Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 16 Jan 2010 07:53:52 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/16/t12636537410e1w5z5o7pk6q1c.htm/, Retrieved Thu, 31 Oct 2024 23:28:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72234, Retrieved Thu, 31 Oct 2024 23:28:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact196
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2010-01-16 14:53:52] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2766
3851
3289
3848
3348
3682
4058
3655
3811
3341
3032
3475
3353
3186
3902
4164
3499
4145
3796
3711
3949
3740
3243
4407
4814
3908
5250
3937
4004
5560
3922
3759
4138
4634
3996
4308
4143
4429
5219
4929
5761
5592
4163
4962
5208
4755
4491
5732
5731
5040
6102
4904
5369
5578
4619
4731
5011
5299
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5526
4248
3830
4430
4837
4408
4569
4104
4807
3944
3794
4390
4041
4104
4823




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72234&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72234&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72234&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.246198542886314
beta0
gamma0.397334337843492

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.246198542886314 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.397334337843492 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72234&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]0.246198542886314[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.397334337843492[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72234&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72234&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
alpha0.246198542886314
beta0
gamma0.397334337843492







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1333533222.9249465812130.075053418801
1431863111.8479822850174.152017714986
1539023853.336181418148.6638185818956
1641644120.2575563971643.7424436028359
1734993455.9256293607243.0743706392841
1841454080.2208904007764.7791095992334
1937964206.10982654648-410.109826546484
2037113720.70679858029-9.70679858029416
2139493891.7990793333257.2009206666844
2237403412.48894307279327.511056927212
2332433179.9787684870163.0212315129947
2444073628.22658427599778.773415724014
2548143743.858813926091070.14118607391
2639083847.4751860169460.5248139830587
2752504577.97438626735672.025613732649
2839374996.89251996398-1059.89251996398
2940044060.6471776821-56.6471776821008
3055604666.89195130402893.108048695985
3139224854.47970881134-932.479708811336
3237594360.39516950586-601.395169505861
3341384405.85424696435-267.854246964353
3446343927.47691612331706.523083876686
3539963709.06128456337286.938715436627
3643084426.81305624074-118.813056240736
3741434408.72871574138-265.728715741384
3844293881.06445052013547.935549479871
3952194914.71480370012304.285196299883
4049294724.36689904177204.633100958234
4157614399.929141271511361.07085872849
4255925639.67635992577-47.6763599257747
4341635048.86038174167-885.860381741668
4449624665.41698143613296.583018563868
4552085031.85622324376176.143776756239
4647554954.6274852554-199.627485255402
4744914387.44868506034103.551314939656
4857324938.52354476708793.476455232923
4957315101.04066679174629.95933320826
5050405037.595056876932.40494312307237
5161025863.96055932165238.039440678354
5249045627.45612721679-723.456127216791
5353695420.89021762652-51.8902176265246
5455785890.83290418776-312.832904187757
5546194983.69026660452-364.690266604521
5647315082.71323434286-351.713234342859
5750115253.46998114473-242.469981144732
5852994960.63144325579338.368556744208
