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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:04:48 -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/2012/Dec/21/t1356080779venw3nlp0l9ansc.htm/, Retrieved Wed, 24 Apr 2024 04:20:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203313, Retrieved Wed, 24 Apr 2024 04:20:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 09:04:48] [5f317879e17cb2eb817d39090eb03de3] [Current]
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Dataseries X:
15,13
15,25
15,33
15,36
15,4
15,4
15,41
15,47
15,54
15,55
15,59
15,65
15,75
15,86
15,89
15,94
15,93
15,95
15,99
15,99
16,06
16,08
16,07
16,11
16,15
16,18
16,3
16,42
16,49
16,5
16,58
16,64
16,66
16,81
16,91
16,92
16,95
17,11
17,16
17,16
17,27
17,34
17,39
17,43
17,45
17,5
17,56
17,65
17,62
17,7
17,72
17,71
17,74
17,75
17,78
17,8
17,86
17,88
17,89
17,94
17,98
18,1
18,14
18,19
18,23
18,24
18,27
18,3
18,34
18,36
18,36
18,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203313&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]3 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=203313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203313&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.239728579543755
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.239728579543755 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203313&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.239728579543755[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203313&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
alpha1
beta0.239728579543755
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
315.3315.37-0.0399999999999991
415.3615.4404108568183-0.0804108568182507
515.415.4511340763333-0.0511340763333124
615.415.4788757768476-0.0788757768476476
715.4115.4599669989035-0.0499669989035496
815.4715.45798848123230.0120115187676628
915.5415.52086798556470.0191320144353266
1015.5515.5954544762091-0.0454544762090627
1115.5915.5945577391936-0.00455773919356162
1215.6515.63346511885080.0165348811492443
1315.7515.69742900242160.0525709975784103
1415.8615.81003177299630.04996822700374
1515.8915.9320105850782-0.0420105850781862
1615.9415.9519394471916-0.0119394471915921
1715.9315.9990772204758-0.0690772204758119
1815.9515.9725174365323-0.0225174365323166
1915.9915.98711936345750.00288063654254422
2015.9916.027809934364-0.0378099343639828
2116.0616.01874581250630.0412541874937347
2216.0816.0986356202744-0.0186356202743667
2316.0716.1141681294971-0.0441681294970735
2416.1116.09357976655160.0164202334483612
2516.1516.1375161657920.0124838342080089
2616.1816.1805088976339-0.000508897633935135
2716.316.2103869003270.0896130996729809
2816.4216.35186972142010.068130278579865
2916.4916.4882024963280.0017975036719875
3016.516.55863340933-0.0586334093300174
3116.5816.55457730539750.0254226946024723
3216.6416.6406718518627-0.000671851862747985
3316.6616.70051078977-0.0405107897700319
3416.8116.71079919568230.0992008043177321
3516.9116.8845804635910.0254195364090464
3616.9216.990674252947-0.0706742529469544
3716.9516.9837316146777-0.0337316146776701
