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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 24 May 2013 13:18:43 -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/2013/May/24/t1369415941zrd8rxxmqwa219a.htm/, Retrieved Wed, 01 May 2024 03:00:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210443, Retrieved Wed, 01 May 2024 03:00:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2013-05-13 06:58:22] [709b7720e5f7ef30901a7a8e706288f1]
- R PD    [Exponential Smoothing] [oef 10 eigen reeks ] [2013-05-24 17:18:43] [09b6c15525a7e41be57b956512900af9] [Current]
- RM D      [Quartiles] [oef3.1] [2013-05-24 18:29:46] [709b7720e5f7ef30901a7a8e706288f1]
- RM D      [Notched Boxplots] [oef3.2] [2013-05-24 18:43:18] [709b7720e5f7ef30901a7a8e706288f1]
- RM        [Quartiles] [oef 3 eigen reeks ] [2013-05-24 19:01:55] [709b7720e5f7ef30901a7a8e706288f1]
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Dataseries X:
15,58
15,66
15,73
15,74
15,77
15,78
15,8
15,81
15,82
15,88
15,85
15,89
15,92
16,02
16,1
16,13
16,21
16,25
16,27
16,21
16,21
16,24
16,32
16,32
16,36
16,48
16,54
16,58
16,56
16,55
16,58
16,53
16,6
16,46
16,48
16,48
16,49
16,54
16,67
16,72
16,79
16,86
16,84
16,86
16,96
17,01
17,02
17,04
17,04
17,39
17,54
17,57
17,58
17,56
17,63
17,67
17,71
17,75
17,82
17,86
17,89
17,96
18
18,08
18
18,02
18,01
18,02
17,95
17,96
18
18,01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210443&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210443&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210443&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.12705129384387
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.12705129384387 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210443&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]0.12705129384387[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210443&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210443&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
beta0.12705129384387
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
315.7315.74-0.00999999999999979
415.7415.8087294870616-0.068729487061562
515.7715.8099973168052-0.0399973168051648
615.7815.8349156059548-0.0549156059547844
715.815.837938507166-0.0379385071660074
815.8115.8531183707441-0.0431183707440628
915.8215.8576401259526-0.0376401259525903
1015.8815.86285789924990.0171421007501333
1115.8515.9250358253294-0.0750358253293744
1215.8915.88550242663660.00449757336336631
1315.9215.9260738491516-0.00607384915160836
1416.0215.95530215875830.064697841241717
1516.116.06352210319690.0364778968030528
1616.1316.1481566671825-0.0181566671824811
1716.2116.17584983912510.0341501608749475
1816.2516.2601886612492-0.0101886612491917
1916.2716.2988941786549-0.0288941786549444
2016.2116.3152231358723-0.105223135872276
2116.2116.2418544003174-0.0318544003173962
2216.2416.23780725754240.00219274245754875
2316.3216.26808584830870.0519141516912534
2416.3216.3546816084499-0.0346816084499295
2516.3616.35027526522380.0097247347762206
2616.4816.39151080535940.0884891946406157
2716.5416.52275347202970.0172465279703218
2816.5816.5849446657226-0.00494466572262198
2916.5616.6243164395449-0.0643164395449354
