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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 23 May 2015 18:07:00 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/23/t1432401002otr4md7vv1biemh.htm/, Retrieved Thu, 02 May 2024 23:13:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279266, Retrieved Thu, 02 May 2024 23:13:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2015-05-23 17:07:00] [cab9dc260884be88f444bea8f40c034b] [Current]
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Dataseries X:
3862,5
3875,7
3875,9
3877,7
3880,4
3883,4
3884,2
3884,8
3894,9
3903,3
3911,2
3928,9
3945,6
3965,7
3992,3
4008,7
4014,8
4020,6
4037,5
4058,5
4082,3
4102,4
4127,1
4144,4
4161
4168,2
4178,3
4174,1
4165,7
4167,9
4158,3
4158,3
4143,7
4157,5
4164,8
4173,9
4181,2
4190,7
4206,6
4222,1
4245,8
4255,4
4266,1
4273,6
4282,1
4299,8
4315,7
4331,7
4348,4
4367,8
4387,2
4410,9
4436
4453,8
4469,1
4472
4458,2
4449
4441,5
4445,7
4453,9
4469,7
4487,5
4504
4524,1
4540,5
4548,4
4554,2
4558
4557,5
4554,5
4550
4543,8
4538,2
4543,3
4545,1




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=279266&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=279266&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279266&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
beta0.825837632297321
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.825837632297321 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279266&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]0.825837632297321[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279266&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279266&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
beta0.825837632297321
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
53880.43875.293755.10624999999936
63883.43888.02943340992-4.62943340991751
73884.23885.75627308379-1.55627308379371
83884.83884.246044205070.553955794935064
93894.93887.403521747157.49647825284774
103903.33904.06939559805-0.769395598051688
113911.23910.383999759060.816000240942685
123928.93917.9328834659910.9671165340092
133945.63946.78994101757-1.18994101756653
143965.73962.882242945052.81775705495465
153992.33983.85925275978.44074724030224
164008.74016.40493947545-7.70493947544992
174014.84028.54191050205-13.7419105020499
184020.64023.6683236698-3.06832366979552
194037.54025.4843865152112.0156134847903
204058.54051.282332306097.21766769391115
214082.34080.342953905141.95704609486256
224102.44106.13415621842-3.73415621841559
234127.14121.700349488375.39965051163017
244144.44149.83458408213-5.43458408212973
2541614164.74650003122-3.74650003122224
264168.24178.62749931603-10.4274993160343
274178.34175.76607797012.53392202990108
284174.14186.9336861397-12.8336861396992
294165.74174.23514516444-8.53514516444375
304167.94159.161501090528.73849890947622
314158.34167.12808233976-8.82808233975902
324158.34149.212519722579.08748027743241
334143.74158.81730291843-15.117302918432
344157.54132.1078652695525.3921347304495
354164.84165.42764569432-0.627645694320563
364173.94171.18431226022.71568773979743
374181.24184.62702939329-3.42702939329502
384190.74189.471859553321.22814044667848
394206.64198.536104151948.06389584806402
404222.14220.070572806192.02942719380553
414245.84239.346550154856.45344984515305
424255.44268.75105189512-13.3510518951161
