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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 11 Jan 2014 10:49:51 -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/2014/Jan/11/t1389455442nt8swe8z7j5gfg7.htm/, Retrieved Tue, 28 May 2024 10:55:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232919, Retrieved Tue, 28 May 2024 10:55:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2013-11-21 14:48:45] [186a8d6923bab97ec27dc2318f4b7e5b]
- RMPD    [Exponential Smoothing] [] [2014-01-11 15:49:51] [ce63f6e18bf6a7ced484324fd1839a76] [Current]
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Dataseries X:
83,7
86,4
85,9
80,4
81,8
87,5
83,7
87
99,7
101,4
101,9
115,7
123,2
136,9
146,8
149,6
146,5
157
147,9
133,6
128,7
100,8
91,8
89,3
96,7
91,6
93,3
93,3
101
100,4
86,9
83,9
80,3
87,7
92,7
95,5
92
87,4
86,8
83,7
85
81,7
90,9
101,5
113,8
120,1
122,1
132,5
140
149,4
144,3
154,4
151,4
145,5
136,8
146,6
145,1
133,6
131,4
127,5
130,1
131,1
132,3
128,6
125,1
128,7
156,1
163,2
159,8
157,4
156,2
152,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232919&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]4 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=232919&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232919&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.99993638629698
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99993638629698 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232919&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]0.99993638629698[/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=232919&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232919&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
alpha0.99993638629698
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
286.483.72.7
385.986.3998282430018-0.499828243001843
480.485.9000317959254-5.50003179592541
581.880.40034987738931.39965012261072
687.581.79991096307285.70008903692724
783.787.4996373962288-3.79963739622882
88783.70024170900493.29975829099509
999.786.99979009015612.700209909844
10101.499.69919209261851.70080790738149
11101.9101.3998918053110.500108194689119
12115.7101.89996818626613.8000318137342
13123.2115.6991221288757.50087787112547
14136.9123.19952284138313.7004771586173
15146.8136.8991284619159.9008715380852
16149.6146.7993701688982.80062983110165
17146.5149.599821841566-3.09982184156564
18157146.50019719114610.499802808854
19147.9156.999332068662-9.09933206866233
20133.6147.900578842208-14.3005788422079
21128.7133.600909712775-4.90090971277547
22100.8128.700311765015-27.900311765015
2391.8100.801774842147-9.00177484214677
2489.391.8005726362315-2.50057263623145
2596.789.30015907068517.39984092931495
2691.696.6995292687167-5.09952926871674
2793.391.60032439994041.69967560005956
2893.393.29989187734110.000108122658858179
2910193.29999999312197.70000000687808
30100.4100.999510174486-0.599510174486312
3186.9100.400038137062-13.5000381370622
3283.986.9008587874168-3.0008587874168
3380.383.9001908957397-3.60019089573971
3487.780.30022902147457.39977097852555
