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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 20:13:31 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/19/t1305835993euagxqvsptu9nq8.htm/, Retrieved Sat, 11 May 2024 12:54:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122215, Retrieved Sat, 11 May 2024 12:54:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [lynn.pelgrims@stu...] [2011-05-16 20:48:06] [74be16979710d4c4e7c6647856088456]
- R  D  [Classical Decomposition] [lynn.pelgrims@stu...] [2011-05-16 20:53:53] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [lynn.pelgrims@stu...] [2011-05-18 12:35:02] [74be16979710d4c4e7c6647856088456]
- R  D        [Exponential Smoothing] [lynn.pelgrims@stu...] [2011-05-19 20:13:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2851
2672
2755
2721
2946
3036
2282
2212
2922
4301
5764
7132
2541
2475
3031
3266
3776
3230
3028
1759
3595
4474
6838
8357
3113
3006
4047
3523
3937
3986
3260
1573
3528
5211
7614
9254
5375
3088
3718
4514
4520
4539
3663
1643
4734
5428
8314
10651
3633
4292
4154
4121
4647
4753
3965
1723
5048
6923
9858
11331
4016
3957
4510
4276
4968
4677
3523
1821
5222
6872
10803
13916
2639
2899
3370
3740
2927
3986
4217
1738
5221
6424
9842
13076
3934
3162
4286
4676
5010
4874
4633
1659
5951
6981
9851
12670




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 216.218.223.82

\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 & 'George Udny Yule' @ 216.218.223.82 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122215&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]'George Udny Yule' @ 216.218.223.82[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122215&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122215&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'George Udny Yule' @ 216.218.223.82







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.308920174800032
beta0
gamma0.63304779631648

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.308920174800032 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.63304779631648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122215&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]0.308920174800032[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.63304779631648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122215&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122215&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
alpha0.308920174800032
beta0
gamma0.63304779631648







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1325412393.50833868648147.491661313524
1424752389.8295795448685.1704204551402
1530312978.4674924846852.5325075153246
1632663224.6845259202741.3154740797308
1737763723.5455651142452.4544348857607
1832303146.0413451321783.9586548678344
1930282495.93638764876532.063612351243
2017592615.42697148435-856.426971484353
2135953129.98059337787465.019406622129
2244744811.19275455775-337.192754557747
2368386258.55829948475579.441700515249
2483577934.86975076983422.130249230167
2531132940.90516043429172.094839565706
2630062897.68831373255108.311686267446
2740473580.46589940871466.534100591291
