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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 15:11:19 +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/2011/May/19/t130581763593dshivmp7se06a.htm/, Retrieved Sun, 12 May 2024 11:37:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122087, Retrieved Sun, 12 May 2024 11:37:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Opdracht 10 Axel ...] [2011-05-18 15:08:23] [6411650949db84072a7f54fa75041d5a]
- R PD    [Exponential Smoothing] [Opgave 10 Oefening 2] [2011-05-19 15:11:19] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
8
8
8,2
8,5
8,7
8,7
8
8
8,3
8,5
8,7
8,6
8,3
7,9
7,9
8,1
8,3
8,1
7,4
7,3
7,7
8
8
7,7
6,9
6,6
6,9
7,5
7,9
7,7
6,5
6,1
6,4
6,8
7,1
7,3
7,2
7
7
7
7,3
7,5
7,2
7,7
8
7,9
8
8
7,9
7,9
8
8,1
8,1
8,2
8
8,3
8,5
8,6
8,7
8,7
8,5
8,4
8,5
8,7
8,7
8,6
7,9
8,1
8,2
8,5
8,6
8,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122087&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122087&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122087&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.947401841274698
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.947401841274698 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122087&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]0.947401841274698[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122087&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122087&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
beta0.947401841274698
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.280.199999999999999
48.58.389480368254940.110519631745062
58.78.79418687086721-0.0941868708672136
68.78.90495405598371-0.204954055983713
788.71078020596802-0.710780205968025
887.337385730092310.66261426990769
98.37.965147709457750.334852290542255
108.58.58238738607253-0.0823873860725293
118.78.7043334248096-0.00433342480960519
128.68.90022793016596-0.300227930165958
138.38.51579143632464-0.215791436324636
147.98.01135023221937-0.111350232219365
157.97.505856817188370.394143182811627
168.17.879268794309980.220731205690021
178.38.288389945007490.0116100549925129
188.18.4993893324847-0.399389332484697
197.47.92100714350322-0.521007143503221
207.36.7274040164310.572595983569
217.77.169882505570770.530117494429233
2288.07211679588495-0.072116795884952
2388.30379321067672-0.303793210676716
247.78.01597896351484-0.315978963514843
256.97.41661991167681-0.51661991167681
266.66.127173256115030.472826743884971
276.96.275130183875570.624869816124431
287.57.167132998228840.332867001771162
297.98.08249180860643-0.182491808606425
307.78.30959873311515-0.609598733115148
316.57.53206377092313-1.03206377092313
326.15.354284654037650.745715345962352
336.45.660776745869180.739223254130822
346.86.66111821794580.138881782054206
357.17.19269507398346-0.0926950739834602
367.37.40487559021444-0.104875590214435
377.27.50551626294051-0.305516262940508
3877.11606959289131-0.116069592891306
3976.806105046870080.193894953129922
4076.989801482479240.0101985175207622
417.36.999463576756680.30053642324332
427.57.58419233750751-0.0841923375075133
437.27.70442836193167-0.504428361931675
447.76.926532003046430.773467996953574
4588.1593170075273-0.159317007527296
467.98.30837978124956-0.408379781249559
4787.821480024554370.178519975445631
4888.09061017799587-0.0906101779958739
497.98.00476592852436-0.104765928524355
507.97.805510494937530.0944895050624721
5187.895030026014850.104969973985151
528.18.094478772646940.00552122735306249
