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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 19 Dec 2010 20:31:05 +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/2010/Dec/19/t1292790789o446ar11cpunc5n.htm/, Retrieved Sat, 04 May 2024 23:52:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112738, Retrieved Sat, 04 May 2024 23:52:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-12-19 20:31:05] [ac6548ae9fe194312a6a7ae1d0184c66] [Current]
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Dataseries X:
95,05
96,84
96,92
97,44
97,78
97,69
96,67
98,29
98,2
98,71
98,54
98,2
96,92
99,06
99,65
99,82
99,99
100,33
99,31
101,1
101,1
100,93
100,85
100,93
99,6
101,88
101,81
102,38
102,74
102,82
101,72
103,47
102,98
102,68
102,9
103,03
101,29
103,69
103,68
104,2
104,08
104,16
103,05
104,66
104,46
104,95
105,85
106,23
104,86
107,44
108,23
108,45
109,39
110,15
109,13
110,28
110,17
109,99
109,26
109,11
107,06
109,53
108,92
109,24
109,12
109
107,23
109,49
109,04
109,02
109,23
109,46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112738&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112738&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112738&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.651524078529005
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.651524078529005 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112738&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]0.651524078529005[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112738&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112738&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
alpha0.651524078529005
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
296.8495.051.79000000000001
396.9296.2162281005670.703771899433079
497.4496.67475243883970.765247561160322
597.7897.17332965097120.606670349028775
697.6997.5685899910930.121410008906935
796.6797.6476915352704-0.977691535270353
898.2997.01070195866771.27929804133227
998.297.84419543621070.355804563789306
1098.7198.076010676770.633989323230054
1198.5498.48906998638460.0509300136153712
1298.298.5222521165749-0.322252116574859
1396.9298.3122971032694-1.3922971032694
1499.0697.40518201602321.65481798397680
1599.6598.4833357781671.16666422183309
1699.8299.24344561024950.576554389750513
1799.9999.61908467775350.370915322246461
18100.3399.86074494129250.469255058707546
1999.31100.166475911012-0.856475911011955
20101.199.60846123230761.49153876769239
21101.1100.5802346535190.519765346481321
22100.93100.9188742919360.0111257080637870
23100.85100.926122958630-0.0761229586304637
24100.93100.8765270181540.0534729818461699
2599.6100.911365953377-1.31136595337736
26101.88100.0569794589891.82302054101115
27101.81101.2447212371110.56527876288942
28102.38101.6130139622140.76698603778587
29102.74102.1127238337270.627276166272807
30102.82102.5214093599410.298590640058706
31101.72102.715948351563-0.99594835156293
32103.47102.0670640195481.40293598045159
33102.98102.981110591447-0.00111059144730064
34102.68102.980387014378-0.300387014377975
35102.9102.7846776416330.115322358366711
36103.03102.8598129349020.170187065098048