2835233995.51499634823-472.514996348226
2939374423.94954379872-486.949543798717
3039863610.75875581215375.24124418785
3132603148.73441559458111.26558440542
3215732417.2388004176-844.238800417595
3335283625.06086969704-97.0608696970385
3452114817.25400517526393.745994824736
3576147041.6915738063572.308426193701
3692548751.14534360582502.854656394184
3753753252.87368814192122.1263118581
3830883743.2519181274-655.2519181274
3937184484.22248389336-766.222483893357
4045144085.57228718524428.427712814763
4145204862.05195726191-342.051957261911
4245394410.93535956836128.064640431644
4336633653.327241700519.6727582994904
4416432264.46469501254-621.464695012545
4547344149.69369766263584.306302337369
4654286067.62647796335-639.626477963354
4783148359.27994241763-45.2799424176301
481065110011.6052518353639.394748164725
4936334499.57305081962-866.57305081962
5042923012.538137174071279.46186282593
5141544324.06523554391-170.06523554391
5241214656.288978844-535.288978843996
5346474799.96689031067-152.966890310666
5447534607.06030980049145.939690199511
5539653774.97903745214190.020962547855
5617232059.85167444573-336.851674445727
5750484770.79937146954277.200628530462
5869236117.09990459278805.900095407219
5998589488.97632961112369.02367038888
601133111853.5444537716-522.544453771616
6140164563.31949339721-547.319493397212
6239573996.87204542113-39.8720454211334
6345104266.86126847803243.13873152197
6442764564.85778587997-288.857785879971
6549684974.17235853488-6.17235853488091
6646774953.99768781614-276.997687816143
6735233980.72313410983-457.72313410983
6818211867.19289066026-46.1928906602607
6952225009.48685230371212.513147696287
7068726581.45741871882290.542581281177
71108039580.81481040081222.18518959919
721391611851.27393113432064.72606886566
7326394698.39199842502-2059.39199842502
7428993891.23363939581-992.233639395808
7533703952.59002165526-582.590021655264
7637403766.1311848531-26.1311848531027
7729274299.77610625762-1372.77610625762
7839863773.76575338307212.234246616928
7942173055.869334976621161.13066502338
8017381733.602368269154.39763173084611
8152214830.86842062341390.131579376592
8264246427.33679785996-3.33679785996355
8398429546.13288845202295.867111547977
841307611678.24507540741397.75492459262
8539343308.1346526193625.865347380701
8631623785.80690373151-623.806903731512
8742864199.6714683831486.3285316168594
8846764505.69936087628170.30063912372
8950104415.17155919637594.828440803634
9048745415.26988008695-541.269880086954
9146334676.44951397193-43.4495139719284
9216592060.96806905497-401.968069054974
9359515568.76517552133382.234824478671
9469817129.87966154635-148.879661546348
95985110660.3884204093-809.388420409317
961267013071.0034899073-401.003489907263

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2541 & 2393.50833868648 & 147.491661313524 \tabularnewline
14 & 2475 & 2389.82957954486 & 85.1704204551402 \tabularnewline
15 & 3031 & 2978.46749248468 & 52.5325075153246 \tabularnewline
16 & 3266 & 3224.68452592027 & 41.3154740797308 \tabularnewline
17 & 3776 & 3723.54556511424 & 52.4544348857607 \tabularnewline
18 & 3230 & 3146.04134513217 & 83.9586548678344 \tabularnewline
