658208.90013454282216.633134642496
75213.024951888987207.972333084726218.077570693248
76213.283269185316207.078179184457219.488359186176
77213.541586481645206.18519097311220.89798199018
78213.799903777974205.278555733874222.321251822075
79214.058221074303204.350606970896223.765835177711
80214.316538370632203.397109402789225.235967338476
81214.574855666961202.415660729474226.734050604448
82214.833172963291201.404910750978228.261435175603
83215.09149025962200.364144288332229.818836230907
84215.349807555949199.293043302096231.406571809801



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')