5941464616.71193179793-470.71193179793
6046255233.04432555503-608.044325555029
6147365001.53386362427-265.533863624275
6242194529.65956327045-310.659563270452
6351165349.52421220215-233.524212202151
6442054708.94280182617-503.942801826167
6541214757.56226645068-636.562266450677
6651035005.40428860497.5957113960058
6743004183.77671714341116.223282856590
6845784405.08666655518172.913333444816
6938094737.72528807202-928.725288072015
7055264449.899342701391076.10065729861
7142484045.27972913278202.720270867217
7238304786.27755947736-956.277559477362
7344304571.6183032043-141.6183032043
7448374116.73618068735720.263819312652
7544085213.51556601744-805.515566017442
7645694351.1173207433217.882679256702
7741044537.72815166057-433.728151660567
7848075055.39617633328-248.396176333275
7939444154.16507259718-210.165072597176
8037944312.09798972122-518.097989721216
8143904144.65752174464245.342478255357
8240414746.3531800518-705.353180051795
8341043641.55501744207462.444982557926
8448234099.36385911524723.636140884755

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3353 & 3222.9249465812 & 130.075053418801 \tabularnewline
14 & 3186 & 3111.84798228501 & 74.152017714986 \tabularnewline
15 & 3902 & 3853.3361814181 & 48.6638185818956 \tabularnewline
16 & 4164 & 4120.25755639716 & 43.7424436028359 \tabularnewline
17 & 3499 & 3455.92562936072 & 43.0743706392841 \tabularnewline
18 & 4145 & 4080.22089040077 & 64.7791095992334 \tabularnewline
19 & 3796 & 4206.10982654648 & -410.109826546484 \tabularnewline
20 & 3711 & 3720.70679858029 & -9.70679858029416 \tabularnewline
21 & 3949 & 3891.79907933332 & 57.2009206666844 \tabularnewline
22 & 3740 & 3412.48894307279 & 327.511056927212 \tabularnewline
23 & 3243 & 3179.97876848701 & 63.0212315129947 \tabularnewline
24 & 4407 & 3628.22658427599 & 778.773415724014 \tabularnewline
25 & 4814 & 3743.85881392609 & 1070.14118607391 \tabularnewline
26 & 3908 & 3847.47518601694 & 60.5248139830587 \tabularnewline
27 & 5250 & 4577.97438626735 & 672.025613732649 \tabularnewline
28 & 3937 & 4996.89251996398 & -1059.89251996398 \tabularnewline
29 & 4004 & 4060.6471776821 & -56.6471776821008 \tabularnewline
30 & 5560 & 4666.89195130402 & 893.108048695985 \tabularnewline
31 & 3922 & 4854.47970881134 & -932.479708811336 \tabularnewline
32 & 3759 & 4360.39516950586 & -601.395169505861 \tabularnewline
33 & 4138 & 4405.85424696435 & -267.854246964353 \tabularnewline
34 & 4634 & 3927.47691612331 & 706.523083876686 \tabularnewline
35 & 3996 & 3709.06128456337 & 286.938715436627 \tabularnewline
36 & 4308 & 4426.81305624074 & -118.813056240736 \tabularnewline
37 & 4143 & 4408.72871574138 & -265.728715741384 \tabularnewline
38 & 4429 & 3881.06445052013 & 547.935549479871 \tabularnewline
39 & 5219 & 4914.71480370012 & 304.285196299883 \tabularnewline
40 & 4929 & 4724.36689904177 & 204.633100958234 \tabularnewline
41 & 5761 & 4399.92914127151 & 1361.07085872849 \tabularnewline
42 & 5592 & 5639.67635992577 & -47.6763599257747 \tabularnewline
43 & 4163 & 5048.86038174167 & -885.860381741668 \tabularnewline
44 & 4962 & 4665.41698143613 & 296.583018563868 \tabularnewline
45 & 5208 & 5031.85622324376 & 176.143776756239 \tabularnewline
46 & 4755 & 4954.6274852554 & -199.627485255402 \tabularnewline
47 & 4491 & 4387.44868506034 & 103.551314939656 \tabularnewline
48 & 5732 & 4938.52354476708 & 793.476455232923 \tabularnewline
49 & 5731 & 5101.04066679174 & 629.95933320826 \tabularnewline
50 & 5040 & 5037.59505687693 & 2.40494312307237 \tabularnewline
51 & 6102 & 5863.96055932165 & 238.039440678354 \tabularnewline