19 & 3028 & 2495.93638764876 & 532.063612351243 \tabularnewline
20 & 1759 & 2615.42697148435 & -856.426971484353 \tabularnewline
21 & 3595 & 3129.98059337787 & 465.019406622129 \tabularnewline
22 & 4474 & 4811.19275455775 & -337.192754557747 \tabularnewline
23 & 6838 & 6258.55829948475 & 579.441700515249 \tabularnewline
24 & 8357 & 7934.86975076983 & 422.130249230167 \tabularnewline
25 & 3113 & 2940.90516043429 & 172.094839565706 \tabularnewline
26 & 3006 & 2897.68831373255 & 108.311686267446 \tabularnewline
27 & 4047 & 3580.46589940871 & 466.534100591291 \tabularnewline
28 & 3523 & 3995.51499634823 & -472.514996348226 \tabularnewline
29 & 3937 & 4423.94954379872 & -486.949543798717 \tabularnewline
30 & 3986 & 3610.75875581215 & 375.24124418785 \tabularnewline
31 & 3260 & 3148.73441559458 & 111.26558440542 \tabularnewline
32 & 1573 & 2417.2388004176 & -844.238800417595 \tabularnewline
33 & 3528 & 3625.06086969704 & -97.0608696970385 \tabularnewline
34 & 5211 & 4817.25400517526 & 393.745994824736 \tabularnewline
35 & 7614 & 7041.6915738063 & 572.308426193701 \tabularnewline
36 & 9254 & 8751.14534360582 & 502.854656394184 \tabularnewline
37 & 5375 & 3252.8736881419 & 2122.1263118581 \tabularnewline
38 & 3088 & 3743.2519181274 & -655.2519181274 \tabularnewline
39 & 3718 & 4484.22248389336 & -766.222483893357 \tabularnewline
40 & 4514 & 4085.57228718524 & 428.427712814763 \tabularnewline
41 & 4520 & 4862.05195726191 & -342.051957261911 \tabularnewline
42 & 4539 & 4410.93535956836 & 128.064640431644 \tabularnewline
43 & 3663 & 3653.32724170051 & 9.6727582994904 \tabularnewline
44 & 1643 & 2264.46469501254 & -621.464695012545 \tabularnewline
45 & 4734 & 4149.69369766263 & 584.306302337369 \tabularnewline
46 & 5428 & 6067.62647796335 & -639.626477963354 \tabularnewline
47 & 8314 & 8359.27994241763 & -45.2799424176301 \tabularnewline
48 & 10651 & 10011.6052518353 & 639.394748164725 \tabularnewline
49 & 3633 & 4499.57305081962 & -866.57305081962 \tabularnewline
50 & 4292 & 3012.53813717407 & 1279.46186282593 \tabularnewline
51 & 4154 & 4324.06523554391 & -170.06523554391 \tabularnewline
52 & 4121 & 4656.288978844 & -535.288978843996 \tabularnewline
53 & 4647 & 4799.96689031067 & -152.966890310666 \tabularnewline
54 & 4753 & 4607.06030980049 & 145.939690199511 \tabularnewline
55 & 3965 & 3774.97903745214 & 190.020962547855 \tabularnewline
56 & 1723 & 2059.85167444573 & -336.851674445727 \tabularnewline
57 & 5048 & 4770.79937146954 & 277.200628530462 \tabularnewline
58 & 6923 & 6117.09990459278 & 805.900095407219 \tabularnewline
59 & 9858 & 9488.97632961112 & 369.02367038888 \tabularnewline
60 & 11331 & 11853.5444537716 & -522.544453771616 \tabularnewline
61 & 4016 & 4563.31949339721 & -547.319493397212 \tabularnewline
62 & 3957 & 3996.87204542113 & -39.8720454211334 \tabularnewline
63 & 4510 & 4266.86126847803 & 243.13873152197 \tabularnewline
64 & 4276 & 4564.85778587997 & -288.857785879971 \tabularnewline
65 & 4968 & 4974.17235853488 & -6.17235853488091 \tabularnewline
66 & 4677 & 4953.99768781614 & -276.997687816143 \tabularnewline
67 & 3523 & 3980.72313410983 & -457.72313410983 \tabularnewline
