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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 computationSun, 12 Jan 2014 13:57:25 -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/2014/Jan/12/t1389553071mcsg2hrcw7lp3z4.htm/, Retrieved Thu, 30 Apr 2026 17:26:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233038, Retrieved Thu, 30 Apr 2026 17:26:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact369
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-01-12 18:57:25] [ab12ae47238ac832614ec82c15c6db51] [Current]
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Dataseries X:
5731
5040
6102
4904
5369
5578
4619
4731
5011
5227
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5657
4249
3830
4736
4840
4413
4571
4106
4801
3956
3829
4453
4027
4121
4798
3233
3554
3952
3951
3685
4312
3867
4140
4114
3818
3377
3453
3502
4017
5410
5184
5529
6434
4962
2980
2937
2969
2731
3163
3145
3173
3723
3224
4114
3446
2955
3879
4278
4177
3698
4449
4162
3961
5246
5170
3682
3495
3770
3291
3580
3898
3477
3054




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233038&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233038&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233038&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.610015165931117
beta0
gamma0.303588602711922

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.610015165931117 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.303588602711922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233038&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]0.610015165931117[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.303588602711922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233038&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233038&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
alpha0.610015165931117
beta0
gamma0.303588602711922







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1347365149.06761681428-413.067616814284
1442194336.55484123937-117.554841239371
1551165180.90100029475-64.9010002947462
1642054210.5556333383-5.55563333830469
1741214058.9103792325962.0896207674109
1851035050.3568068251152.6431931748884
1943004080.08616175122219.913838248784
2045784335.70724697579242.292753024211
2138094771.97273703701-962.972737037015
2256574375.601203222551281.39879677745
2342494118.01548334321130.984516656787
2438304706.58836861052-876.588368610515
2547364210.20414250609525.795857493911
2648404036.66653420593803.33346579407
2744135512.31429393059-1099.31429393059
2845713967.94066850558603.059331494418
2941064192.54585154443-86.5458515444279
3048015100.90697223229-299.906972232287
3139563966.04113281231-10.0411328123082
3238294071.85924299583-242.859242995829
3344534030.21932750016422.780672499845
3440274747.99928429867-720.999284298673
3541213346.00668929311774.993310706889
3647984155.2077879052642.792212094802
3732334776.73864274318-1543.73864274318
3835543433.70201138384120.29798861616
3939524057.55289756198-105.552897561985
4039513411.29531330446539.704686695541
4136853542.85171345588142.14828654412
4243124444.37803043155-132.378030431553
4338673538.76310483849328.236895161509
4441403815.09008683023324.909913169767
4541144202.62611969863-88.6261196986343
4638184448.1785594974-630.178559497402
4733773295.6953865276881.3046134723181
4834533607.18907446694-154.189074466944
4935023445.2263507708656.7736492291424
5040173282.75388374713734.246116252869
5154104288.448977798231121.55102220177
5251844345.80476932697838.19523067303
5355294556.39685390462972.603146095378
5464346276.57252878113157.427471218872
5549625261.63294157095-299.632941570948
