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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 18 Aug 2009 11:06:24 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Aug/18/t1250615254x9hwel9591pflhe.htm/, Retrieved Mon, 06 May 2024 11:06:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42853, Retrieved Mon, 06 May 2024 11:06:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [tijdreeks - insch...] [2009-01-26 21:17:20] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [] [2009-08-18 17:06:24] [b5b38cb8cda4101c154c09cb859ab89a] [Current]
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Dataseries X:
6430
5124
4836
4629
4597
4490
4517
4560
4135
4559
4739
4886
5605
4616
4997
4607
4882
4555
4462
4476
4277
4369
4492
5183
6039
4923
4953
4892
4614
4363
4675
4556
4217
4664
4601
5428
5607
4869
5174
5031
4671
4491
4504
4615
4582
4800
4775
5791
5818
4714
4915
4598
4407
4383
4412
4274
4236
4637
4534
5271
5467
5204
5752
4724
4623
4451
4138
4140
4169
4603
4434
5185




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42853&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42853&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42853&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.82052932810292
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.82052932810292 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42853&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]0.82052932810292[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42853&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42853&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
alpha0.82052932810292
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
251246430-1306
348365358.38869749759-522.388697497587
446294929.75345053133-300.753450531332
545974682.97642384222-85.976423842223
644904612.43024655427-122.430246554272
745174511.972638609625.02736139037916
845604516.097736073443.9022639266004
941354552.12083119529-417.120831195291
1045594209.86095583689349.139044163113
1147394496.33978115854242.660218841458
1248864695.44960748183190.550392518169
1356054851.80179302451753.198206975489
1446165469.82301172243-853.823011722433
1549974769.23618959501227.763810404987
1646074956.12307591278-349.123075912778
1748824669.65735300884212.342646991158
1845554843.89072247209-288.890722472092
1944624606.8474120669-144.847412066899
2044764487.9958623662-11.9958623661996
2142774478.15290547885-201.152905478847
2243694313.1010471003455.8989528996617
2344924358.96777736475133.032222635245
2451834468.12461761969714.875382380309
2560395054.70083480152984.299165198476
2649235862.3471674741-939.347167474095
2749535091.58526729119-138.585267291194
2848924977.87199103579-85.8719910357868
2946144907.41150392833-293.411503928332
3043634666.65875975235-303.658759752350
3146754417.49784164019257.502158359812
3245564628.78591462422-72.7859146242163
3342174569.06293700225-352.062937002252
3446644280.18497185385383.815028146147
3546014595.116459014415.88354098558557
3654284599.94407694618828.055923053817
3756075279.38824712117327.611752878825
3848695548.20329858946-679.203298589458
3951744990.89707235256183.102927647437
4050315141.13839454879-110.138394548792
4146715050.76661167134-379.766611671337
4244914739.15696896073-248.156968960732
4345044535.53689795533-31.536897955325
4446154509.65994826559105.340051734408
4545824596.09455013755-14.0945501375527
4648004584.52955838327215.470441616726
4747754761.3293750690913.6706249309145
4857914772.54652375841018.45347624160
4958185608.217470323209.782529676997
