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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Jan 2013 02:56:16 -0500
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/Jan/16/t13583230426r17j4tdhq17c8k.htm/, Retrieved Fri, 03 May 2024 23:03:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205627, Retrieved Fri, 03 May 2024 23:03:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [gemiddelde prijze...] [2012-11-16 20:22:06] [770959544eacfa1f4175753a9a1bfc9b]
- RMPD    [Exponential Smoothing] [gemiddelde vliegt...] [2013-01-16 07:56:16] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
86,86
86,79
82,52
86,87
81,62
82,66
89,87
92,04
79,74
77,75
79,12
76,37
75,01
77,6
77,81
81,7
76,47
74,72
84,43
86,72
70,99
75,43
74,14
73,3
71,97
69,27
74,13
76,4
72,26
72,1
87,82
91,62
82,69
85,76
86,87
93,09
83,73
84,49
87,37
89,13
83,2
83,77
93,68
93,09
88,59
87,88
87,89
89,38
89,13
89,58
90,22
91,44
91,04
92,1
97,54
99,12
100
99,68
100,08
99,9
99,63
99,45
99,63
99,46
96,91
97,65
102,1
103,57
104,59
104,79
101,31
104,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205627&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205627&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205627&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.559712661816307
beta0.0092101621786818
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.559712661816307 \tabularnewline
beta & 0.0092101621786818 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205627&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]0.559712661816307[/C][/ROW]
[ROW][C]beta[/C][C]0.0092101621786818[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205627&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205627&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
alpha0.559712661816307
beta0.0092101621786818
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
382.5286.72-4.20000000000002
486.8784.27755563393862.5924443660614
581.6285.6502925500271-4.03029255002713
682.6683.2954234213074-0.635423421307422
789.8782.83742989319897.03257010680109
892.0486.70756264456615.33243735543394
979.7489.6535985194921-9.91359851949214
1077.7584.0151300322958-6.26513003229579
1179.1280.386458530203-1.266458530203
1276.3779.5490781101521-3.17907811015213
1375.0177.6247920051927-2.61479200519268
1477.676.00286460921181.59713539078817
1577.8176.74663961124691.06336038875314
1681.777.19713565608724.50286434391285
1776.4779.5959780805672-3.12597808056718
1874.7277.7087462493006-2.98874624930062
1984.4375.88291769201628.5470823079838
2086.7280.55789903147836.16210096852166
2170.9983.9297420210688-12.9397420210688
2275.4376.5433366808603-1.11333668086033
2374.1475.7705808533291-1.63058085332905
2473.374.6999111965379-1.3999111965379
2571.9773.7511336629911-1.78113366299105
2669.2772.5797992649064-3.30979926490645
2774.1370.53578921161823.59421078838182
2876.472.37456931861924.0254306813808
2972.2674.4754599336054-2.21545993360535
3072.173.0718242560739-0.971824256073873
3187.8272.359257416765115.4607425832349
3291.6280.923907117860410.6960928821396