3817.1117.00564518260530.104354817394729
3917.1617.1906620147479-0.0306620147478576
4017.1617.2333114535064-0.0733114535064026
4117.2717.2157366028930.0542633971069719
4217.3417.33874509000270.00125490999730005
4317.3917.4090459277938-0.0190459277938082
4417.4317.4544800745777-0.0244800745777063
4517.4517.4886115010721-0.0386115010720687
4617.517.4993552207660.000644779233994086
4717.5617.54950979277590.0104902072241053
4817.6517.61202459525280.0379754047471543
4917.6217.7111283850905-0.091128385090478
5017.717.65928230677660.0407176932233746
5117.7217.7490435015354-0.0290435015353623
5217.7117.7620809441673-0.0520809441673116
5317.7417.73959565340080.000404346599211181
5417.7517.7696925868367-0.0196925868366549
5517.7817.77497171096680.0050282890332376
5617.817.8061771355542-0.00617713555423904
5717.8617.82469629962220.0353037003778276
5817.8817.8931596055664-0.0131596055663863
5917.8917.9100048720166-0.0200048720165995
6017.9417.91520913246410.024790867535895
6117.9817.97115221192410.00884778807585462
6218.118.01327327959170.0867267204083291
6318.1418.1540641530837-0.0140641530836518
6418.1918.1906925736424-0.000692573642417926
6518.2318.2405265439469-0.0105265439468951
6618.2418.278003030519-0.0380030305190004
6718.2718.2788926179943-0.00889261799432006
6818.318.3067608033141-0.00676080331411555
6918.3418.3351400455390.00485995446095089
7018.3618.3763051155186-0.0163051155186196
7118.3618.392396313336-0.0323963133360436
7218.418.38462999115750.01537000884246

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 15.33 & 15.37 & -0.0399999999999991 \tabularnewline
4 & 15.36 & 15.4404108568183 & -0.0804108568182507 \tabularnewline
5 & 15.4 & 15.4511340763333 & -0.0511340763333124 \tabularnewline
6 & 15.4 & 15.4788757768476 & -0.0788757768476476 \tabularnewline
7 & 15.41 & 15.4599669989035 & -0.0499669989035496 \tabularnewline
8 & 15.47 & 15.4579884812323 & 0.0120115187676628 \tabularnewline
9 & 15.54 & 15.5208679855647 & 0.0191320144353266 \tabularnewline
10 & 15.55 & 15.5954544762091 & -0.0454544762090627 \tabularnewline
11 & 15.59 & 15.5945577391936 & -0.00455773919356162 \tabularnewline
12 & 15.65 & 15.6334651188508 & 0.0165348811492443 \tabularnewline
13 & 15.75 & 15.6974290024216 & 0.0525709975784103 \tabularnewline
14 & 15.86 & 15.8100317729963 & 0.04996822700374 \tabularnewline
15 & 15.89 & 15.9320105850782 & -0.0420105850781862 \tabularnewline
16 & 15.94 & 15.9519394471916 & -0.0119394471915921 \tabularnewline
17 & 15.93 & 15.9990772204758 & -0.0690772204758119 \tabularnewline
18 & 15.95 & 15.9725174365323 & -0.0225174365323166 \tabularnewline
19 & 15.99 & 15.9871193634575 & 0.00288063654254422 \tabularnewline
20 & 15.99 & 16.027809934364 & -0.0378099343639828 \tabularnewline
21 & 16.06 & 16.0187458125063 & 0.0412541874937347 \tabularnewline
22 & 16.08 & 16.0986356202744 & -0.0186356202743667 \tabularnewline
23 & 16.07 & 16.1141681294971 & -0.0441681294970735 \tabularnewline
24 & 16.11 & 16.0935797665516 & 0.0164202334483612 \tabularnewline
25 & 16.15 & 16.137516165792 & 0.0124838342080089 \tabularnewline
26 & 16.18 & 16.1805088976339 & -0.000508897633935135 \tabularnewline