5629805194.18524982359-2214.18524982359
5729373974.01193611086-1037.01193611086
5829693515.81288115566-546.81288115566
5927312627.74606207479103.253937925213
6031632868.60657763952294.393422360483
6131453004.60135842359140.398641576413
6231732972.09747600681200.90252399319
6337233558.88632432131164.113675678694
6432243164.7228497393659.2771502606365
6541142992.346454517631121.65354548237
6634464379.42830921129-933.428309211289
6729553096.53285309737-141.532853097366
6838792871.179516743271007.82048325673
6942783724.78055117916553.219448820837
7041774360.46779707213-183.467797072135
7136983613.3708652294884.6291347705192
7244493951.20898247121497.79101752879
7341624187.12133724357-25.1213372435686
7439614037.58028282926-76.5802828292562
7552464594.00644254261651.993557457394
7651704321.10689469989848.893105300112
7736824700.68340282164-1018.68340282164
7834954557.44587743487-1062.44587743487
7937703256.48586241219513.514137587808
8032913549.81901138467-258.81901138467
8135803558.0249787888421.9750212111571
8238983746.62331339093151.376686609069
8334773286.71420555411190.285794445895
8430543705.5872946898-651.587294689797

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4736 & 5149.06761681428 & -413.067616814284 \tabularnewline
14 & 4219 & 4336.55484123937 & -117.554841239371 \tabularnewline
15 & 5116 & 5180.90100029475 & -64.9010002947462 \tabularnewline
16 & 4205 & 4210.5556333383 & -5.55563333830469 \tabularnewline
17 & 4121 & 4058.91037923259 & 62.0896207674109 \tabularnewline
18 & 5103 & 5050.35680682511 & 52.6431931748884 \tabularnewline
19 & 4300 & 4080.08616175122 & 219.913838248784 \tabularnewline
20 & 4578 & 4335.70724697579 & 242.292753024211 \tabularnewline
21 & 3809 & 4771.97273703701 & -962.972737037015 \tabularnewline
22 & 5657 & 4375.60120322255 & 1281.39879677745 \tabularnewline
23 & 4249 & 4118.01548334321 & 130.984516656787 \tabularnewline
24 & 3830 & 4706.58836861052 & -876.588368610515 \tabularnewline
25 & 4736 & 4210.20414250609 & 525.795857493911 \tabularnewline
26 & 4840 & 4036.66653420593 & 803.33346579407 \tabularnewline
27 & 4413 & 5512.31429393059 & -1099.31429393059 \tabularnewline
28 & 4571 & 3967.94066850558 & 603.059331494418 \tabularnewline
29 & 4106 & 4192.54585154443 & -86.5458515444279 \tabularnewline
30 & 4801 & 5100.90697223229 & -299.906972232287 \tabularnewline
31 & 3956 & 3966.04113281231 & -10.0411328123082 \tabularnewline
32 & 3829 & 4071.85924299583 & -242.859242995829 \tabularnewline
33 & 4453 & 4030.21932750016 & 422.780672499845 \tabularnewline
34 & 4027 & 4747.99928429867 & -720.999284298673 \tabularnewline
35 & 4121 & 3346.00668929311 & 774.993310706889 \tabularnewline
36 & 4798 & 4155.2077879052 & 642.792212094802 \tabularnewline
37 & 3233 & 4776.73864274318 & -1543.73864274318 \tabularnewline
38 & 3554 & 3433.70201138384 & 120.29798861616 \tabularnewline
39 & 3952 & 4057.55289756198 & -105.552897561985 \tabularnewline
40 & 3951 & 3411.29531330446 & 539.704686695541 \tabularnewline
41 & 3685 & 3542.85171345588 & 142.14828654412 \tabularnewline
42 & 4312 & 4444.37803043155 & -132.378030431553 \tabularnewline
43 & 3867 & 3538.76310483849 & 328.236895161509 \tabularnewline
44 & 4140 & 3815.09008683023 & 324.909913169767 \tabularnewline
45 & 4114 & 4202.62611969863 & -88.6261196986343 \tabularnewline
46 & 3818 & 4448.1785594974 & -630.178559497402 \tabularnewline
47 & 3377 & 3295.69538652768 & 81.3046134723181 \tabularnewline
48 & 3453 & 3607.18907446694 & -154.189074466944 \tabularnewline
49 & 3502 & 3445.22635077086 & 56.7736492291424 \tabularnewline
50 & 4017 & 3282.75388374713 & 734.246116252869 \tabularnewline
