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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 06 May 2013 03:11:12 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/06/t1367824354h7ob59buc7wkm0e.htm/, Retrieved Sun, 28 Apr 2024 22:43:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208730, Retrieved Sun, 28 Apr 2024 22:43:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [triple expponenti...] [2013-05-06 07:11:12] [bc4d9ad98829fcb778aa9177827398a7] [Current]
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Dataseries X:
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.00
4.06
4.07
4.07
4.07
4.07
4.07
4.30
4.44
4.52
4.52
4.52
4.53
4.53
4.53
4.53
4.53
4.53
4.53
4.53
4.61
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.63
4.66
4.70
4.72
4.73
4.73
4.74
4.74
4.74
4.76
4.88
4.88
4.88
4.88
4.89
4.97
4.97
4.97
4.97
4.97
4.97
4.97
4.97
4.97
4.97
4.97
4.98
5.00
5.03
5.04
5.04
5.05
5.05
5.05
5.06




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208730&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208730&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208730&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.589894328918783
beta0.0757352352628603
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.589894328918783 \tabularnewline
beta & 0.0757352352628603 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208730&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]0.589894328918783[/C][/ROW]
[ROW][C]beta[/C][C]0.0757352352628603[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208730&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208730&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
alpha0.589894328918783
beta0.0757352352628603
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134.073.861789529914530.208210470085469
144.073.987439312823980.0825606871760192
154.34.27474079827280.0252592017271969
164.444.44228560376877-0.00228560376876974
174.524.53389644023381-0.0138964402338084
184.524.53803727572711-0.0180372757271146
194.524.436846293046140.0831537069538548
204.534.53364558771849-0.00364558771848777
214.534.62949626788018-0.099496267880177
224.534.598943434775-0.0689434347749973
234.534.56416677586129-0.0341667758612916
244.534.54504490992699-0.0150449099269885
254.534.62191907565322-0.0919190756532204
264.534.512004400275630.017995599724367
274.534.7278450938572-0.1978450938572
284.614.73264375118202-0.122643751182022
294.634.72327532585192-0.093275325851919
304.634.6501275093584-0.0201275093584039
314.634.560343805336040.0696561946639598
324.634.584122398859520.0458776011404822
334.634.64262839494087-0.0126283949408705
344.634.65247998322762-0.022479983227619
354.634.6380814127892-0.00808141278920438
364.634.622061981216580.00793801878341593
374.634.6618667362831-0.0318667362831047
384.634.616035733851040.013964266148963
394.664.72438327794075-0.0643832779407454
404.74.82811571601387-0.128115716013867
414.724.81668401841936-0.0966840184193574
424.734.76049193284289-0.0304919328428861
434.734.689920246571830.0400797534281674
444.744.673683904530660.0663160954693387
454.744.708349692961610.0316503070383947
464.744.730355911255110.00964408874488587
474.764.732322319288030.027677680711971