3382.6986.8768608857275-4.1868608857275
3485.7684.4780535307771.28194646922299
3586.8785.14681538837941.72318461162062
3693.0986.0714269143217.01857308567902
3783.7389.9961154742318-6.26611547423184
3884.4986.4528935354594-1.96289353545941
3987.3785.30812059911792.06187940088215
4089.1386.42669311601822.70330688398184
4183.287.9182163838298-4.71821638382976
4283.7785.2314964937883-1.46149649378832
4393.6884.36006988289259.31993011710746
4493.0989.57118891201253.51881108798749
4588.5991.5534877951849-2.96348779518486
4687.8889.8922850046381-2.01228500463813
4787.8988.7531090413936-0.863109041393599
4889.3888.25269205001121.12730794998876
4989.1388.87214797352190.257852026478076
5089.5889.00628764639470.573712353605274
5190.2289.32017585637530.899824143624713
5291.4489.82123159779981.61876840220019
5391.0490.73303436685770.30696563314234
5492.190.91218693773281.18781306226717
5597.5491.59048419687915.94951580312093
5699.1294.96463678994354.15536321005652
5710097.35600054123862.64399945876143
5899.6898.91506479889750.764935201102546
59100.0899.42633627409440.65366372590556
6099.999.87869736124710.0213026387529425
6199.6399.9772277571288-0.34722775712882
6299.4599.8676970496704-0.417697049670352
6399.6399.716570540075-0.0865705400750443
6499.4699.7503334555864-0.290333455586406
6596.9199.6685510054264-2.75855100542636
6697.6598.191055487622-0.541055487621946
67102.197.95193112359814.14806887640189
68103.57100.3587525181353.21124748186465
69104.59102.2577772396022.33222276039793
70104.79103.6768234062691.11317659373128
71101.31104.419292472867-3.10929247286668
72104.8102.7823635980472.0176364019533

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 82.52 & 86.72 & -4.20000000000002 \tabularnewline
4 & 86.87 & 84.2775556339386 & 2.5924443660614 \tabularnewline
5 & 81.62 & 85.6502925500271 & -4.03029255002713 \tabularnewline
6 & 82.66 & 83.2954234213074 & -0.635423421307422 \tabularnewline
7 & 89.87 & 82.8374298931989 & 7.03257010680109 \tabularnewline
8 & 92.04 & 86.7075626445661 & 5.33243735543394 \tabularnewline
9 & 79.74 & 89.6535985194921 & -9.91359851949214 \tabularnewline
10 & 77.75 & 84.0151300322958 & -6.26513003229579 \tabularnewline
11 & 79.12 & 80.386458530203 & -1.266458530203 \tabularnewline
12 & 76.37 & 79.5490781101521 & -3.17907811015213 \tabularnewline
13 & 75.01 & 77.6247920051927 & -2.61479200519268 \tabularnewline
14 & 77.6 & 76.0028646092118 & 1.59713539078817 \tabularnewline
15 & 77.81 & 76.7466396112469 & 1.06336038875314 \tabularnewline
16 & 81.7 & 77.1971356560872 & 4.50286434391285 \tabularnewline
17 & 76.47 & 79.5959780805672 & -3.12597808056718 \tabularnewline
18 & 74.72 & 77.7087462493006 & -2.98874624930062 \tabularnewline
19 & 84.43 & 75.8829176920162 & 8.5470823079838 \tabularnewline
20 & 86.72 & 80.5578990314783 & 6.16210096852166 \tabularnewline
21 & 70.99 & 83.9297420210688 & -12.9397420210688 \tabularnewline
22 & 75.43 & 76.5433366808603 & -1.11333668086033 \tabularnewline
23 & 74.14 & 75.7705808533291 & -1.63058085332905 \tabularnewline
24 & 73.3 & 74.6999111965379 & -1.3999111965379 \tabularnewline