68 & 1821 & 1867.19289066026 & -46.1928906602607 \tabularnewline
69 & 5222 & 5009.48685230371 & 212.513147696287 \tabularnewline
70 & 6872 & 6581.45741871882 & 290.542581281177 \tabularnewline
71 & 10803 & 9580.8148104008 & 1222.18518959919 \tabularnewline
72 & 13916 & 11851.2739311343 & 2064.72606886566 \tabularnewline
73 & 2639 & 4698.39199842502 & -2059.39199842502 \tabularnewline
74 & 2899 & 3891.23363939581 & -992.233639395808 \tabularnewline
75 & 3370 & 3952.59002165526 & -582.590021655264 \tabularnewline
76 & 3740 & 3766.1311848531 & -26.1311848531027 \tabularnewline
77 & 2927 & 4299.77610625762 & -1372.77610625762 \tabularnewline
78 & 3986 & 3773.76575338307 & 212.234246616928 \tabularnewline
79 & 4217 & 3055.86933497662 & 1161.13066502338 \tabularnewline
80 & 1738 & 1733.60236826915 & 4.39763173084611 \tabularnewline
81 & 5221 & 4830.86842062341 & 390.131579376592 \tabularnewline
82 & 6424 & 6427.33679785996 & -3.33679785996355 \tabularnewline
83 & 9842 & 9546.13288845202 & 295.867111547977 \tabularnewline
84 & 13076 & 11678.2450754074 & 1397.75492459262 \tabularnewline
85 & 3934 & 3308.1346526193 & 625.865347380701 \tabularnewline
86 & 3162 & 3785.80690373151 & -623.806903731512 \tabularnewline
87 & 4286 & 4199.67146838314 & 86.3285316168594 \tabularnewline
88 & 4676 & 4505.69936087628 & 170.30063912372 \tabularnewline
89 & 5010 & 4415.17155919637 & 594.828440803634 \tabularnewline
90 & 4874 & 5415.26988008695 & -541.269880086954 \tabularnewline
91 & 4633 & 4676.44951397193 & -43.4495139719284 \tabularnewline
92 & 1659 & 2060.96806905497 & -401.968069054974 \tabularnewline
93 & 5951 & 5568.76517552133 & 382.234824478671 \tabularnewline
94 & 6981 & 7129.87966154635 & -148.879661546348 \tabularnewline
95 & 9851 & 10660.3884204093 & -809.388420409317 \tabularnewline
96 & 12670 & 13071.0034899073 & -401.003489907263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122215&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]13[/C][C]2541[/C][C]2393.50833868648[/C][C]147.491661313524[/C][/ROW]
[ROW][C]14[/C][C]2475[/C][C]2389.82957954486[/C][C]85.1704204551402[/C][/ROW]
[ROW][C]15[/C][C]3031[/C][C]2978.46749248468[/C][C]52.5325075153246[/C][/ROW]
[ROW][C]16[/C][C]3266[/C][C]3224.68452592027[/C][C]41.3154740797308[/C][/ROW]
[ROW][C]17[/C][C]3776[/C][C]3723.54556511424[/C][C]52.4544348857607[/C][/ROW]
[ROW][C]18[/C][C]3230[/C][C]3146.04134513217[/C][C]83.9586548678344[/C][/ROW]
[ROW][C]19[/C][C]3028[/C][C]2495.93638764876[/C][C]532.063612351243[/C][/ROW]
[ROW][C]20[/C][C]1759[/C][C]2615.42697148435[/C][C]-856.426971484353[/C][/ROW]
[ROW][C]21[/C][C]3595[/C][C]3129.98059337787[/C][C]465.019406622129[/C][/ROW]
[ROW][C]22[/C][C]4474[/C][C]4811.19275455775[/C][C]-337.192754557747[/C][/ROW]
[ROW][C]23[/C][C]6838[/C][C]6258.55829948475[/C][C]579.441700515249[/C][/ROW]
[ROW][C]24[/C][C]8357[/C][C]7934.86975076983[/C][C]422.130249230167[/C][/ROW]
[ROW][C]25[/C][C]3113[/C][C]2940.90516043429[/C][C]172.094839565706[/C][/ROW]
[ROW][C]26[/C][C]3006[/C][C]2897.68831373255[/C][C]108.311686267446[/C][/ROW]
[ROW][C]27[/C][C]4047[/C][C]3580.46589940871[/C][C]466.534100591291[/C][/ROW]