37101.29102.970693905668-1.68069390566750
38103.69101.8756813574881.81431864251182
39103.68103.0577536392090.622246360791308
40104.2103.4631621260410.73683787395872
41104.08103.9432297428980.136770257102484
42104.16104.0323388586260.127661141373608
43103.05104.115513166124-1.06551316612378
44104.66103.4213056824041.23869431759553
45104.46104.2283448562550.231655143744987
46104.95104.379273760320.570726239680042
47105.85104.7511156477201.09888435228018
48106.23105.4670652627490.762934737250916
49104.86105.964135614414-1.10413561441426
50107.44105.2447646756622.19523532433804
51108.23106.6750133475061.55498665249438
52108.45107.6881245933970.761875406603068
53109.39108.1845047656381.20549523436209
54110.15108.9699139373771.18008606262322
55109.13109.738768421912-0.608768421912316
56110.28109.3421411367880.93785886321166
57110.17109.9531787684330.216821231567423
58109.99110.094443021535-0.104443021535076
59109.26110.026395878171-0.766395878170641
60109.11109.527070509857-0.417070509857098
61107.06109.255339030241-2.19533903024083
62109.53107.8250227915041.70497720849558
63108.92108.935856496182-0.015856496182451
64109.24108.9255256071180.314474392881507
65109.12109.130413246162-0.0104132461615762
66109109.123628765552-0.123628765551672
67107.23109.043081647996-1.81308164799593
68109.49107.8618152979881.62818470201246
69109.04108.9226168356410.117383164358785
70109.02108.9990947936350.0209052063651001
71109.23109.0127150389480.217284961051632
72109.46109.1542814229760.305718577024251

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 96.84 & 95.05 & 1.79000000000001 \tabularnewline
3 & 96.92 & 96.216228100567 & 0.703771899433079 \tabularnewline
4 & 97.44 & 96.6747524388397 & 0.765247561160322 \tabularnewline
5 & 97.78 & 97.1733296509712 & 0.606670349028775 \tabularnewline
6 & 97.69 & 97.568589991093 & 0.121410008906935 \tabularnewline
7 & 96.67 & 97.6476915352704 & -0.977691535270353 \tabularnewline
8 & 98.29 & 97.0107019586677 & 1.27929804133227 \tabularnewline
9 & 98.2 & 97.8441954362107 & 0.355804563789306 \tabularnewline
10 & 98.71 & 98.07601067677 & 0.633989323230054 \tabularnewline
11 & 98.54 & 98.4890699863846 & 0.0509300136153712 \tabularnewline
12 & 98.2 & 98.5222521165749 & -0.322252116574859 \tabularnewline
13 & 96.92 & 98.3122971032694 & -1.3922971032694 \tabularnewline
14 & 99.06 & 97.4051820160232 & 1.65481798397680 \tabularnewline
15 & 99.65 & 98.483335778167 & 1.16666422183309 \tabularnewline
16 & 99.82 & 99.2434456102495 & 0.576554389750513 \tabularnewline
17 & 99.99 & 99.6190846777535 & 0.370915322246461 \tabularnewline
18 & 100.33 & 99.8607449412925 & 0.469255058707546 \tabularnewline
19 & 99.31 & 100.166475911012 & -0.856475911011955 \tabularnewline
20 & 101.1 & 99.6084612323076 & 1.49153876769239 \tabularnewline
21 & 101.1 & 100.580234653519 & 0.519765346481321 \tabularnewline
22 & 100.93 & 100.918874291936 & 0.0111257080637870 \tabularnewline
23 & 100.85 & 100.926122958630 & -0.0761229586304637 \tabularnewline
24 & 100.93 & 100.876527018154 & 0.0534729818461699 \tabularnewline
25 & 99.6 & 100.911365953377 & -1.31136595337736 \tabularnewline