51 & 5410 & 4288.44897779823 & 1121.55102220177 \tabularnewline
52 & 5184 & 4345.80476932697 & 838.19523067303 \tabularnewline
53 & 5529 & 4556.39685390462 & 972.603146095378 \tabularnewline
54 & 6434 & 6276.57252878113 & 157.427471218872 \tabularnewline
55 & 4962 & 5261.63294157095 & -299.632941570948 \tabularnewline
56 & 2980 & 5194.18524982359 & -2214.18524982359 \tabularnewline
57 & 2937 & 3974.01193611086 & -1037.01193611086 \tabularnewline
58 & 2969 & 3515.81288115566 & -546.81288115566 \tabularnewline
59 & 2731 & 2627.74606207479 & 103.253937925213 \tabularnewline
60 & 3163 & 2868.60657763952 & 294.393422360483 \tabularnewline
61 & 3145 & 3004.60135842359 & 140.398641576413 \tabularnewline
62 & 3173 & 2972.09747600681 & 200.90252399319 \tabularnewline
63 & 3723 & 3558.88632432131 & 164.113675678694 \tabularnewline
64 & 3224 & 3164.72284973936 & 59.2771502606365 \tabularnewline
65 & 4114 & 2992.34645451763 & 1121.65354548237 \tabularnewline
66 & 3446 & 4379.42830921129 & -933.428309211289 \tabularnewline
67 & 2955 & 3096.53285309737 & -141.532853097366 \tabularnewline
68 & 3879 & 2871.17951674327 & 1007.82048325673 \tabularnewline
69 & 4278 & 3724.78055117916 & 553.219448820837 \tabularnewline
70 & 4177 & 4360.46779707213 & -183.467797072135 \tabularnewline
71 & 3698 & 3613.37086522948 & 84.6291347705192 \tabularnewline
72 & 4449 & 3951.20898247121 & 497.79101752879 \tabularnewline
73 & 4162 & 4187.12133724357 & -25.1213372435686 \tabularnewline
74 & 3961 & 4037.58028282926 & -76.5802828292562 \tabularnewline
75 & 5246 & 4594.00644254261 & 651.993557457394 \tabularnewline
76 & 5170 & 4321.10689469989 & 848.893105300112 \tabularnewline
77 & 3682 & 4700.68340282164 & -1018.68340282164 \tabularnewline
78 & 3495 & 4557.44587743487 & -1062.44587743487 \tabularnewline
79 & 3770 & 3256.48586241219 & 513.514137587808 \tabularnewline
80 & 3291 & 3549.81901138467 & -258.81901138467 \tabularnewline
81 & 3580 & 3558.02497878884 & 21.9750212111571 \tabularnewline
82 & 3898 & 3746.62331339093 & 151.376686609069 \tabularnewline
83 & 3477 & 3286.71420555411 & 190.285794445895 \tabularnewline
84 & 3054 & 3705.5872946898 & -651.587294689797 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233038&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]4736[/C][C]5149.06761681428[/C][C]-413.067616814284[/C][/ROW]
[ROW][C]14[/C][C]4219[/C][C]4336.55484123937[/C][C]-117.554841239371[/C][/ROW]
[ROW][C]15[/C][C]5116[/C][C]5180.90100029475[/C][C]-64.9010002947462[/C][/ROW]
[ROW][C]16[/C][C]4205[/C][C]4210.5556333383[/C][C]-5.55563333830469[/C][/ROW]
[ROW][C]17[/C][C]4121[/C][C]4058.91037923259[/C][C]62.0896207674109[/C][/ROW]
[ROW][C]18[/C][C]5103[/C][C]5050.35680682511[/C][C]52.6431931748884[/C][/ROW]
[ROW][C]19[/C][C]4300[/C][C]4080.08616175122[/C][C]219.913838248784[/C][/ROW]
[ROW][C]20[/C][C]4578[/C][C]4335.70724697579[/C][C]242.292753024211[/C][/ROW]
[ROW][C]21[/C][C]3809[/C][C]4771.97273703701[/C][C]-962.972737037015[/C][/ROW]
[ROW][C]22[/C][C]5657[/C][C]4375.60120322255[/C][C]1281.39879677745[/C][/ROW]
[ROW][C]23[/C][C]4249[/C][C]4118.01548334321[/C][C]130.984516656787[/C][/ROW]
[ROW][C]24[/C][C]3830[/C][C]4706.58836861052[/C][C]-876.588368610515[/C][/ROW]
[ROW][C]25[/C][C]4736[/C][C]4210.20414250609[/C][C]525.795857493911[/C][/ROW]
[ROW][C]26[/C][C]4840[/C][C]4036.66653420593[/C][C]803.33346579407[/C][/ROW]
[ROW][C]27[/C][C]4413[/C][C]5512.31429393059[/C][C]-1099.31429393059[/C][/ROW]
[ROW][C]28[/C][C]4571[/C][C]3967.94066850558[/C][C]603.059331494418[/C][/ROW]
[ROW][C]29[/C][C]4106[/C][C]4192.54585154443[/C][C]-86.5458515444279[/C][/ROW]