434266.14265.875250809370.224749190625516
444273.64275.73585714882-2.13585714882265
454282.14283.57198593811-1.4719859381139
464299.84291.231364556218.56863544379485
474315.74314.557666163131.14233383687133
484331.74330.376048434261.32395156573602
494348.44349.56941746059-1.16941746058819
504367.84365.678668513772.12133148623343
514387.24385.380543885681.81945611432275
524410.94405.25811921525.64188078480129
5344364435.717396684220.282603315777123
544453.84461.4257811374-7.62578113740165
554469.14471.47812409847-2.37812409847356
5644724483.78917972368-11.7891797236816
574458.24479.05323145395-20.8532314539489
5844494448.406848164270.593151835730168
594441.54438.246695271883.25330472811675
604445.74432.4083967456913.2916032543062
614453.94449.685102906674.214897093334
624469.74461.74092354267.95907645740044
634487.54482.663828399454.83617160054655
6445044503.432720903430.56727909656729
654524.14522.501201329391.5987986706059
664540.54544.29654943805-3.79654943804599
674548.44556.11121603923-7.71121603923166
684554.24556.61800364326-2.418003643259
6945584562.52112523962-4.52112523962387
704557.54562.96240987641-5.46240987641158
714554.54556.50134623744-2.00134623743907
7245504550.82355919931-0.823559199305237
734543.84547.74343302009-3.94343302009474
744538.24538.66179763165-0.461797631654917
754543.34531.2304277689312.0695722310711
764545.14545.27293472308-0.17293472307847

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 3880.4 & 3875.29375 & 5.10624999999936 \tabularnewline
6 & 3883.4 & 3888.02943340992 & -4.62943340991751 \tabularnewline
7 & 3884.2 & 3885.75627308379 & -1.55627308379371 \tabularnewline
8 & 3884.8 & 3884.24604420507 & 0.553955794935064 \tabularnewline
9 & 3894.9 & 3887.40352174715 & 7.49647825284774 \tabularnewline
10 & 3903.3 & 3904.06939559805 & -0.769395598051688 \tabularnewline
11 & 3911.2 & 3910.38399975906 & 0.816000240942685 \tabularnewline
12 & 3928.9 & 3917.93288346599 & 10.9671165340092 \tabularnewline
13 & 3945.6 & 3946.78994101757 & -1.18994101756653 \tabularnewline
14 & 3965.7 & 3962.88224294505 & 2.81775705495465 \tabularnewline
15 & 3992.3 & 3983.8592527597 & 8.44074724030224 \tabularnewline
16 & 4008.7 & 4016.40493947545 & -7.70493947544992 \tabularnewline
17 & 4014.8 & 4028.54191050205 & -13.7419105020499 \tabularnewline
18 & 4020.6 & 4023.6683236698 & -3.06832366979552 \tabularnewline
19 & 4037.5 & 4025.48438651521 & 12.0156134847903 \tabularnewline
20 & 4058.5 & 4051.28233230609 & 7.21766769391115 \tabularnewline
21 & 4082.3 & 4080.34295390514 & 1.95704609486256 \tabularnewline
22 & 4102.4 & 4106.13415621842 & -3.73415621841559 \tabularnewline
23 & 4127.1 & 4121.70034948837 & 5.39965051163017 \tabularnewline
24 & 4144.4 & 4149.83458408213 & -5.43458408212973 \tabularnewline
25 & 4161 & 4164.74650003122 & -3.74650003122224 \tabularnewline
26 & 4168.2 & 4178.62749931603 & -10.4274993160343 \tabularnewline
27 & 4178.3 & 4175.7660779701 & 2.53392202990108 \tabularnewline
28 & 4174.1 & 4186.9336861397 & -12.8336861396992 \tabularnewline
29 & 4165.7 & 4174.23514516444 & -8.53514516444375 \tabularnewline
30 & 4167.9 & 4159.16150109052 & 8.73849890947622 \tabularnewline
31 & 4158.3 & 4167.12808233976 & -8.82808233975902 \tabularnewline
32 & 4158.3 & 4149.21251972257 & 9.08748027743241 \tabularnewline
33 & 4143.7 & 4158.81730291843 & -15.117302918432 \tabularnewline