538.18.19970959360732-0.099709593607324
548.28.1052445410310.094755458969006
5588.29501603732906-0.295016037329058
568.37.815517300357940.484482699642057
578.58.57451710206457-0.0745171020645667
588.68.70391946236214-0.103919462362141
598.78.70546597237597-0.00546597237597268
608.78.80028750008262-0.100287500082619
618.58.70527493784751-0.205274937847509
628.48.310797083763230.0892029162367702
638.58.295308090853020.20469190914698
648.78.58923358247290.110766417527097
658.78.89417389038947-0.194173890389475
668.68.71021318910701-0.110213189107014
677.98.50579701081427-0.605797010814273
688.17.231863807330120.868136192669876
698.28.25433763474277-0.0543376347427706
708.58.302858059536960.197141940463043
718.68.78963069692411-0.189630696924112
728.58.709974225496-0.209974225496003

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.2 & 8 & 0.199999999999999 \tabularnewline
4 & 8.5 & 8.38948036825494 & 0.110519631745062 \tabularnewline
5 & 8.7 & 8.79418687086721 & -0.0941868708672136 \tabularnewline
6 & 8.7 & 8.90495405598371 & -0.204954055983713 \tabularnewline
7 & 8 & 8.71078020596802 & -0.710780205968025 \tabularnewline
8 & 8 & 7.33738573009231 & 0.66261426990769 \tabularnewline
9 & 8.3 & 7.96514770945775 & 0.334852290542255 \tabularnewline
10 & 8.5 & 8.58238738607253 & -0.0823873860725293 \tabularnewline
11 & 8.7 & 8.7043334248096 & -0.00433342480960519 \tabularnewline
12 & 8.6 & 8.90022793016596 & -0.300227930165958 \tabularnewline
13 & 8.3 & 8.51579143632464 & -0.215791436324636 \tabularnewline
14 & 7.9 & 8.01135023221937 & -0.111350232219365 \tabularnewline
15 & 7.9 & 7.50585681718837 & 0.394143182811627 \tabularnewline
16 & 8.1 & 7.87926879430998 & 0.220731205690021 \tabularnewline
17 & 8.3 & 8.28838994500749 & 0.0116100549925129 \tabularnewline
18 & 8.1 & 8.4993893324847 & -0.399389332484697 \tabularnewline
19 & 7.4 & 7.92100714350322 & -0.521007143503221 \tabularnewline
20 & 7.3 & 6.727404016431 & 0.572595983569 \tabularnewline
21 & 7.7 & 7.16988250557077 & 0.530117494429233 \tabularnewline
22 & 8 & 8.07211679588495 & -0.072116795884952 \tabularnewline
23 & 8 & 8.30379321067672 & -0.303793210676716 \tabularnewline
24 & 7.7 & 8.01597896351484 & -0.315978963514843 \tabularnewline
25 & 6.9 & 7.41661991167681 & -0.51661991167681 \tabularnewline
26 & 6.6 & 6.12717325611503 & 0.472826743884971 \tabularnewline
27 & 6.9 & 6.27513018387557 & 0.624869816124431 \tabularnewline
28 & 7.5 & 7.16713299822884 & 0.332867001771162 \tabularnewline
29 & 7.9 & 8.08249180860643 & -0.182491808606425 \tabularnewline
30 & 7.7 & 8.30959873311515 & -0.609598733115148 \tabularnewline
31 & 6.5 & 7.53206377092313 & -1.03206377092313 \tabularnewline
32 & 6.1 & 5.35428465403765 & 0.745715345962352 \tabularnewline
33 & 6.4 & 5.66077674586918 & 0.739223254130822 \tabularnewline
34 & 6.8 & 6.6611182179458 & 0.138881782054206 \tabularnewline
35 & 7.1 & 7.19269507398346 & -0.0926950739834602 \tabularnewline
36 & 7.3 & 7.40487559021444 & -0.104875590214435 \tabularnewline
37 & 7.2 & 7.50551626294051 & -0.305516262940508 \tabularnewline
38 & 7 & 7.11606959289131 & -0.116069592891306 \tabularnewline
39 & 7 & 6.80610504687008 & 0.193894953129922 \tabularnewline
40 & 7 & 6.98980148247924 & 0.0101985175207622 \tabularnewline
41 & 7.3 & 6.99946357675668 & 0.30053642324332 \tabularnewline
42 & 7.5 & 7.58419233750751 & -0.0841923375075133 \tabularnewline
43 & 7.2 & 7.70442836193167 & -0.504428361931675 \tabularnewline
44 & 7.7 & 6.92653200304643 & 0.773467996953574 \tabularnewline