5047145780.3501884466-1066.3501884466
5149154905.378584798099.62141520191108
5245984913.27323814911-315.273238149112
5344074654.58229988179-247.582299881789
5443834451.43376170961-68.4337617096089
5544124395.2818531944716.7181468055314
5642744408.99958295994-134.999582959937
5742364298.22846585965-62.2284658596454
5846374247.16818457896389.831815421045
5945344567.03662215953-33.0366221595268
6052714539.92910477618731.07089522382
6154675139.79421522978327.205784770219
6252045408.27615795868-204.276157958678
6357525240.6615793214511.338420678602
6447245660.22975007402-936.22975007402
6546234892.02578229582-269.025782295819
6644514671.28223790627-220.282237906268
6741384490.53420124403-352.534201244031
6841404201.26954996397-61.2695499639667
6941694150.9960872988618.0039127011351
7046034165.76882569075437.231174309249
7144344524.52982737237-90.5298273723702
7251854450.24744894525734.752551054754

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 5124 & 6430 & -1306 \tabularnewline
3 & 4836 & 5358.38869749759 & -522.388697497587 \tabularnewline
4 & 4629 & 4929.75345053133 & -300.753450531332 \tabularnewline
5 & 4597 & 4682.97642384222 & -85.976423842223 \tabularnewline
6 & 4490 & 4612.43024655427 & -122.430246554272 \tabularnewline
7 & 4517 & 4511.97263860962 & 5.02736139037916 \tabularnewline
8 & 4560 & 4516.0977360734 & 43.9022639266004 \tabularnewline
9 & 4135 & 4552.12083119529 & -417.120831195291 \tabularnewline
10 & 4559 & 4209.86095583689 & 349.139044163113 \tabularnewline
11 & 4739 & 4496.33978115854 & 242.660218841458 \tabularnewline
12 & 4886 & 4695.44960748183 & 190.550392518169 \tabularnewline
13 & 5605 & 4851.80179302451 & 753.198206975489 \tabularnewline
14 & 4616 & 5469.82301172243 & -853.823011722433 \tabularnewline
15 & 4997 & 4769.23618959501 & 227.763810404987 \tabularnewline
16 & 4607 & 4956.12307591278 & -349.123075912778 \tabularnewline
17 & 4882 & 4669.65735300884 & 212.342646991158 \tabularnewline
18 & 4555 & 4843.89072247209 & -288.890722472092 \tabularnewline
19 & 4462 & 4606.8474120669 & -144.847412066899 \tabularnewline
20 & 4476 & 4487.9958623662 & -11.9958623661996 \tabularnewline
21 & 4277 & 4478.15290547885 & -201.152905478847 \tabularnewline
22 & 4369 & 4313.10104710034 & 55.8989528996617 \tabularnewline
23 & 4492 & 4358.96777736475 & 133.032222635245 \tabularnewline
24 & 5183 & 4468.12461761969 & 714.875382380309 \tabularnewline
25 & 6039 & 5054.70083480152 & 984.299165198476 \tabularnewline
26 & 4923 & 5862.3471674741 & -939.347167474095 \tabularnewline
27 & 4953 & 5091.58526729119 & -138.585267291194 \tabularnewline
28 & 4892 & 4977.87199103579 & -85.8719910357868 \tabularnewline
29 & 4614 & 4907.41150392833 & -293.411503928332 \tabularnewline
30 & 4363 & 4666.65875975235 & -303.658759752350 \tabularnewline
31 & 4675 & 4417.49784164019 & 257.502158359812 \tabularnewline
32 & 4556 & 4628.78591462422 & -72.7859146242163 \tabularnewline
33 & 4217 & 4569.06293700225 & -352.062937002252 \tabularnewline
34 & 4664 & 4280.18497185385 & 383.815028146147 \tabularnewline
35 & 4601 & 4595.11645901441 & 5.88354098558557 \tabularnewline
36 & 5428 & 4599.94407694618 & 828.055923053817 \tabularnewline
37 & 5607 & 5279.38824712117 & 327.611752878825 \tabularnewline
38 & 4869 & 5548.20329858946 & -679.203298589458 \tabularnewline
39 & 5174 & 4990.89707235256 & 183.102927647437 \tabularnewline
40 & 5031 & 5141.13839454879 & -110.138394548792 \tabularnewline
41 & 4671 & 5050.76661167134 & -379.766611671337 \tabularnewline