[ROW][C]28[/C][C]3523[/C][C]3995.51499634823[/C][C]-472.514996348226[/C][/ROW]
[ROW][C]29[/C][C]3937[/C][C]4423.94954379872[/C][C]-486.949543798717[/C][/ROW]
[ROW][C]30[/C][C]3986[/C][C]3610.75875581215[/C][C]375.24124418785[/C][/ROW]
[ROW][C]31[/C][C]3260[/C][C]3148.73441559458[/C][C]111.26558440542[/C][/ROW]
[ROW][C]32[/C][C]1573[/C][C]2417.2388004176[/C][C]-844.238800417595[/C][/ROW]
[ROW][C]33[/C][C]3528[/C][C]3625.06086969704[/C][C]-97.0608696970385[/C][/ROW]
[ROW][C]34[/C][C]5211[/C][C]4817.25400517526[/C][C]393.745994824736[/C][/ROW]
[ROW][C]35[/C][C]7614[/C][C]7041.6915738063[/C][C]572.308426193701[/C][/ROW]
[ROW][C]36[/C][C]9254[/C][C]8751.14534360582[/C][C]502.854656394184[/C][/ROW]
[ROW][C]37[/C][C]5375[/C][C]3252.8736881419[/C][C]2122.1263118581[/C][/ROW]
[ROW][C]38[/C][C]3088[/C][C]3743.2519181274[/C][C]-655.2519181274[/C][/ROW]
[ROW][C]39[/C][C]3718[/C][C]4484.22248389336[/C][C]-766.222483893357[/C][/ROW]
[ROW][C]40[/C][C]4514[/C][C]4085.57228718524[/C][C]428.427712814763[/C][/ROW]
[ROW][C]41[/C][C]4520[/C][C]4862.05195726191[/C][C]-342.051957261911[/C][/ROW]
[ROW][C]42[/C][C]4539[/C][C]4410.93535956836[/C][C]128.064640431644[/C][/ROW]
[ROW][C]43[/C][C]3663[/C][C]3653.32724170051[/C][C]9.6727582994904[/C][/ROW]
[ROW][C]44[/C][C]1643[/C][C]2264.46469501254[/C][C]-621.464695012545[/C][/ROW]
[ROW][C]45[/C][C]4734[/C][C]4149.69369766263[/C][C]584.306302337369[/C][/ROW]
[ROW][C]46[/C][C]5428[/C][C]6067.62647796335[/C][C]-639.626477963354[/C][/ROW]
[ROW][C]47[/C][C]8314[/C][C]8359.27994241763[/C][C]-45.2799424176301[/C][/ROW]
[ROW][C]48[/C][C]10651[/C][C]10011.6052518353[/C][C]639.394748164725[/C][/ROW]
[ROW][C]49[/C][C]3633[/C][C]4499.57305081962[/C][C]-866.57305081962[/C][/ROW]
[ROW][C]50[/C][C]4292[/C][C]3012.53813717407[/C][C]1279.46186282593[/C][/ROW]
[ROW][C]51[/C][C]4154[/C][C]4324.06523554391[/C][C]-170.06523554391[/C][/ROW]
[ROW][C]52[/C][C]4121[/C][C]4656.288978844[/C][C]-535.288978843996[/C][/ROW]
[ROW][C]53[/C][C]4647[/C][C]4799.96689031067[/C][C]-152.966890310666[/C][/ROW]
[ROW][C]54[/C][C]4753[/C][C]4607.06030980049[/C][C]145.939690199511[/C][/ROW]
[ROW][C]55[/C][C]3965[/C][C]3774.97903745214[/C][C]190.020962547855[/C][/ROW]
[ROW][C]56[/C][C]1723[/C][C]2059.85167444573[/C][C]-336.851674445727[/C][/ROW]
[ROW][C]57[/C][C]5048[/C][C]4770.79937146954[/C][C]277.200628530462[/C][/ROW]
[ROW][C]58[/C][C]6923[/C][C]6117.09990459278[/C][C]805.900095407219[/C][/ROW]
[ROW][C]59[/C][C]9858[/C][C]9488.97632961112[/C][C]369.02367038888[/C][/ROW]
[ROW][C]60[/C][C]11331[/C][C]11853.5444537716[/C][C]-522.544453771616[/C][/ROW]
[ROW][C]61[/C][C]4016[/C][C]4563.31949339721[/C][C]-547.319493397212[/C][/ROW]
[ROW][C]62[/C][C]3957[/C][C]3996.87204542113[/C][C]-39.8720454211334[/C][/ROW]
[ROW][C]63[/C][C]4510[/C][C]4266.86126847803[/C][C]243.13873152197[/C][/ROW]
[ROW][C]64[/C][C]4276[/C][C]4564.85778587997[/C][C]-288.857785879971[/C][/ROW]
[ROW][C]65[/C][C]4968[/C][C]4974.17235853488[/C][C]-6.17235853488091[/C][/ROW]
[ROW][C]66[/C][C]4677[/C][C]4953.99768781614[/C][C]-276.997687816143[/C][/ROW]
[ROW][C]67[/C][C]3523[/C][C]3980.72313410983[/C][C]-457.72313410983[/C][/ROW]