45 & 8 & 8.1593170075273 & -0.159317007527296 \tabularnewline
46 & 7.9 & 8.30837978124956 & -0.408379781249559 \tabularnewline
47 & 8 & 7.82148002455437 & 0.178519975445631 \tabularnewline
48 & 8 & 8.09061017799587 & -0.0906101779958739 \tabularnewline
49 & 7.9 & 8.00476592852436 & -0.104765928524355 \tabularnewline
50 & 7.9 & 7.80551049493753 & 0.0944895050624721 \tabularnewline
51 & 8 & 7.89503002601485 & 0.104969973985151 \tabularnewline
52 & 8.1 & 8.09447877264694 & 0.00552122735306249 \tabularnewline
53 & 8.1 & 8.19970959360732 & -0.099709593607324 \tabularnewline
54 & 8.2 & 8.105244541031 & 0.094755458969006 \tabularnewline
55 & 8 & 8.29501603732906 & -0.295016037329058 \tabularnewline
56 & 8.3 & 7.81551730035794 & 0.484482699642057 \tabularnewline
57 & 8.5 & 8.57451710206457 & -0.0745171020645667 \tabularnewline
58 & 8.6 & 8.70391946236214 & -0.103919462362141 \tabularnewline
59 & 8.7 & 8.70546597237597 & -0.00546597237597268 \tabularnewline
60 & 8.7 & 8.80028750008262 & -0.100287500082619 \tabularnewline
61 & 8.5 & 8.70527493784751 & -0.205274937847509 \tabularnewline
62 & 8.4 & 8.31079708376323 & 0.0892029162367702 \tabularnewline
63 & 8.5 & 8.29530809085302 & 0.20469190914698 \tabularnewline
64 & 8.7 & 8.5892335824729 & 0.110766417527097 \tabularnewline
65 & 8.7 & 8.89417389038947 & -0.194173890389475 \tabularnewline
66 & 8.6 & 8.71021318910701 & -0.110213189107014 \tabularnewline
67 & 7.9 & 8.50579701081427 & -0.605797010814273 \tabularnewline
68 & 8.1 & 7.23186380733012 & 0.868136192669876 \tabularnewline
69 & 8.2 & 8.25433763474277 & -0.0543376347427706 \tabularnewline
70 & 8.5 & 8.30285805953696 & 0.197141940463043 \tabularnewline
71 & 8.6 & 8.78963069692411 & -0.189630696924112 \tabularnewline
72 & 8.5 & 8.709974225496 & -0.209974225496003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122087&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]8.2[/C][C]8[/C][C]0.199999999999999[/C][/ROW]
[ROW][C]4[/C][C]8.5[/C][C]8.38948036825494[/C][C]0.110519631745062[/C][/ROW]
[ROW][C]5[/C][C]8.7[/C][C]8.79418687086721[/C][C]-0.0941868708672136[/C][/ROW]
[ROW][C]6[/C][C]8.7[/C][C]8.90495405598371[/C][C]-0.204954055983713[/C][/ROW]
[ROW][C]7[/C][C]8[/C][C]8.71078020596802[/C][C]-0.710780205968025[/C][/ROW]
[ROW][C]8[/C][C]8[/C][C]7.33738573009231[/C][C]0.66261426990769[/C][/ROW]
[ROW][C]9[/C][C]8.3[/C][C]7.96514770945775[/C][C]0.334852290542255[/C][/ROW]
[ROW][C]10[/C][C]8.5[/C][C]8.58238738607253[/C][C]-0.0823873860725293[/C][/ROW]
[ROW][C]11[/C][C]8.7[/C][C]8.7043334248096[/C][C]-0.00433342480960519[/C][/ROW]
[ROW][C]12[/C][C]8.6[/C][C]8.90022793016596[/C][C]-0.300227930165958[/C][/ROW]
[ROW][C]13[/C][C]8.3[/C][C]8.51579143632464[/C][C]-0.215791436324636[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]8.01135023221937[/C][C]-0.111350232219365[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]7.50585681718837[/C][C]0.394143182811627[/C][/ROW]
[ROW][C]16[/C][C]8.1[/C][C]7.87926879430998[/C][C]0.220731205690021[/C][/ROW]
[ROW][C]17[/C][C]8.3[/C][C]8.28838994500749[/C][C]0.0116100549925129[/C][/ROW]
[ROW][C]18[/C][C]8.1[/C][C]8.4993893324847[/C][C]-0.399389332484697[/C][/ROW]
[ROW][C]19[/C][C]7.4[/C][C]7.92100714350322[/C][C]-0.521007143503221[/C][/ROW]
[ROW][C]20[/C][C]7.3[/C][C]6.727404016431[/C][C]0.572595983569[/C][/ROW]
[ROW][C]21[/C][C]7.7[/C][C]7.16988250557077[/C][C]0.530117494429233[/C][/ROW]
[ROW][C]22[/C][C]8[/C][C]8.07211679588495[/C][C]-0.072116795884952[/C][/ROW]