42 & 4491 & 4739.15696896073 & -248.156968960732 \tabularnewline
43 & 4504 & 4535.53689795533 & -31.536897955325 \tabularnewline
44 & 4615 & 4509.65994826559 & 105.340051734408 \tabularnewline
45 & 4582 & 4596.09455013755 & -14.0945501375527 \tabularnewline
46 & 4800 & 4584.52955838327 & 215.470441616726 \tabularnewline
47 & 4775 & 4761.32937506909 & 13.6706249309145 \tabularnewline
48 & 5791 & 4772.5465237584 & 1018.45347624160 \tabularnewline
49 & 5818 & 5608.217470323 & 209.782529676997 \tabularnewline
50 & 4714 & 5780.3501884466 & -1066.3501884466 \tabularnewline
51 & 4915 & 4905.37858479809 & 9.62141520191108 \tabularnewline
52 & 4598 & 4913.27323814911 & -315.273238149112 \tabularnewline
53 & 4407 & 4654.58229988179 & -247.582299881789 \tabularnewline
54 & 4383 & 4451.43376170961 & -68.4337617096089 \tabularnewline
55 & 4412 & 4395.28185319447 & 16.7181468055314 \tabularnewline
56 & 4274 & 4408.99958295994 & -134.999582959937 \tabularnewline
57 & 4236 & 4298.22846585965 & -62.2284658596454 \tabularnewline
58 & 4637 & 4247.16818457896 & 389.831815421045 \tabularnewline
59 & 4534 & 4567.03662215953 & -33.0366221595268 \tabularnewline
60 & 5271 & 4539.92910477618 & 731.07089522382 \tabularnewline
61 & 5467 & 5139.79421522978 & 327.205784770219 \tabularnewline
62 & 5204 & 5408.27615795868 & -204.276157958678 \tabularnewline
63 & 5752 & 5240.6615793214 & 511.338420678602 \tabularnewline
64 & 4724 & 5660.22975007402 & -936.22975007402 \tabularnewline
65 & 4623 & 4892.02578229582 & -269.025782295819 \tabularnewline
66 & 4451 & 4671.28223790627 & -220.282237906268 \tabularnewline
67 & 4138 & 4490.53420124403 & -352.534201244031 \tabularnewline
68 & 4140 & 4201.26954996397 & -61.2695499639667 \tabularnewline
69 & 4169 & 4150.99608729886 & 18.0039127011351 \tabularnewline
70 & 4603 & 4165.76882569075 & 437.231174309249 \tabularnewline
71 & 4434 & 4524.52982737237 & -90.5298273723702 \tabularnewline
72 & 5185 & 4450.24744894525 & 734.752551054754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42853&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]5124[/C][C]6430[/C][C]-1306[/C][/ROW]
[ROW][C]3[/C][C]4836[/C][C]5358.38869749759[/C][C]-522.388697497587[/C][/ROW]
[ROW][C]4[/C][C]4629[/C][C]4929.75345053133[/C][C]-300.753450531332[/C][/ROW]
[ROW][C]5[/C][C]4597[/C][C]4682.97642384222[/C][C]-85.976423842223[/C][/ROW]
[ROW][C]6[/C][C]4490[/C][C]4612.43024655427[/C][C]-122.430246554272[/C][/ROW]
[ROW][C]7[/C][C]4517[/C][C]4511.97263860962[/C][C]5.02736139037916[/C][/ROW]
[ROW][C]8[/C][C]4560[/C][C]4516.0977360734[/C][C]43.9022639266004[/C][/ROW]
[ROW][C]9[/C][C]4135[/C][C]4552.12083119529[/C][C]-417.120831195291[/C][/ROW]
[ROW][C]10[/C][C]4559[/C][C]4209.86095583689[/C][C]349.139044163113[/C][/ROW]
[ROW][C]11[/C][C]4739[/C][C]4496.33978115854[/C][C]242.660218841458[/C][/ROW]
[ROW][C]12[/C][C]4886[/C][C]4695.44960748183[/C][C]190.550392518169[/C][/ROW]
[ROW][C]13[/C][C]5605[/C][C]4851.80179302451[/C][C]753.198206975489[/C][/ROW]
[ROW][C]14[/C][C]4616[/C][C]5469.82301172243[/C][C]-853.823011722433[/C][/ROW]
[ROW][C]15[/C][C]4997[/C][C]4769.23618959501[/C][C]227.763810404987[/C][/ROW]
[ROW][C]16[/C][C]4607[/C][C]4956.12307591278[/C][C]-349.123075912778[/C][/ROW]
[ROW][C]17[/C][C]4882[/C][C]4669.65735300884[/C][C]212.342646991158[/C][/ROW]
[ROW][C]18[/C][C]4555[/C][C]4843.89072247209[/C][C]-288.890722472092[/C][/ROW]
[ROW][C]19[/C][C]4462[/C][C]4606.8474120669[/C][C]-144.847412066899[/C][/ROW]
[ROW][C]20[/C][C]4476[/C][C]4487.9958623662[/C][C]-11.9958623661996[/C][/ROW]