52 & 4904 & 5627.45612721679 & -723.456127216791 \tabularnewline
53 & 5369 & 5420.89021762652 & -51.8902176265246 \tabularnewline
54 & 5578 & 5890.83290418776 & -312.832904187757 \tabularnewline
55 & 4619 & 4983.69026660452 & -364.690266604521 \tabularnewline
56 & 4731 & 5082.71323434286 & -351.713234342859 \tabularnewline
57 & 5011 & 5253.46998114473 & -242.469981144732 \tabularnewline
58 & 5299 & 4960.63144325579 & 338.368556744208 \tabularnewline
59 & 4146 & 4616.71193179793 & -470.71193179793 \tabularnewline
60 & 4625 & 5233.04432555503 & -608.044325555029 \tabularnewline
61 & 4736 & 5001.53386362427 & -265.533863624275 \tabularnewline
62 & 4219 & 4529.65956327045 & -310.659563270452 \tabularnewline
63 & 5116 & 5349.52421220215 & -233.524212202151 \tabularnewline
64 & 4205 & 4708.94280182617 & -503.942801826167 \tabularnewline
65 & 4121 & 4757.56226645068 & -636.562266450677 \tabularnewline
66 & 5103 & 5005.404288604 & 97.5957113960058 \tabularnewline
67 & 4300 & 4183.77671714341 & 116.223282856590 \tabularnewline
68 & 4578 & 4405.08666655518 & 172.913333444816 \tabularnewline
69 & 3809 & 4737.72528807202 & -928.725288072015 \tabularnewline
70 & 5526 & 4449.89934270139 & 1076.10065729861 \tabularnewline
71 & 4248 & 4045.27972913278 & 202.720270867217 \tabularnewline
72 & 3830 & 4786.27755947736 & -956.277559477362 \tabularnewline
73 & 4430 & 4571.6183032043 & -141.6183032043 \tabularnewline
74 & 4837 & 4116.73618068735 & 720.263819312652 \tabularnewline
75 & 4408 & 5213.51556601744 & -805.515566017442 \tabularnewline
76 & 4569 & 4351.1173207433 & 217.882679256702 \tabularnewline
77 & 4104 & 4537.72815166057 & -433.728151660567 \tabularnewline
78 & 4807 & 5055.39617633328 & -248.396176333275 \tabularnewline
79 & 3944 & 4154.16507259718 & -210.165072597176 \tabularnewline
80 & 3794 & 4312.09798972122 & -518.097989721216 \tabularnewline
81 & 4390 & 4144.65752174464 & 245.342478255357 \tabularnewline
82 & 4041 & 4746.3531800518 & -705.353180051795 \tabularnewline
83 & 4104 & 3641.55501744207 & 462.444982557926 \tabularnewline
84 & 4823 & 4099.36385911524 & 723.636140884755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72234&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]3353[/C][C]3222.9249465812[/C][C]130.075053418801[/C][/ROW]
[ROW][C]14[/C][C]3186[/C][C]3111.84798228501[/C][C]74.152017714986[/C][/ROW]
[ROW][C]15[/C][C]3902[/C][C]3853.3361814181[/C][C]48.6638185818956[/C][/ROW]
[ROW][C]16[/C][C]4164[/C][C]4120.25755639716[/C][C]43.7424436028359[/C][/ROW]
[ROW][C]17[/C][C]3499[/C][C]3455.92562936072[/C][C]43.0743706392841[/C][/ROW]
[ROW][C]18[/C][C]4145[/C][C]4080.22089040077[/C][C]64.7791095992334[/C][/ROW]
[ROW][C]19[/C][C]3796[/C][C]4206.10982654648[/C][C]-410.109826546484[/C][/ROW]
[ROW][C]20[/C][C]3711[/C][C]3720.70679858029[/C][C]-9.70679858029416[/C][/ROW]
[ROW][C]21[/C][C]3949[/C][C]3891.79907933332[/C][C]57.2009206666844[/C][/ROW]
[ROW][C]22[/C][C]3740[/C][C]3412.48894307279[/C][C]327.511056927212[/C][/ROW]
[ROW][C]23[/C][C]3243[/C][C]3179.97876848701[/C][C]63.0212315129947[/C][/ROW]
[ROW][C]24[/C][C]4407[/C][C]3628.22658427599[/C][C]778.773415724014[/C][/ROW]
[ROW][C]25[/C][C]4814[/C][C]3743.85881392609[/C][C]1070.14118607391[/C][/ROW]
[ROW][C]26[/C][C]3908[/C][C]3847.47518601694[/C][C]60.5248139830587[/C][/ROW]
[ROW][C]27[/C][C]5250[/C][C]4577.97438626735[/C][C]672.025613732649[/C][/ROW]
[ROW][C]28[/C][C]3937[/C][C]4996.89251996398[/C][C]-1059.89251996398[/C][/ROW]
[ROW][C]29[/C][C]4004[/C][C]4060.6471776821[/C][C]-56.6471776821008[/C][/ROW]
[ROW][C]30[/C][C]5560[/C][C]4666.89195130402[/C][C]893.108048695985[/C][/ROW]