27 & 16.3 & 16.210386900327 & 0.0896130996729809 \tabularnewline
28 & 16.42 & 16.3518697214201 & 0.068130278579865 \tabularnewline
29 & 16.49 & 16.488202496328 & 0.0017975036719875 \tabularnewline
30 & 16.5 & 16.55863340933 & -0.0586334093300174 \tabularnewline
31 & 16.58 & 16.5545773053975 & 0.0254226946024723 \tabularnewline
32 & 16.64 & 16.6406718518627 & -0.000671851862747985 \tabularnewline
33 & 16.66 & 16.70051078977 & -0.0405107897700319 \tabularnewline
34 & 16.81 & 16.7107991956823 & 0.0992008043177321 \tabularnewline
35 & 16.91 & 16.884580463591 & 0.0254195364090464 \tabularnewline
36 & 16.92 & 16.990674252947 & -0.0706742529469544 \tabularnewline
37 & 16.95 & 16.9837316146777 & -0.0337316146776701 \tabularnewline
38 & 17.11 & 17.0056451826053 & 0.104354817394729 \tabularnewline
39 & 17.16 & 17.1906620147479 & -0.0306620147478576 \tabularnewline
40 & 17.16 & 17.2333114535064 & -0.0733114535064026 \tabularnewline
41 & 17.27 & 17.215736602893 & 0.0542633971069719 \tabularnewline
42 & 17.34 & 17.3387450900027 & 0.00125490999730005 \tabularnewline
43 & 17.39 & 17.4090459277938 & -0.0190459277938082 \tabularnewline
44 & 17.43 & 17.4544800745777 & -0.0244800745777063 \tabularnewline
45 & 17.45 & 17.4886115010721 & -0.0386115010720687 \tabularnewline
46 & 17.5 & 17.499355220766 & 0.000644779233994086 \tabularnewline
47 & 17.56 & 17.5495097927759 & 0.0104902072241053 \tabularnewline
48 & 17.65 & 17.6120245952528 & 0.0379754047471543 \tabularnewline
49 & 17.62 & 17.7111283850905 & -0.091128385090478 \tabularnewline
50 & 17.7 & 17.6592823067766 & 0.0407176932233746 \tabularnewline
51 & 17.72 & 17.7490435015354 & -0.0290435015353623 \tabularnewline
52 & 17.71 & 17.7620809441673 & -0.0520809441673116 \tabularnewline
53 & 17.74 & 17.7395956534008 & 0.000404346599211181 \tabularnewline
54 & 17.75 & 17.7696925868367 & -0.0196925868366549 \tabularnewline
55 & 17.78 & 17.7749717109668 & 0.0050282890332376 \tabularnewline
56 & 17.8 & 17.8061771355542 & -0.00617713555423904 \tabularnewline
57 & 17.86 & 17.8246962996222 & 0.0353037003778276 \tabularnewline
58 & 17.88 & 17.8931596055664 & -0.0131596055663863 \tabularnewline
59 & 17.89 & 17.9100048720166 & -0.0200048720165995 \tabularnewline
60 & 17.94 & 17.9152091324641 & 0.024790867535895 \tabularnewline
61 & 17.98 & 17.9711522119241 & 0.00884778807585462 \tabularnewline
62 & 18.1 & 18.0132732795917 & 0.0867267204083291 \tabularnewline
63 & 18.14 & 18.1540641530837 & -0.0140641530836518 \tabularnewline
64 & 18.19 & 18.1906925736424 & -0.000692573642417926 \tabularnewline
65 & 18.23 & 18.2405265439469 & -0.0105265439468951 \tabularnewline
66 & 18.24 & 18.278003030519 & -0.0380030305190004 \tabularnewline
67 & 18.27 & 18.2788926179943 & -0.00889261799432006 \tabularnewline
68 & 18.3 & 18.3067608033141 & -0.00676080331411555 \tabularnewline
69 & 18.34 & 18.335140045539 & 0.00485995446095089 \tabularnewline
70 & 18.36 & 18.3763051155186 & -0.0163051155186196 \tabularnewline
71 & 18.36 & 18.392396313336 & -0.0323963133360436 \tabularnewline