[ROW][C]30[/C][C]4801[/C][C]5100.90697223229[/C][C]-299.906972232287[/C][/ROW]
[ROW][C]31[/C][C]3956[/C][C]3966.04113281231[/C][C]-10.0411328123082[/C][/ROW]
[ROW][C]32[/C][C]3829[/C][C]4071.85924299583[/C][C]-242.859242995829[/C][/ROW]
[ROW][C]33[/C][C]4453[/C][C]4030.21932750016[/C][C]422.780672499845[/C][/ROW]
[ROW][C]34[/C][C]4027[/C][C]4747.99928429867[/C][C]-720.999284298673[/C][/ROW]
[ROW][C]35[/C][C]4121[/C][C]3346.00668929311[/C][C]774.993310706889[/C][/ROW]
[ROW][C]36[/C][C]4798[/C][C]4155.2077879052[/C][C]642.792212094802[/C][/ROW]
[ROW][C]37[/C][C]3233[/C][C]4776.73864274318[/C][C]-1543.73864274318[/C][/ROW]
[ROW][C]38[/C][C]3554[/C][C]3433.70201138384[/C][C]120.29798861616[/C][/ROW]
[ROW][C]39[/C][C]3952[/C][C]4057.55289756198[/C][C]-105.552897561985[/C][/ROW]
[ROW][C]40[/C][C]3951[/C][C]3411.29531330446[/C][C]539.704686695541[/C][/ROW]
[ROW][C]41[/C][C]3685[/C][C]3542.85171345588[/C][C]142.14828654412[/C][/ROW]
[ROW][C]42[/C][C]4312[/C][C]4444.37803043155[/C][C]-132.378030431553[/C][/ROW]
[ROW][C]43[/C][C]3867[/C][C]3538.76310483849[/C][C]328.236895161509[/C][/ROW]
[ROW][C]44[/C][C]4140[/C][C]3815.09008683023[/C][C]324.909913169767[/C][/ROW]
[ROW][C]45[/C][C]4114[/C][C]4202.62611969863[/C][C]-88.6261196986343[/C][/ROW]
[ROW][C]46[/C][C]3818[/C][C]4448.1785594974[/C][C]-630.178559497402[/C][/ROW]
[ROW][C]47[/C][C]3377[/C][C]3295.69538652768[/C][C]81.3046134723181[/C][/ROW]
[ROW][C]48[/C][C]3453[/C][C]3607.18907446694[/C][C]-154.189074466944[/C][/ROW]
[ROW][C]49[/C][C]3502[/C][C]3445.22635077086[/C][C]56.7736492291424[/C][/ROW]
[ROW][C]50[/C][C]4017[/C][C]3282.75388374713[/C][C]734.246116252869[/C][/ROW]
[ROW][C]51[/C][C]5410[/C][C]4288.44897779823[/C][C]1121.55102220177[/C][/ROW]
[ROW][C]52[/C][C]5184[/C][C]4345.80476932697[/C][C]838.19523067303[/C][/ROW]
[ROW][C]53[/C][C]5529[/C][C]4556.39685390462[/C][C]972.603146095378[/C][/ROW]
[ROW][C]54[/C][C]6434[/C][C]6276.57252878113[/C][C]157.427471218872[/C][/ROW]
[ROW][C]55[/C][C]4962[/C][C]5261.63294157095[/C][C]-299.632941570948[/C][/ROW]
[ROW][C]56[/C][C]2980[/C][C]5194.18524982359[/C][C]-2214.18524982359[/C][/ROW]
[ROW][C]57[/C][C]2937[/C][C]3974.01193611086[/C][C]-1037.01193611086[/C][/ROW]
[ROW][C]58[/C][C]2969[/C][C]3515.81288115566[/C][C]-546.81288115566[/C][/ROW]
[ROW][C]59[/C][C]2731[/C][C]2627.74606207479[/C][C]103.253937925213[/C][/ROW]
[ROW][C]60[/C][C]3163[/C][C]2868.60657763952[/C][C]294.393422360483[/C][/ROW]
[ROW][C]61[/C][C]3145[/C][C]3004.60135842359[/C][C]140.398641576413[/C][/ROW]
[ROW][C]62[/C][C]3173[/C][C]2972.09747600681[/C][C]200.90252399319[/C][/ROW]
[ROW][C]63[/C][C]3723[/C][C]3558.88632432131[/C][C]164.113675678694[/C][/ROW]
[ROW][C]64[/C][C]3224[/C][C]3164.72284973936[/C][C]59.2771502606365[/C][/ROW]
[ROW][C]65[/C][C]4114[/C][C]2992.34645451763[/C][C]1121.65354548237[/C][/ROW]
[ROW][C]66[/C][C]3446[/C][C]4379.42830921129[/C][C]-933.428309211289[/C][/ROW]
[ROW][C]67[/C][C]2955[/C][C]3096.53285309737[/C][C]-141.532853097366[/C][/ROW]
[ROW][C]68[/C][C]3879[/C][C]2871.17951674327[/C][C]1007.82048325673[/C][/ROW]
[ROW][C]69[/C][C]4278[/C][C]3724.78055117916[/C][C]553.219448820837[/C][/ROW]
[ROW][C]70[/C][C]4177[/C][C]4360.46779707213[/C][C]-183.467797072135[/C][/ROW]
[ROW][C]71[/C][C]3698[/C][C]3613.37086522948[/C][C]84.6291347705192[/C][/ROW]
[ROW][C]72[/C][C]4449[/C][C]3951.20898247121[/C][C]497.79101752879[/C][/ROW]
[ROW][C]73[/C][C]4162[/C][C]4187.12133724357[/C][C]-25.1213372435686[/C][/ROW]
[ROW][C]74[/C][C]3961[/C][C]4037.58028282926[/C][C]-76.5802828292562[/C][/ROW]
[ROW][C]75[/C][C]5246[/C][C]4594.00644254261[/C][C]651.993557457394[/C][/ROW]
[ROW][C]76[/C][C]5170[/C][C]4321.10689469989[/C][C]848.893105300112[/C][/ROW]
