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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 21:32:20 +0000
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/Nov/30/t1417383181n0bzn51gh6wma0l.htm/, Retrieved Sun, 19 May 2024 16:32:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261680, Retrieved Sun, 19 May 2024 16:32:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2014-11-28 09:37:57] [ff75f90af5b40beed49c921323a87bd7]
- RMPD  [Exponential Smoothing] [] [2014-11-30 21:31:05] [ff75f90af5b40beed49c921323a87bd7]
- R PD      [Exponential Smoothing] [] [2014-11-30 21:32:20] [a4941b106213b8203102126a01fbfecf] [Current]
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Dataseries X:
44.91
44.86
44.76
44.89
44.89
45
45.01
45.11
45.05
44.67
44.48
44.48
44.48
44.58
44.79
44.79
44.41
44.41
44.44
44.43
44.36
44.39
44.39
44.41
44.32
44.43
44.82
44.97
44.91
44.79
44.76
44.8
44.65
44.49
44.56
44.4
44.45
44.46
44.39
44.5
44.44
44.41
44.4
44.42
44.49
44.46
44.49
44.5
44.5
44.5
44.55
44.53
44.49
44.49
44.62
44.59
44.56
44.57
44.04
44.06
44.07
44.1
44.21
44.48
44.51
44.24
44.25
44.27
44.45
44.39
44.23
44.23




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261680&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261680&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261680&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0247165894496602
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0247165894496602 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261680&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]0.0247165894496602[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261680&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261680&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
beta0.0247165894496602
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
344.7644.81-0.0500000000000043
444.8944.70876417052750.181235829472485
544.8944.84324370211820.0467562978818421
64544.84439935833710.155600641662907
745.0144.95824527551520.0517547244848231
845.1144.96952447579230.140475524207652
945.0545.0729965516519-0.0229965516519144
1044.6745.012428155326-0.342428155325969
1144.4844.6239644991948-0.143964499194787
1244.4844.43040618777290.049593812227144
1344.4844.43163197766890.0483680223310827
1444.5844.43282747021940.147172529780633
1544.7944.53646507321620.253534926783779
1644.7944.75273159191270.0372684080873142
1744.4144.7536527398548-0.343652739854825
1844.4144.36515881617060.0448411838294192
1944.4444.36626713730170.0737328626982716
2044.4344.3980895621980.0319104378020114
2144.3644.3888782793883-0.0288782793883016
2244.3944.31816450681260.0718354931873506
2344.3944.34994003520570.0400599647943238
2444.4144.35093018090890.0590698190911283
2544.3244.3723901853762-0.0523901853762041
2644.4344.28109527867310.148904721326929
2744.8244.39477569553720.425224304462773
2844.9744.79528579009460.174714209905353
2944.9144.9496041294919-0.0396041294919058
3044.7944.8886252504827-0.0986252504827334
3144.7644.7661875706572-0.00618757065718967
3244.844.73603463501360.0639653649864371
3344.6544.7776156406789-0.127615640678926