[ROW][C]23[/C][C]8[/C][C]8.30379321067672[/C][C]-0.303793210676716[/C][/ROW]
[ROW][C]24[/C][C]7.7[/C][C]8.01597896351484[/C][C]-0.315978963514843[/C][/ROW]
[ROW][C]25[/C][C]6.9[/C][C]7.41661991167681[/C][C]-0.51661991167681[/C][/ROW]
[ROW][C]26[/C][C]6.6[/C][C]6.12717325611503[/C][C]0.472826743884971[/C][/ROW]
[ROW][C]27[/C][C]6.9[/C][C]6.27513018387557[/C][C]0.624869816124431[/C][/ROW]
[ROW][C]28[/C][C]7.5[/C][C]7.16713299822884[/C][C]0.332867001771162[/C][/ROW]
[ROW][C]29[/C][C]7.9[/C][C]8.08249180860643[/C][C]-0.182491808606425[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]8.30959873311515[/C][C]-0.609598733115148[/C][/ROW]
[ROW][C]31[/C][C]6.5[/C][C]7.53206377092313[/C][C]-1.03206377092313[/C][/ROW]
[ROW][C]32[/C][C]6.1[/C][C]5.35428465403765[/C][C]0.745715345962352[/C][/ROW]
[ROW][C]33[/C][C]6.4[/C][C]5.66077674586918[/C][C]0.739223254130822[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]6.6611182179458[/C][C]0.138881782054206[/C][/ROW]
[ROW][C]35[/C][C]7.1[/C][C]7.19269507398346[/C][C]-0.0926950739834602[/C][/ROW]
[ROW][C]36[/C][C]7.3[/C][C]7.40487559021444[/C][C]-0.104875590214435[/C][/ROW]
[ROW][C]37[/C][C]7.2[/C][C]7.50551626294051[/C][C]-0.305516262940508[/C][/ROW]
[ROW][C]38[/C][C]7[/C][C]7.11606959289131[/C][C]-0.116069592891306[/C][/ROW]
[ROW][C]39[/C][C]7[/C][C]6.80610504687008[/C][C]0.193894953129922[/C][/ROW]
[ROW][C]40[/C][C]7[/C][C]6.98980148247924[/C][C]0.0101985175207622[/C][/ROW]
[ROW][C]41[/C][C]7.3[/C][C]6.99946357675668[/C][C]0.30053642324332[/C][/ROW]
[ROW][C]42[/C][C]7.5[/C][C]7.58419233750751[/C][C]-0.0841923375075133[/C][/ROW]
[ROW][C]43[/C][C]7.2[/C][C]7.70442836193167[/C][C]-0.504428361931675[/C][/ROW]
[ROW][C]44[/C][C]7.7[/C][C]6.92653200304643[/C][C]0.773467996953574[/C][/ROW]
[ROW][C]45[/C][C]8[/C][C]8.1593170075273[/C][C]-0.159317007527296[/C][/ROW]
[ROW][C]46[/C][C]7.9[/C][C]8.30837978124956[/C][C]-0.408379781249559[/C][/ROW]
[ROW][C]47[/C][C]8[/C][C]7.82148002455437[/C][C]0.178519975445631[/C][/ROW]
[ROW][C]48[/C][C]8[/C][C]8.09061017799587[/C][C]-0.0906101779958739[/C][/ROW]
[ROW][C]49[/C][C]7.9[/C][C]8.00476592852436[/C][C]-0.104765928524355[/C][/ROW]
[ROW][C]50[/C][C]7.9[/C][C]7.80551049493753[/C][C]0.0944895050624721[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]7.89503002601485[/C][C]0.104969973985151[/C][/ROW]
[ROW][C]52[/C][C]8.1[/C][C]8.09447877264694[/C][C]0.00552122735306249[/C][/ROW]
[ROW][C]53[/C][C]8.1[/C][C]8.19970959360732[/C][C]-0.099709593607324[/C][/ROW]
[ROW][C]54[/C][C]8.2[/C][C]8.105244541031[/C][C]0.094755458969006[/C][/ROW]
[ROW][C]55[/C][C]8[/C][C]8.29501603732906[/C][C]-0.295016037329058[/C][/ROW]
[ROW][C]56[/C][C]8.3[/C][C]7.81551730035794[/C][C]0.484482699642057[/C][/ROW]
[ROW][C]57[/C][C]8.5[/C][C]8.57451710206457[/C][C]-0.0745171020645667[/C][/ROW]
[ROW][C]58[/C][C]8.6[/C][C]8.70391946236214[/C][C]-0.103919462362141[/C][/ROW]
[ROW][C]59[/C][C]8.7[/C][C]8.70546597237597[/C][C]-0.00546597237597268[/C][/ROW]
[ROW][C]60[/C][C]8.7[/C][C]8.80028750008262[/C][C]-0.100287500082619[/C][/ROW]
[ROW][C]61[/C][C]8.5[/C][C]8.70527493784751[/C][C]-0.205274937847509[/C][/ROW]
[ROW][C]62[/C][C]8.4[/C][C]8.31079708376323[/C][C]0.0892029162367702[/C][/ROW]
[ROW][C]63[/C][C]8.5[/C][C]8.29530809085302[/C][C]0.20469190914698[/C][/ROW]
[ROW][C]64[/C][C]8.7[/C][C]8.5892335824729[/C][C]0.110766417527097[/C][/ROW]
[ROW][C]65[/C][C]8.7[/C][C]8.89417389038947[/C][C]-0.194173890389475[/C][/ROW]
[ROW][C]66[/C][C]8.6[/C][C]8.71021318910701[/C][C]-0.110213189107014[/C][/ROW]
