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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 May 2012 07:45:48 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/25/t1337946367zvbe4m068d0yo6n.htm/, Retrieved Fri, 03 May 2024 18:49:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167470, Retrieved Fri, 03 May 2024 18:49:51 +0000
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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)
-     [Classical Decomposition] [opgave 9-1] [2012-05-03 14:22:17] [7df349cccf6cf4c74b65932dd692edc2]
- RMPD    [Exponential Smoothing] [oefening 10/2] [2012-05-25 11:45:48] [649f27debd29df6d3b5186bbc318d779] [Current]
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Dataseries X:
66,6
71,7
75,4
80,9
80,7
85
91,5
87,7
95,3
102,4
114,2
111,7
113,7
118,8
129
136,4
155
166
168,7
145,5
127,3
91,5
69
54
56,3
54,2
59,3
63,4
73,3
86,7
81,3
89,6
85,3
92,4
96,8
93,6
97,6
94,2
99,9
106,4
96
94,9
94,8
95,9
96,2
103,1
106,9
114,2
118,2
123,9
137,1
146,2
136,4
133,2
135,9
127,1
128,5
126,6
132,6
130,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167470&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167470&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167470&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999926998533081
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999926998533081 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167470&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]0.999926998533081[/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=167470&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167470&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
alpha0.999926998533081
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
271.766.65.10000000000001
375.471.69962769251873.70037230748129
480.975.39972986739345.50027013260659
580.780.8995984722119-0.199598472211875
68580.70001457098134.29998542901873
791.584.99968609475596.50031390524406
887.791.4995254675495-3.79952546754947
995.387.70027737093277.59972262906727
10102.495.29944520909997.10055479090011
11114.2102.39948164908411.8005183509157
12111.7114.19913854485-2.49913854484997
13113.7111.700182440781.99981755922019
14118.8113.6998540103855.10014598961538
15129118.79962768186110.2003723181387
16136.4128.9992553578587.40074464214234
17155136.39945973478518.6005402652152
18166154.99864213327511.0013578667248
19168.7165.9991968847382.70080311526237
20145.5168.699802837411-23.1998028374107
21127.3145.501693619639-18.2016936196394
2291.5127.301328750335-35.8013287503346
236991.5026135495164-22.5026135495164
245469.0016427237986-15.0016427237986
2556.354.0010951419252.29890485807496
2654.256.299832176573-2.09983217657305
2759.354.20015329082925.09984670917082
2863.459.29962770370924.10037229629084
2973.363.39970066680759.90029933319254
3086.773.299277263625713.4007227363743
3181.386.6990217275825-5.39902172758246
3289.681.3003941365068.29960586349395
3385.389.5993941165971-4.29939411659711
3492.485.30031386207747.09968613792263
3596.892.39948171249734.40051828750272
3693.696.7996787557098-3.19967875570981