[ROW][C]68[/C][C]1821[/C][C]1867.19289066026[/C][C]-46.1928906602607[/C][/ROW]
[ROW][C]69[/C][C]5222[/C][C]5009.48685230371[/C][C]212.513147696287[/C][/ROW]
[ROW][C]70[/C][C]6872[/C][C]6581.45741871882[/C][C]290.542581281177[/C][/ROW]
[ROW][C]71[/C][C]10803[/C][C]9580.8148104008[/C][C]1222.18518959919[/C][/ROW]
[ROW][C]72[/C][C]13916[/C][C]11851.2739311343[/C][C]2064.72606886566[/C][/ROW]
[ROW][C]73[/C][C]2639[/C][C]4698.39199842502[/C][C]-2059.39199842502[/C][/ROW]
[ROW][C]74[/C][C]2899[/C][C]3891.23363939581[/C][C]-992.233639395808[/C][/ROW]
[ROW][C]75[/C][C]3370[/C][C]3952.59002165526[/C][C]-582.590021655264[/C][/ROW]
[ROW][C]76[/C][C]3740[/C][C]3766.1311848531[/C][C]-26.1311848531027[/C][/ROW]
[ROW][C]77[/C][C]2927[/C][C]4299.77610625762[/C][C]-1372.77610625762[/C][/ROW]
[ROW][C]78[/C][C]3986[/C][C]3773.76575338307[/C][C]212.234246616928[/C][/ROW]
[ROW][C]79[/C][C]4217[/C][C]3055.86933497662[/C][C]1161.13066502338[/C][/ROW]
[ROW][C]80[/C][C]1738[/C][C]1733.60236826915[/C][C]4.39763173084611[/C][/ROW]
[ROW][C]81[/C][C]5221[/C][C]4830.86842062341[/C][C]390.131579376592[/C][/ROW]
[ROW][C]82[/C][C]6424[/C][C]6427.33679785996[/C][C]-3.33679785996355[/C][/ROW]
[ROW][C]83[/C][C]9842[/C][C]9546.13288845202[/C][C]295.867111547977[/C][/ROW]
[ROW][C]84[/C][C]13076[/C][C]11678.2450754074[/C][C]1397.75492459262[/C][/ROW]
[ROW][C]85[/C][C]3934[/C][C]3308.1346526193[/C][C]625.865347380701[/C][/ROW]
[ROW][C]86[/C][C]3162[/C][C]3785.80690373151[/C][C]-623.806903731512[/C][/ROW]
[ROW][C]87[/C][C]4286[/C][C]4199.67146838314[/C][C]86.3285316168594[/C][/ROW]
[ROW][C]88[/C][C]4676[/C][C]4505.69936087628[/C][C]170.30063912372[/C][/ROW]
[ROW][C]89[/C][C]5010[/C][C]4415.17155919637[/C][C]594.828440803634[/C][/ROW]
[ROW][C]90[/C][C]4874[/C][C]5415.26988008695[/C][C]-541.269880086954[/C][/ROW]
[ROW][C]91[/C][C]4633[/C][C]4676.44951397193[/C][C]-43.4495139719284[/C][/ROW]
[ROW][C]92[/C][C]1659[/C][C]2060.96806905497[/C][C]-401.968069054974[/C][/ROW]
[ROW][C]93[/C][C]5951[/C][C]5568.76517552133[/C][C]382.234824478671[/C][/ROW]
[ROW][C]94[/C][C]6981[/C][C]7129.87966154635[/C][C]-148.879661546348[/C][/ROW]
[ROW][C]95[/C][C]9851[/C][C]10660.3884204093[/C][C]-809.388420409317[/C][/ROW]
[ROW][C]96[/C][C]12670[/C][C]13071.0034899073[/C][C]-401.003489907263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122215&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122215&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
1325412393.50833868648147.491661313524
1424752389.8295795448685.1704204551402
1530312978.4674924846852.5325075153246
1632663224.6845259202741.3154740797308
1737763723.5455651142452.4544348857607
1832303146.0413451321783.9586548678344
1930282495.93638764876532.063612351243
2017592615.42697148435-856.426971484353
2135953129.98059337787465.019406622129
2244744811.19275455775-337.192754557747
2368386258.55829948475579.441700515249
2483577934.86975076983422.130249230167
2531132940.90516043429172.094839565706
2630062897.68831373255108.311686267446
2740473580.46589940871466.534100591291
2835233995.51499634823-472.514996348226
2939374423.94954379872-486.949543798717
3039863610.75875581215375.24124418785