[ROW][C]67[/C][C]7.9[/C][C]8.50579701081427[/C][C]-0.605797010814273[/C][/ROW]
[ROW][C]68[/C][C]8.1[/C][C]7.23186380733012[/C][C]0.868136192669876[/C][/ROW]
[ROW][C]69[/C][C]8.2[/C][C]8.25433763474277[/C][C]-0.0543376347427706[/C][/ROW]
[ROW][C]70[/C][C]8.5[/C][C]8.30285805953696[/C][C]0.197141940463043[/C][/ROW]
[ROW][C]71[/C][C]8.6[/C][C]8.78963069692411[/C][C]-0.189630696924112[/C][/ROW]
[ROW][C]72[/C][C]8.5[/C][C]8.709974225496[/C][C]-0.209974225496003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122087&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122087&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
38.280.199999999999999
48.58.389480368254940.110519631745062
58.78.79418687086721-0.0941868708672136
68.78.90495405598371-0.204954055983713
788.71078020596802-0.710780205968025
887.337385730092310.66261426990769
98.37.965147709457750.334852290542255
108.58.58238738607253-0.0823873860725293
118.78.7043334248096-0.00433342480960519
128.68.90022793016596-0.300227930165958
138.38.51579143632464-0.215791436324636
147.98.01135023221937-0.111350232219365
157.97.505856817188370.394143182811627
168.17.879268794309980.220731205690021
178.38.288389945007490.0116100549925129
188.18.4993893324847-0.399389332484697
197.47.92100714350322-0.521007143503221
207.36.7274040164310.572595983569
217.77.169882505570770.530117494429233
2288.07211679588495-0.072116795884952
2388.30379321067672-0.303793210676716
247.78.01597896351484-0.315978963514843
256.97.41661991167681-0.51661991167681
266.66.127173256115030.472826743884971
276.96.275130183875570.624869816124431
287.57.167132998228840.332867001771162
297.98.08249180860643-0.182491808606425
307.78.30959873311515-0.609598733115148
316.57.53206377092313-1.03206377092313
326.15.354284654037650.745715345962352
336.45.660776745869180.739223254130822
346.86.66111821794580.138881782054206
357.17.19269507398346-0.0926950739834602
367.37.40487559021444-0.104875590214435
377.27.50551626294051-0.305516262940508
3877.11606959289131-0.116069592891306
3976.806105046870080.193894953129922
4076.989801482479240.0101985175207622
417.36.999463576756680.30053642324332
427.57.58419233750751-0.0841923375075133
437.27.70442836193167-0.504428361931675
447.76.926532003046430.773467996953574
4588.1593170075273-0.159317007527296
467.98.30837978124956-0.408379781249559
4787.821480024554370.178519975445631
4888.09061017799587-0.0906101779958739
497.98.00476592852436-0.104765928524355
507.97.805510494937530.0944895050624721
5187.895030026014850.104969973985151
528.18.094478772646940.00552122735306249
538.18.19970959360732-0.099709593607324
548.28.1052445410310.094755458969006
5588.29501603732906-0.295016037329058
568.37.815517300357940.484482699642057
578.58.57451710206457-0.0745171020645667
588.68.70391946236214-0.103919462362141
598.78.70546597237597-0.00546597237597268
608.78.80028750008262-0.100287500082619
618.58.70527493784751-0.205274937847509
628.48.310797083763230.0892029162367702
638.58.295308090853020.20469190914698
648.78.58923358247290.110766417527097
658.78.89417389038947-0.194173890389475
668.68.71021318910701-0.110213189107014
677.98.50579701081427-0.605797010814273
688.17.231863807330120.868136192669876
698.28.25433763474277-0.0543376347427706
708.58.302858059536960.197141940463043
718.68.78963069692411-0.189630696924112
728.58.709974225496-0.209974225496003







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.411044257640867.684502594726189.13758592055554
748.322088515281726.731580463012979.91259656755047
