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Author's title

Michiel van Schaik - Exponential Smoothing - Gemiddelde consumptieprijs hot...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 May 2008 09:46:46 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/28/t1211989669tuub98ag5xx4r12.htm/, Retrieved Tue, 14 May 2024 19:31:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13450, Retrieved Tue, 14 May 2024 19:31:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Michiel van Schai...] [2008-05-28 15:46:46] [f1389fff7fe55b9c206fc4c1b90cd78e] [Current]
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Dataseries X:
65,05
65,84
66,6
67,55
68,07
69,06
69,06
69,11
69,29
69,38
69,28
69,75
69,9
70,21
70,48
71,55
72,18
72,64
72,77
72,74
73,13
73,44
73,34
73,34
73,81
74,26
74,72
75,11
75,26
75,89
75,91
76,43
76,56
76,76
76,76
76,56
76,82
77,09
77,51
77,76
77,86
77,89
77,94
77,99
78,17
78,91
78,87
78,88
79,08
79,41
79,51
79,73
80,38
80,56
80,46
80,45
80,58
80,68
80,52
81,49
81,66
81,95
82,3
82,4
83,14
83,17
83,11
83,21
83,33
83,88
83,8
83,73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13450&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13450&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13450&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.917656813396868
beta0.0281982938785126
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.917656813396868 \tabularnewline
beta & 0.0281982938785126 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13450&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]0.917656813396868[/C][/ROW]
[ROW][C]beta[/C][C]0.0281982938785126[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13450&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13450&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
alpha0.917656813396868
beta0.0281982938785126
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1369.968.02802916666671.87197083333331
1470.2170.10975244390180.100247556098211
1570.4870.5228191591618-0.0428191591618372
1671.5571.5855750578989-0.0355750578988676
1772.1872.2048913359693-0.0248913359692864
1872.6472.6829508405107-0.0429508405107413
1972.7772.819576506402-0.0495765064019906
2072.7472.7696725588243-0.0296725588243021
2173.1373.1435157866442-0.0135157866442341
2273.4473.4722523138908-0.0322523138907655
2373.3473.4212939002112-0.0812939002111506
2473.3473.436145217428-0.0961452174280453
2573.8173.8711076112687-0.0611076112687385
2674.2674.02244121005440.237558789945581
2774.7274.54268732731490.177312672685119
2875.1175.8066967954683-0.696696795468341
2975.2675.8017541082026-0.541754108202568
3075.8975.77219353562350.117806464376542
3175.9176.0281231170997-0.118123117099742
3276.4375.88751158100870.542488418991283
3376.5676.7730937913862-0.213093791386186
3476.7676.8973401886155-0.137340188615454
3576.7676.72338645008270.0366135499172628
3676.5676.8257419725764-0.265741972576421
3776.8277.0840978456703-0.264097845670292
3877.0977.04463655734250.0453634426575462
3977.5177.34946647339120.160533526608802
4077.7678.491589561936-0.731589561936005
4177.8678.431962709569-0.571962709569021
4277.8978.3927865840641-0.502786584064097
4377.9478.0075341024115-0.0675341024115284
4477.9977.91678840837210.0732115916278957
4578.1778.2464209483747-0.0764209483747322