3797.693.60023358124283.99976641875716
3894.297.5997080111841-3.39970801118409
3999.994.20024818367195.69975181632809
40106.499.89958390975636.50041609024368
4196106.39952546009-10.3995254600898
4294.996.0007591806139-1.10075918061385
4394.894.9000803570349-0.100080357034912
4495.994.80000730601291.09999269398713
4596.295.89991969891970.300080301080257
46103.196.19997809369786.90002190630216
47106.9103.0994962882793.80050371172095
48114.2106.8997225576547.30027744234599
49118.2114.1994670690384.00053293096221
50123.9118.1997079552285.70029204477243
51137.1123.89958387031913.2004161296811
52146.2137.0990363502599.1009636497414
53136.4146.199335616303-9.79933561630318
54133.2136.400715365875-3.20071536587486
55135.9133.2002336569172.69976634308313
56127.1135.899802913097-8.79980291309661
57128.5127.1006423985211.39935760147875
58126.6128.499897844842-1.89989784484234
59132.6126.600138695335.99986130467033
60130.9132.599562001323-1.69956200132344

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 71.7 & 66.6 & 5.10000000000001 \tabularnewline
3 & 75.4 & 71.6996276925187 & 3.70037230748129 \tabularnewline
4 & 80.9 & 75.3997298673934 & 5.50027013260659 \tabularnewline
5 & 80.7 & 80.8995984722119 & -0.199598472211875 \tabularnewline
6 & 85 & 80.7000145709813 & 4.29998542901873 \tabularnewline
7 & 91.5 & 84.9996860947559 & 6.50031390524406 \tabularnewline
8 & 87.7 & 91.4995254675495 & -3.79952546754947 \tabularnewline
9 & 95.3 & 87.7002773709327 & 7.59972262906727 \tabularnewline
10 & 102.4 & 95.2994452090999 & 7.10055479090011 \tabularnewline
11 & 114.2 & 102.399481649084 & 11.8005183509157 \tabularnewline
12 & 111.7 & 114.19913854485 & -2.49913854484997 \tabularnewline
13 & 113.7 & 111.70018244078 & 1.99981755922019 \tabularnewline
14 & 118.8 & 113.699854010385 & 5.10014598961538 \tabularnewline
15 & 129 & 118.799627681861 & 10.2003723181387 \tabularnewline
16 & 136.4 & 128.999255357858 & 7.40074464214234 \tabularnewline
17 & 155 & 136.399459734785 & 18.6005402652152 \tabularnewline
18 & 166 & 154.998642133275 & 11.0013578667248 \tabularnewline
19 & 168.7 & 165.999196884738 & 2.70080311526237 \tabularnewline
20 & 145.5 & 168.699802837411 & -23.1998028374107 \tabularnewline
21 & 127.3 & 145.501693619639 & -18.2016936196394 \tabularnewline
22 & 91.5 & 127.301328750335 & -35.8013287503346 \tabularnewline
23 & 69 & 91.5026135495164 & -22.5026135495164 \tabularnewline
24 & 54 & 69.0016427237986 & -15.0016427237986 \tabularnewline
25 & 56.3 & 54.001095141925 & 2.29890485807496 \tabularnewline
26 & 54.2 & 56.299832176573 & -2.09983217657305 \tabularnewline
27 & 59.3 & 54.2001532908292 & 5.09984670917082 \tabularnewline
28 & 63.4 & 59.2996277037092 & 4.10037229629084 \tabularnewline
29 & 73.3 & 63.3997006668075 & 9.90029933319254 \tabularnewline
30 & 86.7 & 73.2992772636257 & 13.4007227363743 \tabularnewline
31 & 81.3 & 86.6990217275825 & -5.39902172758246 \tabularnewline
32 & 89.6 & 81.300394136506 & 8.29960586349395 \tabularnewline
33 & 85.3 & 89.5993941165971 & -4.29939411659711 \tabularnewline
34 & 92.4 & 85.3003138620774 & 7.09968613792263 \tabularnewline