484.884.737074434716150.142925565283852
494.884.839321897661390.0406781023386102
504.884.857459711315330.0225402886846666
514.884.94149804404472-0.061498044044721
524.895.02368694476422-0.133686944764221
534.975.02450174315693-0.0545017431569272
544.975.02486563330458-0.0548656333045763
554.974.97229611498373-0.00229611498373217
564.974.943367212793240.0266327872067631
574.974.940179574970660.0298204250293423
584.974.951771898577910.0182281014220864
594.974.966271560110350.00372843988965421
604.975.00316392885212-0.0331639288521224
614.974.950741960512190.0192580394878084
624.974.938985849280860.0310141507191419
634.974.98411691372887-0.0141169137288708
644.985.05732603157429-0.0773260315742936
6555.1190555159884-0.1190555159884
665.035.073499680406-0.0434996804059988
675.045.04201112589581-0.00201112589581154
685.045.017944171173640.0220558288263559
695.055.005989327870110.0440106721298896
705.055.014457728518190.0355422714818143
715.055.027257459910730.0227425400892649
725.065.055118771311620.00488122868837504

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4.07 & 3.86178952991453 & 0.208210470085469 \tabularnewline
14 & 4.07 & 3.98743931282398 & 0.0825606871760192 \tabularnewline
15 & 4.3 & 4.2747407982728 & 0.0252592017271969 \tabularnewline
16 & 4.44 & 4.44228560376877 & -0.00228560376876974 \tabularnewline
17 & 4.52 & 4.53389644023381 & -0.0138964402338084 \tabularnewline
18 & 4.52 & 4.53803727572711 & -0.0180372757271146 \tabularnewline
19 & 4.52 & 4.43684629304614 & 0.0831537069538548 \tabularnewline
20 & 4.53 & 4.53364558771849 & -0.00364558771848777 \tabularnewline
21 & 4.53 & 4.62949626788018 & -0.099496267880177 \tabularnewline
22 & 4.53 & 4.598943434775 & -0.0689434347749973 \tabularnewline
23 & 4.53 & 4.56416677586129 & -0.0341667758612916 \tabularnewline
24 & 4.53 & 4.54504490992699 & -0.0150449099269885 \tabularnewline
25 & 4.53 & 4.62191907565322 & -0.0919190756532204 \tabularnewline
26 & 4.53 & 4.51200440027563 & 0.017995599724367 \tabularnewline
27 & 4.53 & 4.7278450938572 & -0.1978450938572 \tabularnewline
28 & 4.61 & 4.73264375118202 & -0.122643751182022 \tabularnewline
29 & 4.63 & 4.72327532585192 & -0.093275325851919 \tabularnewline
30 & 4.63 & 4.6501275093584 & -0.0201275093584039 \tabularnewline
31 & 4.63 & 4.56034380533604 & 0.0696561946639598 \tabularnewline
32 & 4.63 & 4.58412239885952 & 0.0458776011404822 \tabularnewline
33 & 4.63 & 4.64262839494087 & -0.0126283949408705 \tabularnewline
34 & 4.63 & 4.65247998322762 & -0.022479983227619 \tabularnewline
35 & 4.63 & 4.6380814127892 & -0.00808141278920438 \tabularnewline
36 & 4.63 & 4.62206198121658 & 0.00793801878341593 \tabularnewline
37 & 4.63 & 4.6618667362831 & -0.0318667362831047 \tabularnewline
38 & 4.63 & 4.61603573385104 & 0.013964266148963 \tabularnewline
39 & 4.66 & 4.72438327794075 & -0.0643832779407454 \tabularnewline
40 & 4.7 & 4.82811571601387 & -0.128115716013867 \tabularnewline
41 & 4.72 & 4.81668401841936 & -0.0966840184193574 \tabularnewline
42 & 4.73 & 4.76049193284289 & -0.0304919328428861 \tabularnewline
43 & 4.73 & 4.68992024657183 & 0.0400797534281674 \tabularnewline
44 & 4.74 & 4.67368390453066 & 0.0663160954693387 \tabularnewline
45 & 4.74 & 4.70834969296161 & 0.0316503070383947 \tabularnewline