72 & 18.4 & 18.3846299911575 & 0.01537000884246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203313&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]15.33[/C][C]15.37[/C][C]-0.0399999999999991[/C][/ROW]
[ROW][C]4[/C][C]15.36[/C][C]15.4404108568183[/C][C]-0.0804108568182507[/C][/ROW]
[ROW][C]5[/C][C]15.4[/C][C]15.4511340763333[/C][C]-0.0511340763333124[/C][/ROW]
[ROW][C]6[/C][C]15.4[/C][C]15.4788757768476[/C][C]-0.0788757768476476[/C][/ROW]
[ROW][C]7[/C][C]15.41[/C][C]15.4599669989035[/C][C]-0.0499669989035496[/C][/ROW]
[ROW][C]8[/C][C]15.47[/C][C]15.4579884812323[/C][C]0.0120115187676628[/C][/ROW]
[ROW][C]9[/C][C]15.54[/C][C]15.5208679855647[/C][C]0.0191320144353266[/C][/ROW]
[ROW][C]10[/C][C]15.55[/C][C]15.5954544762091[/C][C]-0.0454544762090627[/C][/ROW]
[ROW][C]11[/C][C]15.59[/C][C]15.5945577391936[/C][C]-0.00455773919356162[/C][/ROW]
[ROW][C]12[/C][C]15.65[/C][C]15.6334651188508[/C][C]0.0165348811492443[/C][/ROW]
[ROW][C]13[/C][C]15.75[/C][C]15.6974290024216[/C][C]0.0525709975784103[/C][/ROW]
[ROW][C]14[/C][C]15.86[/C][C]15.8100317729963[/C][C]0.04996822700374[/C][/ROW]
[ROW][C]15[/C][C]15.89[/C][C]15.9320105850782[/C][C]-0.0420105850781862[/C][/ROW]
[ROW][C]16[/C][C]15.94[/C][C]15.9519394471916[/C][C]-0.0119394471915921[/C][/ROW]
[ROW][C]17[/C][C]15.93[/C][C]15.9990772204758[/C][C]-0.0690772204758119[/C][/ROW]
[ROW][C]18[/C][C]15.95[/C][C]15.9725174365323[/C][C]-0.0225174365323166[/C][/ROW]
[ROW][C]19[/C][C]15.99[/C][C]15.9871193634575[/C][C]0.00288063654254422[/C][/ROW]
[ROW][C]20[/C][C]15.99[/C][C]16.027809934364[/C][C]-0.0378099343639828[/C][/ROW]
[ROW][C]21[/C][C]16.06[/C][C]16.0187458125063[/C][C]0.0412541874937347[/C][/ROW]
[ROW][C]22[/C][C]16.08[/C][C]16.0986356202744[/C][C]-0.0186356202743667[/C][/ROW]
[ROW][C]23[/C][C]16.07[/C][C]16.1141681294971[/C][C]-0.0441681294970735[/C][/ROW]
[ROW][C]24[/C][C]16.11[/C][C]16.0935797665516[/C][C]0.0164202334483612[/C][/ROW]
[ROW][C]25[/C][C]16.15[/C][C]16.137516165792[/C][C]0.0124838342080089[/C][/ROW]
[ROW][C]26[/C][C]16.18[/C][C]16.1805088976339[/C][C]-0.000508897633935135[/C][/ROW]
[ROW][C]27[/C][C]16.3[/C][C]16.210386900327[/C][C]0.0896130996729809[/C][/ROW]
[ROW][C]28[/C][C]16.42[/C][C]16.3518697214201[/C][C]0.068130278579865[/C][/ROW]
[ROW][C]29[/C][C]16.49[/C][C]16.488202496328[/C][C]0.0017975036719875[/C][/ROW]
[ROW][C]30[/C][C]16.5[/C][C]16.55863340933[/C][C]-0.0586334093300174[/C][/ROW]
[ROW][C]31[/C][C]16.58[/C][C]16.5545773053975[/C][C]0.0254226946024723[/C][/ROW]
[ROW][C]32[/C][C]16.64[/C][C]16.6406718518627[/C][C]-0.000671851862747985[/C][/ROW]
[ROW][C]33[/C][C]16.66[/C][C]16.70051078977[/C][C]-0.0405107897700319[/C][/ROW]
[ROW][C]34[/C][C]16.81[/C][C]16.7107991956823[/C][C]0.0992008043177321[/C][/ROW]
[ROW][C]35[/C][C]16.91[/C][C]16.884580463591[/C][C]0.0254195364090464[/C][/ROW]
[ROW][C]36[/C][C]16.92[/C][C]16.990674252947[/C][C]-0.0706742529469544[/C][/ROW]
[ROW][C]37[/C][C]16.95[/C][C]16.9837316146777[/C][C]-0.0337316146776701[/C][/ROW]
[ROW][C]38[/C][C]17.11[/C][C]17.0056451826053[/C][C]0.104354817394729[/C][/ROW]
[ROW][C]39[/C][C]17.16[/C][C]17.1906620147479[/C][C]-0.0306620147478576[/C][/ROW]
[ROW][C]40[/C][C]17.16[/C][C]17.2333114535064[/C][C]-0.0733114535064026[/C][/ROW]