3016.5516.5961449526853-0.0461449526853208
3116.5816.5802821767423-0.000282176742288698
3216.5316.6102463258221-0.0802463258220847
3316.616.55005092630020.0499490736998247
3416.4616.62639702074-0.166397020740042
3516.4816.46525606396330.0147439360367478
3616.4816.4871293001131-0.00712930011307122
3716.4916.48622351330950.0037764866904908
3816.5416.49670332082970.0432966791702825
3916.6716.55220421993740.117795780062558
4016.7216.69717032620370.0228296737962559
4116.7916.75007086579760.0399291342024135
4216.8616.82514391396010.0348560860399303
4316.8416.8995724247898-0.0595724247897778
4416.8616.8720036711428-0.0120036711428178
4516.9616.89047858919320.0695214108067539
4617.0116.99931137438610.0106886256139056
4717.0217.0506693780998-0.0306693780997591
4817.0417.0567727939308-0.0167727939307944
4917.0417.0746417887605-0.0346417887605099
5017.3917.07024050467740.319759495322579
5117.5417.4608663622770.079133637722979
5217.5717.6209203933363-0.0509203933362947
5317.5817.6444508914799-0.0644508914798827
5417.5617.646262322328-0.0862623223279684
5517.6317.61530258266620.0146974173337746
5617.6717.6871699085546-0.0171699085546422
5717.7117.7249884494576-0.0149884494575971
5817.7517.7630841475613-0.0130841475612975
5917.8217.80142178968480.0185782103152121
6017.8617.8737821753426-0.0137821753426408
6117.8917.9120311321334-0.022031132133371
6217.9617.9392320482910.0207679517090149
631818.0118706434261-0.0118706434261036
6418.0818.05036246282010.0296375371799442
651818.1341279502651-0.13412795026511
6618.0218.0370868206433-0.0170868206433035
6718.0118.0549159179729-0.0449159179728937
6818.0218.0392092924803-0.0192092924802552
6917.9518.0467687270168-0.0967687270168121
7017.9617.9644741350457-0.00447413504570093
711817.97390569039930.0260943096006869
7218.0118.017221006196-0.00722100619604049

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 15.73 & 15.74 & -0.00999999999999979 \tabularnewline
4 & 15.74 & 15.8087294870616 & -0.068729487061562 \tabularnewline
5 & 15.77 & 15.8099973168052 & -0.0399973168051648 \tabularnewline
6 & 15.78 & 15.8349156059548 & -0.0549156059547844 \tabularnewline
7 & 15.8 & 15.837938507166 & -0.0379385071660074 \tabularnewline
8 & 15.81 & 15.8531183707441 & -0.0431183707440628 \tabularnewline
9 & 15.82 & 15.8576401259526 & -0.0376401259525903 \tabularnewline
10 & 15.88 & 15.8628578992499 & 0.0171421007501333 \tabularnewline
11 & 15.85 & 15.9250358253294 & -0.0750358253293744 \tabularnewline
12 & 15.89 & 15.8855024266366 & 0.00449757336336631 \tabularnewline
13 & 15.92 & 15.9260738491516 & -0.00607384915160836 \tabularnewline
14 & 16.02 & 15.9553021587583 & 0.064697841241717 \tabularnewline
15 & 16.1 & 16.0635221031969 & 0.0364778968030528 \tabularnewline
16 & 16.13 & 16.1481566671825 & -0.0181566671824811 \tabularnewline
17 & 16.21 & 16.1758498391251 & 0.0341501608749475 \tabularnewline
18 & 16.25 & 16.2601886612492 & -0.0101886612491917 \tabularnewline
19 & 16.27 & 16.2988941786549 & -0.0288941786549444 \tabularnewline
20 & 16.21 & 16.3152231358723 & -0.105223135872276 \tabularnewline
21 & 16.21 & 16.2418544003174 & -0.0318544003173962 \tabularnewline