46 & 4.74 & 4.73035591125511 & 0.00964408874488587 \tabularnewline
47 & 4.76 & 4.73232231928803 & 0.027677680711971 \tabularnewline
48 & 4.88 & 4.73707443471615 & 0.142925565283852 \tabularnewline
49 & 4.88 & 4.83932189766139 & 0.0406781023386102 \tabularnewline
50 & 4.88 & 4.85745971131533 & 0.0225402886846666 \tabularnewline
51 & 4.88 & 4.94149804404472 & -0.061498044044721 \tabularnewline
52 & 4.89 & 5.02368694476422 & -0.133686944764221 \tabularnewline
53 & 4.97 & 5.02450174315693 & -0.0545017431569272 \tabularnewline
54 & 4.97 & 5.02486563330458 & -0.0548656333045763 \tabularnewline
55 & 4.97 & 4.97229611498373 & -0.00229611498373217 \tabularnewline
56 & 4.97 & 4.94336721279324 & 0.0266327872067631 \tabularnewline
57 & 4.97 & 4.94017957497066 & 0.0298204250293423 \tabularnewline
58 & 4.97 & 4.95177189857791 & 0.0182281014220864 \tabularnewline
59 & 4.97 & 4.96627156011035 & 0.00372843988965421 \tabularnewline
60 & 4.97 & 5.00316392885212 & -0.0331639288521224 \tabularnewline
61 & 4.97 & 4.95074196051219 & 0.0192580394878084 \tabularnewline
62 & 4.97 & 4.93898584928086 & 0.0310141507191419 \tabularnewline
63 & 4.97 & 4.98411691372887 & -0.0141169137288708 \tabularnewline
64 & 4.98 & 5.05732603157429 & -0.0773260315742936 \tabularnewline
65 & 5 & 5.1190555159884 & -0.1190555159884 \tabularnewline
66 & 5.03 & 5.073499680406 & -0.0434996804059988 \tabularnewline
67 & 5.04 & 5.04201112589581 & -0.00201112589581154 \tabularnewline
68 & 5.04 & 5.01794417117364 & 0.0220558288263559 \tabularnewline
69 & 5.05 & 5.00598932787011 & 0.0440106721298896 \tabularnewline
70 & 5.05 & 5.01445772851819 & 0.0355422714818143 \tabularnewline
71 & 5.05 & 5.02725745991073 & 0.0227425400892649 \tabularnewline
72 & 5.06 & 5.05511877131162 & 0.00488122868837504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208730&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]4.07[/C][C]3.86178952991453[/C][C]0.208210470085469[/C][/ROW]
[ROW][C]14[/C][C]4.07[/C][C]3.98743931282398[/C][C]0.0825606871760192[/C][/ROW]
[ROW][C]15[/C][C]4.3[/C][C]4.2747407982728[/C][C]0.0252592017271969[/C][/ROW]
[ROW][C]16[/C][C]4.44[/C][C]4.44228560376877[/C][C]-0.00228560376876974[/C][/ROW]
[ROW][C]17[/C][C]4.52[/C][C]4.53389644023381[/C][C]-0.0138964402338084[/C][/ROW]
[ROW][C]18[/C][C]4.52[/C][C]4.53803727572711[/C][C]-0.0180372757271146[/C][/ROW]
[ROW][C]19[/C][C]4.52[/C][C]4.43684629304614[/C][C]0.0831537069538548[/C][/ROW]
[ROW][C]20[/C][C]4.53[/C][C]4.53364558771849[/C][C]-0.00364558771848777[/C][/ROW]
[ROW][C]21[/C][C]4.53[/C][C]4.62949626788018[/C][C]-0.099496267880177[/C][/ROW]
[ROW][C]22[/C][C]4.53[/C][C]4.598943434775[/C][C]-0.0689434347749973[/C][/ROW]
[ROW][C]23[/C][C]4.53[/C][C]4.56416677586129[/C][C]-0.0341667758612916[/C][/ROW]
[ROW][C]24[/C][C]4.53[/C][C]4.54504490992699[/C][C]-0.0150449099269885[/C][/ROW]
[ROW][C]25[/C][C]4.53[/C][C]4.62191907565322[/C][C]-0.0919190756532204[/C][/ROW]
[ROW][C]26[/C][C]4.53[/C][C]4.51200440027563[/C][C]0.017995599724367[/C][/ROW]
[ROW][C]27[/C][C]4.53[/C][C]4.7278450938572[/C][C]-0.1978450938572[/C][/ROW]
[ROW][C]28[/C][C]4.61[/C][C]4.73264375118202[/C][C]-0.122643751182022[/C][/ROW]
[ROW][C]29[/C][C]4.63[/C][C]4.72327532585192[/C][C]-0.093275325851919[/C][/ROW]