35 & 96.8 & 92.3994817124973 & 4.40051828750272 \tabularnewline
36 & 93.6 & 96.7996787557098 & -3.19967875570981 \tabularnewline
37 & 97.6 & 93.6002335812428 & 3.99976641875716 \tabularnewline
38 & 94.2 & 97.5997080111841 & -3.39970801118409 \tabularnewline
39 & 99.9 & 94.2002481836719 & 5.69975181632809 \tabularnewline
40 & 106.4 & 99.8995839097563 & 6.50041609024368 \tabularnewline
41 & 96 & 106.39952546009 & -10.3995254600898 \tabularnewline
42 & 94.9 & 96.0007591806139 & -1.10075918061385 \tabularnewline
43 & 94.8 & 94.9000803570349 & -0.100080357034912 \tabularnewline
44 & 95.9 & 94.8000073060129 & 1.09999269398713 \tabularnewline
45 & 96.2 & 95.8999196989197 & 0.300080301080257 \tabularnewline
46 & 103.1 & 96.1999780936978 & 6.90002190630216 \tabularnewline
47 & 106.9 & 103.099496288279 & 3.80050371172095 \tabularnewline
48 & 114.2 & 106.899722557654 & 7.30027744234599 \tabularnewline
49 & 118.2 & 114.199467069038 & 4.00053293096221 \tabularnewline
50 & 123.9 & 118.199707955228 & 5.70029204477243 \tabularnewline
51 & 137.1 & 123.899583870319 & 13.2004161296811 \tabularnewline
52 & 146.2 & 137.099036350259 & 9.1009636497414 \tabularnewline
53 & 136.4 & 146.199335616303 & -9.79933561630318 \tabularnewline
54 & 133.2 & 136.400715365875 & -3.20071536587486 \tabularnewline
55 & 135.9 & 133.200233656917 & 2.69976634308313 \tabularnewline
56 & 127.1 & 135.899802913097 & -8.79980291309661 \tabularnewline
57 & 128.5 & 127.100642398521 & 1.39935760147875 \tabularnewline
58 & 126.6 & 128.499897844842 & -1.89989784484234 \tabularnewline
59 & 132.6 & 126.60013869533 & 5.99986130467033 \tabularnewline
60 & 130.9 & 132.599562001323 & -1.69956200132344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167470&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]71.7[/C][C]66.6[/C][C]5.10000000000001[/C][/ROW]
[ROW][C]3[/C][C]75.4[/C][C]71.6996276925187[/C][C]3.70037230748129[/C][/ROW]
[ROW][C]4[/C][C]80.9[/C][C]75.3997298673934[/C][C]5.50027013260659[/C][/ROW]
[ROW][C]5[/C][C]80.7[/C][C]80.8995984722119[/C][C]-0.199598472211875[/C][/ROW]
[ROW][C]6[/C][C]85[/C][C]80.7000145709813[/C][C]4.29998542901873[/C][/ROW]
[ROW][C]7[/C][C]91.5[/C][C]84.9996860947559[/C][C]6.50031390524406[/C][/ROW]
[ROW][C]8[/C][C]87.7[/C][C]91.4995254675495[/C][C]-3.79952546754947[/C][/ROW]
[ROW][C]9[/C][C]95.3[/C][C]87.7002773709327[/C][C]7.59972262906727[/C][/ROW]
[ROW][C]10[/C][C]102.4[/C][C]95.2994452090999[/C][C]7.10055479090011[/C][/ROW]
[ROW][C]11[/C][C]114.2[/C][C]102.399481649084[/C][C]11.8005183509157[/C][/ROW]
[ROW][C]12[/C][C]111.7[/C][C]114.19913854485[/C][C]-2.49913854484997[/C][/ROW]
[ROW][C]13[/C][C]113.7[/C][C]111.70018244078[/C][C]1.99981755922019[/C][/ROW]
[ROW][C]14[/C][C]118.8[/C][C]113.699854010385[/C][C]5.10014598961538[/C][/ROW]
[ROW][C]15[/C][C]129[/C][C]118.799627681861[/C][C]10.2003723181387[/C][/ROW]
[ROW][C]16[/C][C]136.4[/C][C]128.999255357858[/C][C]7.40074464214234[/C][/ROW]
[ROW][C]17[/C][C]155[/C][C]136.399459734785[/C][C]18.6005402652152[/C][/ROW]
[ROW][C]18[/C][C]166[/C][C]154.998642133275[/C][C]11.0013578667248[/C][/ROW]
[ROW][C]19[/C][C]168.7[/C][C]165.999196884738[/C][C]2.70080311526237[/C][/ROW]