26 & 101.88 & 100.056979458989 & 1.82302054101115 \tabularnewline
27 & 101.81 & 101.244721237111 & 0.56527876288942 \tabularnewline
28 & 102.38 & 101.613013962214 & 0.76698603778587 \tabularnewline
29 & 102.74 & 102.112723833727 & 0.627276166272807 \tabularnewline
30 & 102.82 & 102.521409359941 & 0.298590640058706 \tabularnewline
31 & 101.72 & 102.715948351563 & -0.99594835156293 \tabularnewline
32 & 103.47 & 102.067064019548 & 1.40293598045159 \tabularnewline
33 & 102.98 & 102.981110591447 & -0.00111059144730064 \tabularnewline
34 & 102.68 & 102.980387014378 & -0.300387014377975 \tabularnewline
35 & 102.9 & 102.784677641633 & 0.115322358366711 \tabularnewline
36 & 103.03 & 102.859812934902 & 0.170187065098048 \tabularnewline
37 & 101.29 & 102.970693905668 & -1.68069390566750 \tabularnewline
38 & 103.69 & 101.875681357488 & 1.81431864251182 \tabularnewline
39 & 103.68 & 103.057753639209 & 0.622246360791308 \tabularnewline
40 & 104.2 & 103.463162126041 & 0.73683787395872 \tabularnewline
41 & 104.08 & 103.943229742898 & 0.136770257102484 \tabularnewline
42 & 104.16 & 104.032338858626 & 0.127661141373608 \tabularnewline
43 & 103.05 & 104.115513166124 & -1.06551316612378 \tabularnewline
44 & 104.66 & 103.421305682404 & 1.23869431759553 \tabularnewline
45 & 104.46 & 104.228344856255 & 0.231655143744987 \tabularnewline
46 & 104.95 & 104.37927376032 & 0.570726239680042 \tabularnewline
47 & 105.85 & 104.751115647720 & 1.09888435228018 \tabularnewline
48 & 106.23 & 105.467065262749 & 0.762934737250916 \tabularnewline
49 & 104.86 & 105.964135614414 & -1.10413561441426 \tabularnewline
50 & 107.44 & 105.244764675662 & 2.19523532433804 \tabularnewline
51 & 108.23 & 106.675013347506 & 1.55498665249438 \tabularnewline
52 & 108.45 & 107.688124593397 & 0.761875406603068 \tabularnewline
53 & 109.39 & 108.184504765638 & 1.20549523436209 \tabularnewline
54 & 110.15 & 108.969913937377 & 1.18008606262322 \tabularnewline
55 & 109.13 & 109.738768421912 & -0.608768421912316 \tabularnewline
56 & 110.28 & 109.342141136788 & 0.93785886321166 \tabularnewline
57 & 110.17 & 109.953178768433 & 0.216821231567423 \tabularnewline
58 & 109.99 & 110.094443021535 & -0.104443021535076 \tabularnewline
59 & 109.26 & 110.026395878171 & -0.766395878170641 \tabularnewline
60 & 109.11 & 109.527070509857 & -0.417070509857098 \tabularnewline
61 & 107.06 & 109.255339030241 & -2.19533903024083 \tabularnewline
62 & 109.53 & 107.825022791504 & 1.70497720849558 \tabularnewline
63 & 108.92 & 108.935856496182 & -0.015856496182451 \tabularnewline
64 & 109.24 & 108.925525607118 & 0.314474392881507 \tabularnewline
65 & 109.12 & 109.130413246162 & -0.0104132461615762 \tabularnewline
66 & 109 & 109.123628765552 & -0.123628765551672 \tabularnewline
67 & 107.23 & 109.043081647996 & -1.81308164799593 \tabularnewline
68 & 109.49 & 107.861815297988 & 1.62818470201246 \tabularnewline
69 & 109.04 & 108.922616835641 & 0.117383164358785 \tabularnewline
70 & 109.02 & 108.999094793635 & 0.0209052063651001 \tabularnewline
71 & 109.23 & 109.012715038948 & 0.217284961051632 \tabularnewline