[ROW][C]30[/C][C]4.63[/C][C]4.6501275093584[/C][C]-0.0201275093584039[/C][/ROW]
[ROW][C]31[/C][C]4.63[/C][C]4.56034380533604[/C][C]0.0696561946639598[/C][/ROW]
[ROW][C]32[/C][C]4.63[/C][C]4.58412239885952[/C][C]0.0458776011404822[/C][/ROW]
[ROW][C]33[/C][C]4.63[/C][C]4.64262839494087[/C][C]-0.0126283949408705[/C][/ROW]
[ROW][C]34[/C][C]4.63[/C][C]4.65247998322762[/C][C]-0.022479983227619[/C][/ROW]
[ROW][C]35[/C][C]4.63[/C][C]4.6380814127892[/C][C]-0.00808141278920438[/C][/ROW]
[ROW][C]36[/C][C]4.63[/C][C]4.62206198121658[/C][C]0.00793801878341593[/C][/ROW]
[ROW][C]37[/C][C]4.63[/C][C]4.6618667362831[/C][C]-0.0318667362831047[/C][/ROW]
[ROW][C]38[/C][C]4.63[/C][C]4.61603573385104[/C][C]0.013964266148963[/C][/ROW]
[ROW][C]39[/C][C]4.66[/C][C]4.72438327794075[/C][C]-0.0643832779407454[/C][/ROW]
[ROW][C]40[/C][C]4.7[/C][C]4.82811571601387[/C][C]-0.128115716013867[/C][/ROW]
[ROW][C]41[/C][C]4.72[/C][C]4.81668401841936[/C][C]-0.0966840184193574[/C][/ROW]
[ROW][C]42[/C][C]4.73[/C][C]4.76049193284289[/C][C]-0.0304919328428861[/C][/ROW]
[ROW][C]43[/C][C]4.73[/C][C]4.68992024657183[/C][C]0.0400797534281674[/C][/ROW]
[ROW][C]44[/C][C]4.74[/C][C]4.67368390453066[/C][C]0.0663160954693387[/C][/ROW]
[ROW][C]45[/C][C]4.74[/C][C]4.70834969296161[/C][C]0.0316503070383947[/C][/ROW]
[ROW][C]46[/C][C]4.74[/C][C]4.73035591125511[/C][C]0.00964408874488587[/C][/ROW]
[ROW][C]47[/C][C]4.76[/C][C]4.73232231928803[/C][C]0.027677680711971[/C][/ROW]
[ROW][C]48[/C][C]4.88[/C][C]4.73707443471615[/C][C]0.142925565283852[/C][/ROW]
[ROW][C]49[/C][C]4.88[/C][C]4.83932189766139[/C][C]0.0406781023386102[/C][/ROW]
[ROW][C]50[/C][C]4.88[/C][C]4.85745971131533[/C][C]0.0225402886846666[/C][/ROW]
[ROW][C]51[/C][C]4.88[/C][C]4.94149804404472[/C][C]-0.061498044044721[/C][/ROW]
[ROW][C]52[/C][C]4.89[/C][C]5.02368694476422[/C][C]-0.133686944764221[/C][/ROW]
[ROW][C]53[/C][C]4.97[/C][C]5.02450174315693[/C][C]-0.0545017431569272[/C][/ROW]
[ROW][C]54[/C][C]4.97[/C][C]5.02486563330458[/C][C]-0.0548656333045763[/C][/ROW]
[ROW][C]55[/C][C]4.97[/C][C]4.97229611498373[/C][C]-0.00229611498373217[/C][/ROW]
[ROW][C]56[/C][C]4.97[/C][C]4.94336721279324[/C][C]0.0266327872067631[/C][/ROW]
[ROW][C]57[/C][C]4.97[/C][C]4.94017957497066[/C][C]0.0298204250293423[/C][/ROW]
[ROW][C]58[/C][C]4.97[/C][C]4.95177189857791[/C][C]0.0182281014220864[/C][/ROW]
[ROW][C]59[/C][C]4.97[/C][C]4.96627156011035[/C][C]0.00372843988965421[/C][/ROW]
[ROW][C]60[/C][C]4.97[/C][C]5.00316392885212[/C][C]-0.0331639288521224[/C][/ROW]
[ROW][C]61[/C][C]4.97[/C][C]4.95074196051219[/C][C]0.0192580394878084[/C][/ROW]
[ROW][C]62[/C][C]4.97[/C][C]4.93898584928086[/C][C]0.0310141507191419[/C][/ROW]
[ROW][C]63[/C][C]4.97[/C][C]4.98411691372887[/C][C]-0.0141169137288708[/C][/ROW]
[ROW][C]64[/C][C]4.98[/C][C]5.05732603157429[/C][C]-0.0773260315742936[/C][/ROW]
[ROW][C]65[/C][C]5[/C][C]5.1190555159884[/C][C]-0.1190555159884[/C][/ROW]
[ROW][C]66[/C][C]5.03[/C][C]5.073499680406[/C][C]-0.0434996804059988[/C][/ROW]
[ROW][C]67[/C][C]5.04[/C][C]5.04201112589581[/C][C]-0.00201112589581154[/C][/ROW]
[ROW][C]68[/C][C]5.04[/C][C]5.01794417117364[/C][C]0.0220558288263559[/C][/ROW]
[ROW][C]69[/C][C]5.05[/C][C]5.00598932787011[/C][C]0.0440106721298896[/C][/ROW]