22 & 16.24 & 16.2378072575424 & 0.00219274245754875 \tabularnewline
23 & 16.32 & 16.2680858483087 & 0.0519141516912534 \tabularnewline
24 & 16.32 & 16.3546816084499 & -0.0346816084499295 \tabularnewline
25 & 16.36 & 16.3502752652238 & 0.0097247347762206 \tabularnewline
26 & 16.48 & 16.3915108053594 & 0.0884891946406157 \tabularnewline
27 & 16.54 & 16.5227534720297 & 0.0172465279703218 \tabularnewline
28 & 16.58 & 16.5849446657226 & -0.00494466572262198 \tabularnewline
29 & 16.56 & 16.6243164395449 & -0.0643164395449354 \tabularnewline
30 & 16.55 & 16.5961449526853 & -0.0461449526853208 \tabularnewline
31 & 16.58 & 16.5802821767423 & -0.000282176742288698 \tabularnewline
32 & 16.53 & 16.6102463258221 & -0.0802463258220847 \tabularnewline
33 & 16.6 & 16.5500509263002 & 0.0499490736998247 \tabularnewline
34 & 16.46 & 16.62639702074 & -0.166397020740042 \tabularnewline
35 & 16.48 & 16.4652560639633 & 0.0147439360367478 \tabularnewline
36 & 16.48 & 16.4871293001131 & -0.00712930011307122 \tabularnewline
37 & 16.49 & 16.4862235133095 & 0.0037764866904908 \tabularnewline
38 & 16.54 & 16.4967033208297 & 0.0432966791702825 \tabularnewline
39 & 16.67 & 16.5522042199374 & 0.117795780062558 \tabularnewline
40 & 16.72 & 16.6971703262037 & 0.0228296737962559 \tabularnewline
41 & 16.79 & 16.7500708657976 & 0.0399291342024135 \tabularnewline
42 & 16.86 & 16.8251439139601 & 0.0348560860399303 \tabularnewline
43 & 16.84 & 16.8995724247898 & -0.0595724247897778 \tabularnewline
44 & 16.86 & 16.8720036711428 & -0.0120036711428178 \tabularnewline
45 & 16.96 & 16.8904785891932 & 0.0695214108067539 \tabularnewline
46 & 17.01 & 16.9993113743861 & 0.0106886256139056 \tabularnewline
47 & 17.02 & 17.0506693780998 & -0.0306693780997591 \tabularnewline
48 & 17.04 & 17.0567727939308 & -0.0167727939307944 \tabularnewline
49 & 17.04 & 17.0746417887605 & -0.0346417887605099 \tabularnewline
50 & 17.39 & 17.0702405046774 & 0.319759495322579 \tabularnewline
51 & 17.54 & 17.460866362277 & 0.079133637722979 \tabularnewline
52 & 17.57 & 17.6209203933363 & -0.0509203933362947 \tabularnewline
53 & 17.58 & 17.6444508914799 & -0.0644508914798827 \tabularnewline
54 & 17.56 & 17.646262322328 & -0.0862623223279684 \tabularnewline
55 & 17.63 & 17.6153025826662 & 0.0146974173337746 \tabularnewline
56 & 17.67 & 17.6871699085546 & -0.0171699085546422 \tabularnewline
57 & 17.71 & 17.7249884494576 & -0.0149884494575971 \tabularnewline
58 & 17.75 & 17.7630841475613 & -0.0130841475612975 \tabularnewline
59 & 17.82 & 17.8014217896848 & 0.0185782103152121 \tabularnewline
60 & 17.86 & 17.8737821753426 & -0.0137821753426408 \tabularnewline
61 & 17.89 & 17.9120311321334 & -0.022031132133371 \tabularnewline
62 & 17.96 & 17.939232048291 & 0.0207679517090149 \tabularnewline
63 & 18 & 18.0118706434261 & -0.0118706434261036 \tabularnewline
64 & 18.08 & 18.0503624628201 & 0.0296375371799442 \tabularnewline
65 & 18 & 18.1341279502651 & -0.13412795026511 \tabularnewline
66 & 18.02 & 18.0370868206433 & -0.0170868206433035 \tabularnewline
67 & 18.01 & 18.0549159179729 & -0.0449159179728937 \tabularnewline
68 & 18.02 & 18.0392092924803 & -0.0192092924802552 \tabularnewline
69 & 17.95 & 18.0467687270168 & -0.0967687270168121 \tabularnewline