72 & 109.46 & 109.154281422976 & 0.305718577024251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112738&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]2[/C][C]96.84[/C][C]95.05[/C][C]1.79000000000001[/C][/ROW]
[ROW][C]3[/C][C]96.92[/C][C]96.216228100567[/C][C]0.703771899433079[/C][/ROW]
[ROW][C]4[/C][C]97.44[/C][C]96.6747524388397[/C][C]0.765247561160322[/C][/ROW]
[ROW][C]5[/C][C]97.78[/C][C]97.1733296509712[/C][C]0.606670349028775[/C][/ROW]
[ROW][C]6[/C][C]97.69[/C][C]97.568589991093[/C][C]0.121410008906935[/C][/ROW]
[ROW][C]7[/C][C]96.67[/C][C]97.6476915352704[/C][C]-0.977691535270353[/C][/ROW]
[ROW][C]8[/C][C]98.29[/C][C]97.0107019586677[/C][C]1.27929804133227[/C][/ROW]
[ROW][C]9[/C][C]98.2[/C][C]97.8441954362107[/C][C]0.355804563789306[/C][/ROW]
[ROW][C]10[/C][C]98.71[/C][C]98.07601067677[/C][C]0.633989323230054[/C][/ROW]
[ROW][C]11[/C][C]98.54[/C][C]98.4890699863846[/C][C]0.0509300136153712[/C][/ROW]
[ROW][C]12[/C][C]98.2[/C][C]98.5222521165749[/C][C]-0.322252116574859[/C][/ROW]
[ROW][C]13[/C][C]96.92[/C][C]98.3122971032694[/C][C]-1.3922971032694[/C][/ROW]
[ROW][C]14[/C][C]99.06[/C][C]97.4051820160232[/C][C]1.65481798397680[/C][/ROW]
[ROW][C]15[/C][C]99.65[/C][C]98.483335778167[/C][C]1.16666422183309[/C][/ROW]
[ROW][C]16[/C][C]99.82[/C][C]99.2434456102495[/C][C]0.576554389750513[/C][/ROW]
[ROW][C]17[/C][C]99.99[/C][C]99.6190846777535[/C][C]0.370915322246461[/C][/ROW]
[ROW][C]18[/C][C]100.33[/C][C]99.8607449412925[/C][C]0.469255058707546[/C][/ROW]
[ROW][C]19[/C][C]99.31[/C][C]100.166475911012[/C][C]-0.856475911011955[/C][/ROW]
[ROW][C]20[/C][C]101.1[/C][C]99.6084612323076[/C][C]1.49153876769239[/C][/ROW]
[ROW][C]21[/C][C]101.1[/C][C]100.580234653519[/C][C]0.519765346481321[/C][/ROW]
[ROW][C]22[/C][C]100.93[/C][C]100.918874291936[/C][C]0.0111257080637870[/C][/ROW]
[ROW][C]23[/C][C]100.85[/C][C]100.926122958630[/C][C]-0.0761229586304637[/C][/ROW]
[ROW][C]24[/C][C]100.93[/C][C]100.876527018154[/C][C]0.0534729818461699[/C][/ROW]
[ROW][C]25[/C][C]99.6[/C][C]100.911365953377[/C][C]-1.31136595337736[/C][/ROW]
[ROW][C]26[/C][C]101.88[/C][C]100.056979458989[/C][C]1.82302054101115[/C][/ROW]
[ROW][C]27[/C][C]101.81[/C][C]101.244721237111[/C][C]0.56527876288942[/C][/ROW]
[ROW][C]28[/C][C]102.38[/C][C]101.613013962214[/C][C]0.76698603778587[/C][/ROW]
[ROW][C]29[/C][C]102.74[/C][C]102.112723833727[/C][C]0.627276166272807[/C][/ROW]
[ROW][C]30[/C][C]102.82[/C][C]102.521409359941[/C][C]0.298590640058706[/C][/ROW]
[ROW][C]31[/C][C]101.72[/C][C]102.715948351563[/C][C]-0.99594835156293[/C][/ROW]
[ROW][C]32[/C][C]103.47[/C][C]102.067064019548[/C][C]1.40293598045159[/C][/ROW]
[ROW][C]33[/C][C]102.98[/C][C]102.981110591447[/C][C]-0.00111059144730064[/C][/ROW]
[ROW][C]34[/C][C]102.68[/C][C]102.980387014378[/C][C]-0.300387014377975[/C][/ROW]
[ROW][C]35[/C][C]102.9[/C][C]102.784677641633[/C][C]0.115322358366711[/C][/ROW]
[ROW][C]36[/C][C]103.03[/C][C]102.859812934902[/C][C]0.170187065098048[/C][/ROW]
[ROW][C]37[/C][C]101.29[/C][C]102.970693905668[/C][C]-1.68069390566750[/C][/ROW]
[ROW][C]38[/C][C]103.69[/C][C]101.875681357488[/C][C]1.81431864251182[/C][/ROW]
[ROW][C]39[/C][C]103.68[/C][C]103.057753639209[/C][C]0.622246360791308[/C][/ROW]