[ROW][C]77[/C][C]3682[/C][C]4700.68340282164[/C][C]-1018.68340282164[/C][/ROW]
[ROW][C]78[/C][C]3495[/C][C]4557.44587743487[/C][C]-1062.44587743487[/C][/ROW]
[ROW][C]79[/C][C]3770[/C][C]3256.48586241219[/C][C]513.514137587808[/C][/ROW]
[ROW][C]80[/C][C]3291[/C][C]3549.81901138467[/C][C]-258.81901138467[/C][/ROW]
[ROW][C]81[/C][C]3580[/C][C]3558.02497878884[/C][C]21.9750212111571[/C][/ROW]
[ROW][C]82[/C][C]3898[/C][C]3746.62331339093[/C][C]151.376686609069[/C][/ROW]
[ROW][C]83[/C][C]3477[/C][C]3286.71420555411[/C][C]190.285794445895[/C][/ROW]
[ROW][C]84[/C][C]3054[/C][C]3705.5872946898[/C][C]-651.587294689797[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233038&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233038&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
1347365149.06761681428-413.067616814284
1442194336.55484123937-117.554841239371
1551165180.90100029475-64.9010002947462
1642054210.5556333383-5.55563333830469
1741214058.9103792325962.0896207674109
1851035050.3568068251152.6431931748884
1943004080.08616175122219.913838248784
2045784335.70724697579242.292753024211
2138094771.97273703701-962.972737037015
2256574375.601203222551281.39879677745
2342494118.01548334321130.984516656787
2438304706.58836861052-876.588368610515
2547364210.20414250609525.795857493911
2648404036.66653420593803.33346579407
2744135512.31429393059-1099.31429393059
2845713967.94066850558603.059331494418
2941064192.54585154443-86.5458515444279
3048015100.90697223229-299.906972232287
3139563966.04113281231-10.0411328123082
3238294071.85924299583-242.859242995829
3344534030.21932750016422.780672499845
3440274747.99928429867-720.999284298673
3541213346.00668929311774.993310706889
3647984155.2077879052642.792212094802
3732334776.73864274318-1543.73864274318
3835543433.70201138384120.29798861616
3939524057.55289756198-105.552897561985
4039513411.29531330446539.704686695541
4136853542.85171345588142.14828654412
4243124444.37803043155-132.378030431553
4338673538.76310483849328.236895161509
4441403815.09008683023324.909913169767
4541144202.62611969863-88.6261196986343
4638184448.1785594974-630.178559497402
4733773295.6953865276881.3046134723181
4834533607.18907446694-154.189074466944
4935023445.2263507708656.7736492291424
5040173282.75388374713734.246116252869
5154104288.448977798231121.55102220177
5251844345.80476932697838.19523067303
5355294556.39685390462972.603146095378
5464346276.57252878113157.427471218872
5549625261.63294157095-299.632941570948
5629805194.18524982359-2214.18524982359
5729373974.01193611086-1037.01193611086
5829693515.81288115566-546.81288115566
5927312627.74606207479103.253937925213
6031632868.60657763952294.393422360483
6131453004.60135842359140.398641576413
6231732972.09747600681200.90252399319
6337233558.88632432131164.113675678694
6432243164.7228497393659.2771502606365
6541142992.346454517631121.65354548237
6634464379.42830921129-933.428309211289
6729553096.53285309737-141.532853097366
6838792871.179516743271007.82048325673
6942783724.78055117916553.219448820837
7041774360.46779707213-183.467797072135
7136983613.3708652294884.6291347705192
7244493951.20898247121497.79101752879
7341624187.12133724357-25.1213372435686
7439614037.58028282926-76.5802828292562
7552464594.00644254261651.993557457394
7651704321.10689469989848.893105300112
7736824700.68340282164-1018.68340282164
7834954557.44587743487-1062.44587743487
7937703256.48586241219513.514137587808
8032913549.81901138467-258.81901138467
8135803558.0249787888421.9750212111571
8238983746.62331339093151.376686609069
8334773286.71420555411190.285794445895