70 & 17.96 & 17.9644741350457 & -0.00447413504570093 \tabularnewline
71 & 18 & 17.9739056903993 & 0.0260943096006869 \tabularnewline
72 & 18.01 & 18.017221006196 & -0.00722100619604049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210443&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]15.73[/C][C]15.74[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]15.74[/C][C]15.8087294870616[/C][C]-0.068729487061562[/C][/ROW]
[ROW][C]5[/C][C]15.77[/C][C]15.8099973168052[/C][C]-0.0399973168051648[/C][/ROW]
[ROW][C]6[/C][C]15.78[/C][C]15.8349156059548[/C][C]-0.0549156059547844[/C][/ROW]
[ROW][C]7[/C][C]15.8[/C][C]15.837938507166[/C][C]-0.0379385071660074[/C][/ROW]
[ROW][C]8[/C][C]15.81[/C][C]15.8531183707441[/C][C]-0.0431183707440628[/C][/ROW]
[ROW][C]9[/C][C]15.82[/C][C]15.8576401259526[/C][C]-0.0376401259525903[/C][/ROW]
[ROW][C]10[/C][C]15.88[/C][C]15.8628578992499[/C][C]0.0171421007501333[/C][/ROW]
[ROW][C]11[/C][C]15.85[/C][C]15.9250358253294[/C][C]-0.0750358253293744[/C][/ROW]
[ROW][C]12[/C][C]15.89[/C][C]15.8855024266366[/C][C]0.00449757336336631[/C][/ROW]
[ROW][C]13[/C][C]15.92[/C][C]15.9260738491516[/C][C]-0.00607384915160836[/C][/ROW]
[ROW][C]14[/C][C]16.02[/C][C]15.9553021587583[/C][C]0.064697841241717[/C][/ROW]
[ROW][C]15[/C][C]16.1[/C][C]16.0635221031969[/C][C]0.0364778968030528[/C][/ROW]
[ROW][C]16[/C][C]16.13[/C][C]16.1481566671825[/C][C]-0.0181566671824811[/C][/ROW]
[ROW][C]17[/C][C]16.21[/C][C]16.1758498391251[/C][C]0.0341501608749475[/C][/ROW]
[ROW][C]18[/C][C]16.25[/C][C]16.2601886612492[/C][C]-0.0101886612491917[/C][/ROW]
[ROW][C]19[/C][C]16.27[/C][C]16.2988941786549[/C][C]-0.0288941786549444[/C][/ROW]
[ROW][C]20[/C][C]16.21[/C][C]16.3152231358723[/C][C]-0.105223135872276[/C][/ROW]
[ROW][C]21[/C][C]16.21[/C][C]16.2418544003174[/C][C]-0.0318544003173962[/C][/ROW]
[ROW][C]22[/C][C]16.24[/C][C]16.2378072575424[/C][C]0.00219274245754875[/C][/ROW]
[ROW][C]23[/C][C]16.32[/C][C]16.2680858483087[/C][C]0.0519141516912534[/C][/ROW]
[ROW][C]24[/C][C]16.32[/C][C]16.3546816084499[/C][C]-0.0346816084499295[/C][/ROW]
[ROW][C]25[/C][C]16.36[/C][C]16.3502752652238[/C][C]0.0097247347762206[/C][/ROW]
[ROW][C]26[/C][C]16.48[/C][C]16.3915108053594[/C][C]0.0884891946406157[/C][/ROW]
[ROW][C]27[/C][C]16.54[/C][C]16.5227534720297[/C][C]0.0172465279703218[/C][/ROW]
[ROW][C]28[/C][C]16.58[/C][C]16.5849446657226[/C][C]-0.00494466572262198[/C][/ROW]
[ROW][C]29[/C][C]16.56[/C][C]16.6243164395449[/C][C]-0.0643164395449354[/C][/ROW]
[ROW][C]30[/C][C]16.55[/C][C]16.5961449526853[/C][C]-0.0461449526853208[/C][/ROW]
[ROW][C]31[/C][C]16.58[/C][C]16.5802821767423[/C][C]-0.000282176742288698[/C][/ROW]
[ROW][C]32[/C][C]16.53[/C][C]16.6102463258221[/C][C]-0.0802463258220847[/C][/ROW]
[ROW][C]33[/C][C]16.6[/C][C]16.5500509263002[/C][C]0.0499490736998247[/C][/ROW]
[ROW][C]34[/C][C]16.46[/C][C]16.62639702074[/C][C]-0.166397020740042[/C][/ROW]
[ROW][C]35[/C][C]16.48[/C][C]16.4652560639633[/C][C]0.0147439360367478[/C][/ROW]
[ROW][C]36[/C][C]16.48[/C][C]16.4871293001131[/C][C]-0.00712930011307122[/C][/ROW]
[ROW][C]37[/C][C]16.49[/C][C]16.4862235133095[/C][C]0.0037764866904908[/C][/ROW]