3592.787.69952927316665.00047072683344
3695.592.69968190154022.80031809845977
379295.4998218613961-3.49982186139613
3887.492.0002226366285-4.6002226366285
3986.887.4002926371966-0.600292637196645
4083.786.8000381868375-3.10003818683754
418583.70019720490861.29980279509142
4281.784.999917314731-3.299917314731
4390.981.700209919969.19979008003996
44101.590.89941476728610.600585232714
45113.8101.49932565751912.3006743424808
46120.1113.7992175085556.30078249144456
47122.1120.0995991838942.00040081610621
48132.5122.09987274709710.4001272529034
49140132.4993384093947.50066159060643
50149.4139.9995228551419.40047714485888
51144.3149.399402000839-5.09940200083867
52154.4144.30032439184410.0996756081555
53151.4154.399357522235-2.99935752223527
54145.5151.400190800239-5.90019080023868
55136.8145.500375332985-8.70037533298532
56146.6136.8005534630939.7994465369074
57145.1146.599376620918-1.49937662091824
58133.6145.100095380899-11.5000953808991
59131.4133.600731563652-2.20073156365225
60127.5131.400139996684-3.90013999668412
61130.1127.5002481023472.59975189765251
62131.1130.0998346201551.00016537984513
63132.3131.0999363757771.20006362422347
64128.6132.299923659509-3.69992365950901
65125.1128.600235365845-3.50023536584487
66128.7125.1002226629333.59977733706694
67156.1128.69977100483427.4002289951665
68163.2156.098256969977.10174303002995
69159.8163.199548231828-3.39954823182794
70157.4159.800216257852-2.40021625785164
71156.2157.400152686644-1.20015268664423
72152.5156.200076346157-3.70007634615658

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 86.4 & 83.7 & 2.7 \tabularnewline
3 & 85.9 & 86.3998282430018 & -0.499828243001843 \tabularnewline
4 & 80.4 & 85.9000317959254 & -5.50003179592541 \tabularnewline
5 & 81.8 & 80.4003498773893 & 1.39965012261072 \tabularnewline
6 & 87.5 & 81.7999109630728 & 5.70008903692724 \tabularnewline
7 & 83.7 & 87.4996373962288 & -3.79963739622882 \tabularnewline
8 & 87 & 83.7002417090049 & 3.29975829099509 \tabularnewline
9 & 99.7 & 86.999790090156 & 12.700209909844 \tabularnewline
10 & 101.4 & 99.6991920926185 & 1.70080790738149 \tabularnewline
11 & 101.9 & 101.399891805311 & 0.500108194689119 \tabularnewline
12 & 115.7 & 101.899968186266 & 13.8000318137342 \tabularnewline
13 & 123.2 & 115.699122128875 & 7.50087787112547 \tabularnewline
14 & 136.9 & 123.199522841383 & 13.7004771586173 \tabularnewline
15 & 146.8 & 136.899128461915 & 9.9008715380852 \tabularnewline
16 & 149.6 & 146.799370168898 & 2.80062983110165 \tabularnewline
17 & 146.5 & 149.599821841566 & -3.09982184156564 \tabularnewline
18 & 157 & 146.500197191146 & 10.499802808854 \tabularnewline
19 & 147.9 & 156.999332068662 & -9.09933206866233 \tabularnewline
20 & 133.6 & 147.900578842208 & -14.3005788422079 \tabularnewline
21 & 128.7 & 133.600909712775 & -4.90090971277547 \tabularnewline
22 & 100.8 & 128.700311765015 & -27.900311765015 \tabularnewline
23 & 91.8 & 100.801774842147 & -9.00177484214677 \tabularnewline
24 & 89.3 & 91.8005726362315 & -2.50057263623145 \tabularnewline
25 & 96.7 & 89.3001590706851 & 7.39984092931495 \tabularnewline