[ROW][C]41[/C][C]17.27[/C][C]17.215736602893[/C][C]0.0542633971069719[/C][/ROW]
[ROW][C]42[/C][C]17.34[/C][C]17.3387450900027[/C][C]0.00125490999730005[/C][/ROW]
[ROW][C]43[/C][C]17.39[/C][C]17.4090459277938[/C][C]-0.0190459277938082[/C][/ROW]
[ROW][C]44[/C][C]17.43[/C][C]17.4544800745777[/C][C]-0.0244800745777063[/C][/ROW]
[ROW][C]45[/C][C]17.45[/C][C]17.4886115010721[/C][C]-0.0386115010720687[/C][/ROW]
[ROW][C]46[/C][C]17.5[/C][C]17.499355220766[/C][C]0.000644779233994086[/C][/ROW]
[ROW][C]47[/C][C]17.56[/C][C]17.5495097927759[/C][C]0.0104902072241053[/C][/ROW]
[ROW][C]48[/C][C]17.65[/C][C]17.6120245952528[/C][C]0.0379754047471543[/C][/ROW]
[ROW][C]49[/C][C]17.62[/C][C]17.7111283850905[/C][C]-0.091128385090478[/C][/ROW]
[ROW][C]50[/C][C]17.7[/C][C]17.6592823067766[/C][C]0.0407176932233746[/C][/ROW]
[ROW][C]51[/C][C]17.72[/C][C]17.7490435015354[/C][C]-0.0290435015353623[/C][/ROW]
[ROW][C]52[/C][C]17.71[/C][C]17.7620809441673[/C][C]-0.0520809441673116[/C][/ROW]
[ROW][C]53[/C][C]17.74[/C][C]17.7395956534008[/C][C]0.000404346599211181[/C][/ROW]
[ROW][C]54[/C][C]17.75[/C][C]17.7696925868367[/C][C]-0.0196925868366549[/C][/ROW]
[ROW][C]55[/C][C]17.78[/C][C]17.7749717109668[/C][C]0.0050282890332376[/C][/ROW]
[ROW][C]56[/C][C]17.8[/C][C]17.8061771355542[/C][C]-0.00617713555423904[/C][/ROW]
[ROW][C]57[/C][C]17.86[/C][C]17.8246962996222[/C][C]0.0353037003778276[/C][/ROW]
[ROW][C]58[/C][C]17.88[/C][C]17.8931596055664[/C][C]-0.0131596055663863[/C][/ROW]
[ROW][C]59[/C][C]17.89[/C][C]17.9100048720166[/C][C]-0.0200048720165995[/C][/ROW]
[ROW][C]60[/C][C]17.94[/C][C]17.9152091324641[/C][C]0.024790867535895[/C][/ROW]
[ROW][C]61[/C][C]17.98[/C][C]17.9711522119241[/C][C]0.00884778807585462[/C][/ROW]
[ROW][C]62[/C][C]18.1[/C][C]18.0132732795917[/C][C]0.0867267204083291[/C][/ROW]
[ROW][C]63[/C][C]18.14[/C][C]18.1540641530837[/C][C]-0.0140641530836518[/C][/ROW]
[ROW][C]64[/C][C]18.19[/C][C]18.1906925736424[/C][C]-0.000692573642417926[/C][/ROW]
[ROW][C]65[/C][C]18.23[/C][C]18.2405265439469[/C][C]-0.0105265439468951[/C][/ROW]
[ROW][C]66[/C][C]18.24[/C][C]18.278003030519[/C][C]-0.0380030305190004[/C][/ROW]
[ROW][C]67[/C][C]18.27[/C][C]18.2788926179943[/C][C]-0.00889261799432006[/C][/ROW]
[ROW][C]68[/C][C]18.3[/C][C]18.3067608033141[/C][C]-0.00676080331411555[/C][/ROW]
[ROW][C]69[/C][C]18.34[/C][C]18.335140045539[/C][C]0.00485995446095089[/C][/ROW]
[ROW][C]70[/C][C]18.36[/C][C]18.3763051155186[/C][C]-0.0163051155186196[/C][/ROW]
[ROW][C]71[/C][C]18.36[/C][C]18.392396313336[/C][C]-0.0323963133360436[/C][/ROW]
[ROW][C]72[/C][C]18.4[/C][C]18.3846299911575[/C][C]0.01537000884246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203313&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203313&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
315.3315.37-0.0399999999999991
415.3615.4404108568183-0.0804108568182507
515.415.4511340763333-0.0511340763333124
615.415.4788757768476-0.0788757768476476
715.4115.4599669989035-0.0499669989035496
815.4715.45798848123230.0120115187676628
915.5415.52086798556470.0191320144353266
1015.5515.5954544762091-0.0454544762090627