4678.9178.44276295402630.467237045973690
4778.8778.79401084502530.0759891549747493
4878.8878.86470494560040.0152950543995871
4979.0879.345466161293-0.265466161293062
5079.4179.29457026772830.115429732271693
5179.5179.6393325341397-0.129332534139706
5279.7380.4006491921818-0.67064919218177
5380.3880.37031717682390.0096828231761208
5480.5680.8458673950013-0.285867395001333
5580.4680.6764046146996-0.216404614699641
5680.4580.43767635647890.0123236435211425
5780.5880.6745779044181-0.0945779044181023
5880.6880.8740192199891-0.194019219989102
5980.5280.5441279248172-0.0241279248171793
6081.4980.47324422387351.01675577612649
6181.6681.8310911402325-0.171091140232477
6281.9581.88181261028760.0681873897124063
6382.382.1454949553830.154505044617025
6482.483.1124748864526-0.712474886452625
6583.1483.08847117085670.051528829143308
6683.1783.567857163918-0.397857163918033
6783.1183.288220157795-0.178220157794911
6883.2183.09122857686180.118771423138156
6983.3383.407626758217-0.077626758217022
7083.8883.6054904449820.274509555018000
7183.883.72271633189450.0772836681054514
7283.7383.836406682311-0.106406682310975

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 69.9 & 68.0280291666667 & 1.87197083333331 \tabularnewline
14 & 70.21 & 70.1097524439018 & 0.100247556098211 \tabularnewline
15 & 70.48 & 70.5228191591618 & -0.0428191591618372 \tabularnewline
16 & 71.55 & 71.5855750578989 & -0.0355750578988676 \tabularnewline
17 & 72.18 & 72.2048913359693 & -0.0248913359692864 \tabularnewline
18 & 72.64 & 72.6829508405107 & -0.0429508405107413 \tabularnewline
19 & 72.77 & 72.819576506402 & -0.0495765064019906 \tabularnewline
20 & 72.74 & 72.7696725588243 & -0.0296725588243021 \tabularnewline
21 & 73.13 & 73.1435157866442 & -0.0135157866442341 \tabularnewline
22 & 73.44 & 73.4722523138908 & -0.0322523138907655 \tabularnewline
23 & 73.34 & 73.4212939002112 & -0.0812939002111506 \tabularnewline
24 & 73.34 & 73.436145217428 & -0.0961452174280453 \tabularnewline
25 & 73.81 & 73.8711076112687 & -0.0611076112687385 \tabularnewline
26 & 74.26 & 74.0224412100544 & 0.237558789945581 \tabularnewline
27 & 74.72 & 74.5426873273149 & 0.177312672685119 \tabularnewline
28 & 75.11 & 75.8066967954683 & -0.696696795468341 \tabularnewline
29 & 75.26 & 75.8017541082026 & -0.541754108202568 \tabularnewline
30 & 75.89 & 75.7721935356235 & 0.117806464376542 \tabularnewline
31 & 75.91 & 76.0281231170997 & -0.118123117099742 \tabularnewline
32 & 76.43 & 75.8875115810087 & 0.542488418991283 \tabularnewline
33 & 76.56 & 76.7730937913862 & -0.213093791386186 \tabularnewline
34 & 76.76 & 76.8973401886155 & -0.137340188615454 \tabularnewline
35 & 76.76 & 76.7233864500827 & 0.0366135499172628 \tabularnewline
36 & 76.56 & 76.8257419725764 & -0.265741972576421 \tabularnewline
37 & 76.82 & 77.0840978456703 & -0.264097845670292 \tabularnewline
38 & 77.09 & 77.0446365573425 & 0.0453634426575462 \tabularnewline
39 & 77.51 & 77.3494664733912 & 0.160533526608802 \tabularnewline
40 & 77.76 & 78.491589561936 & -0.731589561936005 \tabularnewline
41 & 77.86 & 78.431962709569 & -0.571962709569021 \tabularnewline
42 & 77.89 & 78.3927865840641 & -0.502786584064097 \tabularnewline
43 & 77.94 & 78.0075341024115 & -0.0675341024115284 \tabularnewline