[ROW][C]31[/C][C]3922[/C][C]4854.47970881134[/C][C]-932.479708811336[/C][/ROW]
[ROW][C]32[/C][C]3759[/C][C]4360.39516950586[/C][C]-601.395169505861[/C][/ROW]
[ROW][C]33[/C][C]4138[/C][C]4405.85424696435[/C][C]-267.854246964353[/C][/ROW]
[ROW][C]34[/C][C]4634[/C][C]3927.47691612331[/C][C]706.523083876686[/C][/ROW]
[ROW][C]35[/C][C]3996[/C][C]3709.06128456337[/C][C]286.938715436627[/C][/ROW]
[ROW][C]36[/C][C]4308[/C][C]4426.81305624074[/C][C]-118.813056240736[/C][/ROW]
[ROW][C]37[/C][C]4143[/C][C]4408.72871574138[/C][C]-265.728715741384[/C][/ROW]
[ROW][C]38[/C][C]4429[/C][C]3881.06445052013[/C][C]547.935549479871[/C][/ROW]
[ROW][C]39[/C][C]5219[/C][C]4914.71480370012[/C][C]304.285196299883[/C][/ROW]
[ROW][C]40[/C][C]4929[/C][C]4724.36689904177[/C][C]204.633100958234[/C][/ROW]
[ROW][C]41[/C][C]5761[/C][C]4399.92914127151[/C][C]1361.07085872849[/C][/ROW]
[ROW][C]42[/C][C]5592[/C][C]5639.67635992577[/C][C]-47.6763599257747[/C][/ROW]
[ROW][C]43[/C][C]4163[/C][C]5048.86038174167[/C][C]-885.860381741668[/C][/ROW]
[ROW][C]44[/C][C]4962[/C][C]4665.41698143613[/C][C]296.583018563868[/C][/ROW]
[ROW][C]45[/C][C]5208[/C][C]5031.85622324376[/C][C]176.143776756239[/C][/ROW]
[ROW][C]46[/C][C]4755[/C][C]4954.6274852554[/C][C]-199.627485255402[/C][/ROW]
[ROW][C]47[/C][C]4491[/C][C]4387.44868506034[/C][C]103.551314939656[/C][/ROW]
[ROW][C]48[/C][C]5732[/C][C]4938.52354476708[/C][C]793.476455232923[/C][/ROW]
[ROW][C]49[/C][C]5731[/C][C]5101.04066679174[/C][C]629.95933320826[/C][/ROW]
[ROW][C]50[/C][C]5040[/C][C]5037.59505687693[/C][C]2.40494312307237[/C][/ROW]
[ROW][C]51[/C][C]6102[/C][C]5863.96055932165[/C][C]238.039440678354[/C][/ROW]
[ROW][C]52[/C][C]4904[/C][C]5627.45612721679[/C][C]-723.456127216791[/C][/ROW]
[ROW][C]53[/C][C]5369[/C][C]5420.89021762652[/C][C]-51.8902176265246[/C][/ROW]
[ROW][C]54[/C][C]5578[/C][C]5890.83290418776[/C][C]-312.832904187757[/C][/ROW]
[ROW][C]55[/C][C]4619[/C][C]4983.69026660452[/C][C]-364.690266604521[/C][/ROW]
[ROW][C]56[/C][C]4731[/C][C]5082.71323434286[/C][C]-351.713234342859[/C][/ROW]
[ROW][C]57[/C][C]5011[/C][C]5253.46998114473[/C][C]-242.469981144732[/C][/ROW]
[ROW][C]58[/C][C]5299[/C][C]4960.63144325579[/C][C]338.368556744208[/C][/ROW]
[ROW][C]59[/C][C]4146[/C][C]4616.71193179793[/C][C]-470.71193179793[/C][/ROW]
[ROW][C]60[/C][C]4625[/C][C]5233.04432555503[/C][C]-608.044325555029[/C][/ROW]
[ROW][C]61[/C][C]4736[/C][C]5001.53386362427[/C][C]-265.533863624275[/C][/ROW]
[ROW][C]62[/C][C]4219[/C][C]4529.65956327045[/C][C]-310.659563270452[/C][/ROW]
[ROW][C]63[/C][C]5116[/C][C]5349.52421220215[/C][C]-233.524212202151[/C][/ROW]
[ROW][C]64[/C][C]4205[/C][C]4708.94280182617[/C][C]-503.942801826167[/C][/ROW]
[ROW][C]65[/C][C]4121[/C][C]4757.56226645068[/C][C]-636.562266450677[/C][/ROW]
[ROW][C]66[/C][C]5103[/C][C]5005.404288604[/C][C]97.5957113960058[/C][/ROW]
[ROW][C]67[/C][C]4300[/C][C]4183.77671714341[/C][C]116.223282856590[/C][/ROW]
[ROW][C]68[/C][C]4578[/C][C]4405.08666655518[/C][C]172.913333444816[/C][/ROW]
[ROW][C]69[/C][C]3809[/C][C]4737.72528807202[/C][C]-928.725288072015[/C][/ROW]
[ROW][C]70[/C][C]5526[/C][C]4449.89934270139[/C][C]1076.10065729861[/C][/ROW]
[ROW][C]71[/C][C]4248[/C][C]4045.27972913278[/C][C]202.720270867217[/C][/ROW]
[ROW][C]72[/C][C]3830[/C][C]4786.27755947736[/C][C]-956.277559477362[/C][/ROW]
[ROW][C]73[/C][C]4430[/C][C]4571.6183032043[/C][C]-141.6183032043[/C][/ROW]
[ROW][C]74[/C][C]4837[/C][C]4116.73618068735[/C][C]720.263819312652[/C][/ROW]
[ROW][C]75[/C][C]4408[/C][C]5213.51556601744[/C][C]-805.515566017442[/C][/ROW]
[ROW][C]76[/C][C]4569[/C][C]4351.1173207433[/C][C]217.882679256702[/C][/ROW]