[ROW][C]40[/C][C]104.2[/C][C]103.463162126041[/C][C]0.73683787395872[/C][/ROW]
[ROW][C]41[/C][C]104.08[/C][C]103.943229742898[/C][C]0.136770257102484[/C][/ROW]
[ROW][C]42[/C][C]104.16[/C][C]104.032338858626[/C][C]0.127661141373608[/C][/ROW]
[ROW][C]43[/C][C]103.05[/C][C]104.115513166124[/C][C]-1.06551316612378[/C][/ROW]
[ROW][C]44[/C][C]104.66[/C][C]103.421305682404[/C][C]1.23869431759553[/C][/ROW]
[ROW][C]45[/C][C]104.46[/C][C]104.228344856255[/C][C]0.231655143744987[/C][/ROW]
[ROW][C]46[/C][C]104.95[/C][C]104.37927376032[/C][C]0.570726239680042[/C][/ROW]
[ROW][C]47[/C][C]105.85[/C][C]104.751115647720[/C][C]1.09888435228018[/C][/ROW]
[ROW][C]48[/C][C]106.23[/C][C]105.467065262749[/C][C]0.762934737250916[/C][/ROW]
[ROW][C]49[/C][C]104.86[/C][C]105.964135614414[/C][C]-1.10413561441426[/C][/ROW]
[ROW][C]50[/C][C]107.44[/C][C]105.244764675662[/C][C]2.19523532433804[/C][/ROW]
[ROW][C]51[/C][C]108.23[/C][C]106.675013347506[/C][C]1.55498665249438[/C][/ROW]
[ROW][C]52[/C][C]108.45[/C][C]107.688124593397[/C][C]0.761875406603068[/C][/ROW]
[ROW][C]53[/C][C]109.39[/C][C]108.184504765638[/C][C]1.20549523436209[/C][/ROW]
[ROW][C]54[/C][C]110.15[/C][C]108.969913937377[/C][C]1.18008606262322[/C][/ROW]
[ROW][C]55[/C][C]109.13[/C][C]109.738768421912[/C][C]-0.608768421912316[/C][/ROW]
[ROW][C]56[/C][C]110.28[/C][C]109.342141136788[/C][C]0.93785886321166[/C][/ROW]
[ROW][C]57[/C][C]110.17[/C][C]109.953178768433[/C][C]0.216821231567423[/C][/ROW]
[ROW][C]58[/C][C]109.99[/C][C]110.094443021535[/C][C]-0.104443021535076[/C][/ROW]
[ROW][C]59[/C][C]109.26[/C][C]110.026395878171[/C][C]-0.766395878170641[/C][/ROW]
[ROW][C]60[/C][C]109.11[/C][C]109.527070509857[/C][C]-0.417070509857098[/C][/ROW]
[ROW][C]61[/C][C]107.06[/C][C]109.255339030241[/C][C]-2.19533903024083[/C][/ROW]
[ROW][C]62[/C][C]109.53[/C][C]107.825022791504[/C][C]1.70497720849558[/C][/ROW]
[ROW][C]63[/C][C]108.92[/C][C]108.935856496182[/C][C]-0.015856496182451[/C][/ROW]
[ROW][C]64[/C][C]109.24[/C][C]108.925525607118[/C][C]0.314474392881507[/C][/ROW]
[ROW][C]65[/C][C]109.12[/C][C]109.130413246162[/C][C]-0.0104132461615762[/C][/ROW]
[ROW][C]66[/C][C]109[/C][C]109.123628765552[/C][C]-0.123628765551672[/C][/ROW]
[ROW][C]67[/C][C]107.23[/C][C]109.043081647996[/C][C]-1.81308164799593[/C][/ROW]
[ROW][C]68[/C][C]109.49[/C][C]107.861815297988[/C][C]1.62818470201246[/C][/ROW]
[ROW][C]69[/C][C]109.04[/C][C]108.922616835641[/C][C]0.117383164358785[/C][/ROW]
[ROW][C]70[/C][C]109.02[/C][C]108.999094793635[/C][C]0.0209052063651001[/C][/ROW]
[ROW][C]71[/C][C]109.23[/C][C]109.012715038948[/C][C]0.217284961051632[/C][/ROW]
[ROW][C]72[/C][C]109.46[/C][C]109.154281422976[/C][C]0.305718577024251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112738&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112738&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
296.8495.051.79000000000001
396.9296.2162281005670.703771899433079
497.4496.67475243883970.765247561160322
597.7897.17332965097120.606670349028775
697.6997.5685899910930.121410008906935
796.6797.6476915352704-0.977691535270353
898.2997.01070195866771.27929804133227
998.297.84419543621070.355804563789306