3444.4944.6244614172809-0.13446141728091
3544.5644.46113798963320.0988620103668367
3644.444.5335815213556-0.133581521355573
3744.4544.37027984173420.0797201582658431
3844.4644.42225025215690.0377497478431223
3944.3944.4331832971761-0.0431832971761423
4044.544.36211595334880.137884046651237
4144.4444.4755239767215-0.0355239767214997
4244.4144.4146459451732-0.00464594517325168
4344.444.38453111325380.0154688867462056
4444.4244.37491345137670.045086548623253
4544.4944.39602783708880.0939721629112285
4644.4644.4683505084591-0.00835050845914509
4744.4944.43814411236990.0518558876301398
4844.544.4694258130550.0305741869450316
4944.544.48018150268140.0198184973185604
5044.544.48067134834320.0193286516568278
5144.5544.48114908669080.0688509133092055
5244.5344.5328508464483-0.0028508464482826
5344.4944.512780383247-0.0227803832470457
5444.4944.47221732986680.0177826701331796
5544.6244.47265685682380.147343143176172
5644.5944.6062986768019-0.0162986768019238
5744.5644.5758958290988-0.0158958290988451
5844.5744.5455029384170.0244970615829558
5944.0444.5561084222309-0.516108422230914
6044.0644.01335198224710.0466480177528794
6144.0744.03450496215060.0354950378494365
6244.144.04538227842860.0546177215714181
6344.2144.07673224222930.13326775777066
6444.4844.1900261666850.28997383331496
6544.5144.46719333087420.042806669125774
6644.2444.4982513657407-0.258251365740712
6744.2544.22186827275890.0281317272411101
6844.2744.23256359311160.0374364068883892
6944.4544.25348889341120.196511106588851
7044.3944.438345977755-0.0483459777550053
7144.2344.3771510300713-0.147151030071292
7244.2344.21351395847390.016486041526079

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 44.76 & 44.81 & -0.0500000000000043 \tabularnewline
4 & 44.89 & 44.7087641705275 & 0.181235829472485 \tabularnewline
5 & 44.89 & 44.8432437021182 & 0.0467562978818421 \tabularnewline
6 & 45 & 44.8443993583371 & 0.155600641662907 \tabularnewline
7 & 45.01 & 44.9582452755152 & 0.0517547244848231 \tabularnewline
8 & 45.11 & 44.9695244757923 & 0.140475524207652 \tabularnewline
9 & 45.05 & 45.0729965516519 & -0.0229965516519144 \tabularnewline
10 & 44.67 & 45.012428155326 & -0.342428155325969 \tabularnewline
11 & 44.48 & 44.6239644991948 & -0.143964499194787 \tabularnewline
12 & 44.48 & 44.4304061877729 & 0.049593812227144 \tabularnewline
13 & 44.48 & 44.4316319776689 & 0.0483680223310827 \tabularnewline
14 & 44.58 & 44.4328274702194 & 0.147172529780633 \tabularnewline
15 & 44.79 & 44.5364650732162 & 0.253534926783779 \tabularnewline
16 & 44.79 & 44.7527315919127 & 0.0372684080873142 \tabularnewline
17 & 44.41 & 44.7536527398548 & -0.343652739854825 \tabularnewline
18 & 44.41 & 44.3651588161706 & 0.0448411838294192 \tabularnewline
19 & 44.44 & 44.3662671373017 & 0.0737328626982716 \tabularnewline
20 & 44.43 & 44.398089562198 & 0.0319104378020114 \tabularnewline
21 & 44.36 & 44.3888782793883 & -0.0288782793883016 \tabularnewline
22 & 44.39 & 44.3181645068126 & 0.0718354931873506 \tabularnewline
23 & 44.39 & 44.3499400352057 & 0.0400599647943238 \tabularnewline
24 & 44.41 & 44.3509301809089 & 0.0590698190911283 \tabularnewline