44 & 77.99 & 77.9167884083721 & 0.0732115916278957 \tabularnewline
45 & 78.17 & 78.2464209483747 & -0.0764209483747322 \tabularnewline
46 & 78.91 & 78.4427629540263 & 0.467237045973690 \tabularnewline
47 & 78.87 & 78.7940108450253 & 0.0759891549747493 \tabularnewline
48 & 78.88 & 78.8647049456004 & 0.0152950543995871 \tabularnewline
49 & 79.08 & 79.345466161293 & -0.265466161293062 \tabularnewline
50 & 79.41 & 79.2945702677283 & 0.115429732271693 \tabularnewline
51 & 79.51 & 79.6393325341397 & -0.129332534139706 \tabularnewline
52 & 79.73 & 80.4006491921818 & -0.67064919218177 \tabularnewline
53 & 80.38 & 80.3703171768239 & 0.0096828231761208 \tabularnewline
54 & 80.56 & 80.8458673950013 & -0.285867395001333 \tabularnewline
55 & 80.46 & 80.6764046146996 & -0.216404614699641 \tabularnewline
56 & 80.45 & 80.4376763564789 & 0.0123236435211425 \tabularnewline
57 & 80.58 & 80.6745779044181 & -0.0945779044181023 \tabularnewline
58 & 80.68 & 80.8740192199891 & -0.194019219989102 \tabularnewline
59 & 80.52 & 80.5441279248172 & -0.0241279248171793 \tabularnewline
60 & 81.49 & 80.4732442238735 & 1.01675577612649 \tabularnewline
61 & 81.66 & 81.8310911402325 & -0.171091140232477 \tabularnewline
62 & 81.95 & 81.8818126102876 & 0.0681873897124063 \tabularnewline
63 & 82.3 & 82.145494955383 & 0.154505044617025 \tabularnewline
64 & 82.4 & 83.1124748864526 & -0.712474886452625 \tabularnewline
65 & 83.14 & 83.0884711708567 & 0.051528829143308 \tabularnewline
66 & 83.17 & 83.567857163918 & -0.397857163918033 \tabularnewline
67 & 83.11 & 83.288220157795 & -0.178220157794911 \tabularnewline
68 & 83.21 & 83.0912285768618 & 0.118771423138156 \tabularnewline
69 & 83.33 & 83.407626758217 & -0.077626758217022 \tabularnewline
70 & 83.88 & 83.605490444982 & 0.274509555018000 \tabularnewline
71 & 83.8 & 83.7227163318945 & 0.0772836681054514 \tabularnewline
72 & 83.73 & 83.836406682311 & -0.106406682310975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13450&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]69.9[/C][C]68.0280291666667[/C][C]1.87197083333331[/C][/ROW]
[ROW][C]14[/C][C]70.21[/C][C]70.1097524439018[/C][C]0.100247556098211[/C][/ROW]
[ROW][C]15[/C][C]70.48[/C][C]70.5228191591618[/C][C]-0.0428191591618372[/C][/ROW]
[ROW][C]16[/C][C]71.55[/C][C]71.5855750578989[/C][C]-0.0355750578988676[/C][/ROW]
[ROW][C]17[/C][C]72.18[/C][C]72.2048913359693[/C][C]-0.0248913359692864[/C][/ROW]
[ROW][C]18[/C][C]72.64[/C][C]72.6829508405107[/C][C]-0.0429508405107413[/C][/ROW]
[ROW][C]19[/C][C]72.77[/C][C]72.819576506402[/C][C]-0.0495765064019906[/C][/ROW]
[ROW][C]20[/C][C]72.74[/C][C]72.7696725588243[/C][C]-0.0296725588243021[/C][/ROW]
[ROW][C]21[/C][C]73.13[/C][C]73.1435157866442[/C][C]-0.0135157866442341[/C][/ROW]
[ROW][C]22[/C][C]73.44[/C][C]73.4722523138908[/C][C]-0.0322523138907655[/C][/ROW]
[ROW][C]23[/C][C]73.34[/C][C]73.4212939002112[/C][C]-0.0812939002111506[/C][/ROW]
[ROW][C]24[/C][C]73.34[/C][C]73.436145217428[/C][C]-0.0961452174280453[/C][/ROW]
[ROW][C]25[/C][C]73.81[/C][C]73.8711076112687[/C][C]-0.0611076112687385[/C][/ROW]
[ROW][C]26[/C][C]74.26[/C][C]74.0224412100544[/C][C]0.237558789945581[/C][/ROW]
[ROW][C]27[/C][C]74.72[/C][C]74.5426873273149[/C][C]0.177312672685119[/C][/ROW]
[ROW][C]28[/C][C]75.11[/C][C]75.8066967954683[/C][C]-0.696696795468341[/C][/ROW]