34 & 4157.5 & 4132.10786526955 & 25.3921347304495 \tabularnewline
35 & 4164.8 & 4165.42764569432 & -0.627645694320563 \tabularnewline
36 & 4173.9 & 4171.1843122602 & 2.71568773979743 \tabularnewline
37 & 4181.2 & 4184.62702939329 & -3.42702939329502 \tabularnewline
38 & 4190.7 & 4189.47185955332 & 1.22814044667848 \tabularnewline
39 & 4206.6 & 4198.53610415194 & 8.06389584806402 \tabularnewline
40 & 4222.1 & 4220.07057280619 & 2.02942719380553 \tabularnewline
41 & 4245.8 & 4239.34655015485 & 6.45344984515305 \tabularnewline
42 & 4255.4 & 4268.75105189512 & -13.3510518951161 \tabularnewline
43 & 4266.1 & 4265.87525080937 & 0.224749190625516 \tabularnewline
44 & 4273.6 & 4275.73585714882 & -2.13585714882265 \tabularnewline
45 & 4282.1 & 4283.57198593811 & -1.4719859381139 \tabularnewline
46 & 4299.8 & 4291.23136455621 & 8.56863544379485 \tabularnewline
47 & 4315.7 & 4314.55766616313 & 1.14233383687133 \tabularnewline
48 & 4331.7 & 4330.37604843426 & 1.32395156573602 \tabularnewline
49 & 4348.4 & 4349.56941746059 & -1.16941746058819 \tabularnewline
50 & 4367.8 & 4365.67866851377 & 2.12133148623343 \tabularnewline
51 & 4387.2 & 4385.38054388568 & 1.81945611432275 \tabularnewline
52 & 4410.9 & 4405.2581192152 & 5.64188078480129 \tabularnewline
53 & 4436 & 4435.71739668422 & 0.282603315777123 \tabularnewline
54 & 4453.8 & 4461.4257811374 & -7.62578113740165 \tabularnewline
55 & 4469.1 & 4471.47812409847 & -2.37812409847356 \tabularnewline
56 & 4472 & 4483.78917972368 & -11.7891797236816 \tabularnewline
57 & 4458.2 & 4479.05323145395 & -20.8532314539489 \tabularnewline
58 & 4449 & 4448.40684816427 & 0.593151835730168 \tabularnewline
59 & 4441.5 & 4438.24669527188 & 3.25330472811675 \tabularnewline
60 & 4445.7 & 4432.40839674569 & 13.2916032543062 \tabularnewline
61 & 4453.9 & 4449.68510290667 & 4.214897093334 \tabularnewline
62 & 4469.7 & 4461.7409235426 & 7.95907645740044 \tabularnewline
63 & 4487.5 & 4482.66382839945 & 4.83617160054655 \tabularnewline
64 & 4504 & 4503.43272090343 & 0.56727909656729 \tabularnewline
65 & 4524.1 & 4522.50120132939 & 1.5987986706059 \tabularnewline
66 & 4540.5 & 4544.29654943805 & -3.79654943804599 \tabularnewline
67 & 4548.4 & 4556.11121603923 & -7.71121603923166 \tabularnewline
68 & 4554.2 & 4556.61800364326 & -2.418003643259 \tabularnewline
69 & 4558 & 4562.52112523962 & -4.52112523962387 \tabularnewline
70 & 4557.5 & 4562.96240987641 & -5.46240987641158 \tabularnewline
71 & 4554.5 & 4556.50134623744 & -2.00134623743907 \tabularnewline
72 & 4550 & 4550.82355919931 & -0.823559199305237 \tabularnewline
73 & 4543.8 & 4547.74343302009 & -3.94343302009474 \tabularnewline
74 & 4538.2 & 4538.66179763165 & -0.461797631654917 \tabularnewline
75 & 4543.3 & 4531.23042776893 & 12.0695722310711 \tabularnewline
76 & 4545.1 & 4545.27293472308 & -0.17293472307847 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279266&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]5[/C][C]3880.4[/C][C]3875.29375[/C][C]5.10624999999936[/C][/ROW]
[ROW][C]6[/C][C]3883.4[/C][C]3888.02943340992[/C][C]-4.62943340991751[/C][/ROW]
[ROW][C]7[/C][C]3884.2[/C][C]3885.75627308379[/C][C]-1.55627308379371[/C][/ROW]
[ROW][C]8[/C][C]3884.8[/C][C]3884.24604420507[/C][C]0.553955794935064[/C][/ROW]
[ROW][C]9[/C][C]3894.9[/C][C]3887.40352174715[/C][C]7.49647825284774[/C][/ROW]