[ROW][C]20[/C][C]145.5[/C][C]168.699802837411[/C][C]-23.1998028374107[/C][/ROW]
[ROW][C]21[/C][C]127.3[/C][C]145.501693619639[/C][C]-18.2016936196394[/C][/ROW]
[ROW][C]22[/C][C]91.5[/C][C]127.301328750335[/C][C]-35.8013287503346[/C][/ROW]
[ROW][C]23[/C][C]69[/C][C]91.5026135495164[/C][C]-22.5026135495164[/C][/ROW]
[ROW][C]24[/C][C]54[/C][C]69.0016427237986[/C][C]-15.0016427237986[/C][/ROW]
[ROW][C]25[/C][C]56.3[/C][C]54.001095141925[/C][C]2.29890485807496[/C][/ROW]
[ROW][C]26[/C][C]54.2[/C][C]56.299832176573[/C][C]-2.09983217657305[/C][/ROW]
[ROW][C]27[/C][C]59.3[/C][C]54.2001532908292[/C][C]5.09984670917082[/C][/ROW]
[ROW][C]28[/C][C]63.4[/C][C]59.2996277037092[/C][C]4.10037229629084[/C][/ROW]
[ROW][C]29[/C][C]73.3[/C][C]63.3997006668075[/C][C]9.90029933319254[/C][/ROW]
[ROW][C]30[/C][C]86.7[/C][C]73.2992772636257[/C][C]13.4007227363743[/C][/ROW]
[ROW][C]31[/C][C]81.3[/C][C]86.6990217275825[/C][C]-5.39902172758246[/C][/ROW]
[ROW][C]32[/C][C]89.6[/C][C]81.300394136506[/C][C]8.29960586349395[/C][/ROW]
[ROW][C]33[/C][C]85.3[/C][C]89.5993941165971[/C][C]-4.29939411659711[/C][/ROW]
[ROW][C]34[/C][C]92.4[/C][C]85.3003138620774[/C][C]7.09968613792263[/C][/ROW]
[ROW][C]35[/C][C]96.8[/C][C]92.3994817124973[/C][C]4.40051828750272[/C][/ROW]
[ROW][C]36[/C][C]93.6[/C][C]96.7996787557098[/C][C]-3.19967875570981[/C][/ROW]
[ROW][C]37[/C][C]97.6[/C][C]93.6002335812428[/C][C]3.99976641875716[/C][/ROW]
[ROW][C]38[/C][C]94.2[/C][C]97.5997080111841[/C][C]-3.39970801118409[/C][/ROW]
[ROW][C]39[/C][C]99.9[/C][C]94.2002481836719[/C][C]5.69975181632809[/C][/ROW]
[ROW][C]40[/C][C]106.4[/C][C]99.8995839097563[/C][C]6.50041609024368[/C][/ROW]
[ROW][C]41[/C][C]96[/C][C]106.39952546009[/C][C]-10.3995254600898[/C][/ROW]
[ROW][C]42[/C][C]94.9[/C][C]96.0007591806139[/C][C]-1.10075918061385[/C][/ROW]
[ROW][C]43[/C][C]94.8[/C][C]94.9000803570349[/C][C]-0.100080357034912[/C][/ROW]
[ROW][C]44[/C][C]95.9[/C][C]94.8000073060129[/C][C]1.09999269398713[/C][/ROW]
[ROW][C]45[/C][C]96.2[/C][C]95.8999196989197[/C][C]0.300080301080257[/C][/ROW]
[ROW][C]46[/C][C]103.1[/C][C]96.1999780936978[/C][C]6.90002190630216[/C][/ROW]
[ROW][C]47[/C][C]106.9[/C][C]103.099496288279[/C][C]3.80050371172095[/C][/ROW]
[ROW][C]48[/C][C]114.2[/C][C]106.899722557654[/C][C]7.30027744234599[/C][/ROW]
[ROW][C]49[/C][C]118.2[/C][C]114.199467069038[/C][C]4.00053293096221[/C][/ROW]
[ROW][C]50[/C][C]123.9[/C][C]118.199707955228[/C][C]5.70029204477243[/C][/ROW]
[ROW][C]51[/C][C]137.1[/C][C]123.899583870319[/C][C]13.2004161296811[/C][/ROW]
[ROW][C]52[/C][C]146.2[/C][C]137.099036350259[/C][C]9.1009636497414[/C][/ROW]
[ROW][C]53[/C][C]136.4[/C][C]146.199335616303[/C][C]-9.79933561630318[/C][/ROW]
[ROW][C]54[/C][C]133.2[/C][C]136.400715365875[/C][C]-3.20071536587486[/C][/ROW]
[ROW][C]55[/C][C]135.9[/C][C]133.200233656917[/C][C]2.69976634308313[/C][/ROW]
[ROW][C]56[/C][C]127.1[/C][C]135.899802913097[/C][C]-8.79980291309661[/C][/ROW]
[ROW][C]57[/C][C]128.5[/C][C]127.100642398521[/C][C]1.39935760147875[/C][/ROW]
[ROW][C]58[/C][C]126.6[/C][C]128.499897844842[/C][C]-1.89989784484234[/C][/ROW]