[ROW][C]29[/C][C]75.26[/C][C]75.8017541082026[/C][C]-0.541754108202568[/C][/ROW]
[ROW][C]30[/C][C]75.89[/C][C]75.7721935356235[/C][C]0.117806464376542[/C][/ROW]
[ROW][C]31[/C][C]75.91[/C][C]76.0281231170997[/C][C]-0.118123117099742[/C][/ROW]
[ROW][C]32[/C][C]76.43[/C][C]75.8875115810087[/C][C]0.542488418991283[/C][/ROW]
[ROW][C]33[/C][C]76.56[/C][C]76.7730937913862[/C][C]-0.213093791386186[/C][/ROW]
[ROW][C]34[/C][C]76.76[/C][C]76.8973401886155[/C][C]-0.137340188615454[/C][/ROW]
[ROW][C]35[/C][C]76.76[/C][C]76.7233864500827[/C][C]0.0366135499172628[/C][/ROW]
[ROW][C]36[/C][C]76.56[/C][C]76.8257419725764[/C][C]-0.265741972576421[/C][/ROW]
[ROW][C]37[/C][C]76.82[/C][C]77.0840978456703[/C][C]-0.264097845670292[/C][/ROW]
[ROW][C]38[/C][C]77.09[/C][C]77.0446365573425[/C][C]0.0453634426575462[/C][/ROW]
[ROW][C]39[/C][C]77.51[/C][C]77.3494664733912[/C][C]0.160533526608802[/C][/ROW]
[ROW][C]40[/C][C]77.76[/C][C]78.491589561936[/C][C]-0.731589561936005[/C][/ROW]
[ROW][C]41[/C][C]77.86[/C][C]78.431962709569[/C][C]-0.571962709569021[/C][/ROW]
[ROW][C]42[/C][C]77.89[/C][C]78.3927865840641[/C][C]-0.502786584064097[/C][/ROW]
[ROW][C]43[/C][C]77.94[/C][C]78.0075341024115[/C][C]-0.0675341024115284[/C][/ROW]
[ROW][C]44[/C][C]77.99[/C][C]77.9167884083721[/C][C]0.0732115916278957[/C][/ROW]
[ROW][C]45[/C][C]78.17[/C][C]78.2464209483747[/C][C]-0.0764209483747322[/C][/ROW]
[ROW][C]46[/C][C]78.91[/C][C]78.4427629540263[/C][C]0.467237045973690[/C][/ROW]
[ROW][C]47[/C][C]78.87[/C][C]78.7940108450253[/C][C]0.0759891549747493[/C][/ROW]
[ROW][C]48[/C][C]78.88[/C][C]78.8647049456004[/C][C]0.0152950543995871[/C][/ROW]
[ROW][C]49[/C][C]79.08[/C][C]79.345466161293[/C][C]-0.265466161293062[/C][/ROW]
[ROW][C]50[/C][C]79.41[/C][C]79.2945702677283[/C][C]0.115429732271693[/C][/ROW]
[ROW][C]51[/C][C]79.51[/C][C]79.6393325341397[/C][C]-0.129332534139706[/C][/ROW]
[ROW][C]52[/C][C]79.73[/C][C]80.4006491921818[/C][C]-0.67064919218177[/C][/ROW]
[ROW][C]53[/C][C]80.38[/C][C]80.3703171768239[/C][C]0.0096828231761208[/C][/ROW]
[ROW][C]54[/C][C]80.56[/C][C]80.8458673950013[/C][C]-0.285867395001333[/C][/ROW]
[ROW][C]55[/C][C]80.46[/C][C]80.6764046146996[/C][C]-0.216404614699641[/C][/ROW]
[ROW][C]56[/C][C]80.45[/C][C]80.4376763564789[/C][C]0.0123236435211425[/C][/ROW]
[ROW][C]57[/C][C]80.58[/C][C]80.6745779044181[/C][C]-0.0945779044181023[/C][/ROW]
[ROW][C]58[/C][C]80.68[/C][C]80.8740192199891[/C][C]-0.194019219989102[/C][/ROW]
[ROW][C]59[/C][C]80.52[/C][C]80.5441279248172[/C][C]-0.0241279248171793[/C][/ROW]
[ROW][C]60[/C][C]81.49[/C][C]80.4732442238735[/C][C]1.01675577612649[/C][/ROW]
[ROW][C]61[/C][C]81.66[/C][C]81.8310911402325[/C][C]-0.171091140232477[/C][/ROW]
[ROW][C]62[/C][C]81.95[/C][C]81.8818126102876[/C][C]0.0681873897124063[/C][/ROW]
[ROW][C]63[/C][C]82.3[/C][C]82.145494955383[/C][C]0.154505044617025[/C][/ROW]
[ROW][C]64[/C][C]82.4[/C][C]83.1124748864526[/C][C]-0.712474886452625[/C][/ROW]
[ROW][C]65[/C][C]83.14[/C][C]83.0884711708567[/C][C]0.051528829143308[/C][/ROW]
[ROW][C]66[/C][C]83.17[/C][C]83.567857163918[/C][C]-0.397857163918033[/C][/ROW]
[ROW][C]67[/C][C]83.11[/C][C]83.288220157795[/C][C]-0.178220157794911[/C][/ROW]
[ROW][C]68[/C][C]83.21[/C][C]83.0912285768618[/C][C]0.118771423138156[/C][/ROW]