8430543705.5872946898-651.587294689797







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853197.510520330482280.634854205944114.38618645501
863078.908323577771893.974884671054263.84176248449
873594.649138071862025.83918728145163.45908886232
883113.78106088871516.471375044814711.09074673258
892858.827364564241173.015584035794544.6391450927
903171.092064581571138.245284148135203.938845015
912768.45943774686794.3494710285624742.56940446516
922671.84549850325585.8932298553214757.79776715119
932820.44638234011461.1494461122485179.74331856798
942959.65273381767333.2896978193175586.01576981603
952528.46166977417106.8784742675484950.04486528079
962659.0797505548122.789503101255195.36999800836

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3197.51052033048 & 2280.63485420594 & 4114.38618645501 \tabularnewline
86 & 3078.90832357777 & 1893.97488467105 & 4263.84176248449 \tabularnewline
87 & 3594.64913807186 & 2025.8391872814 & 5163.45908886232 \tabularnewline
88 & 3113.7810608887 & 1516.47137504481 & 4711.09074673258 \tabularnewline
89 & 2858.82736456424 & 1173.01558403579 & 4544.6391450927 \tabularnewline
90 & 3171.09206458157 & 1138.24528414813 & 5203.938845015 \tabularnewline
91 & 2768.45943774686 & 794.349471028562 & 4742.56940446516 \tabularnewline
92 & 2671.84549850325 & 585.893229855321 & 4757.79776715119 \tabularnewline
93 & 2820.44638234011 & 461.149446112248 & 5179.74331856798 \tabularnewline
94 & 2959.65273381767 & 333.289697819317 & 5586.01576981603 \tabularnewline
95 & 2528.46166977417 & 106.878474267548 & 4950.04486528079 \tabularnewline
96 & 2659.0797505548 & 122.78950310125 & 5195.36999800836 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233038&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]85[/C][C]3197.51052033048[/C][C]2280.63485420594[/C][C]4114.38618645501[/C][/ROW]
[ROW][C]86[/C][C]3078.90832357777[/C][C]1893.97488467105[/C][C]4263.84176248449[/C][/ROW]
[ROW][C]87[/C][C]3594.64913807186[/C][C]2025.8391872814[/C][C]5163.45908886232[/C][/ROW]
[ROW][C]88[/C][C]3113.7810608887[/C][C]1516.47137504481[/C][C]4711.09074673258[/C][/ROW]
[ROW][C]89[/C][C]2858.82736456424[/C][C]1173.01558403579[/C][C]4544.6391450927[/C][/ROW]
[ROW][C]90[/C][C]3171.09206458157[/C][C]1138.24528414813[/C][C]5203.938845015[/C][/ROW]
[ROW][C]91[/C][C]2768.45943774686[/C][C]794.349471028562[/C][C]4742.56940446516[/C][/ROW]
[ROW][C]92[/C][C]2671.84549850325[/C][C]585.893229855321[/C][C]4757.79776715119[/C][/ROW]
[ROW][C]93[/C][C]2820.44638234011[/C][C]461.149446112248[/C][C]5179.74331856798[/C][/ROW]
[ROW][C]94[/C][C]2959.65273381767[/C][C]333.289697819317[/C][C]5586.01576981603[/C][/ROW]
[ROW][C]95[/C][C]2528.46166977417[/C][C]106.878474267548[/C][C]4950.04486528079[/C][/ROW]
[ROW][C]96[/C][C]2659.0797505548[/C][C]122.78950310125[/C][C]5195.36999800836[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233038&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233038&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
853197.510520330482280.634854205944114.38618645501
863078.908323577771893.974884671054263.84176248449
873594.649138071862025.83918728145163.45908886232
883113.78106088871516.471375044814711.09074673258
892858.827364564241173.015584035794544.6391450927
903171.092064581571138.245284148135203.938845015
912768.45943774686794.3494710285624742.56940446516
922671.84549850325585.8932298553214757.79776715119
932820.44638234011461.1494461122485179.74331856798
942959.65273381767333.2896978193175586.01576981603
952528.46166977417106.8784742675484950.04486528079
962659.0797505548122.789503101255195.36999800836



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