[ROW][C]21[/C][C]4277[/C][C]4478.15290547885[/C][C]-201.152905478847[/C][/ROW]
[ROW][C]22[/C][C]4369[/C][C]4313.10104710034[/C][C]55.8989528996617[/C][/ROW]
[ROW][C]23[/C][C]4492[/C][C]4358.96777736475[/C][C]133.032222635245[/C][/ROW]
[ROW][C]24[/C][C]5183[/C][C]4468.12461761969[/C][C]714.875382380309[/C][/ROW]
[ROW][C]25[/C][C]6039[/C][C]5054.70083480152[/C][C]984.299165198476[/C][/ROW]
[ROW][C]26[/C][C]4923[/C][C]5862.3471674741[/C][C]-939.347167474095[/C][/ROW]
[ROW][C]27[/C][C]4953[/C][C]5091.58526729119[/C][C]-138.585267291194[/C][/ROW]
[ROW][C]28[/C][C]4892[/C][C]4977.87199103579[/C][C]-85.8719910357868[/C][/ROW]
[ROW][C]29[/C][C]4614[/C][C]4907.41150392833[/C][C]-293.411503928332[/C][/ROW]
[ROW][C]30[/C][C]4363[/C][C]4666.65875975235[/C][C]-303.658759752350[/C][/ROW]
[ROW][C]31[/C][C]4675[/C][C]4417.49784164019[/C][C]257.502158359812[/C][/ROW]
[ROW][C]32[/C][C]4556[/C][C]4628.78591462422[/C][C]-72.7859146242163[/C][/ROW]
[ROW][C]33[/C][C]4217[/C][C]4569.06293700225[/C][C]-352.062937002252[/C][/ROW]
[ROW][C]34[/C][C]4664[/C][C]4280.18497185385[/C][C]383.815028146147[/C][/ROW]
[ROW][C]35[/C][C]4601[/C][C]4595.11645901441[/C][C]5.88354098558557[/C][/ROW]
[ROW][C]36[/C][C]5428[/C][C]4599.94407694618[/C][C]828.055923053817[/C][/ROW]
[ROW][C]37[/C][C]5607[/C][C]5279.38824712117[/C][C]327.611752878825[/C][/ROW]
[ROW][C]38[/C][C]4869[/C][C]5548.20329858946[/C][C]-679.203298589458[/C][/ROW]
[ROW][C]39[/C][C]5174[/C][C]4990.89707235256[/C][C]183.102927647437[/C][/ROW]
[ROW][C]40[/C][C]5031[/C][C]5141.13839454879[/C][C]-110.138394548792[/C][/ROW]
[ROW][C]41[/C][C]4671[/C][C]5050.76661167134[/C][C]-379.766611671337[/C][/ROW]
[ROW][C]42[/C][C]4491[/C][C]4739.15696896073[/C][C]-248.156968960732[/C][/ROW]
[ROW][C]43[/C][C]4504[/C][C]4535.53689795533[/C][C]-31.536897955325[/C][/ROW]
[ROW][C]44[/C][C]4615[/C][C]4509.65994826559[/C][C]105.340051734408[/C][/ROW]
[ROW][C]45[/C][C]4582[/C][C]4596.09455013755[/C][C]-14.0945501375527[/C][/ROW]
[ROW][C]46[/C][C]4800[/C][C]4584.52955838327[/C][C]215.470441616726[/C][/ROW]
[ROW][C]47[/C][C]4775[/C][C]4761.32937506909[/C][C]13.6706249309145[/C][/ROW]
[ROW][C]48[/C][C]5791[/C][C]4772.5465237584[/C][C]1018.45347624160[/C][/ROW]
[ROW][C]49[/C][C]5818[/C][C]5608.217470323[/C][C]209.782529676997[/C][/ROW]
[ROW][C]50[/C][C]4714[/C][C]5780.3501884466[/C][C]-1066.3501884466[/C][/ROW]
[ROW][C]51[/C][C]4915[/C][C]4905.37858479809[/C][C]9.62141520191108[/C][/ROW]
[ROW][C]52[/C][C]4598[/C][C]4913.27323814911[/C][C]-315.273238149112[/C][/ROW]
[ROW][C]53[/C][C]4407[/C][C]4654.58229988179[/C][C]-247.582299881789[/C][/ROW]
[ROW][C]54[/C][C]4383[/C][C]4451.43376170961[/C][C]-68.4337617096089[/C][/ROW]
[ROW][C]55[/C][C]4412[/C][C]4395.28185319447[/C][C]16.7181468055314[/C][/ROW]
[ROW][C]56[/C][C]4274[/C][C]4408.99958295994[/C][C]-134.999582959937[/C][/ROW]
[ROW][C]57[/C][C]4236[/C][C]4298.22846585965[/C][C]-62.2284658596454[/C][/ROW]
[ROW][C]58[/C][C]4637[/C][C]4247.16818457896[/C][C]389.831815421045[/C][/ROW]
[ROW][C]59[/C][C]4534[/C][C]4567.03662215953[/C][C]-33.0366221595268[/C][/ROW]
[ROW][C]60[/C][C]5271[/C][C]4539.92910477618[/C][C]731.07089522382[/C][/ROW]
[ROW][C]61[/C][C]5467[/C][C]5139.79421522978[/C][C]327.205784770219[/C][/ROW]
[ROW][C]62[/C][C]5204[/C][C]5408.27615795868[/C][C]-204.276157958678[/C][/ROW]
[ROW][C]63[/C][C]5752[/C][C]5240.6615793214[/C][C]511.338420678602[/C][/ROW]
[ROW][C]64[/C][C]4724[/C][C]5660.22975007402[/C][C]-936.22975007402[/C][/ROW]
[ROW][C]65[/C][C]4623[/C][C]4892.02578229582[/C][C]-269.025782295819[/C][/ROW]