[ROW][C]59[/C][C]132.6[/C][C]126.60013869533[/C][C]5.99986130467033[/C][/ROW]
[ROW][C]60[/C][C]130.9[/C][C]132.599562001323[/C][C]-1.69956200132344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167470&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167470&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
271.766.65.10000000000001
375.471.69962769251873.70037230748129
480.975.39972986739345.50027013260659
580.780.8995984722119-0.199598472211875
68580.70001457098134.29998542901873
791.584.99968609475596.50031390524406
887.791.4995254675495-3.79952546754947
995.387.70027737093277.59972262906727
10102.495.29944520909997.10055479090011
11114.2102.39948164908411.8005183509157
12111.7114.19913854485-2.49913854484997
13113.7111.700182440781.99981755922019
14118.8113.6998540103855.10014598961538
15129118.79962768186110.2003723181387
16136.4128.9992553578587.40074464214234
17155136.39945973478518.6005402652152
18166154.99864213327511.0013578667248
19168.7165.9991968847382.70080311526237
20145.5168.699802837411-23.1998028374107
21127.3145.501693619639-18.2016936196394
2291.5127.301328750335-35.8013287503346
236991.5026135495164-22.5026135495164
245469.0016427237986-15.0016427237986
2556.354.0010951419252.29890485807496
2654.256.299832176573-2.09983217657305
2759.354.20015329082925.09984670917082
2863.459.29962770370924.10037229629084
2973.363.39970066680759.90029933319254
3086.773.299277263625713.4007227363743
3181.386.6990217275825-5.39902172758246
3289.681.3003941365068.29960586349395
3385.389.5993941165971-4.29939411659711
3492.485.30031386207747.09968613792263
3596.892.39948171249734.40051828750272
3693.696.7996787557098-3.19967875570981
3797.693.60023358124283.99976641875716
3894.297.5997080111841-3.39970801118409
3999.994.20024818367195.69975181632809
40106.499.89958390975636.50041609024368
4196106.39952546009-10.3995254600898
4294.996.0007591806139-1.10075918061385
4394.894.9000803570349-0.100080357034912
4495.994.80000730601291.09999269398713
4596.295.89991969891970.300080301080257
46103.196.19997809369786.90002190630216
47106.9103.0994962882793.80050371172095
48114.2106.8997225576547.30027744234599
49118.2114.1994670690384.00053293096221
50123.9118.1997079552285.70029204477243
51137.1123.89958387031913.2004161296811
52146.2137.0990363502599.1009636497414
53136.4146.199335616303-9.79933561630318
54133.2136.400715365875-3.20071536587486
55135.9133.2002336569172.69976634308313
56127.1135.899802913097-8.79980291309661
57128.5127.1006423985211.39935760147875
58126.6128.499897844842-1.89989784484234
59132.6126.600138695335.99986130467033
60130.9132.599562001323-1.69956200132344







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61130.900124070519112.216437696932149.583810444106
62130.900124070519104.478365837022157.321882304016
63130.90012407051998.5406049178468163.259643223192
64130.90012407051993.5347972094442168.265450931594
65130.90012407051989.1245711348873172.675677006151
66130.90012407051985.1374100478502176.662838093188
67130.90012407051981.4708294532238180.329418687815
68130.90012407051978.0580542964633183.742193844575
69130.90012407051974.8527020990404186.947546041998