25 & 44.32 & 44.3723901853762 & -0.0523901853762041 \tabularnewline
26 & 44.43 & 44.2810952786731 & 0.148904721326929 \tabularnewline
27 & 44.82 & 44.3947756955372 & 0.425224304462773 \tabularnewline
28 & 44.97 & 44.7952857900946 & 0.174714209905353 \tabularnewline
29 & 44.91 & 44.9496041294919 & -0.0396041294919058 \tabularnewline
30 & 44.79 & 44.8886252504827 & -0.0986252504827334 \tabularnewline
31 & 44.76 & 44.7661875706572 & -0.00618757065718967 \tabularnewline
32 & 44.8 & 44.7360346350136 & 0.0639653649864371 \tabularnewline
33 & 44.65 & 44.7776156406789 & -0.127615640678926 \tabularnewline
34 & 44.49 & 44.6244614172809 & -0.13446141728091 \tabularnewline
35 & 44.56 & 44.4611379896332 & 0.0988620103668367 \tabularnewline
36 & 44.4 & 44.5335815213556 & -0.133581521355573 \tabularnewline
37 & 44.45 & 44.3702798417342 & 0.0797201582658431 \tabularnewline
38 & 44.46 & 44.4222502521569 & 0.0377497478431223 \tabularnewline
39 & 44.39 & 44.4331832971761 & -0.0431832971761423 \tabularnewline
40 & 44.5 & 44.3621159533488 & 0.137884046651237 \tabularnewline
41 & 44.44 & 44.4755239767215 & -0.0355239767214997 \tabularnewline
42 & 44.41 & 44.4146459451732 & -0.00464594517325168 \tabularnewline
43 & 44.4 & 44.3845311132538 & 0.0154688867462056 \tabularnewline
44 & 44.42 & 44.3749134513767 & 0.045086548623253 \tabularnewline
45 & 44.49 & 44.3960278370888 & 0.0939721629112285 \tabularnewline
46 & 44.46 & 44.4683505084591 & -0.00835050845914509 \tabularnewline
47 & 44.49 & 44.4381441123699 & 0.0518558876301398 \tabularnewline
48 & 44.5 & 44.469425813055 & 0.0305741869450316 \tabularnewline
49 & 44.5 & 44.4801815026814 & 0.0198184973185604 \tabularnewline
50 & 44.5 & 44.4806713483432 & 0.0193286516568278 \tabularnewline
51 & 44.55 & 44.4811490866908 & 0.0688509133092055 \tabularnewline
52 & 44.53 & 44.5328508464483 & -0.0028508464482826 \tabularnewline
53 & 44.49 & 44.512780383247 & -0.0227803832470457 \tabularnewline
54 & 44.49 & 44.4722173298668 & 0.0177826701331796 \tabularnewline
55 & 44.62 & 44.4726568568238 & 0.147343143176172 \tabularnewline
56 & 44.59 & 44.6062986768019 & -0.0162986768019238 \tabularnewline
57 & 44.56 & 44.5758958290988 & -0.0158958290988451 \tabularnewline
58 & 44.57 & 44.545502938417 & 0.0244970615829558 \tabularnewline
59 & 44.04 & 44.5561084222309 & -0.516108422230914 \tabularnewline
60 & 44.06 & 44.0133519822471 & 0.0466480177528794 \tabularnewline
61 & 44.07 & 44.0345049621506 & 0.0354950378494365 \tabularnewline
62 & 44.1 & 44.0453822784286 & 0.0546177215714181 \tabularnewline
63 & 44.21 & 44.0767322422293 & 0.13326775777066 \tabularnewline
64 & 44.48 & 44.190026166685 & 0.28997383331496 \tabularnewline
65 & 44.51 & 44.4671933308742 & 0.042806669125774 \tabularnewline
66 & 44.24 & 44.4982513657407 & -0.258251365740712 \tabularnewline
67 & 44.25 & 44.2218682727589 & 0.0281317272411101 \tabularnewline
68 & 44.27 & 44.2325635931116 & 0.0374364068883892 \tabularnewline
69 & 44.45 & 44.2534888934112 & 0.196511106588851 \tabularnewline
70 & 44.39 & 44.438345977755 & -0.0483459777550053 \tabularnewline
71 & 44.23 & 44.3771510300713 & -0.147151030071292 \tabularnewline