26 & 91.6 & 96.6995292687167 & -5.09952926871674 \tabularnewline
27 & 93.3 & 91.6003243999404 & 1.69967560005956 \tabularnewline
28 & 93.3 & 93.2998918773411 & 0.000108122658858179 \tabularnewline
29 & 101 & 93.2999999931219 & 7.70000000687808 \tabularnewline
30 & 100.4 & 100.999510174486 & -0.599510174486312 \tabularnewline
31 & 86.9 & 100.400038137062 & -13.5000381370622 \tabularnewline
32 & 83.9 & 86.9008587874168 & -3.0008587874168 \tabularnewline
33 & 80.3 & 83.9001908957397 & -3.60019089573971 \tabularnewline
34 & 87.7 & 80.3002290214745 & 7.39977097852555 \tabularnewline
35 & 92.7 & 87.6995292731666 & 5.00047072683344 \tabularnewline
36 & 95.5 & 92.6996819015402 & 2.80031809845977 \tabularnewline
37 & 92 & 95.4998218613961 & -3.49982186139613 \tabularnewline
38 & 87.4 & 92.0002226366285 & -4.6002226366285 \tabularnewline
39 & 86.8 & 87.4002926371966 & -0.600292637196645 \tabularnewline
40 & 83.7 & 86.8000381868375 & -3.10003818683754 \tabularnewline
41 & 85 & 83.7001972049086 & 1.29980279509142 \tabularnewline
42 & 81.7 & 84.999917314731 & -3.299917314731 \tabularnewline
43 & 90.9 & 81.70020991996 & 9.19979008003996 \tabularnewline
44 & 101.5 & 90.899414767286 & 10.600585232714 \tabularnewline
45 & 113.8 & 101.499325657519 & 12.3006743424808 \tabularnewline
46 & 120.1 & 113.799217508555 & 6.30078249144456 \tabularnewline
47 & 122.1 & 120.099599183894 & 2.00040081610621 \tabularnewline
48 & 132.5 & 122.099872747097 & 10.4001272529034 \tabularnewline
49 & 140 & 132.499338409394 & 7.50066159060643 \tabularnewline
50 & 149.4 & 139.999522855141 & 9.40047714485888 \tabularnewline
51 & 144.3 & 149.399402000839 & -5.09940200083867 \tabularnewline
52 & 154.4 & 144.300324391844 & 10.0996756081555 \tabularnewline
53 & 151.4 & 154.399357522235 & -2.99935752223527 \tabularnewline
54 & 145.5 & 151.400190800239 & -5.90019080023868 \tabularnewline
55 & 136.8 & 145.500375332985 & -8.70037533298532 \tabularnewline
56 & 146.6 & 136.800553463093 & 9.7994465369074 \tabularnewline
57 & 145.1 & 146.599376620918 & -1.49937662091824 \tabularnewline
58 & 133.6 & 145.100095380899 & -11.5000953808991 \tabularnewline
59 & 131.4 & 133.600731563652 & -2.20073156365225 \tabularnewline
60 & 127.5 & 131.400139996684 & -3.90013999668412 \tabularnewline
61 & 130.1 & 127.500248102347 & 2.59975189765251 \tabularnewline
62 & 131.1 & 130.099834620155 & 1.00016537984513 \tabularnewline
63 & 132.3 & 131.099936375777 & 1.20006362422347 \tabularnewline
64 & 128.6 & 132.299923659509 & -3.69992365950901 \tabularnewline
65 & 125.1 & 128.600235365845 & -3.50023536584487 \tabularnewline
66 & 128.7 & 125.100222662933 & 3.59977733706694 \tabularnewline
67 & 156.1 & 128.699771004834 & 27.4002289951665 \tabularnewline
68 & 163.2 & 156.09825696997 & 7.10174303002995 \tabularnewline
69 & 159.8 & 163.199548231828 & -3.39954823182794 \tabularnewline
70 & 157.4 & 159.800216257852 & -2.40021625785164 \tabularnewline
71 & 156.2 & 157.400152686644 & -1.20015268664423 \tabularnewline