25 & 71.97 & 73.7511336629911 & -1.78113366299105 \tabularnewline
26 & 69.27 & 72.5797992649064 & -3.30979926490645 \tabularnewline
27 & 74.13 & 70.5357892116182 & 3.59421078838182 \tabularnewline
28 & 76.4 & 72.3745693186192 & 4.0254306813808 \tabularnewline
29 & 72.26 & 74.4754599336054 & -2.21545993360535 \tabularnewline
30 & 72.1 & 73.0718242560739 & -0.971824256073873 \tabularnewline
31 & 87.82 & 72.3592574167651 & 15.4607425832349 \tabularnewline
32 & 91.62 & 80.9239071178604 & 10.6960928821396 \tabularnewline
33 & 82.69 & 86.8768608857275 & -4.1868608857275 \tabularnewline
34 & 85.76 & 84.478053530777 & 1.28194646922299 \tabularnewline
35 & 86.87 & 85.1468153883794 & 1.72318461162062 \tabularnewline
36 & 93.09 & 86.071426914321 & 7.01857308567902 \tabularnewline
37 & 83.73 & 89.9961154742318 & -6.26611547423184 \tabularnewline
38 & 84.49 & 86.4528935354594 & -1.96289353545941 \tabularnewline
39 & 87.37 & 85.3081205991179 & 2.06187940088215 \tabularnewline
40 & 89.13 & 86.4266931160182 & 2.70330688398184 \tabularnewline
41 & 83.2 & 87.9182163838298 & -4.71821638382976 \tabularnewline
42 & 83.77 & 85.2314964937883 & -1.46149649378832 \tabularnewline
43 & 93.68 & 84.3600698828925 & 9.31993011710746 \tabularnewline
44 & 93.09 & 89.5711889120125 & 3.51881108798749 \tabularnewline
45 & 88.59 & 91.5534877951849 & -2.96348779518486 \tabularnewline
46 & 87.88 & 89.8922850046381 & -2.01228500463813 \tabularnewline
47 & 87.89 & 88.7531090413936 & -0.863109041393599 \tabularnewline
48 & 89.38 & 88.2526920500112 & 1.12730794998876 \tabularnewline
49 & 89.13 & 88.8721479735219 & 0.257852026478076 \tabularnewline
50 & 89.58 & 89.0062876463947 & 0.573712353605274 \tabularnewline
51 & 90.22 & 89.3201758563753 & 0.899824143624713 \tabularnewline
52 & 91.44 & 89.8212315977998 & 1.61876840220019 \tabularnewline
53 & 91.04 & 90.7330343668577 & 0.30696563314234 \tabularnewline
54 & 92.1 & 90.9121869377328 & 1.18781306226717 \tabularnewline
55 & 97.54 & 91.5904841968791 & 5.94951580312093 \tabularnewline
56 & 99.12 & 94.9646367899435 & 4.15536321005652 \tabularnewline
57 & 100 & 97.3560005412386 & 2.64399945876143 \tabularnewline
58 & 99.68 & 98.9150647988975 & 0.764935201102546 \tabularnewline
59 & 100.08 & 99.4263362740944 & 0.65366372590556 \tabularnewline
60 & 99.9 & 99.8786973612471 & 0.0213026387529425 \tabularnewline
61 & 99.63 & 99.9772277571288 & -0.34722775712882 \tabularnewline
62 & 99.45 & 99.8676970496704 & -0.417697049670352 \tabularnewline
63 & 99.63 & 99.716570540075 & -0.0865705400750443 \tabularnewline
64 & 99.46 & 99.7503334555864 & -0.290333455586406 \tabularnewline
65 & 96.91 & 99.6685510054264 & -2.75855100542636 \tabularnewline
66 & 97.65 & 98.191055487622 & -0.541055487621946 \tabularnewline
67 & 102.1 & 97.9519311235981 & 4.14806887640189 \tabularnewline
68 & 103.57 & 100.358752518135 & 3.21124748186465 \tabularnewline
69 & 104.59 & 102.257777239602 & 2.33222276039793 \tabularnewline
70 & 104.79 & 103.676823406269 & 1.11317659373128 \tabularnewline
71 & 101.31 & 104.419292472867 & -3.10929247286668 \tabularnewline