72 & 44.23 & 44.2135139584739 & 0.016486041526079 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261680&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]44.76[/C][C]44.81[/C][C]-0.0500000000000043[/C][/ROW]
[ROW][C]4[/C][C]44.89[/C][C]44.7087641705275[/C][C]0.181235829472485[/C][/ROW]
[ROW][C]5[/C][C]44.89[/C][C]44.8432437021182[/C][C]0.0467562978818421[/C][/ROW]
[ROW][C]6[/C][C]45[/C][C]44.8443993583371[/C][C]0.155600641662907[/C][/ROW]
[ROW][C]7[/C][C]45.01[/C][C]44.9582452755152[/C][C]0.0517547244848231[/C][/ROW]
[ROW][C]8[/C][C]45.11[/C][C]44.9695244757923[/C][C]0.140475524207652[/C][/ROW]
[ROW][C]9[/C][C]45.05[/C][C]45.0729965516519[/C][C]-0.0229965516519144[/C][/ROW]
[ROW][C]10[/C][C]44.67[/C][C]45.012428155326[/C][C]-0.342428155325969[/C][/ROW]
[ROW][C]11[/C][C]44.48[/C][C]44.6239644991948[/C][C]-0.143964499194787[/C][/ROW]
[ROW][C]12[/C][C]44.48[/C][C]44.4304061877729[/C][C]0.049593812227144[/C][/ROW]
[ROW][C]13[/C][C]44.48[/C][C]44.4316319776689[/C][C]0.0483680223310827[/C][/ROW]
[ROW][C]14[/C][C]44.58[/C][C]44.4328274702194[/C][C]0.147172529780633[/C][/ROW]
[ROW][C]15[/C][C]44.79[/C][C]44.5364650732162[/C][C]0.253534926783779[/C][/ROW]
[ROW][C]16[/C][C]44.79[/C][C]44.7527315919127[/C][C]0.0372684080873142[/C][/ROW]
[ROW][C]17[/C][C]44.41[/C][C]44.7536527398548[/C][C]-0.343652739854825[/C][/ROW]
[ROW][C]18[/C][C]44.41[/C][C]44.3651588161706[/C][C]0.0448411838294192[/C][/ROW]
[ROW][C]19[/C][C]44.44[/C][C]44.3662671373017[/C][C]0.0737328626982716[/C][/ROW]
[ROW][C]20[/C][C]44.43[/C][C]44.398089562198[/C][C]0.0319104378020114[/C][/ROW]
[ROW][C]21[/C][C]44.36[/C][C]44.3888782793883[/C][C]-0.0288782793883016[/C][/ROW]
[ROW][C]22[/C][C]44.39[/C][C]44.3181645068126[/C][C]0.0718354931873506[/C][/ROW]
[ROW][C]23[/C][C]44.39[/C][C]44.3499400352057[/C][C]0.0400599647943238[/C][/ROW]
[ROW][C]24[/C][C]44.41[/C][C]44.3509301809089[/C][C]0.0590698190911283[/C][/ROW]
[ROW][C]25[/C][C]44.32[/C][C]44.3723901853762[/C][C]-0.0523901853762041[/C][/ROW]
[ROW][C]26[/C][C]44.43[/C][C]44.2810952786731[/C][C]0.148904721326929[/C][/ROW]
[ROW][C]27[/C][C]44.82[/C][C]44.3947756955372[/C][C]0.425224304462773[/C][/ROW]
[ROW][C]28[/C][C]44.97[/C][C]44.7952857900946[/C][C]0.174714209905353[/C][/ROW]
[ROW][C]29[/C][C]44.91[/C][C]44.9496041294919[/C][C]-0.0396041294919058[/C][/ROW]
[ROW][C]30[/C][C]44.79[/C][C]44.8886252504827[/C][C]-0.0986252504827334[/C][/ROW]
[ROW][C]31[/C][C]44.76[/C][C]44.7661875706572[/C][C]-0.00618757065718967[/C][/ROW]
[ROW][C]32[/C][C]44.8[/C][C]44.7360346350136[/C][C]0.0639653649864371[/C][/ROW]
[ROW][C]33[/C][C]44.65[/C][C]44.7776156406789[/C][C]-0.127615640678926[/C][/ROW]
[ROW][C]34[/C][C]44.49[/C][C]44.6244614172809[/C][C]-0.13446141728091[/C][/ROW]
[ROW][C]35[/C][C]44.56[/C][C]44.4611379896332[/C][C]0.0988620103668367[/C][/ROW]
[ROW][C]36[/C][C]44.4[/C][C]44.5335815213556[/C][C]-0.133581521355573[/C][/ROW]
[ROW][C]37[/C][C]44.45[/C][C]44.3702798417342[/C][C]0.0797201582658431[/C][/ROW]
[ROW][C]38[/C][C]44.46[/C][C]44.4222502521569[/C][C]0.0377497478431223[/C][/ROW]
[ROW][C]39[/C][C]44.39[/C][C]44.4331832971761[/C][C]-0.0431832971761423[/C][/ROW]