[ROW][C]10[/C][C]3903.3[/C][C]3904.06939559805[/C][C]-0.769395598051688[/C][/ROW]
[ROW][C]11[/C][C]3911.2[/C][C]3910.38399975906[/C][C]0.816000240942685[/C][/ROW]
[ROW][C]12[/C][C]3928.9[/C][C]3917.93288346599[/C][C]10.9671165340092[/C][/ROW]
[ROW][C]13[/C][C]3945.6[/C][C]3946.78994101757[/C][C]-1.18994101756653[/C][/ROW]
[ROW][C]14[/C][C]3965.7[/C][C]3962.88224294505[/C][C]2.81775705495465[/C][/ROW]
[ROW][C]15[/C][C]3992.3[/C][C]3983.8592527597[/C][C]8.44074724030224[/C][/ROW]
[ROW][C]16[/C][C]4008.7[/C][C]4016.40493947545[/C][C]-7.70493947544992[/C][/ROW]
[ROW][C]17[/C][C]4014.8[/C][C]4028.54191050205[/C][C]-13.7419105020499[/C][/ROW]
[ROW][C]18[/C][C]4020.6[/C][C]4023.6683236698[/C][C]-3.06832366979552[/C][/ROW]
[ROW][C]19[/C][C]4037.5[/C][C]4025.48438651521[/C][C]12.0156134847903[/C][/ROW]
[ROW][C]20[/C][C]4058.5[/C][C]4051.28233230609[/C][C]7.21766769391115[/C][/ROW]
[ROW][C]21[/C][C]4082.3[/C][C]4080.34295390514[/C][C]1.95704609486256[/C][/ROW]
[ROW][C]22[/C][C]4102.4[/C][C]4106.13415621842[/C][C]-3.73415621841559[/C][/ROW]
[ROW][C]23[/C][C]4127.1[/C][C]4121.70034948837[/C][C]5.39965051163017[/C][/ROW]
[ROW][C]24[/C][C]4144.4[/C][C]4149.83458408213[/C][C]-5.43458408212973[/C][/ROW]
[ROW][C]25[/C][C]4161[/C][C]4164.74650003122[/C][C]-3.74650003122224[/C][/ROW]
[ROW][C]26[/C][C]4168.2[/C][C]4178.62749931603[/C][C]-10.4274993160343[/C][/ROW]
[ROW][C]27[/C][C]4178.3[/C][C]4175.7660779701[/C][C]2.53392202990108[/C][/ROW]
[ROW][C]28[/C][C]4174.1[/C][C]4186.9336861397[/C][C]-12.8336861396992[/C][/ROW]
[ROW][C]29[/C][C]4165.7[/C][C]4174.23514516444[/C][C]-8.53514516444375[/C][/ROW]
[ROW][C]30[/C][C]4167.9[/C][C]4159.16150109052[/C][C]8.73849890947622[/C][/ROW]
[ROW][C]31[/C][C]4158.3[/C][C]4167.12808233976[/C][C]-8.82808233975902[/C][/ROW]
[ROW][C]32[/C][C]4158.3[/C][C]4149.21251972257[/C][C]9.08748027743241[/C][/ROW]
[ROW][C]33[/C][C]4143.7[/C][C]4158.81730291843[/C][C]-15.117302918432[/C][/ROW]
[ROW][C]34[/C][C]4157.5[/C][C]4132.10786526955[/C][C]25.3921347304495[/C][/ROW]
[ROW][C]35[/C][C]4164.8[/C][C]4165.42764569432[/C][C]-0.627645694320563[/C][/ROW]
[ROW][C]36[/C][C]4173.9[/C][C]4171.1843122602[/C][C]2.71568773979743[/C][/ROW]
[ROW][C]37[/C][C]4181.2[/C][C]4184.62702939329[/C][C]-3.42702939329502[/C][/ROW]
[ROW][C]38[/C][C]4190.7[/C][C]4189.47185955332[/C][C]1.22814044667848[/C][/ROW]
[ROW][C]39[/C][C]4206.6[/C][C]4198.53610415194[/C][C]8.06389584806402[/C][/ROW]
[ROW][C]40[/C][C]4222.1[/C][C]4220.07057280619[/C][C]2.02942719380553[/C][/ROW]
[ROW][C]41[/C][C]4245.8[/C][C]4239.34655015485[/C][C]6.45344984515305[/C][/ROW]
[ROW][C]42[/C][C]4255.4[/C][C]4268.75105189512[/C][C]-13.3510518951161[/C][/ROW]
[ROW][C]43[/C][C]4266.1[/C][C]4265.87525080937[/C][C]0.224749190625516[/C][/ROW]
[ROW][C]44[/C][C]4273.6[/C][C]4275.73585714882[/C][C]-2.13585714882265[/C][/ROW]
[ROW][C]45[/C][C]4282.1[/C][C]4283.57198593811[/C][C]-1.4719859381139[/C][/ROW]
[ROW][C]46[/C][C]4299.8[/C][C]4291.23136455621[/C][C]8.56863544379485[/C][/ROW]
[ROW][C]47[/C][C]4315.7[/C][C]4314.55766616313[/C][C]1.14233383687133[/C][/ROW]
[ROW][C]48[/C][C]4331.7[/C][C]4330.37604843426[/C][C]1.32395156573602[/C][/ROW]
[ROW][C]49[/C][C]4348.4[/C][C]4349.56941746059[/C][C]-1.16941746058819[/C][/ROW]
[ROW][C]50[/C][C]4367.8[/C][C]4365.67866851377[/C][C]2.12133148623343[/C][/ROW]
[ROW][C]51[/C][C]4387.2[/C][C]4385.38054388568[/C][C]1.81945611432275[/C][/ROW]