[ROW][C]70[/C][C]5.05[/C][C]5.01445772851819[/C][C]0.0355422714818143[/C][/ROW]
[ROW][C]71[/C][C]5.05[/C][C]5.02725745991073[/C][C]0.0227425400892649[/C][/ROW]
[ROW][C]72[/C][C]5.06[/C][C]5.05511877131162[/C][C]0.00488122868837504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208730&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208730&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
134.073.861789529914530.208210470085469
144.073.987439312823980.0825606871760192
154.34.27474079827280.0252592017271969
164.444.44228560376877-0.00228560376876974
174.524.53389644023381-0.0138964402338084
184.524.53803727572711-0.0180372757271146
194.524.436846293046140.0831537069538548
204.534.53364558771849-0.00364558771848777
214.534.62949626788018-0.099496267880177
224.534.598943434775-0.0689434347749973
234.534.56416677586129-0.0341667758612916
244.534.54504490992699-0.0150449099269885
254.534.62191907565322-0.0919190756532204
264.534.512004400275630.017995599724367
274.534.7278450938572-0.1978450938572
284.614.73264375118202-0.122643751182022
294.634.72327532585192-0.093275325851919
304.634.6501275093584-0.0201275093584039
314.634.560343805336040.0696561946639598
324.634.584122398859520.0458776011404822
334.634.64262839494087-0.0126283949408705
344.634.65247998322762-0.022479983227619
354.634.6380814127892-0.00808141278920438
364.634.622061981216580.00793801878341593
374.634.6618667362831-0.0318667362831047
384.634.616035733851040.013964266148963
394.664.72438327794075-0.0643832779407454
404.74.82811571601387-0.128115716013867
414.724.81668401841936-0.0966840184193574
424.734.76049193284289-0.0304919328428861
434.734.689920246571830.0400797534281674
444.744.673683904530660.0663160954693387
454.744.708349692961610.0316503070383947
464.744.730355911255110.00964408874488587
474.764.732322319288030.027677680711971
484.884.737074434716150.142925565283852
494.884.839321897661390.0406781023386102
504.884.857459711315330.0225402886846666
514.884.94149804404472-0.061498044044721
524.895.02368694476422-0.133686944764221
534.975.02450174315693-0.0545017431569272
544.975.02486563330458-0.0548656333045763
554.974.97229611498373-0.00229611498373217
564.974.943367212793240.0266327872067631
574.974.940179574970660.0298204250293423
584.974.951771898577910.0182281014220864
594.974.966271560110350.00372843988965421
604.975.00316392885212-0.0331639288521224
614.974.950741960512190.0192580394878084
624.974.938985849280860.0310141507191419
634.974.98411691372887-0.0141169137288708
644.985.05732603157429-0.0773260315742936
6555.1190555159884-0.1190555159884
665.035.073499680406-0.0434996804059988
675.045.04201112589581-0.00201112589581154
685.045.017944171173640.0220558288263559
695.055.005989327870110.0440106721298896
705.055.014457728518190.0355422714818143
715.055.027257459910730.0227425400892649
725.065.055118771311620.00488122868837504







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
735.043220071883874.910744133007395.17569601076035
745.020646731942474.863749172076575.17754429180837
755.023310369423314.842440478431865.20418026041477
765.073891391270774.869169261536995.27861352100455
775.162543000544714.933897861533085.39118813955635
785.221943549620214.969186113457845.47470098578258