[ROW][C]40[/C][C]44.5[/C][C]44.3621159533488[/C][C]0.137884046651237[/C][/ROW]
[ROW][C]41[/C][C]44.44[/C][C]44.4755239767215[/C][C]-0.0355239767214997[/C][/ROW]
[ROW][C]42[/C][C]44.41[/C][C]44.4146459451732[/C][C]-0.00464594517325168[/C][/ROW]
[ROW][C]43[/C][C]44.4[/C][C]44.3845311132538[/C][C]0.0154688867462056[/C][/ROW]
[ROW][C]44[/C][C]44.42[/C][C]44.3749134513767[/C][C]0.045086548623253[/C][/ROW]
[ROW][C]45[/C][C]44.49[/C][C]44.3960278370888[/C][C]0.0939721629112285[/C][/ROW]
[ROW][C]46[/C][C]44.46[/C][C]44.4683505084591[/C][C]-0.00835050845914509[/C][/ROW]
[ROW][C]47[/C][C]44.49[/C][C]44.4381441123699[/C][C]0.0518558876301398[/C][/ROW]
[ROW][C]48[/C][C]44.5[/C][C]44.469425813055[/C][C]0.0305741869450316[/C][/ROW]
[ROW][C]49[/C][C]44.5[/C][C]44.4801815026814[/C][C]0.0198184973185604[/C][/ROW]
[ROW][C]50[/C][C]44.5[/C][C]44.4806713483432[/C][C]0.0193286516568278[/C][/ROW]
[ROW][C]51[/C][C]44.55[/C][C]44.4811490866908[/C][C]0.0688509133092055[/C][/ROW]
[ROW][C]52[/C][C]44.53[/C][C]44.5328508464483[/C][C]-0.0028508464482826[/C][/ROW]
[ROW][C]53[/C][C]44.49[/C][C]44.512780383247[/C][C]-0.0227803832470457[/C][/ROW]
[ROW][C]54[/C][C]44.49[/C][C]44.4722173298668[/C][C]0.0177826701331796[/C][/ROW]
[ROW][C]55[/C][C]44.62[/C][C]44.4726568568238[/C][C]0.147343143176172[/C][/ROW]
[ROW][C]56[/C][C]44.59[/C][C]44.6062986768019[/C][C]-0.0162986768019238[/C][/ROW]
[ROW][C]57[/C][C]44.56[/C][C]44.5758958290988[/C][C]-0.0158958290988451[/C][/ROW]
[ROW][C]58[/C][C]44.57[/C][C]44.545502938417[/C][C]0.0244970615829558[/C][/ROW]
[ROW][C]59[/C][C]44.04[/C][C]44.5561084222309[/C][C]-0.516108422230914[/C][/ROW]
[ROW][C]60[/C][C]44.06[/C][C]44.0133519822471[/C][C]0.0466480177528794[/C][/ROW]
[ROW][C]61[/C][C]44.07[/C][C]44.0345049621506[/C][C]0.0354950378494365[/C][/ROW]
[ROW][C]62[/C][C]44.1[/C][C]44.0453822784286[/C][C]0.0546177215714181[/C][/ROW]
[ROW][C]63[/C][C]44.21[/C][C]44.0767322422293[/C][C]0.13326775777066[/C][/ROW]
[ROW][C]64[/C][C]44.48[/C][C]44.190026166685[/C][C]0.28997383331496[/C][/ROW]
[ROW][C]65[/C][C]44.51[/C][C]44.4671933308742[/C][C]0.042806669125774[/C][/ROW]
[ROW][C]66[/C][C]44.24[/C][C]44.4982513657407[/C][C]-0.258251365740712[/C][/ROW]
[ROW][C]67[/C][C]44.25[/C][C]44.2218682727589[/C][C]0.0281317272411101[/C][/ROW]
[ROW][C]68[/C][C]44.27[/C][C]44.2325635931116[/C][C]0.0374364068883892[/C][/ROW]
[ROW][C]69[/C][C]44.45[/C][C]44.2534888934112[/C][C]0.196511106588851[/C][/ROW]
[ROW][C]70[/C][C]44.39[/C][C]44.438345977755[/C][C]-0.0483459777550053[/C][/ROW]
[ROW][C]71[/C][C]44.23[/C][C]44.3771510300713[/C][C]-0.147151030071292[/C][/ROW]
[ROW][C]72[/C][C]44.23[/C][C]44.2135139584739[/C][C]0.016486041526079[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261680&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261680&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
344.7644.81-0.0500000000000043
444.8944.70876417052750.181235829472485
544.8944.84324370211820.0467562978818421
64544.84439935833710.155600641662907
745.0144.95824527551520.0517547244848231
845.1144.96952447579230.140475524207652
945.0545.0729965516519-0.0229965516519144