1098.7198.076010676770.633989323230054
1198.5498.48906998638460.0509300136153712
1298.298.5222521165749-0.322252116574859
1396.9298.3122971032694-1.3922971032694
1499.0697.40518201602321.65481798397680
1599.6598.4833357781671.16666422183309
1699.8299.24344561024950.576554389750513
1799.9999.61908467775350.370915322246461
18100.3399.86074494129250.469255058707546
1999.31100.166475911012-0.856475911011955
20101.199.60846123230761.49153876769239
21101.1100.5802346535190.519765346481321
22100.93100.9188742919360.0111257080637870
23100.85100.926122958630-0.0761229586304637
24100.93100.8765270181540.0534729818461699
2599.6100.911365953377-1.31136595337736
26101.88100.0569794589891.82302054101115
27101.81101.2447212371110.56527876288942
28102.38101.6130139622140.76698603778587
29102.74102.1127238337270.627276166272807
30102.82102.5214093599410.298590640058706
31101.72102.715948351563-0.99594835156293
32103.47102.0670640195481.40293598045159
33102.98102.981110591447-0.00111059144730064
34102.68102.980387014378-0.300387014377975
35102.9102.7846776416330.115322358366711
36103.03102.8598129349020.170187065098048
37101.29102.970693905668-1.68069390566750
38103.69101.8756813574881.81431864251182
39103.68103.0577536392090.622246360791308
40104.2103.4631621260410.73683787395872
41104.08103.9432297428980.136770257102484
42104.16104.0323388586260.127661141373608
43103.05104.115513166124-1.06551316612378
44104.66103.4213056824041.23869431759553
45104.46104.2283448562550.231655143744987
46104.95104.379273760320.570726239680042
47105.85104.7511156477201.09888435228018
48106.23105.4670652627490.762934737250916
49104.86105.964135614414-1.10413561441426
50107.44105.2447646756622.19523532433804
51108.23106.6750133475061.55498665249438
52108.45107.6881245933970.761875406603068
53109.39108.1845047656381.20549523436209
54110.15108.9699139373771.18008606262322
55109.13109.738768421912-0.608768421912316
56110.28109.3421411367880.93785886321166
57110.17109.9531787684330.216821231567423
58109.99110.094443021535-0.104443021535076
59109.26110.026395878171-0.766395878170641
60109.11109.527070509857-0.417070509857098
61107.06109.255339030241-2.19533903024083
62109.53107.8250227915041.70497720849558
63108.92108.935856496182-0.015856496182451
64109.24108.9255256071180.314474392881507
65109.12109.130413246162-0.0104132461615762
66109109.123628765552-0.123628765551672
67107.23109.043081647996-1.81308164799593
68109.49107.8618152979881.62818470201246
69109.04108.9226168356410.117383164358785
70109.02108.9990947936350.0209052063651001
71109.23109.0127150389480.217284961051632
72109.46109.1542814229760.305718577024251







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73109.353464437161107.532780286888111.174148587433
74109.353464437161107.180446345334111.526482528987
75109.353464437161106.877757572494111.829171301827
76109.353464437161106.608242891983112.098685982339
77109.353464437161106.362919639893112.344009234428
78109.353464437161106.136249020560112.570679853761
79109.353464437161105.92452992493112.782398949391
80109.353464437161105.725144062453112.981784811868
81109.353464437161105.536158372163113.170770502159