72 & 104.8 & 102.782363598047 & 2.0176364019533 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205627&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]82.52[/C][C]86.72[/C][C]-4.20000000000002[/C][/ROW]
[ROW][C]4[/C][C]86.87[/C][C]84.2775556339386[/C][C]2.5924443660614[/C][/ROW]
[ROW][C]5[/C][C]81.62[/C][C]85.6502925500271[/C][C]-4.03029255002713[/C][/ROW]
[ROW][C]6[/C][C]82.66[/C][C]83.2954234213074[/C][C]-0.635423421307422[/C][/ROW]
[ROW][C]7[/C][C]89.87[/C][C]82.8374298931989[/C][C]7.03257010680109[/C][/ROW]
[ROW][C]8[/C][C]92.04[/C][C]86.7075626445661[/C][C]5.33243735543394[/C][/ROW]
[ROW][C]9[/C][C]79.74[/C][C]89.6535985194921[/C][C]-9.91359851949214[/C][/ROW]
[ROW][C]10[/C][C]77.75[/C][C]84.0151300322958[/C][C]-6.26513003229579[/C][/ROW]
[ROW][C]11[/C][C]79.12[/C][C]80.386458530203[/C][C]-1.266458530203[/C][/ROW]
[ROW][C]12[/C][C]76.37[/C][C]79.5490781101521[/C][C]-3.17907811015213[/C][/ROW]
[ROW][C]13[/C][C]75.01[/C][C]77.6247920051927[/C][C]-2.61479200519268[/C][/ROW]
[ROW][C]14[/C][C]77.6[/C][C]76.0028646092118[/C][C]1.59713539078817[/C][/ROW]
[ROW][C]15[/C][C]77.81[/C][C]76.7466396112469[/C][C]1.06336038875314[/C][/ROW]
[ROW][C]16[/C][C]81.7[/C][C]77.1971356560872[/C][C]4.50286434391285[/C][/ROW]
[ROW][C]17[/C][C]76.47[/C][C]79.5959780805672[/C][C]-3.12597808056718[/C][/ROW]
[ROW][C]18[/C][C]74.72[/C][C]77.7087462493006[/C][C]-2.98874624930062[/C][/ROW]
[ROW][C]19[/C][C]84.43[/C][C]75.8829176920162[/C][C]8.5470823079838[/C][/ROW]
[ROW][C]20[/C][C]86.72[/C][C]80.5578990314783[/C][C]6.16210096852166[/C][/ROW]
[ROW][C]21[/C][C]70.99[/C][C]83.9297420210688[/C][C]-12.9397420210688[/C][/ROW]
[ROW][C]22[/C][C]75.43[/C][C]76.5433366808603[/C][C]-1.11333668086033[/C][/ROW]
[ROW][C]23[/C][C]74.14[/C][C]75.7705808533291[/C][C]-1.63058085332905[/C][/ROW]
[ROW][C]24[/C][C]73.3[/C][C]74.6999111965379[/C][C]-1.3999111965379[/C][/ROW]
[ROW][C]25[/C][C]71.97[/C][C]73.7511336629911[/C][C]-1.78113366299105[/C][/ROW]
[ROW][C]26[/C][C]69.27[/C][C]72.5797992649064[/C][C]-3.30979926490645[/C][/ROW]
[ROW][C]27[/C][C]74.13[/C][C]70.5357892116182[/C][C]3.59421078838182[/C][/ROW]
[ROW][C]28[/C][C]76.4[/C][C]72.3745693186192[/C][C]4.0254306813808[/C][/ROW]
[ROW][C]29[/C][C]72.26[/C][C]74.4754599336054[/C][C]-2.21545993360535[/C][/ROW]
[ROW][C]30[/C][C]72.1[/C][C]73.0718242560739[/C][C]-0.971824256073873[/C][/ROW]
[ROW][C]31[/C][C]87.82[/C][C]72.3592574167651[/C][C]15.4607425832349[/C][/ROW]
[ROW][C]32[/C][C]91.62[/C][C]80.9239071178604[/C][C]10.6960928821396[/C][/ROW]
[ROW][C]33[/C][C]82.69[/C][C]86.8768608857275[/C][C]-4.1868608857275[/C][/ROW]
[ROW][C]34[/C][C]85.76[/C][C]84.478053530777[/C][C]1.28194646922299[/C][/ROW]
[ROW][C]35[/C][C]86.87[/C][C]85.1468153883794[/C][C]1.72318461162062[/C][/ROW]
[ROW][C]36[/C][C]93.09[/C][C]86.071426914321[/C][C]7.01857308567902[/C][/ROW]
[ROW][C]37[/C][C]83.73[/C][C]89.9961154742318[/C][C]-6.26611547423184[/C][/ROW]
[ROW][C]38[/C][C]84.49[/C][C]86.4528935354594[/C][C]-1.96289353545941[/C][/ROW]
[ROW][C]39[/C][C]87.37[/C][C]85.3081205991179[/C][C]2.06187940088215[/C][/ROW]