[ROW][C]52[/C][C]4410.9[/C][C]4405.2581192152[/C][C]5.64188078480129[/C][/ROW]
[ROW][C]53[/C][C]4436[/C][C]4435.71739668422[/C][C]0.282603315777123[/C][/ROW]
[ROW][C]54[/C][C]4453.8[/C][C]4461.4257811374[/C][C]-7.62578113740165[/C][/ROW]
[ROW][C]55[/C][C]4469.1[/C][C]4471.47812409847[/C][C]-2.37812409847356[/C][/ROW]
[ROW][C]56[/C][C]4472[/C][C]4483.78917972368[/C][C]-11.7891797236816[/C][/ROW]
[ROW][C]57[/C][C]4458.2[/C][C]4479.05323145395[/C][C]-20.8532314539489[/C][/ROW]
[ROW][C]58[/C][C]4449[/C][C]4448.40684816427[/C][C]0.593151835730168[/C][/ROW]
[ROW][C]59[/C][C]4441.5[/C][C]4438.24669527188[/C][C]3.25330472811675[/C][/ROW]
[ROW][C]60[/C][C]4445.7[/C][C]4432.40839674569[/C][C]13.2916032543062[/C][/ROW]
[ROW][C]61[/C][C]4453.9[/C][C]4449.68510290667[/C][C]4.214897093334[/C][/ROW]
[ROW][C]62[/C][C]4469.7[/C][C]4461.7409235426[/C][C]7.95907645740044[/C][/ROW]
[ROW][C]63[/C][C]4487.5[/C][C]4482.66382839945[/C][C]4.83617160054655[/C][/ROW]
[ROW][C]64[/C][C]4504[/C][C]4503.43272090343[/C][C]0.56727909656729[/C][/ROW]
[ROW][C]65[/C][C]4524.1[/C][C]4522.50120132939[/C][C]1.5987986706059[/C][/ROW]
[ROW][C]66[/C][C]4540.5[/C][C]4544.29654943805[/C][C]-3.79654943804599[/C][/ROW]
[ROW][C]67[/C][C]4548.4[/C][C]4556.11121603923[/C][C]-7.71121603923166[/C][/ROW]
[ROW][C]68[/C][C]4554.2[/C][C]4556.61800364326[/C][C]-2.418003643259[/C][/ROW]
[ROW][C]69[/C][C]4558[/C][C]4562.52112523962[/C][C]-4.52112523962387[/C][/ROW]
[ROW][C]70[/C][C]4557.5[/C][C]4562.96240987641[/C][C]-5.46240987641158[/C][/ROW]
[ROW][C]71[/C][C]4554.5[/C][C]4556.50134623744[/C][C]-2.00134623743907[/C][/ROW]
[ROW][C]72[/C][C]4550[/C][C]4550.82355919931[/C][C]-0.823559199305237[/C][/ROW]
[ROW][C]73[/C][C]4543.8[/C][C]4547.74343302009[/C][C]-3.94343302009474[/C][/ROW]
[ROW][C]74[/C][C]4538.2[/C][C]4538.66179763165[/C][C]-0.461797631654917[/C][/ROW]
[ROW][C]75[/C][C]4543.3[/C][C]4531.23042776893[/C][C]12.0695722310711[/C][/ROW]
[ROW][C]76[/C][C]4545.1[/C][C]4545.27293472308[/C][C]-0.17293472307847[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279266&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279266&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
53880.43875.293755.10624999999936
63883.43888.02943340992-4.62943340991751
73884.23885.75627308379-1.55627308379371
83884.83884.246044205070.553955794935064
93894.93887.403521747157.49647825284774
103903.33904.06939559805-0.769395598051688
113911.23910.383999759060.816000240942685
123928.93917.9328834659910.9671165340092
133945.63946.78994101757-1.18994101756653
143965.73962.882242945052.81775705495465
153992.33983.85925275978.44074724030224
164008.74016.40493947545-7.70493947544992
174014.84028.54191050205-13.7419105020499
184020.64023.6683236698-3.06832366979552
194037.54025.4843865152112.0156134847903
204058.54051.282332306097.21766769391115
214082.34080.342953905141.95704609486256
224102.44106.13415621842-3.73415621841559
234127.14121.700349488375.39965051163017
244144.44149.83458408213-5.43458408212973
2541614164.74650003122-3.74650003122224
264168.24178.62749931603-10.4274993160343
274178.34175.76607797012.53392202990108
284174.14186.9336861397-12.8336861396992
294165.74174.23514516444-8.53514516444375
304167.94159.161501090528.73849890947622
314158.34167.12808233976-8.82808233975902
324158.34149.212519722579.08748027743241
334143.74158.81730291843-15.117302918432