1044.6745.012428155326-0.342428155325969
1144.4844.6239644991948-0.143964499194787
1244.4844.43040618777290.049593812227144
1344.4844.43163197766890.0483680223310827
1444.5844.43282747021940.147172529780633
1544.7944.53646507321620.253534926783779
1644.7944.75273159191270.0372684080873142
1744.4144.7536527398548-0.343652739854825
1844.4144.36515881617060.0448411838294192
1944.4444.36626713730170.0737328626982716
2044.4344.3980895621980.0319104378020114
2144.3644.3888782793883-0.0288782793883016
2244.3944.31816450681260.0718354931873506
2344.3944.34994003520570.0400599647943238
2444.4144.35093018090890.0590698190911283
2544.3244.3723901853762-0.0523901853762041
2644.4344.28109527867310.148904721326929
2744.8244.39477569553720.425224304462773
2844.9744.79528579009460.174714209905353
2944.9144.9496041294919-0.0396041294919058
3044.7944.8886252504827-0.0986252504827334
3144.7644.7661875706572-0.00618757065718967
3244.844.73603463501360.0639653649864371
3344.6544.7776156406789-0.127615640678926
3444.4944.6244614172809-0.13446141728091
3544.5644.46113798963320.0988620103668367
3644.444.5335815213556-0.133581521355573
3744.4544.37027984173420.0797201582658431
3844.4644.42225025215690.0377497478431223
3944.3944.4331832971761-0.0431832971761423
4044.544.36211595334880.137884046651237
4144.4444.4755239767215-0.0355239767214997
4244.4144.4146459451732-0.00464594517325168
4344.444.38453111325380.0154688867462056
4444.4244.37491345137670.045086548623253
4544.4944.39602783708880.0939721629112285
4644.4644.4683505084591-0.00835050845914509
4744.4944.43814411236990.0518558876301398
4844.544.4694258130550.0305741869450316
4944.544.48018150268140.0198184973185604
5044.544.48067134834320.0193286516568278
5144.5544.48114908669080.0688509133092055
5244.5344.5328508464483-0.0028508464482826
5344.4944.512780383247-0.0227803832470457
5444.4944.47221732986680.0177826701331796
5544.6244.47265685682380.147343143176172
5644.5944.6062986768019-0.0162986768019238
5744.5644.5758958290988-0.0158958290988451
5844.5744.5455029384170.0244970615829558
5944.0444.5561084222309-0.516108422230914
6044.0644.01335198224710.0466480177528794
6144.0744.03450496215060.0354950378494365
6244.144.04538227842860.0546177215714181
6344.2144.07673224222930.13326775777066
6444.4844.1900261666850.28997383331496
6544.5144.46719333087420.042806669125774
6644.2444.4982513657407-0.258251365740712
6744.2544.22186827275890.0281317272411101
6844.2744.23256359311160.0374364068883892
6944.4544.25348889341120.196511106588851
7044.3944.438345977755-0.0483459777550053
7144.2344.3771510300713-0.147151030071292
7244.2344.21351395847390.016486041526079







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7344.21392143719443.942694546659744.4851483277282
7444.197842874387943.809500889860244.5861848589157
7544.181764311581943.700280880545744.6632477426181
7644.165685748775943.602920877481244.7284506200706
7744.149607185969943.512792144597644.7864222273421
7844.133528623163843.427551664620444.8395055817072
7944.117450060357843.345825547035244.8890745736804
8044.101371497551843.266730227553444.9360127675501
8144.085292934745743.189660014384644.9809258551069