795.238813618078464.961677599626765.51594963653017
805.231576575061474.92974415524435.53340899487864
815.220403133003554.893521367193645.54728489881345
825.202258941102794.849950742620885.5545671395847
835.19007735925534.81194907435225.56820564415839
845.19741602286114.793062780394915.60176926532728

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 5.04322007188387 & 4.91074413300739 & 5.17569601076035 \tabularnewline
74 & 5.02064673194247 & 4.86374917207657 & 5.17754429180837 \tabularnewline
75 & 5.02331036942331 & 4.84244047843186 & 5.20418026041477 \tabularnewline
76 & 5.07389139127077 & 4.86916926153699 & 5.27861352100455 \tabularnewline
77 & 5.16254300054471 & 4.93389786153308 & 5.39118813955635 \tabularnewline
78 & 5.22194354962021 & 4.96918611345784 & 5.47470098578258 \tabularnewline
79 & 5.23881361807846 & 4.96167759962676 & 5.51594963653017 \tabularnewline
80 & 5.23157657506147 & 4.9297441552443 & 5.53340899487864 \tabularnewline
81 & 5.22040313300355 & 4.89352136719364 & 5.54728489881345 \tabularnewline
82 & 5.20225894110279 & 4.84995074262088 & 5.5545671395847 \tabularnewline
83 & 5.1900773592553 & 4.8119490743522 & 5.56820564415839 \tabularnewline
84 & 5.1974160228611 & 4.79306278039491 & 5.60176926532728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208730&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]5.04322007188387[/C][C]4.91074413300739[/C][C]5.17569601076035[/C][/ROW]
[ROW][C]74[/C][C]5.02064673194247[/C][C]4.86374917207657[/C][C]5.17754429180837[/C][/ROW]
[ROW][C]75[/C][C]5.02331036942331[/C][C]4.84244047843186[/C][C]5.20418026041477[/C][/ROW]
[ROW][C]76[/C][C]5.07389139127077[/C][C]4.86916926153699[/C][C]5.27861352100455[/C][/ROW]
[ROW][C]77[/C][C]5.16254300054471[/C][C]4.93389786153308[/C][C]5.39118813955635[/C][/ROW]
[ROW][C]78[/C][C]5.22194354962021[/C][C]4.96918611345784[/C][C]5.47470098578258[/C][/ROW]
[ROW][C]79[/C][C]5.23881361807846[/C][C]4.96167759962676[/C][C]5.51594963653017[/C][/ROW]
[ROW][C]80[/C][C]5.23157657506147[/C][C]4.9297441552443[/C][C]5.53340899487864[/C][/ROW]
[ROW][C]81[/C][C]5.22040313300355[/C][C]4.89352136719364[/C][C]5.54728489881345[/C][/ROW]
[ROW][C]82[/C][C]5.20225894110279[/C][C]4.84995074262088[/C][C]5.5545671395847[/C][/ROW]
[ROW][C]83[/C][C]5.1900773592553[/C][C]4.8119490743522[/C][C]5.56820564415839[/C][/ROW]
[ROW][C]84[/C][C]5.1974160228611[/C][C]4.79306278039491[/C][C]5.60176926532728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208730&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208730&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
735.043220071883874.910744133007395.17569601076035
745.020646731942474.863749172076575.17754429180837
755.023310369423314.842440478431865.20418026041477
765.073891391270774.869169261536995.27861352100455
775.162543000544714.933897861533085.39118813955635
785.221943549620214.969186113457845.47470098578258
795.238813618078464.961677599626765.51594963653017
805.231576575061474.92974415524435.53340899487864
815.220403133003554.893521367193645.54728489881345
825.202258941102794.849950742620885.5545671395847
835.19007735925534.81194907435225.56820564415839
845.19741602286114.793062780394915.60176926532728



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')