1115.5915.5945577391936-0.00455773919356162
1215.6515.63346511885080.0165348811492443
1315.7515.69742900242160.0525709975784103
1415.8615.81003177299630.04996822700374
1515.8915.9320105850782-0.0420105850781862
1615.9415.9519394471916-0.0119394471915921
1715.9315.9990772204758-0.0690772204758119
1815.9515.9725174365323-0.0225174365323166
1915.9915.98711936345750.00288063654254422
2015.9916.027809934364-0.0378099343639828
2116.0616.01874581250630.0412541874937347
2216.0816.0986356202744-0.0186356202743667
2316.0716.1141681294971-0.0441681294970735
2416.1116.09357976655160.0164202334483612
2516.1516.1375161657920.0124838342080089
2616.1816.1805088976339-0.000508897633935135
2716.316.2103869003270.0896130996729809
2816.4216.35186972142010.068130278579865
2916.4916.4882024963280.0017975036719875
3016.516.55863340933-0.0586334093300174
3116.5816.55457730539750.0254226946024723
3216.6416.6406718518627-0.000671851862747985
3316.6616.70051078977-0.0405107897700319
3416.8116.71079919568230.0992008043177321
3516.9116.8845804635910.0254195364090464
3616.9216.990674252947-0.0706742529469544
3716.9516.9837316146777-0.0337316146776701
3817.1117.00564518260530.104354817394729
3917.1617.1906620147479-0.0306620147478576
4017.1617.2333114535064-0.0733114535064026
4117.2717.2157366028930.0542633971069719
4217.3417.33874509000270.00125490999730005
4317.3917.4090459277938-0.0190459277938082
4417.4317.4544800745777-0.0244800745777063
4517.4517.4886115010721-0.0386115010720687
4617.517.4993552207660.000644779233994086
4717.5617.54950979277590.0104902072241053
4817.6517.61202459525280.0379754047471543
4917.6217.7111283850905-0.091128385090478
5017.717.65928230677660.0407176932233746
5117.7217.7490435015354-0.0290435015353623
5217.7117.7620809441673-0.0520809441673116
5317.7417.73959565340080.000404346599211181
5417.7517.7696925868367-0.0196925868366549
5517.7817.77497171096680.0050282890332376
5617.817.8061771355542-0.00617713555423904
5717.8617.82469629962220.0353037003778276
5817.8817.8931596055664-0.0131596055663863
5917.8917.9100048720166-0.0200048720165995
6017.9417.91520913246410.024790867535895
6117.9817.97115221192410.00884778807585462
6218.118.01327327959170.0867267204083291
6318.1418.1540641530837-0.0140641530836518
6418.1918.1906925736424-0.000692573642417926
6518.2318.2405265439469-0.0105265439468951
6618.2418.278003030519-0.0380030305190004
6718.2718.2788926179943-0.00889261799432006
6818.318.3067608033141-0.00676080331411555
6918.3418.3351400455390.00485995446095089
7018.3618.3763051155186-0.0163051155186196
7118.3618.392396313336-0.0323963133360436
7218.418.38462999115750.01537000884246







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7318.428314621544918.344851585385818.511777657704
7418.456629243089818.323691543216118.5895669429636
7518.484943864634818.303505888785318.6663818404842
7618.513258486179718.281939058429518.7445779139299
7718.541573107724618.258306579658618.8248396357906
7818.569887729269518.232376007938318.9073994506007
7918.598202350814418.204080460853218.9923242407757
8018.626516972359318.17342282054719.0796111241717
8118.654831593904318.140437213134519.169225974674