72 & 152.5 & 156.200076346157 & -3.70007634615658 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232919&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]86.4[/C][C]83.7[/C][C]2.7[/C][/ROW]
[ROW][C]3[/C][C]85.9[/C][C]86.3998282430018[/C][C]-0.499828243001843[/C][/ROW]
[ROW][C]4[/C][C]80.4[/C][C]85.9000317959254[/C][C]-5.50003179592541[/C][/ROW]
[ROW][C]5[/C][C]81.8[/C][C]80.4003498773893[/C][C]1.39965012261072[/C][/ROW]
[ROW][C]6[/C][C]87.5[/C][C]81.7999109630728[/C][C]5.70008903692724[/C][/ROW]
[ROW][C]7[/C][C]83.7[/C][C]87.4996373962288[/C][C]-3.79963739622882[/C][/ROW]
[ROW][C]8[/C][C]87[/C][C]83.7002417090049[/C][C]3.29975829099509[/C][/ROW]
[ROW][C]9[/C][C]99.7[/C][C]86.999790090156[/C][C]12.700209909844[/C][/ROW]
[ROW][C]10[/C][C]101.4[/C][C]99.6991920926185[/C][C]1.70080790738149[/C][/ROW]
[ROW][C]11[/C][C]101.9[/C][C]101.399891805311[/C][C]0.500108194689119[/C][/ROW]
[ROW][C]12[/C][C]115.7[/C][C]101.899968186266[/C][C]13.8000318137342[/C][/ROW]
[ROW][C]13[/C][C]123.2[/C][C]115.699122128875[/C][C]7.50087787112547[/C][/ROW]
[ROW][C]14[/C][C]136.9[/C][C]123.199522841383[/C][C]13.7004771586173[/C][/ROW]
[ROW][C]15[/C][C]146.8[/C][C]136.899128461915[/C][C]9.9008715380852[/C][/ROW]
[ROW][C]16[/C][C]149.6[/C][C]146.799370168898[/C][C]2.80062983110165[/C][/ROW]
[ROW][C]17[/C][C]146.5[/C][C]149.599821841566[/C][C]-3.09982184156564[/C][/ROW]
[ROW][C]18[/C][C]157[/C][C]146.500197191146[/C][C]10.499802808854[/C][/ROW]
[ROW][C]19[/C][C]147.9[/C][C]156.999332068662[/C][C]-9.09933206866233[/C][/ROW]
[ROW][C]20[/C][C]133.6[/C][C]147.900578842208[/C][C]-14.3005788422079[/C][/ROW]
[ROW][C]21[/C][C]128.7[/C][C]133.600909712775[/C][C]-4.90090971277547[/C][/ROW]
[ROW][C]22[/C][C]100.8[/C][C]128.700311765015[/C][C]-27.900311765015[/C][/ROW]
[ROW][C]23[/C][C]91.8[/C][C]100.801774842147[/C][C]-9.00177484214677[/C][/ROW]
[ROW][C]24[/C][C]89.3[/C][C]91.8005726362315[/C][C]-2.50057263623145[/C][/ROW]
[ROW][C]25[/C][C]96.7[/C][C]89.3001590706851[/C][C]7.39984092931495[/C][/ROW]
[ROW][C]26[/C][C]91.6[/C][C]96.6995292687167[/C][C]-5.09952926871674[/C][/ROW]
[ROW][C]27[/C][C]93.3[/C][C]91.6003243999404[/C][C]1.69967560005956[/C][/ROW]
[ROW][C]28[/C][C]93.3[/C][C]93.2998918773411[/C][C]0.000108122658858179[/C][/ROW]
[ROW][C]29[/C][C]101[/C][C]93.2999999931219[/C][C]7.70000000687808[/C][/ROW]
[ROW][C]30[/C][C]100.4[/C][C]100.999510174486[/C][C]-0.599510174486312[/C][/ROW]
[ROW][C]31[/C][C]86.9[/C][C]100.400038137062[/C][C]-13.5000381370622[/C][/ROW]
[ROW][C]32[/C][C]83.9[/C][C]86.9008587874168[/C][C]-3.0008587874168[/C][/ROW]
[ROW][C]33[/C][C]80.3[/C][C]83.9001908957397[/C][C]-3.60019089573971[/C][/ROW]
[ROW][C]34[/C][C]87.7[/C][C]80.3002290214745[/C][C]7.39977097852555[/C][/ROW]
[ROW][C]35[/C][C]92.7[/C][C]87.6995292731666[/C][C]5.00047072683344[/C][/ROW]
[ROW][C]36[/C][C]95.5[/C][C]92.6996819015402[/C][C]2.80031809845977[/C][/ROW]
[ROW][C]37[/C][C]92[/C][C]95.4998218613961[/C][C]-3.49982186139613[/C][/ROW]
[ROW][C]38[/C][C]87.4[/C][C]92.0002226366285[/C][C]-4.6002226366285[/C][/ROW]
[ROW][C]39[/C][C]86.8[/C][C]87.4002926371966[/C][C]-0.600292637196645[/C][/ROW]