[ROW][C]77[/C][C]4104[/C][C]4537.72815166057[/C][C]-433.728151660567[/C][/ROW]
[ROW][C]78[/C][C]4807[/C][C]5055.39617633328[/C][C]-248.396176333275[/C][/ROW]
[ROW][C]79[/C][C]3944[/C][C]4154.16507259718[/C][C]-210.165072597176[/C][/ROW]
[ROW][C]80[/C][C]3794[/C][C]4312.09798972122[/C][C]-518.097989721216[/C][/ROW]
[ROW][C]81[/C][C]4390[/C][C]4144.65752174464[/C][C]245.342478255357[/C][/ROW]
[ROW][C]82[/C][C]4041[/C][C]4746.3531800518[/C][C]-705.353180051795[/C][/ROW]
[ROW][C]83[/C][C]4104[/C][C]3641.55501744207[/C][C]462.444982557926[/C][/ROW]
[ROW][C]84[/C][C]4823[/C][C]4099.36385911524[/C][C]723.636140884755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72234&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72234&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
1333533222.9249465812130.075053418801
1431863111.8479822850174.152017714986
1539023853.336181418148.6638185818956
1641644120.2575563971643.7424436028359
1734993455.9256293607243.0743706392841
1841454080.2208904007764.7791095992334
1937964206.10982654648-410.109826546484
2037113720.70679858029-9.70679858029416
2139493891.7990793333257.2009206666844
2237403412.48894307279327.511056927212
2332433179.9787684870163.0212315129947
2444073628.22658427599778.773415724014
2548143743.858813926091070.14118607391
2639083847.4751860169460.5248139830587
2752504577.97438626735672.025613732649
2839374996.89251996398-1059.89251996398
2940044060.6471776821-56.6471776821008
3055604666.89195130402893.108048695985
3139224854.47970881134-932.479708811336
3237594360.39516950586-601.395169505861
3341384405.85424696435-267.854246964353
3446343927.47691612331706.523083876686
3539963709.06128456337286.938715436627
3643084426.81305624074-118.813056240736
3741434408.72871574138-265.728715741384
3844293881.06445052013547.935549479871
3952194914.71480370012304.285196299883
4049294724.36689904177204.633100958234
4157614399.929141271511361.07085872849
4255925639.67635992577-47.6763599257747
4341635048.86038174167-885.860381741668
4449624665.41698143613296.583018563868
4552085031.85622324376176.143776756239
4647554954.6274852554-199.627485255402
4744914387.44868506034103.551314939656
4857324938.52354476708793.476455232923
4957315101.04066679174629.95933320826
5050405037.595056876932.40494312307237
5161025863.96055932165238.039440678354
5249045627.45612721679-723.456127216791
5353695420.89021762652-51.8902176265246
5455785890.83290418776-312.832904187757
5546194983.69026660452-364.690266604521
5647315082.71323434286-351.713234342859
5750115253.46998114473-242.469981144732
5852994960.63144325579338.368556744208
5941464616.71193179793-470.71193179793
6046255233.04432555503-608.044325555029
6147365001.53386362427-265.533863624275
6242194529.65956327045-310.659563270452
6351165349.52421220215-233.524212202151
6442054708.94280182617-503.942801826167
6541214757.56226645068-636.562266450677
6651035005.40428860497.5957113960058
6743004183.77671714341116.223282856590
6845784405.08666655518172.913333444816
6938094737.72528807202-928.725288072015
7055264449.899342701391076.10065729861
7142484045.27972913278202.720270867217
7238304786.27755947736-956.277559477362
7344304571.6183032043-141.6183032043
7448374116.73618068735720.263819312652
7544085213.51556601744-805.515566017442
7645694351.1173207433217.882679256702
7741044537.72815166057-433.728151660567
7848075055.39617633328-248.396176333275
7939444154.16507259718-210.165072597176
8037944312.09798972122-518.097989721216
8143904144.65752174464245.342478255357
8240414746.3531800518-705.353180051795
8341043641.55501744207462.444982557926
8448234099.36385911524723.636140884755