[ROW][C]40[/C][C]89.13[/C][C]86.4266931160182[/C][C]2.70330688398184[/C][/ROW]
[ROW][C]41[/C][C]83.2[/C][C]87.9182163838298[/C][C]-4.71821638382976[/C][/ROW]
[ROW][C]42[/C][C]83.77[/C][C]85.2314964937883[/C][C]-1.46149649378832[/C][/ROW]
[ROW][C]43[/C][C]93.68[/C][C]84.3600698828925[/C][C]9.31993011710746[/C][/ROW]
[ROW][C]44[/C][C]93.09[/C][C]89.5711889120125[/C][C]3.51881108798749[/C][/ROW]
[ROW][C]45[/C][C]88.59[/C][C]91.5534877951849[/C][C]-2.96348779518486[/C][/ROW]
[ROW][C]46[/C][C]87.88[/C][C]89.8922850046381[/C][C]-2.01228500463813[/C][/ROW]
[ROW][C]47[/C][C]87.89[/C][C]88.7531090413936[/C][C]-0.863109041393599[/C][/ROW]
[ROW][C]48[/C][C]89.38[/C][C]88.2526920500112[/C][C]1.12730794998876[/C][/ROW]
[ROW][C]49[/C][C]89.13[/C][C]88.8721479735219[/C][C]0.257852026478076[/C][/ROW]
[ROW][C]50[/C][C]89.58[/C][C]89.0062876463947[/C][C]0.573712353605274[/C][/ROW]
[ROW][C]51[/C][C]90.22[/C][C]89.3201758563753[/C][C]0.899824143624713[/C][/ROW]
[ROW][C]52[/C][C]91.44[/C][C]89.8212315977998[/C][C]1.61876840220019[/C][/ROW]
[ROW][C]53[/C][C]91.04[/C][C]90.7330343668577[/C][C]0.30696563314234[/C][/ROW]
[ROW][C]54[/C][C]92.1[/C][C]90.9121869377328[/C][C]1.18781306226717[/C][/ROW]
[ROW][C]55[/C][C]97.54[/C][C]91.5904841968791[/C][C]5.94951580312093[/C][/ROW]
[ROW][C]56[/C][C]99.12[/C][C]94.9646367899435[/C][C]4.15536321005652[/C][/ROW]
[ROW][C]57[/C][C]100[/C][C]97.3560005412386[/C][C]2.64399945876143[/C][/ROW]
[ROW][C]58[/C][C]99.68[/C][C]98.9150647988975[/C][C]0.764935201102546[/C][/ROW]
[ROW][C]59[/C][C]100.08[/C][C]99.4263362740944[/C][C]0.65366372590556[/C][/ROW]
[ROW][C]60[/C][C]99.9[/C][C]99.8786973612471[/C][C]0.0213026387529425[/C][/ROW]
[ROW][C]61[/C][C]99.63[/C][C]99.9772277571288[/C][C]-0.34722775712882[/C][/ROW]
[ROW][C]62[/C][C]99.45[/C][C]99.8676970496704[/C][C]-0.417697049670352[/C][/ROW]
[ROW][C]63[/C][C]99.63[/C][C]99.716570540075[/C][C]-0.0865705400750443[/C][/ROW]
[ROW][C]64[/C][C]99.46[/C][C]99.7503334555864[/C][C]-0.290333455586406[/C][/ROW]
[ROW][C]65[/C][C]96.91[/C][C]99.6685510054264[/C][C]-2.75855100542636[/C][/ROW]
[ROW][C]66[/C][C]97.65[/C][C]98.191055487622[/C][C]-0.541055487621946[/C][/ROW]
[ROW][C]67[/C][C]102.1[/C][C]97.9519311235981[/C][C]4.14806887640189[/C][/ROW]
[ROW][C]68[/C][C]103.57[/C][C]100.358752518135[/C][C]3.21124748186465[/C][/ROW]
[ROW][C]69[/C][C]104.59[/C][C]102.257777239602[/C][C]2.33222276039793[/C][/ROW]
[ROW][C]70[/C][C]104.79[/C][C]103.676823406269[/C][C]1.11317659373128[/C][/ROW]
[ROW][C]71[/C][C]101.31[/C][C]104.419292472867[/C][C]-3.10929247286668[/C][/ROW]
[ROW][C]72[/C][C]104.8[/C][C]102.782363598047[/C][C]2.0176364019533[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205627&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205627&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
382.5286.72-4.20000000000002
486.8784.27755563393862.5924443660614
581.6285.6502925500271-4.03029255002713
682.6683.2954234213074-0.635423421307422
789.8782.83742989319897.03257010680109
892.0486.70756264456615.33243735543394
979.7489.6535985194921-9.91359851949214