[ROW][C]40[/C][C]83.7[/C][C]86.8000381868375[/C][C]-3.10003818683754[/C][/ROW]
[ROW][C]41[/C][C]85[/C][C]83.7001972049086[/C][C]1.29980279509142[/C][/ROW]
[ROW][C]42[/C][C]81.7[/C][C]84.999917314731[/C][C]-3.299917314731[/C][/ROW]
[ROW][C]43[/C][C]90.9[/C][C]81.70020991996[/C][C]9.19979008003996[/C][/ROW]
[ROW][C]44[/C][C]101.5[/C][C]90.899414767286[/C][C]10.600585232714[/C][/ROW]
[ROW][C]45[/C][C]113.8[/C][C]101.499325657519[/C][C]12.3006743424808[/C][/ROW]
[ROW][C]46[/C][C]120.1[/C][C]113.799217508555[/C][C]6.30078249144456[/C][/ROW]
[ROW][C]47[/C][C]122.1[/C][C]120.099599183894[/C][C]2.00040081610621[/C][/ROW]
[ROW][C]48[/C][C]132.5[/C][C]122.099872747097[/C][C]10.4001272529034[/C][/ROW]
[ROW][C]49[/C][C]140[/C][C]132.499338409394[/C][C]7.50066159060643[/C][/ROW]
[ROW][C]50[/C][C]149.4[/C][C]139.999522855141[/C][C]9.40047714485888[/C][/ROW]
[ROW][C]51[/C][C]144.3[/C][C]149.399402000839[/C][C]-5.09940200083867[/C][/ROW]
[ROW][C]52[/C][C]154.4[/C][C]144.300324391844[/C][C]10.0996756081555[/C][/ROW]
[ROW][C]53[/C][C]151.4[/C][C]154.399357522235[/C][C]-2.99935752223527[/C][/ROW]
[ROW][C]54[/C][C]145.5[/C][C]151.400190800239[/C][C]-5.90019080023868[/C][/ROW]
[ROW][C]55[/C][C]136.8[/C][C]145.500375332985[/C][C]-8.70037533298532[/C][/ROW]
[ROW][C]56[/C][C]146.6[/C][C]136.800553463093[/C][C]9.7994465369074[/C][/ROW]
[ROW][C]57[/C][C]145.1[/C][C]146.599376620918[/C][C]-1.49937662091824[/C][/ROW]
[ROW][C]58[/C][C]133.6[/C][C]145.100095380899[/C][C]-11.5000953808991[/C][/ROW]
[ROW][C]59[/C][C]131.4[/C][C]133.600731563652[/C][C]-2.20073156365225[/C][/ROW]
[ROW][C]60[/C][C]127.5[/C][C]131.400139996684[/C][C]-3.90013999668412[/C][/ROW]
[ROW][C]61[/C][C]130.1[/C][C]127.500248102347[/C][C]2.59975189765251[/C][/ROW]
[ROW][C]62[/C][C]131.1[/C][C]130.099834620155[/C][C]1.00016537984513[/C][/ROW]
[ROW][C]63[/C][C]132.3[/C][C]131.099936375777[/C][C]1.20006362422347[/C][/ROW]
[ROW][C]64[/C][C]128.6[/C][C]132.299923659509[/C][C]-3.69992365950901[/C][/ROW]
[ROW][C]65[/C][C]125.1[/C][C]128.600235365845[/C][C]-3.50023536584487[/C][/ROW]
[ROW][C]66[/C][C]128.7[/C][C]125.100222662933[/C][C]3.59977733706694[/C][/ROW]
[ROW][C]67[/C][C]156.1[/C][C]128.699771004834[/C][C]27.4002289951665[/C][/ROW]
[ROW][C]68[/C][C]163.2[/C][C]156.09825696997[/C][C]7.10174303002995[/C][/ROW]
[ROW][C]69[/C][C]159.8[/C][C]163.199548231828[/C][C]-3.39954823182794[/C][/ROW]
[ROW][C]70[/C][C]157.4[/C][C]159.800216257852[/C][C]-2.40021625785164[/C][/ROW]
[ROW][C]71[/C][C]156.2[/C][C]157.400152686644[/C][C]-1.20015268664423[/C][/ROW]
[ROW][C]72[/C][C]152.5[/C][C]156.200076346157[/C][C]-3.70007634615658[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232919&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232919&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
286.483.72.7
385.986.3998282430018-0.499828243001843
480.485.9000317959254-5.50003179592541
581.880.40034987738931.39965012261072
687.581.79991096307285.70008903692724
783.787.4996373962288-3.79963739622882
88783.70024170900493.29975829099509
999.786.99979009015612.700209909844