[ROW][C]69[/C][C]83.33[/C][C]83.407626758217[/C][C]-0.077626758217022[/C][/ROW]
[ROW][C]70[/C][C]83.88[/C][C]83.605490444982[/C][C]0.274509555018000[/C][/ROW]
[ROW][C]71[/C][C]83.8[/C][C]83.7227163318945[/C][C]0.0772836681054514[/C][/ROW]
[ROW][C]72[/C][C]83.73[/C][C]83.836406682311[/C][C]-0.106406682310975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13450&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13450&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
1369.968.02802916666671.87197083333331
1470.2170.10975244390180.100247556098211
1570.4870.5228191591618-0.0428191591618372
1671.5571.5855750578989-0.0355750578988676
1772.1872.2048913359693-0.0248913359692864
1872.6472.6829508405107-0.0429508405107413
1972.7772.819576506402-0.0495765064019906
2072.7472.7696725588243-0.0296725588243021
2173.1373.1435157866442-0.0135157866442341
2273.4473.4722523138908-0.0322523138907655
2373.3473.4212939002112-0.0812939002111506
2473.3473.436145217428-0.0961452174280453
2573.8173.8711076112687-0.0611076112687385
2674.2674.02244121005440.237558789945581
2774.7274.54268732731490.177312672685119
2875.1175.8066967954683-0.696696795468341
2975.2675.8017541082026-0.541754108202568
3075.8975.77219353562350.117806464376542
3175.9176.0281231170997-0.118123117099742
3276.4375.88751158100870.542488418991283
3376.5676.7730937913862-0.213093791386186
3476.7676.8973401886155-0.137340188615454
3576.7676.72338645008270.0366135499172628
3676.5676.8257419725764-0.265741972576421
3776.8277.0840978456703-0.264097845670292
3877.0977.04463655734250.0453634426575462
3977.5177.34946647339120.160533526608802
4077.7678.491589561936-0.731589561936005
4177.8678.431962709569-0.571962709569021
4277.8978.3927865840641-0.502786584064097
4377.9478.0075341024115-0.0675341024115284
4477.9977.91678840837210.0732115916278957
4578.1778.2464209483747-0.0764209483747322
4678.9178.44276295402630.467237045973690
4778.8778.79401084502530.0759891549747493
4878.8878.86470494560040.0152950543995871
4979.0879.345466161293-0.265466161293062
5079.4179.29457026772830.115429732271693
5179.5179.6393325341397-0.129332534139706
5279.7380.4006491921818-0.67064919218177
5380.3880.37031717682390.0096828231761208
5480.5680.8458673950013-0.285867395001333
5580.4680.6764046146996-0.216404614699641
5680.4580.43767635647890.0123236435211425
5780.5880.6745779044181-0.0945779044181023
5880.6880.8740192199891-0.194019219989102
5980.5280.5441279248172-0.0241279248171793
6081.4980.47324422387351.01675577612649
6181.6681.8310911402325-0.171091140232477
6281.9581.88181261028760.0681873897124063
6382.382.1454949553830.154505044617025
6482.483.1124748864526-0.712474886452625
6583.1483.08847117085670.051528829143308
6683.1783.567857163918-0.397857163918033
6783.1183.288220157795-0.178220157794911
6883.2183.09122857686180.118771423138156
6983.3383.407626758217-0.077626758217022
7083.8883.6054904449820.274509555018000
7183.883.72271633189450.0772836681054514
7283.7383.836406682311-0.106406682310975







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7384.042504794995683.283118735890684.8018908541005
7484.251099366729683.207045755842485.2951529776167
7584.438719513118683.161232246488485.7162067797488
7685.16793167271683.683608000096186.6522553453358
7785.85448687139884.179807993270187.5291657495258