344157.54132.1078652695525.3921347304495
354164.84165.42764569432-0.627645694320563
364173.94171.18431226022.71568773979743
374181.24184.62702939329-3.42702939329502
384190.74189.471859553321.22814044667848
394206.64198.536104151948.06389584806402
404222.14220.070572806192.02942719380553
414245.84239.346550154856.45344984515305
424255.44268.75105189512-13.3510518951161
434266.14265.875250809370.224749190625516
444273.64275.73585714882-2.13585714882265
454282.14283.57198593811-1.4719859381139
464299.84291.231364556218.56863544379485
474315.74314.557666163131.14233383687133
484331.74330.376048434261.32395156573602
494348.44349.56941746059-1.16941746058819
504367.84365.678668513772.12133148623343
514387.24385.380543885681.81945611432275
524410.94405.25811921525.64188078480129
5344364435.717396684220.282603315777123
544453.84461.4257811374-7.62578113740165
554469.14471.47812409847-2.37812409847356
5644724483.78917972368-11.7891797236816
574458.24479.05323145395-20.8532314539489
5844494448.406848164270.593151835730168
594441.54438.246695271883.25330472811675
604445.74432.4083967456913.2916032543062
614453.94449.685102906674.214897093334
624469.74461.74092354267.95907645740044
634487.54482.663828399454.83617160054655
6445044503.432720903430.56727909656729
654524.14522.501201329391.5987986706059
664540.54544.29654943805-3.79654943804599
674548.44556.11121603923-7.71121603923166
684554.24556.61800364326-2.418003643259
6945584562.52112523962-4.52112523962387
704557.54562.96240987641-5.46240987641158
714554.54556.50134623744-2.00134623743907
7245504550.82355919931-0.823559199305237
734543.84547.74343302009-3.94343302009474
744538.24538.66179763165-0.461797631654917
754543.34531.2304277689312.0695722310711
764545.14545.27293472308-0.17293472307847







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
774549.030118720834534.357155605814563.70308183585
784553.335237441664522.789796487494583.88067839583
794556.190356162494506.724698978094605.65601334689
804558.020474883324486.953994947064629.08695481957

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
77 & 4549.03011872083 & 4534.35715560581 & 4563.70308183585 \tabularnewline
78 & 4553.33523744166 & 4522.78979648749 & 4583.88067839583 \tabularnewline
79 & 4556.19035616249 & 4506.72469897809 & 4605.65601334689 \tabularnewline
80 & 4558.02047488332 & 4486.95399494706 & 4629.08695481957 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279266&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]77[/C][C]4549.03011872083[/C][C]4534.35715560581[/C][C]4563.70308183585[/C][/ROW]
[ROW][C]78[/C][C]4553.33523744166[/C][C]4522.78979648749[/C][C]4583.88067839583[/C][/ROW]
[ROW][C]79[/C][C]4556.19035616249[/C][C]4506.72469897809[/C][C]4605.65601334689[/C][/ROW]
[ROW][C]80[/C][C]4558.02047488332[/C][C]4486.95399494706[/C][C]4629.08695481957[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279266&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279266&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
774549.030118720834534.357155605814563.70308183585
784553.335237441664522.789796487494583.88067839583
794556.190356162494506.724698978094605.65601334689
804558.020474883324486.953994947064629.08695481957



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 4 ; 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')