3132603148.73441559458111.26558440542
3215732417.2388004176-844.238800417595
3335283625.06086969704-97.0608696970385
3452114817.25400517526393.745994824736
3576147041.6915738063572.308426193701
3692548751.14534360582502.854656394184
3753753252.87368814192122.1263118581
3830883743.2519181274-655.2519181274
3937184484.22248389336-766.222483893357
4045144085.57228718524428.427712814763
4145204862.05195726191-342.051957261911
4245394410.93535956836128.064640431644
4336633653.327241700519.6727582994904
4416432264.46469501254-621.464695012545
4547344149.69369766263584.306302337369
4654286067.62647796335-639.626477963354
4783148359.27994241763-45.2799424176301
481065110011.6052518353639.394748164725
4936334499.57305081962-866.57305081962
5042923012.538137174071279.46186282593
5141544324.06523554391-170.06523554391
5241214656.288978844-535.288978843996
5346474799.96689031067-152.966890310666
5447534607.06030980049145.939690199511
5539653774.97903745214190.020962547855
5617232059.85167444573-336.851674445727
5750484770.79937146954277.200628530462
5869236117.09990459278805.900095407219
5998589488.97632961112369.02367038888
601133111853.5444537716-522.544453771616
6140164563.31949339721-547.319493397212
6239573996.87204542113-39.8720454211334
6345104266.86126847803243.13873152197
6442764564.85778587997-288.857785879971
6549684974.17235853488-6.17235853488091
6646774953.99768781614-276.997687816143
6735233980.72313410983-457.72313410983
6818211867.19289066026-46.1928906602607
6952225009.48685230371212.513147696287
7068726581.45741871882290.542581281177
71108039580.81481040081222.18518959919
721391611851.27393113432064.72606886566
7326394698.39199842502-2059.39199842502
7428993891.23363939581-992.233639395808
7533703952.59002165526-582.590021655264
7637403766.1311848531-26.1311848531027
7729274299.77610625762-1372.77610625762
7839863773.76575338307212.234246616928
7942173055.869334976621161.13066502338
8017381733.602368269154.39763173084611
8152214830.86842062341390.131579376592
8264246427.33679785996-3.33679785996355
8398429546.13288845202295.867111547977
841307611678.24507540741397.75492459262
8539343308.1346526193625.865347380701
8631623785.80690373151-623.806903731512
8742864199.6714683831486.3285316168594
8846764505.69936087628170.30063912372
8950104415.17155919637594.828440803634
9048745415.26988008695-541.269880086954
9146334676.44951397193-43.4495139719284
9216592060.96806905497-401.968069054974
9359515568.76517552133382.234824478671
9469817129.87966154635-148.879661546348
95985110660.3884204093-809.388420409317
961267013071.0034899073-401.003489907263







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
973629.692575287392668.826936215894590.55821435889
983364.115703800352335.755158711774392.47624888892
994292.922766624163112.292387372785473.55314587553
1004610.108303348853329.485540716085890.73106598162
1014642.272169646613300.561058808025983.98328048519
1024941.392964319423498.26807942526384.51784921364
1034592.815878060673161.560507428196024.07124869315
1041853.29345270853790.3399742864992916.24693113056
1056031.389223646953853.537276077328209.24117121658