[ROW][C]38[/C][C]16.54[/C][C]16.4967033208297[/C][C]0.0432966791702825[/C][/ROW]
[ROW][C]39[/C][C]16.67[/C][C]16.5522042199374[/C][C]0.117795780062558[/C][/ROW]
[ROW][C]40[/C][C]16.72[/C][C]16.6971703262037[/C][C]0.0228296737962559[/C][/ROW]
[ROW][C]41[/C][C]16.79[/C][C]16.7500708657976[/C][C]0.0399291342024135[/C][/ROW]
[ROW][C]42[/C][C]16.86[/C][C]16.8251439139601[/C][C]0.0348560860399303[/C][/ROW]
[ROW][C]43[/C][C]16.84[/C][C]16.8995724247898[/C][C]-0.0595724247897778[/C][/ROW]
[ROW][C]44[/C][C]16.86[/C][C]16.8720036711428[/C][C]-0.0120036711428178[/C][/ROW]
[ROW][C]45[/C][C]16.96[/C][C]16.8904785891932[/C][C]0.0695214108067539[/C][/ROW]
[ROW][C]46[/C][C]17.01[/C][C]16.9993113743861[/C][C]0.0106886256139056[/C][/ROW]
[ROW][C]47[/C][C]17.02[/C][C]17.0506693780998[/C][C]-0.0306693780997591[/C][/ROW]
[ROW][C]48[/C][C]17.04[/C][C]17.0567727939308[/C][C]-0.0167727939307944[/C][/ROW]
[ROW][C]49[/C][C]17.04[/C][C]17.0746417887605[/C][C]-0.0346417887605099[/C][/ROW]
[ROW][C]50[/C][C]17.39[/C][C]17.0702405046774[/C][C]0.319759495322579[/C][/ROW]
[ROW][C]51[/C][C]17.54[/C][C]17.460866362277[/C][C]0.079133637722979[/C][/ROW]
[ROW][C]52[/C][C]17.57[/C][C]17.6209203933363[/C][C]-0.0509203933362947[/C][/ROW]
[ROW][C]53[/C][C]17.58[/C][C]17.6444508914799[/C][C]-0.0644508914798827[/C][/ROW]
[ROW][C]54[/C][C]17.56[/C][C]17.646262322328[/C][C]-0.0862623223279684[/C][/ROW]
[ROW][C]55[/C][C]17.63[/C][C]17.6153025826662[/C][C]0.0146974173337746[/C][/ROW]
[ROW][C]56[/C][C]17.67[/C][C]17.6871699085546[/C][C]-0.0171699085546422[/C][/ROW]
[ROW][C]57[/C][C]17.71[/C][C]17.7249884494576[/C][C]-0.0149884494575971[/C][/ROW]
[ROW][C]58[/C][C]17.75[/C][C]17.7630841475613[/C][C]-0.0130841475612975[/C][/ROW]
[ROW][C]59[/C][C]17.82[/C][C]17.8014217896848[/C][C]0.0185782103152121[/C][/ROW]
[ROW][C]60[/C][C]17.86[/C][C]17.8737821753426[/C][C]-0.0137821753426408[/C][/ROW]
[ROW][C]61[/C][C]17.89[/C][C]17.9120311321334[/C][C]-0.022031132133371[/C][/ROW]
[ROW][C]62[/C][C]17.96[/C][C]17.939232048291[/C][C]0.0207679517090149[/C][/ROW]
[ROW][C]63[/C][C]18[/C][C]18.0118706434261[/C][C]-0.0118706434261036[/C][/ROW]
[ROW][C]64[/C][C]18.08[/C][C]18.0503624628201[/C][C]0.0296375371799442[/C][/ROW]
[ROW][C]65[/C][C]18[/C][C]18.1341279502651[/C][C]-0.13412795026511[/C][/ROW]
[ROW][C]66[/C][C]18.02[/C][C]18.0370868206433[/C][C]-0.0170868206433035[/C][/ROW]
[ROW][C]67[/C][C]18.01[/C][C]18.0549159179729[/C][C]-0.0449159179728937[/C][/ROW]
[ROW][C]68[/C][C]18.02[/C][C]18.0392092924803[/C][C]-0.0192092924802552[/C][/ROW]
[ROW][C]69[/C][C]17.95[/C][C]18.0467687270168[/C][C]-0.0967687270168121[/C][/ROW]
[ROW][C]70[/C][C]17.96[/C][C]17.9644741350457[/C][C]-0.00447413504570093[/C][/ROW]
[ROW][C]71[/C][C]18[/C][C]17.9739056903993[/C][C]0.0260943096006869[/C][/ROW]
[ROW][C]72[/C][C]18.01[/C][C]18.017221006196[/C][C]-0.00722100619604049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210443&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210443&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
315.7315.74-0.00999999999999979
415.7415.8087294870616-0.068729487061562
515.7715.8099973168052-0.0399973168051648
615.7815.8349156059548-0.0549156059547844
715.815.837938507166-0.0379385071660074