10101.499.69919209261851.70080790738149
11101.9101.3998918053110.500108194689119
12115.7101.89996818626613.8000318137342
13123.2115.6991221288757.50087787112547
14136.9123.19952284138313.7004771586173
15146.8136.8991284619159.9008715380852
16149.6146.7993701688982.80062983110165
17146.5149.599821841566-3.09982184156564
18157146.50019719114610.499802808854
19147.9156.999332068662-9.09933206866233
20133.6147.900578842208-14.3005788422079
21128.7133.600909712775-4.90090971277547
22100.8128.700311765015-27.900311765015
2391.8100.801774842147-9.00177484214677
2489.391.8005726362315-2.50057263623145
2596.789.30015907068517.39984092931495
2691.696.6995292687167-5.09952926871674
2793.391.60032439994041.69967560005956
2893.393.29989187734110.000108122658858179
2910193.29999999312197.70000000687808
30100.4100.999510174486-0.599510174486312
3186.9100.400038137062-13.5000381370622
3283.986.9008587874168-3.0008587874168
3380.383.9001908957397-3.60019089573971
3487.780.30022902147457.39977097852555
3592.787.69952927316665.00047072683344
3695.592.69968190154022.80031809845977
379295.4998218613961-3.49982186139613
3887.492.0002226366285-4.6002226366285
3986.887.4002926371966-0.600292637196645
4083.786.8000381868375-3.10003818683754
418583.70019720490861.29980279509142
4281.784.999917314731-3.299917314731
4390.981.700209919969.19979008003996
44101.590.89941476728610.600585232714
45113.8101.49932565751912.3006743424808
46120.1113.7992175085556.30078249144456
47122.1120.0995991838942.00040081610621
48132.5122.09987274709710.4001272529034
49140132.4993384093947.50066159060643
50149.4139.9995228551419.40047714485888
51144.3149.399402000839-5.09940200083867
52154.4144.30032439184410.0996756081555
53151.4154.399357522235-2.99935752223527
54145.5151.400190800239-5.90019080023868
55136.8145.500375332985-8.70037533298532
56146.6136.8005534630939.7994465369074
57145.1146.599376620918-1.49937662091824
58133.6145.100095380899-11.5000953808991
59131.4133.600731563652-2.20073156365225
60127.5131.400139996684-3.90013999668412
61130.1127.5002481023472.59975189765251
62131.1130.0998346201551.00016537984513
63132.3131.0999363757771.20006362422347
64128.6132.299923659509-3.69992365950901
65125.1128.600235365845-3.50023536584487
66128.7125.1002226629333.59977733706694
67156.1128.69977100483427.4002289951665
68163.2156.098256969977.10174303002995
69159.8163.199548231828-3.39954823182794
70157.4159.800216257852-2.40021625785164
71156.2157.400152686644-1.20015268664423
72152.5156.200076346157-3.70007634615658







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73152.500235375558136.701563353693168.298907397423
74152.500235375558130.158249774272174.842220976844
75152.500235375558125.137293217199179.863177533917
76152.500235375558120.904398837885184.09607191323
77152.500235375558117.175128589181187.825342161935
78152.500235375558113.803601769745191.196868981371
79152.500235375558110.703157303327194.297313447789
80152.500235375558107.817330161933197.183140589183
81152.500235375558105.106899332572199.893571418544
82152.500235375558102.543308085771202.457162665345