7886.242090810104884.388245155257888.0959364649517
7986.348438447479784.32345150359888.3734253913613
8086.346861425429184.156700053775388.537022797083
8186.542437160950384.191645783280988.8932285386198
8286.846881307056884.338976966464689.354785647649
8386.695207824957584.032939744740589.3574759051745
8486.720099224725283.905627017398189.5345714320524

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 84.0425047949956 & 83.2831187358906 & 84.8018908541005 \tabularnewline
74 & 84.2510993667296 & 83.2070457558424 & 85.2951529776167 \tabularnewline
75 & 84.4387195131186 & 83.1612322464884 & 85.7162067797488 \tabularnewline
76 & 85.167931672716 & 83.6836080000961 & 86.6522553453358 \tabularnewline
77 & 85.854486871398 & 84.1798079932701 & 87.5291657495258 \tabularnewline
78 & 86.2420908101048 & 84.3882451552578 & 88.0959364649517 \tabularnewline
79 & 86.3484384474797 & 84.323451503598 & 88.3734253913613 \tabularnewline
80 & 86.3468614254291 & 84.1567000537753 & 88.537022797083 \tabularnewline
81 & 86.5424371609503 & 84.1916457832809 & 88.8932285386198 \tabularnewline
82 & 86.8468813070568 & 84.3389769664646 & 89.354785647649 \tabularnewline
83 & 86.6952078249575 & 84.0329397447405 & 89.3574759051745 \tabularnewline
84 & 86.7200992247252 & 83.9056270173981 & 89.5345714320524 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13450&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]84.0425047949956[/C][C]83.2831187358906[/C][C]84.8018908541005[/C][/ROW]
[ROW][C]74[/C][C]84.2510993667296[/C][C]83.2070457558424[/C][C]85.2951529776167[/C][/ROW]
[ROW][C]75[/C][C]84.4387195131186[/C][C]83.1612322464884[/C][C]85.7162067797488[/C][/ROW]
[ROW][C]76[/C][C]85.167931672716[/C][C]83.6836080000961[/C][C]86.6522553453358[/C][/ROW]
[ROW][C]77[/C][C]85.854486871398[/C][C]84.1798079932701[/C][C]87.5291657495258[/C][/ROW]
[ROW][C]78[/C][C]86.2420908101048[/C][C]84.3882451552578[/C][C]88.0959364649517[/C][/ROW]
[ROW][C]79[/C][C]86.3484384474797[/C][C]84.323451503598[/C][C]88.3734253913613[/C][/ROW]
[ROW][C]80[/C][C]86.3468614254291[/C][C]84.1567000537753[/C][C]88.537022797083[/C][/ROW]
[ROW][C]81[/C][C]86.5424371609503[/C][C]84.1916457832809[/C][C]88.8932285386198[/C][/ROW]
[ROW][C]82[/C][C]86.8468813070568[/C][C]84.3389769664646[/C][C]89.354785647649[/C][/ROW]
[ROW][C]83[/C][C]86.6952078249575[/C][C]84.0329397447405[/C][C]89.3574759051745[/C][/ROW]
[ROW][C]84[/C][C]86.7200992247252[/C][C]83.9056270173981[/C][C]89.5345714320524[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13450&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13450&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
7384.042504794995683.283118735890684.8018908541005
7484.251099366729683.207045755842485.2951529776167
7584.438719513118683.161232246488485.7162067797488
7685.16793167271683.683608000096186.6522553453358
7785.85448687139884.179807993270187.5291657495258
7886.242090810104884.388245155257888.0959364649517
7986.348438447479784.32345150359888.3734253913613
8086.346861425429184.156700053775388.537022797083
8186.542437160950384.191645783280988.8932285386198
8286.846881307056884.338976966464689.354785647649
8386.695207824957584.032939744740589.3574759051745
8486.720099224725283.905627017398189.5345714320524



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')