1067277.068458811184698.452628371499855.68428925086
10710674.58962682137008.036445917314341.1428077252
10813682.04007233419142.9390331587918221.1411115094

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 3629.69257528739 & 2668.82693621589 & 4590.55821435889 \tabularnewline
98 & 3364.11570380035 & 2335.75515871177 & 4392.47624888892 \tabularnewline
99 & 4292.92276662416 & 3112.29238737278 & 5473.55314587553 \tabularnewline
100 & 4610.10830334885 & 3329.48554071608 & 5890.73106598162 \tabularnewline
101 & 4642.27216964661 & 3300.56105880802 & 5983.98328048519 \tabularnewline
102 & 4941.39296431942 & 3498.2680794252 & 6384.51784921364 \tabularnewline
103 & 4592.81587806067 & 3161.56050742819 & 6024.07124869315 \tabularnewline
104 & 1853.29345270853 & 790.339974286499 & 2916.24693113056 \tabularnewline
105 & 6031.38922364695 & 3853.53727607732 & 8209.24117121658 \tabularnewline
106 & 7277.06845881118 & 4698.45262837149 & 9855.68428925086 \tabularnewline
107 & 10674.5896268213 & 7008.0364459173 & 14341.1428077252 \tabularnewline
108 & 13682.0400723341 & 9142.93903315879 & 18221.1411115094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122215&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]97[/C][C]3629.69257528739[/C][C]2668.82693621589[/C][C]4590.55821435889[/C][/ROW]
[ROW][C]98[/C][C]3364.11570380035[/C][C]2335.75515871177[/C][C]4392.47624888892[/C][/ROW]
[ROW][C]99[/C][C]4292.92276662416[/C][C]3112.29238737278[/C][C]5473.55314587553[/C][/ROW]
[ROW][C]100[/C][C]4610.10830334885[/C][C]3329.48554071608[/C][C]5890.73106598162[/C][/ROW]
[ROW][C]101[/C][C]4642.27216964661[/C][C]3300.56105880802[/C][C]5983.98328048519[/C][/ROW]
[ROW][C]102[/C][C]4941.39296431942[/C][C]3498.2680794252[/C][C]6384.51784921364[/C][/ROW]
[ROW][C]103[/C][C]4592.81587806067[/C][C]3161.56050742819[/C][C]6024.07124869315[/C][/ROW]
[ROW][C]104[/C][C]1853.29345270853[/C][C]790.339974286499[/C][C]2916.24693113056[/C][/ROW]
[ROW][C]105[/C][C]6031.38922364695[/C][C]3853.53727607732[/C][C]8209.24117121658[/C][/ROW]
[ROW][C]106[/C][C]7277.06845881118[/C][C]4698.45262837149[/C][C]9855.68428925086[/C][/ROW]
[ROW][C]107[/C][C]10674.5896268213[/C][C]7008.0364459173[/C][C]14341.1428077252[/C][/ROW]
[ROW][C]108[/C][C]13682.0400723341[/C][C]9142.93903315879[/C][C]18221.1411115094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122215&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122215&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
973629.692575287392668.826936215894590.55821435889
983364.115703800352335.755158711774392.47624888892
994292.922766624163112.292387372785473.55314587553
1004610.108303348853329.485540716085890.73106598162
1014642.272169646613300.561058808025983.98328048519
1024941.392964319423498.26807942526384.51784921364
1034592.815878060673161.560507428196024.07124869315
1041853.29345270853790.3399742864992916.24693113056
1056031.389223646953853.537276077328209.24117121658
1067277.068458811184698.452628371499855.68428925086
10710674.58962682137008.036445917314341.1428077252
10813682.04007233419142.9390331587918221.1411115094



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')