70130.90012407051971.8210018589307189.979246282108
71130.90012407051968.9374590783272192.862789062711
72130.90012407051966.182266993995195.617981147043

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 130.900124070519 & 112.216437696932 & 149.583810444106 \tabularnewline
62 & 130.900124070519 & 104.478365837022 & 157.321882304016 \tabularnewline
63 & 130.900124070519 & 98.5406049178468 & 163.259643223192 \tabularnewline
64 & 130.900124070519 & 93.5347972094442 & 168.265450931594 \tabularnewline
65 & 130.900124070519 & 89.1245711348873 & 172.675677006151 \tabularnewline
66 & 130.900124070519 & 85.1374100478502 & 176.662838093188 \tabularnewline
67 & 130.900124070519 & 81.4708294532238 & 180.329418687815 \tabularnewline
68 & 130.900124070519 & 78.0580542964633 & 183.742193844575 \tabularnewline
69 & 130.900124070519 & 74.8527020990404 & 186.947546041998 \tabularnewline
70 & 130.900124070519 & 71.8210018589307 & 189.979246282108 \tabularnewline
71 & 130.900124070519 & 68.9374590783272 & 192.862789062711 \tabularnewline
72 & 130.900124070519 & 66.182266993995 & 195.617981147043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167470&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]61[/C][C]130.900124070519[/C][C]112.216437696932[/C][C]149.583810444106[/C][/ROW]
[ROW][C]62[/C][C]130.900124070519[/C][C]104.478365837022[/C][C]157.321882304016[/C][/ROW]
[ROW][C]63[/C][C]130.900124070519[/C][C]98.5406049178468[/C][C]163.259643223192[/C][/ROW]
[ROW][C]64[/C][C]130.900124070519[/C][C]93.5347972094442[/C][C]168.265450931594[/C][/ROW]
[ROW][C]65[/C][C]130.900124070519[/C][C]89.1245711348873[/C][C]172.675677006151[/C][/ROW]
[ROW][C]66[/C][C]130.900124070519[/C][C]85.1374100478502[/C][C]176.662838093188[/C][/ROW]
[ROW][C]67[/C][C]130.900124070519[/C][C]81.4708294532238[/C][C]180.329418687815[/C][/ROW]
[ROW][C]68[/C][C]130.900124070519[/C][C]78.0580542964633[/C][C]183.742193844575[/C][/ROW]
[ROW][C]69[/C][C]130.900124070519[/C][C]74.8527020990404[/C][C]186.947546041998[/C][/ROW]
[ROW][C]70[/C][C]130.900124070519[/C][C]71.8210018589307[/C][C]189.979246282108[/C][/ROW]
[ROW][C]71[/C][C]130.900124070519[/C][C]68.9374590783272[/C][C]192.862789062711[/C][/ROW]
[ROW][C]72[/C][C]130.900124070519[/C][C]66.182266993995[/C][C]195.617981147043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167470&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167470&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
61130.900124070519112.216437696932149.583810444106
62130.900124070519104.478365837022157.321882304016
63130.90012407051998.5406049178468163.259643223192
64130.90012407051993.5347972094442168.265450931594
65130.90012407051989.1245711348873172.675677006151
66130.90012407051985.1374100478502176.662838093188
67130.90012407051981.4708294532238180.329418687815
68130.90012407051978.0580542964633183.742193844575
69130.90012407051974.8527020990404186.947546041998
70130.90012407051971.8210018589307189.979246282108
71130.90012407051968.9374590783272192.862789062711
72130.90012407051966.182266993995195.617981147043



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