[ROW][C]66[/C][C]4451[/C][C]4671.28223790627[/C][C]-220.282237906268[/C][/ROW]
[ROW][C]67[/C][C]4138[/C][C]4490.53420124403[/C][C]-352.534201244031[/C][/ROW]
[ROW][C]68[/C][C]4140[/C][C]4201.26954996397[/C][C]-61.2695499639667[/C][/ROW]
[ROW][C]69[/C][C]4169[/C][C]4150.99608729886[/C][C]18.0039127011351[/C][/ROW]
[ROW][C]70[/C][C]4603[/C][C]4165.76882569075[/C][C]437.231174309249[/C][/ROW]
[ROW][C]71[/C][C]4434[/C][C]4524.52982737237[/C][C]-90.5298273723702[/C][/ROW]
[ROW][C]72[/C][C]5185[/C][C]4450.24744894525[/C][C]734.752551054754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42853&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42853&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
251246430-1306
348365358.38869749759-522.388697497587
446294929.75345053133-300.753450531332
545974682.97642384222-85.976423842223
644904612.43024655427-122.430246554272
745174511.972638609625.02736139037916
845604516.097736073443.9022639266004
941354552.12083119529-417.120831195291
1045594209.86095583689349.139044163113
1147394496.33978115854242.660218841458
1248864695.44960748183190.550392518169
1356054851.80179302451753.198206975489
1446165469.82301172243-853.823011722433
1549974769.23618959501227.763810404987
1646074956.12307591278-349.123075912778
1748824669.65735300884212.342646991158
1845554843.89072247209-288.890722472092
1944624606.8474120669-144.847412066899
2044764487.9958623662-11.9958623661996
2142774478.15290547885-201.152905478847
2243694313.1010471003455.8989528996617
2344924358.96777736475133.032222635245
2451834468.12461761969714.875382380309
2560395054.70083480152984.299165198476
2649235862.3471674741-939.347167474095
2749535091.58526729119-138.585267291194
2848924977.87199103579-85.8719910357868
2946144907.41150392833-293.411503928332
3043634666.65875975235-303.658759752350
3146754417.49784164019257.502158359812
3245564628.78591462422-72.7859146242163
3342174569.06293700225-352.062937002252
3446644280.18497185385383.815028146147
3546014595.116459014415.88354098558557
3654284599.94407694618828.055923053817
3756075279.38824712117327.611752878825
3848695548.20329858946-679.203298589458
3951744990.89707235256183.102927647437
4050315141.13839454879-110.138394548792
4146715050.76661167134-379.766611671337
4244914739.15696896073-248.156968960732
4345044535.53689795533-31.536897955325
4446154509.65994826559105.340051734408
4545824596.09455013755-14.0945501375527
4648004584.52955838327215.470441616726
4747754761.3293750690913.6706249309145
4857914772.54652375841018.45347624160
4958185608.217470323209.782529676997
5047145780.3501884466-1066.3501884466
5149154905.378584798099.62141520191108
5245984913.27323814911-315.273238149112
5344074654.58229988179-247.582299881789
5443834451.43376170961-68.4337617096089
5544124395.2818531944716.7181468055314
5642744408.99958295994-134.999582959937
5742364298.22846585965-62.2284658596454
5846374247.16818457896389.831815421045
5945344567.03662215953-33.0366221595268
6052714539.92910477618731.07089522382
6154675139.79421522978327.205784770219
6252045408.27615795868-204.276157958678
6357525240.6615793214511.338420678602
6447245660.22975007402-936.22975007402
6546234892.02578229582-269.025782295819
6644514671.28223790627-220.282237906268
6741384490.53420124403-352.534201244031
6841404201.26954996397-61.2695499639667
6941694150.9960872988618.0039127011351
7046034165.76882569075437.231174309249
7144344524.52982737237-90.5298273723702
7251854450.24744894525734.752551054754







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
735053.133465984114177.565829939285928.70110202894