1077.7584.0151300322958-6.26513003229579
1179.1280.386458530203-1.266458530203
1276.3779.5490781101521-3.17907811015213
1375.0177.6247920051927-2.61479200519268
1477.676.00286460921181.59713539078817
1577.8176.74663961124691.06336038875314
1681.777.19713565608724.50286434391285
1776.4779.5959780805672-3.12597808056718
1874.7277.7087462493006-2.98874624930062
1984.4375.88291769201628.5470823079838
2086.7280.55789903147836.16210096852166
2170.9983.9297420210688-12.9397420210688
2275.4376.5433366808603-1.11333668086033
2374.1475.7705808533291-1.63058085332905
2473.374.6999111965379-1.3999111965379
2571.9773.7511336629911-1.78113366299105
2669.2772.5797992649064-3.30979926490645
2774.1370.53578921161823.59421078838182
2876.472.37456931861924.0254306813808
2972.2674.4754599336054-2.21545993360535
3072.173.0718242560739-0.971824256073873
3187.8272.359257416765115.4607425832349
3291.6280.923907117860410.6960928821396
3382.6986.8768608857275-4.1868608857275
3485.7684.4780535307771.28194646922299
3586.8785.14681538837941.72318461162062
3693.0986.0714269143217.01857308567902
3783.7389.9961154742318-6.26611547423184
3884.4986.4528935354594-1.96289353545941
3987.3785.30812059911792.06187940088215
4089.1386.42669311601822.70330688398184
4183.287.9182163838298-4.71821638382976
4283.7785.2314964937883-1.46149649378832
4393.6884.36006988289259.31993011710746
4493.0989.57118891201253.51881108798749
4588.5991.5534877951849-2.96348779518486
4687.8889.8922850046381-2.01228500463813
4787.8988.7531090413936-0.863109041393599
4889.3888.25269205001121.12730794998876
4989.1388.87214797352190.257852026478076
5089.5889.00628764639470.573712353605274
5190.2289.32017585637530.899824143624713
5291.4489.82123159779981.61876840220019
5391.0490.73303436685770.30696563314234
5492.190.91218693773281.18781306226717
5597.5491.59048419687915.94951580312093
5699.1294.96463678994354.15536321005652
5710097.35600054123862.64399945876143
5899.6898.91506479889750.764935201102546
59100.0899.42633627409440.65366372590556
6099.999.87869736124710.0213026387529425
6199.6399.9772277571288-0.34722775712882
6299.4599.8676970496704-0.417697049670352
6399.6399.716570540075-0.0865705400750443
6499.4699.7503334555864-0.290333455586406
6596.9199.6685510054264-2.75855100542636
6697.6598.191055487622-0.541055487621946
67102.197.95193112359814.14806887640189
68103.57100.3587525181353.21124748186465
69104.59102.2577772396022.33222276039793
70104.79103.6768234062691.11317659373128
71101.31104.419292472867-3.10929247286668
72104.8102.7823635980472.0176364019533







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73104.02544273590895.2820434912462112.768841980569
74104.13922523265494.0973426036391114.181107861668
75104.253007729493.0423418418988115.463673616901
76104.36679022614692.0798067822354116.653773670057
77104.48057272289291.187105630191117.774039815593
78104.59435521963890.3492856057988118.839424833478
79104.70813771638589.5558689718464119.860406460923
80104.82192021313188.7991848088368120.844655617425
81104.93570270987788.0734230131213121.797982406632