8218.683146215449218.105171693535419.261120737363
8318.711460836994118.067679899407119.3552417745811
8418.73977545853918.028016861839319.4515340552387

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 18.4283146215449 & 18.3448515853858 & 18.511777657704 \tabularnewline
74 & 18.4566292430898 & 18.3236915432161 & 18.5895669429636 \tabularnewline
75 & 18.4849438646348 & 18.3035058887853 & 18.6663818404842 \tabularnewline
76 & 18.5132584861797 & 18.2819390584295 & 18.7445779139299 \tabularnewline
77 & 18.5415731077246 & 18.2583065796586 & 18.8248396357906 \tabularnewline
78 & 18.5698877292695 & 18.2323760079383 & 18.9073994506007 \tabularnewline
79 & 18.5982023508144 & 18.2040804608532 & 18.9923242407757 \tabularnewline
80 & 18.6265169723593 & 18.173422820547 & 19.0796111241717 \tabularnewline
81 & 18.6548315939043 & 18.1404372131345 & 19.169225974674 \tabularnewline
82 & 18.6831462154492 & 18.1051716935354 & 19.261120737363 \tabularnewline
83 & 18.7114608369941 & 18.0676798994071 & 19.3552417745811 \tabularnewline
84 & 18.739775458539 & 18.0280168618393 & 19.4515340552387 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203313&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]18.4283146215449[/C][C]18.3448515853858[/C][C]18.511777657704[/C][/ROW]
[ROW][C]74[/C][C]18.4566292430898[/C][C]18.3236915432161[/C][C]18.5895669429636[/C][/ROW]
[ROW][C]75[/C][C]18.4849438646348[/C][C]18.3035058887853[/C][C]18.6663818404842[/C][/ROW]
[ROW][C]76[/C][C]18.5132584861797[/C][C]18.2819390584295[/C][C]18.7445779139299[/C][/ROW]
[ROW][C]77[/C][C]18.5415731077246[/C][C]18.2583065796586[/C][C]18.8248396357906[/C][/ROW]
[ROW][C]78[/C][C]18.5698877292695[/C][C]18.2323760079383[/C][C]18.9073994506007[/C][/ROW]
[ROW][C]79[/C][C]18.5982023508144[/C][C]18.2040804608532[/C][C]18.9923242407757[/C][/ROW]
[ROW][C]80[/C][C]18.6265169723593[/C][C]18.173422820547[/C][C]19.0796111241717[/C][/ROW]
[ROW][C]81[/C][C]18.6548315939043[/C][C]18.1404372131345[/C][C]19.169225974674[/C][/ROW]
[ROW][C]82[/C][C]18.6831462154492[/C][C]18.1051716935354[/C][C]19.261120737363[/C][/ROW]
[ROW][C]83[/C][C]18.7114608369941[/C][C]18.0676798994071[/C][C]19.3552417745811[/C][/ROW]
[ROW][C]84[/C][C]18.739775458539[/C][C]18.0280168618393[/C][C]19.4515340552387[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203313&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203313&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
7318.428314621544918.344851585385818.511777657704
7418.456629243089818.323691543216118.5895669429636
7518.484943864634818.303505888785318.6663818404842
7618.513258486179718.281939058429518.7445779139299
7718.541573107724618.258306579658618.8248396357906
7818.569887729269518.232376007938318.9073994506007
7918.598202350814418.204080460853218.9923242407757
8018.626516972359318.17342282054719.0796111241717
8118.654831593904318.140437213134519.169225974674
8218.683146215449218.105171693535419.261120737363
8318.711460836994118.067679899407119.3552417745811
8418.73977545853918.028016861839319.4515340552387



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')