8244.069214371939743.114179761635445.024248982244
8344.053135809133743.039965404865145.0663062134023
8444.037057246327742.96676864336945.1073458492863

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 44.213921437194 & 43.9426945466597 & 44.4851483277282 \tabularnewline
74 & 44.1978428743879 & 43.8095008898602 & 44.5861848589157 \tabularnewline
75 & 44.1817643115819 & 43.7002808805457 & 44.6632477426181 \tabularnewline
76 & 44.1656857487759 & 43.6029208774812 & 44.7284506200706 \tabularnewline
77 & 44.1496071859699 & 43.5127921445976 & 44.7864222273421 \tabularnewline
78 & 44.1335286231638 & 43.4275516646204 & 44.8395055817072 \tabularnewline
79 & 44.1174500603578 & 43.3458255470352 & 44.8890745736804 \tabularnewline
80 & 44.1013714975518 & 43.2667302275534 & 44.9360127675501 \tabularnewline
81 & 44.0852929347457 & 43.1896600143846 & 44.9809258551069 \tabularnewline
82 & 44.0692143719397 & 43.1141797616354 & 45.024248982244 \tabularnewline
83 & 44.0531358091337 & 43.0399654048651 & 45.0663062134023 \tabularnewline
84 & 44.0370572463277 & 42.966768643369 & 45.1073458492863 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261680&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]44.213921437194[/C][C]43.9426945466597[/C][C]44.4851483277282[/C][/ROW]
[ROW][C]74[/C][C]44.1978428743879[/C][C]43.8095008898602[/C][C]44.5861848589157[/C][/ROW]
[ROW][C]75[/C][C]44.1817643115819[/C][C]43.7002808805457[/C][C]44.6632477426181[/C][/ROW]
[ROW][C]76[/C][C]44.1656857487759[/C][C]43.6029208774812[/C][C]44.7284506200706[/C][/ROW]
[ROW][C]77[/C][C]44.1496071859699[/C][C]43.5127921445976[/C][C]44.7864222273421[/C][/ROW]
[ROW][C]78[/C][C]44.1335286231638[/C][C]43.4275516646204[/C][C]44.8395055817072[/C][/ROW]
[ROW][C]79[/C][C]44.1174500603578[/C][C]43.3458255470352[/C][C]44.8890745736804[/C][/ROW]
[ROW][C]80[/C][C]44.1013714975518[/C][C]43.2667302275534[/C][C]44.9360127675501[/C][/ROW]
[ROW][C]81[/C][C]44.0852929347457[/C][C]43.1896600143846[/C][C]44.9809258551069[/C][/ROW]
[ROW][C]82[/C][C]44.0692143719397[/C][C]43.1141797616354[/C][C]45.024248982244[/C][/ROW]
[ROW][C]83[/C][C]44.0531358091337[/C][C]43.0399654048651[/C][C]45.0663062134023[/C][/ROW]
[ROW][C]84[/C][C]44.0370572463277[/C][C]42.966768643369[/C][C]45.1073458492863[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261680&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261680&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
7344.21392143719443.942694546659744.4851483277282
7444.197842874387943.809500889860244.5861848589157
7544.181764311581943.700280880545744.6632477426181
7644.165685748775943.602920877481244.7284506200706
7744.149607185969943.512792144597644.7864222273421
7844.133528623163843.427551664620444.8395055817072
7944.117450060357843.345825547035244.8890745736804
8044.101371497551843.266730227553444.9360127675501
8144.085292934745743.189660014384644.9809258551069
8244.069214371939743.114179761635445.024248982244
8344.053135809133743.039965404865145.0663062134023
8444.037057246327742.96676864336945.1073458492863



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')