82105.04948520662387.374061834209122.724908579037
83105.16326770336986.697503235469123.629032171269
84105.27705020011586.0408307788818124.513269621349

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 104.025442735908 & 95.2820434912462 & 112.768841980569 \tabularnewline
74 & 104.139225232654 & 94.0973426036391 & 114.181107861668 \tabularnewline
75 & 104.2530077294 & 93.0423418418988 & 115.463673616901 \tabularnewline
76 & 104.366790226146 & 92.0798067822354 & 116.653773670057 \tabularnewline
77 & 104.480572722892 & 91.187105630191 & 117.774039815593 \tabularnewline
78 & 104.594355219638 & 90.3492856057988 & 118.839424833478 \tabularnewline
79 & 104.708137716385 & 89.5558689718464 & 119.860406460923 \tabularnewline
80 & 104.821920213131 & 88.7991848088368 & 120.844655617425 \tabularnewline
81 & 104.935702709877 & 88.0734230131213 & 121.797982406632 \tabularnewline
82 & 105.049485206623 & 87.374061834209 & 122.724908579037 \tabularnewline
83 & 105.163267703369 & 86.697503235469 & 123.629032171269 \tabularnewline
84 & 105.277050200115 & 86.0408307788818 & 124.513269621349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205627&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]104.025442735908[/C][C]95.2820434912462[/C][C]112.768841980569[/C][/ROW]
[ROW][C]74[/C][C]104.139225232654[/C][C]94.0973426036391[/C][C]114.181107861668[/C][/ROW]
[ROW][C]75[/C][C]104.2530077294[/C][C]93.0423418418988[/C][C]115.463673616901[/C][/ROW]
[ROW][C]76[/C][C]104.366790226146[/C][C]92.0798067822354[/C][C]116.653773670057[/C][/ROW]
[ROW][C]77[/C][C]104.480572722892[/C][C]91.187105630191[/C][C]117.774039815593[/C][/ROW]
[ROW][C]78[/C][C]104.594355219638[/C][C]90.3492856057988[/C][C]118.839424833478[/C][/ROW]
[ROW][C]79[/C][C]104.708137716385[/C][C]89.5558689718464[/C][C]119.860406460923[/C][/ROW]
[ROW][C]80[/C][C]104.821920213131[/C][C]88.7991848088368[/C][C]120.844655617425[/C][/ROW]
[ROW][C]81[/C][C]104.935702709877[/C][C]88.0734230131213[/C][C]121.797982406632[/C][/ROW]
[ROW][C]82[/C][C]105.049485206623[/C][C]87.374061834209[/C][C]122.724908579037[/C][/ROW]
[ROW][C]83[/C][C]105.163267703369[/C][C]86.697503235469[/C][C]123.629032171269[/C][/ROW]
[ROW][C]84[/C][C]105.277050200115[/C][C]86.0408307788818[/C][C]124.513269621349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205627&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205627&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
73104.02544273590895.2820434912462112.768841980569
74104.13922523265494.0973426036391114.181107861668
75104.253007729493.0423418418988115.463673616901
76104.36679022614692.0798067822354116.653773670057
77104.48057272289291.187105630191117.774039815593
78104.59435521963890.3492856057988118.839424833478
79104.70813771638589.5558689718464119.860406460923
80104.82192021313188.7991848088368120.844655617425
81104.93570270987788.0734230131213121.797982406632
82105.04948520662387.374061834209122.724908579037
83105.16326770336986.697503235469123.629032171269
84105.27705020011586.0408307788818124.513269621349



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')