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
854542.296481787183518.128741032895566.46422254147
864380.423930375923325.673495235205435.17436551664
874842.887393947543758.416370979515927.35841691558
884485.325146712983371.926602217295598.72369120868
894423.128835733483281.535546460575564.72212500638
905103.089102206513933.980827776496272.19737663652
914274.463419007623078.473002420385470.45383559486
924391.909312372613169.627840780945614.19078396429
934580.682787388763332.663991446925828.70158333059
944837.231484898653563.995515310966110.46745448634
954255.858879781162957.895570022485553.82218953983
964678.044118581923355.815820326476000.27241683736

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 4542.29648178718 & 3518.12874103289 & 5566.46422254147 \tabularnewline
86 & 4380.42393037592 & 3325.67349523520 & 5435.17436551664 \tabularnewline
87 & 4842.88739394754 & 3758.41637097951 & 5927.35841691558 \tabularnewline
88 & 4485.32514671298 & 3371.92660221729 & 5598.72369120868 \tabularnewline
89 & 4423.12883573348 & 3281.53554646057 & 5564.72212500638 \tabularnewline
90 & 5103.08910220651 & 3933.98082777649 & 6272.19737663652 \tabularnewline
91 & 4274.46341900762 & 3078.47300242038 & 5470.45383559486 \tabularnewline
92 & 4391.90931237261 & 3169.62784078094 & 5614.19078396429 \tabularnewline
93 & 4580.68278738876 & 3332.66399144692 & 5828.70158333059 \tabularnewline
94 & 4837.23148489865 & 3563.99551531096 & 6110.46745448634 \tabularnewline
95 & 4255.85887978116 & 2957.89557002248 & 5553.82218953983 \tabularnewline
96 & 4678.04411858192 & 3355.81582032647 & 6000.27241683736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72234&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]4542.29648178718[/C][C]3518.12874103289[/C][C]5566.46422254147[/C][/ROW]
[ROW][C]86[/C][C]4380.42393037592[/C][C]3325.67349523520[/C][C]5435.17436551664[/C][/ROW]
[ROW][C]87[/C][C]4842.88739394754[/C][C]3758.41637097951[/C][C]5927.35841691558[/C][/ROW]
[ROW][C]88[/C][C]4485.32514671298[/C][C]3371.92660221729[/C][C]5598.72369120868[/C][/ROW]
[ROW][C]89[/C][C]4423.12883573348[/C][C]3281.53554646057[/C][C]5564.72212500638[/C][/ROW]
[ROW][C]90[/C][C]5103.08910220651[/C][C]3933.98082777649[/C][C]6272.19737663652[/C][/ROW]
[ROW][C]91[/C][C]4274.46341900762[/C][C]3078.47300242038[/C][C]5470.45383559486[/C][/ROW]
[ROW][C]92[/C][C]4391.90931237261[/C][C]3169.62784078094[/C][C]5614.19078396429[/C][/ROW]
[ROW][C]93[/C][C]4580.68278738876[/C][C]3332.66399144692[/C][C]5828.70158333059[/C][/ROW]
[ROW][C]94[/C][C]4837.23148489865[/C][C]3563.99551531096[/C][C]6110.46745448634[/C][/ROW]
[ROW][C]95[/C][C]4255.85887978116[/C][C]2957.89557002248[/C][C]5553.82218953983[/C][/ROW]
[ROW][C]96[/C][C]4678.04411858192[/C][C]3355.81582032647[/C][C]6000.27241683736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72234&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72234&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
854542.296481787183518.128741032895566.46422254147
864380.423930375923325.673495235205435.17436551664
874842.887393947543758.416370979515927.35841691558
884485.325146712983371.926602217295598.72369120868
894423.128835733483281.535546460575564.72212500638
905103.089102206513933.980827776496272.19737663652
914274.463419007623078.473002420385470.45383559486
924391.909312372613169.627840780945614.19078396429
934580.682787388763332.663991446925828.70158333059
944837.231484898653563.995515310966110.46745448634
954255.858879781162957.895570022485553.82218953983
964678.044118581923355.815820326476000.27241683736



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')