758.233132772922585.5962506942124210.8700148516327
768.144177030563454.3041582345281811.9841958265987
778.05522128820432.8730310656385813.23741151077
787.966265545845171.3157927497382714.6167383419521
797.87730980348603-0.3576407700444916.1122603770166
807.7883540611269-2.1393622412728717.7160703635267
817.69939831876775-4.0228794623193319.4216760998548
827.61044257640861-6.0027398217109721.2236249745282
837.52148683404948-8.0742803715524523.1172540396514
847.43253109169034-10.233454400928425.0985165843091

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.41104425764086 & 7.68450259472618 & 9.13758592055554 \tabularnewline
74 & 8.32208851528172 & 6.73158046301297 & 9.91259656755047 \tabularnewline
75 & 8.23313277292258 & 5.59625069421242 & 10.8700148516327 \tabularnewline
76 & 8.14417703056345 & 4.30415823452818 & 11.9841958265987 \tabularnewline
77 & 8.0552212882043 & 2.87303106563858 & 13.23741151077 \tabularnewline
78 & 7.96626554584517 & 1.31579274973827 & 14.6167383419521 \tabularnewline
79 & 7.87730980348603 & -0.35764077004449 & 16.1122603770166 \tabularnewline
80 & 7.7883540611269 & -2.13936224127287 & 17.7160703635267 \tabularnewline
81 & 7.69939831876775 & -4.02287946231933 & 19.4216760998548 \tabularnewline
82 & 7.61044257640861 & -6.00273982171097 & 21.2236249745282 \tabularnewline
83 & 7.52148683404948 & -8.07428037155245 & 23.1172540396514 \tabularnewline
84 & 7.43253109169034 & -10.2334544009284 & 25.0985165843091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122087&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]8.41104425764086[/C][C]7.68450259472618[/C][C]9.13758592055554[/C][/ROW]
[ROW][C]74[/C][C]8.32208851528172[/C][C]6.73158046301297[/C][C]9.91259656755047[/C][/ROW]
[ROW][C]75[/C][C]8.23313277292258[/C][C]5.59625069421242[/C][C]10.8700148516327[/C][/ROW]
[ROW][C]76[/C][C]8.14417703056345[/C][C]4.30415823452818[/C][C]11.9841958265987[/C][/ROW]
[ROW][C]77[/C][C]8.0552212882043[/C][C]2.87303106563858[/C][C]13.23741151077[/C][/ROW]
[ROW][C]78[/C][C]7.96626554584517[/C][C]1.31579274973827[/C][C]14.6167383419521[/C][/ROW]
[ROW][C]79[/C][C]7.87730980348603[/C][C]-0.35764077004449[/C][C]16.1122603770166[/C][/ROW]
[ROW][C]80[/C][C]7.7883540611269[/C][C]-2.13936224127287[/C][C]17.7160703635267[/C][/ROW]
[ROW][C]81[/C][C]7.69939831876775[/C][C]-4.02287946231933[/C][C]19.4216760998548[/C][/ROW]
[ROW][C]82[/C][C]7.61044257640861[/C][C]-6.00273982171097[/C][C]21.2236249745282[/C][/ROW]
[ROW][C]83[/C][C]7.52148683404948[/C][C]-8.07428037155245[/C][C]23.1172540396514[/C][/ROW]
[ROW][C]84[/C][C]7.43253109169034[/C][C]-10.2334544009284[/C][C]25.0985165843091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122087&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122087&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
738.411044257640867.684502594726189.13758592055554
748.322088515281726.731580463012979.91259656755047
758.233132772922585.5962506942124210.8700148516327
768.144177030563454.3041582345281811.9841958265987
778.05522128820432.8730310656385813.23741151077
787.966265545845171.3157927497382714.6167383419521
797.87730980348603-0.3576407700444916.1122603770166
807.7883540611269-2.1393622412728717.7160703635267
817.69939831876775-4.0228794623193319.4216760998548
827.61044257640861-6.0027398217109721.2236249745282
837.52148683404948-8.0742803715524523.1172540396514
847.43253109169034-10.233454400928425.0985165843091



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')