83152.500235375558100.104998309669204.895472441446
84152.50023537555897.7752214409384207.225249310177

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 152.500235375558 & 136.701563353693 & 168.298907397423 \tabularnewline
74 & 152.500235375558 & 130.158249774272 & 174.842220976844 \tabularnewline
75 & 152.500235375558 & 125.137293217199 & 179.863177533917 \tabularnewline
76 & 152.500235375558 & 120.904398837885 & 184.09607191323 \tabularnewline
77 & 152.500235375558 & 117.175128589181 & 187.825342161935 \tabularnewline
78 & 152.500235375558 & 113.803601769745 & 191.196868981371 \tabularnewline
79 & 152.500235375558 & 110.703157303327 & 194.297313447789 \tabularnewline
80 & 152.500235375558 & 107.817330161933 & 197.183140589183 \tabularnewline
81 & 152.500235375558 & 105.106899332572 & 199.893571418544 \tabularnewline
82 & 152.500235375558 & 102.543308085771 & 202.457162665345 \tabularnewline
83 & 152.500235375558 & 100.104998309669 & 204.895472441446 \tabularnewline
84 & 152.500235375558 & 97.7752214409384 & 207.225249310177 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232919&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]152.500235375558[/C][C]136.701563353693[/C][C]168.298907397423[/C][/ROW]
[ROW][C]74[/C][C]152.500235375558[/C][C]130.158249774272[/C][C]174.842220976844[/C][/ROW]
[ROW][C]75[/C][C]152.500235375558[/C][C]125.137293217199[/C][C]179.863177533917[/C][/ROW]
[ROW][C]76[/C][C]152.500235375558[/C][C]120.904398837885[/C][C]184.09607191323[/C][/ROW]
[ROW][C]77[/C][C]152.500235375558[/C][C]117.175128589181[/C][C]187.825342161935[/C][/ROW]
[ROW][C]78[/C][C]152.500235375558[/C][C]113.803601769745[/C][C]191.196868981371[/C][/ROW]
[ROW][C]79[/C][C]152.500235375558[/C][C]110.703157303327[/C][C]194.297313447789[/C][/ROW]
[ROW][C]80[/C][C]152.500235375558[/C][C]107.817330161933[/C][C]197.183140589183[/C][/ROW]
[ROW][C]81[/C][C]152.500235375558[/C][C]105.106899332572[/C][C]199.893571418544[/C][/ROW]
[ROW][C]82[/C][C]152.500235375558[/C][C]102.543308085771[/C][C]202.457162665345[/C][/ROW]
[ROW][C]83[/C][C]152.500235375558[/C][C]100.104998309669[/C][C]204.895472441446[/C][/ROW]
[ROW][C]84[/C][C]152.500235375558[/C][C]97.7752214409384[/C][C]207.225249310177[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232919&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232919&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
73152.500235375558136.701563353693168.298907397423
74152.500235375558130.158249774272174.842220976844
75152.500235375558125.137293217199179.863177533917
76152.500235375558120.904398837885184.09607191323
77152.500235375558117.175128589181187.825342161935
78152.500235375558113.803601769745191.196868981371
79152.500235375558110.703157303327194.297313447789
80152.500235375558107.817330161933197.183140589183
81152.500235375558105.106899332572199.893571418544
82152.500235375558102.543308085771202.457162665345
83152.500235375558100.104998309669204.895472441446
84152.50023537555897.7752214409384207.225249310177



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')