815.8115.8531183707441-0.0431183707440628
915.8215.8576401259526-0.0376401259525903
1015.8815.86285789924990.0171421007501333
1115.8515.9250358253294-0.0750358253293744
1215.8915.88550242663660.00449757336336631
1315.9215.9260738491516-0.00607384915160836
1416.0215.95530215875830.064697841241717
1516.116.06352210319690.0364778968030528
1616.1316.1481566671825-0.0181566671824811
1716.2116.17584983912510.0341501608749475
1816.2516.2601886612492-0.0101886612491917
1916.2716.2988941786549-0.0288941786549444
2016.2116.3152231358723-0.105223135872276
2116.2116.2418544003174-0.0318544003173962
2216.2416.23780725754240.00219274245754875
2316.3216.26808584830870.0519141516912534
2416.3216.3546816084499-0.0346816084499295
2516.3616.35027526522380.0097247347762206
2616.4816.39151080535940.0884891946406157
2716.5416.52275347202970.0172465279703218
2816.5816.5849446657226-0.00494466572262198
2916.5616.6243164395449-0.0643164395449354
3016.5516.5961449526853-0.0461449526853208
3116.5816.5802821767423-0.000282176742288698
3216.5316.6102463258221-0.0802463258220847
3316.616.55005092630020.0499490736998247
3416.4616.62639702074-0.166397020740042
3516.4816.46525606396330.0147439360367478
3616.4816.4871293001131-0.00712930011307122
3716.4916.48622351330950.0037764866904908
3816.5416.49670332082970.0432966791702825
3916.6716.55220421993740.117795780062558
4016.7216.69717032620370.0228296737962559
4116.7916.75007086579760.0399291342024135
4216.8616.82514391396010.0348560860399303
4316.8416.8995724247898-0.0595724247897778
4416.8616.8720036711428-0.0120036711428178
4516.9616.89047858919320.0695214108067539
4617.0116.99931137438610.0106886256139056
4717.0217.0506693780998-0.0306693780997591
4817.0417.0567727939308-0.0167727939307944
4917.0417.0746417887605-0.0346417887605099
5017.3917.07024050467740.319759495322579
5117.5417.4608663622770.079133637722979
5217.5717.6209203933363-0.0509203933362947
5317.5817.6444508914799-0.0644508914798827
5417.5617.646262322328-0.0862623223279684
5517.6317.61530258266620.0146974173337746
5617.6717.6871699085546-0.0171699085546422
5717.7117.7249884494576-0.0149884494575971
5817.7517.7630841475613-0.0130841475612975
5917.8217.80142178968480.0185782103152121
6017.8617.8737821753426-0.0137821753426408
6117.8917.9120311321334-0.022031132133371
6217.9617.9392320482910.0207679517090149
631818.0118706434261-0.0118706434261036
6418.0818.05036246282010.0296375371799442
651818.1341279502651-0.13412795026511
6618.0218.0370868206433-0.0170868206433035
6718.0118.0549159179729-0.0449159179728937
6818.0218.0392092924803-0.0192092924802552
6917.9518.0467687270168-0.0967687270168121
7017.9617.9644741350457-0.00447413504570093
711817.97390569039930.0260943096006869
7218.0118.017221006196-0.00722100619604049







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7318.02630356801617.901693563061418.1509135729706
7418.04260713603217.854853117624118.2303611544398
7518.058910704047917.814630025295418.3031913828005
7618.075214272063917.776394284752818.374034259375
7718.091517840079917.738510939900918.4445247402589
7818.107821408095917.700223805042118.5154190111497
7918.124124976111917.661134172886218.5871157793375