745053.133465984113920.54404157186185.72289039642
755053.133465984113711.903089317946394.36384265028
765053.133465984113531.608230474186574.65870149404
775053.133465984113370.522649040686735.74428292754
785053.133465984113223.565407589866882.70152437836
795053.133465984113087.564998772147018.70193319607
805053.133465984112960.384193304877145.88273866335
815053.133465984112840.501630973837265.76530099439
825053.133465984112726.788745977547379.47818599068
835053.133465984112618.380937429337487.88599453889
845053.133465984112514.598456514017591.66847545421

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 5053.13346598411 & 4177.56582993928 & 5928.70110202894 \tabularnewline
74 & 5053.13346598411 & 3920.5440415718 & 6185.72289039642 \tabularnewline
75 & 5053.13346598411 & 3711.90308931794 & 6394.36384265028 \tabularnewline
76 & 5053.13346598411 & 3531.60823047418 & 6574.65870149404 \tabularnewline
77 & 5053.13346598411 & 3370.52264904068 & 6735.74428292754 \tabularnewline
78 & 5053.13346598411 & 3223.56540758986 & 6882.70152437836 \tabularnewline
79 & 5053.13346598411 & 3087.56499877214 & 7018.70193319607 \tabularnewline
80 & 5053.13346598411 & 2960.38419330487 & 7145.88273866335 \tabularnewline
81 & 5053.13346598411 & 2840.50163097383 & 7265.76530099439 \tabularnewline
82 & 5053.13346598411 & 2726.78874597754 & 7379.47818599068 \tabularnewline
83 & 5053.13346598411 & 2618.38093742933 & 7487.88599453889 \tabularnewline
84 & 5053.13346598411 & 2514.59845651401 & 7591.66847545421 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42853&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]5053.13346598411[/C][C]4177.56582993928[/C][C]5928.70110202894[/C][/ROW]
[ROW][C]74[/C][C]5053.13346598411[/C][C]3920.5440415718[/C][C]6185.72289039642[/C][/ROW]
[ROW][C]75[/C][C]5053.13346598411[/C][C]3711.90308931794[/C][C]6394.36384265028[/C][/ROW]
[ROW][C]76[/C][C]5053.13346598411[/C][C]3531.60823047418[/C][C]6574.65870149404[/C][/ROW]
[ROW][C]77[/C][C]5053.13346598411[/C][C]3370.52264904068[/C][C]6735.74428292754[/C][/ROW]
[ROW][C]78[/C][C]5053.13346598411[/C][C]3223.56540758986[/C][C]6882.70152437836[/C][/ROW]
[ROW][C]79[/C][C]5053.13346598411[/C][C]3087.56499877214[/C][C]7018.70193319607[/C][/ROW]
[ROW][C]80[/C][C]5053.13346598411[/C][C]2960.38419330487[/C][C]7145.88273866335[/C][/ROW]
[ROW][C]81[/C][C]5053.13346598411[/C][C]2840.50163097383[/C][C]7265.76530099439[/C][/ROW]
[ROW][C]82[/C][C]5053.13346598411[/C][C]2726.78874597754[/C][C]7379.47818599068[/C][/ROW]
[ROW][C]83[/C][C]5053.13346598411[/C][C]2618.38093742933[/C][C]7487.88599453889[/C][/ROW]
[ROW][C]84[/C][C]5053.13346598411[/C][C]2514.59845651401[/C][C]7591.66847545421[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42853&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42853&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
735053.133465984114177.565829939285928.70110202894
745053.133465984113920.54404157186185.72289039642
755053.133465984113711.903089317946394.36384265028
765053.133465984113531.608230474186574.65870149404
775053.133465984113370.522649040686735.74428292754
785053.133465984113223.565407589866882.70152437836
795053.133465984113087.564998772147018.70193319607
805053.133465984112960.384193304877145.88273866335
815053.133465984112840.501630973837265.76530099439
825053.133465984112726.788745977547379.47818599068
835053.133465984112618.380937429337487.88599453889
845053.133465984112514.598456514017591.66847545421



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')