82109.353464437161105.356097498009113.350831376312
83109.353464437161105.183805062754113.523123811567
84109.353464437161105.018354732559113.688574141762

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 109.353464437161 & 107.532780286888 & 111.174148587433 \tabularnewline
74 & 109.353464437161 & 107.180446345334 & 111.526482528987 \tabularnewline
75 & 109.353464437161 & 106.877757572494 & 111.829171301827 \tabularnewline
76 & 109.353464437161 & 106.608242891983 & 112.098685982339 \tabularnewline
77 & 109.353464437161 & 106.362919639893 & 112.344009234428 \tabularnewline
78 & 109.353464437161 & 106.136249020560 & 112.570679853761 \tabularnewline
79 & 109.353464437161 & 105.92452992493 & 112.782398949391 \tabularnewline
80 & 109.353464437161 & 105.725144062453 & 112.981784811868 \tabularnewline
81 & 109.353464437161 & 105.536158372163 & 113.170770502159 \tabularnewline
82 & 109.353464437161 & 105.356097498009 & 113.350831376312 \tabularnewline
83 & 109.353464437161 & 105.183805062754 & 113.523123811567 \tabularnewline
84 & 109.353464437161 & 105.018354732559 & 113.688574141762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112738&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]109.353464437161[/C][C]107.532780286888[/C][C]111.174148587433[/C][/ROW]
[ROW][C]74[/C][C]109.353464437161[/C][C]107.180446345334[/C][C]111.526482528987[/C][/ROW]
[ROW][C]75[/C][C]109.353464437161[/C][C]106.877757572494[/C][C]111.829171301827[/C][/ROW]
[ROW][C]76[/C][C]109.353464437161[/C][C]106.608242891983[/C][C]112.098685982339[/C][/ROW]
[ROW][C]77[/C][C]109.353464437161[/C][C]106.362919639893[/C][C]112.344009234428[/C][/ROW]
[ROW][C]78[/C][C]109.353464437161[/C][C]106.136249020560[/C][C]112.570679853761[/C][/ROW]
[ROW][C]79[/C][C]109.353464437161[/C][C]105.92452992493[/C][C]112.782398949391[/C][/ROW]
[ROW][C]80[/C][C]109.353464437161[/C][C]105.725144062453[/C][C]112.981784811868[/C][/ROW]
[ROW][C]81[/C][C]109.353464437161[/C][C]105.536158372163[/C][C]113.170770502159[/C][/ROW]
[ROW][C]82[/C][C]109.353464437161[/C][C]105.356097498009[/C][C]113.350831376312[/C][/ROW]
[ROW][C]83[/C][C]109.353464437161[/C][C]105.183805062754[/C][C]113.523123811567[/C][/ROW]
[ROW][C]84[/C][C]109.353464437161[/C][C]105.018354732559[/C][C]113.688574141762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112738&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112738&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
73109.353464437161107.532780286888111.174148587433
74109.353464437161107.180446345334111.526482528987
75109.353464437161106.877757572494111.829171301827
76109.353464437161106.608242891983112.098685982339
77109.353464437161106.362919639893112.344009234428
78109.353464437161106.136249020560112.570679853761
79109.353464437161105.92452992493112.782398949391
80109.353464437161105.725144062453112.981784811868
81109.353464437161105.536158372163113.170770502159
82109.353464437161105.356097498009113.350831376312
83109.353464437161105.183805062754113.523123811567
84109.353464437161105.018354732559113.688574141762



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')