8018.140428544127917.621016183017518.6598409052382
8118.156732112143817.579737092447218.7337271318404
8218.173035680159817.537218147180418.8088532131392
8318.189339248175817.493413573930618.885264922421
8418.205642816191817.448298525281318.9629871071023

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 18.026303568016 & 17.9016935630614 & 18.1509135729706 \tabularnewline
74 & 18.042607136032 & 17.8548531176241 & 18.2303611544398 \tabularnewline
75 & 18.0589107040479 & 17.8146300252954 & 18.3031913828005 \tabularnewline
76 & 18.0752142720639 & 17.7763942847528 & 18.374034259375 \tabularnewline
77 & 18.0915178400799 & 17.7385109399009 & 18.4445247402589 \tabularnewline
78 & 18.1078214080959 & 17.7002238050421 & 18.5154190111497 \tabularnewline
79 & 18.1241249761119 & 17.6611341728862 & 18.5871157793375 \tabularnewline
80 & 18.1404285441279 & 17.6210161830175 & 18.6598409052382 \tabularnewline
81 & 18.1567321121438 & 17.5797370924472 & 18.7337271318404 \tabularnewline
82 & 18.1730356801598 & 17.5372181471804 & 18.8088532131392 \tabularnewline
83 & 18.1893392481758 & 17.4934135739306 & 18.885264922421 \tabularnewline
84 & 18.2056428161918 & 17.4482985252813 & 18.9629871071023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210443&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]18.026303568016[/C][C]17.9016935630614[/C][C]18.1509135729706[/C][/ROW]
[ROW][C]74[/C][C]18.042607136032[/C][C]17.8548531176241[/C][C]18.2303611544398[/C][/ROW]
[ROW][C]75[/C][C]18.0589107040479[/C][C]17.8146300252954[/C][C]18.3031913828005[/C][/ROW]
[ROW][C]76[/C][C]18.0752142720639[/C][C]17.7763942847528[/C][C]18.374034259375[/C][/ROW]
[ROW][C]77[/C][C]18.0915178400799[/C][C]17.7385109399009[/C][C]18.4445247402589[/C][/ROW]
[ROW][C]78[/C][C]18.1078214080959[/C][C]17.7002238050421[/C][C]18.5154190111497[/C][/ROW]
[ROW][C]79[/C][C]18.1241249761119[/C][C]17.6611341728862[/C][C]18.5871157793375[/C][/ROW]
[ROW][C]80[/C][C]18.1404285441279[/C][C]17.6210161830175[/C][C]18.6598409052382[/C][/ROW]
[ROW][C]81[/C][C]18.1567321121438[/C][C]17.5797370924472[/C][C]18.7337271318404[/C][/ROW]
[ROW][C]82[/C][C]18.1730356801598[/C][C]17.5372181471804[/C][C]18.8088532131392[/C][/ROW]
[ROW][C]83[/C][C]18.1893392481758[/C][C]17.4934135739306[/C][C]18.885264922421[/C][/ROW]
[ROW][C]84[/C][C]18.2056428161918[/C][C]17.4482985252813[/C][C]18.9629871071023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210443&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210443&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
7318.02630356801617.901693563061418.1509135729706
7418.04260713603217.854853117624118.2303611544398
7518.058910704047917.814630025295418.3031913828005
7618.075214272063917.776394284752818.374034259375
7718.091517840079917.738510939900918.4445247402589
7818.107821408095917.700223805042118.5154190111497
7918.124124976111917.661134172886218.5871157793375
8018.140428544127917.621016183017518.6598409052382
8118.156732112143817.579737092447218.7337271318404
8218.173035680159817.537218147180418.8088532131392
8318.189339248175817.493413573930618.885264922421
8418.205642816191817.448298525281318.9629871071023



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')