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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 24 Dec 2010 14:38:01 +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/2010/Dec/24/t1293201372vf9uoe46njhcimo.htm/, Retrieved Tue, 30 Apr 2024 00:28:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115014, Retrieved Tue, 30 Apr 2024 00:28:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact173
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
-    D    [Exponential Smoothing] [Exponential Smoot...] [2010-12-12 11:16:02] [aeb27d5c05332f2e597ad139ee63fbe4]
-   PD        [Exponential Smoothing] [Exponential Smoot...] [2010-12-24 14:38:01] [18ef3d986e8801a4b28404e69e5bf56b] [Current]
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Dataseries X:
44164
40399
36763
37903
35532
35533
32110
33374
35462
33508
36080
34560
38737
38144
37594
36424
36843
37246
38661
40454
44928
48441
48140
45998
47369
49554
47510
44873
45344
42413
36912
43452
42142
44382
43636
44167
44423
42868
43908
42013
38846
35087
33026
34646
37135
37985
43121
43722
43630
42234
39351
39327
35704
30466
28155
29257
29998
32529
34787
33855
34556
31348
30805
28353
24514
21106
21346
23335
24379
26290
30084
29429
30632
27349
27264
27474
24482
21453
18788
19282
19713
21917
23812
23785
24696
24562
23580
24939
23899
21454
19761
19815
20780
23462
25005
24725
26198
27543
26471
26558
25317
22896




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115014&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115014&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115014&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.855314864777257
beta0.0252228018917085
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.855314864777257 \tabularnewline
beta & 0.0252228018917085 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115014&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]0.855314864777257[/C][/ROW]
[ROW][C]beta[/C][C]0.0252228018917085[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115014&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115014&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
alpha0.855314864777257
beta0.0252228018917085
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133873738442.7943376068294.205662393157
143814437937.7174870782206.282512921782
153759437283.4305493924310.569450607611
163642435777.8334969757646.166503024266
173684336054.1342913292788.865708670812
183724636599.1313824386646.86861756137
193866136911.42309705381749.57690294621
204045440489.9969874451-35.9969874451199
214492843103.81640847171824.18359152826
224844143273.69650702945167.30349297063
234814050920.4732504005-2780.4732504005
244599847484.4140376552-1486.41403765516
254736950644.3496980102-3275.34969801022
264955447154.60818547822399.39181452175
274751048519.6721805846-1009.67218058464
284487346033.3897680229-1160.38976802291
294534444846.1699821568497.83001784324
304241345176.4238107366-2763.42381073661
313691242712.5442437365-5800.54424373655
324345239393.31624904314058.68375095692
334214245685.1287516123-3543.12875161225
344438241538.78649826452843.21350173555
354363645788.4906863834-2152.49068638339
364416742831.01448433761335.98551566244
374442347961.2759558062-3538.27595580615
384286844877.1461433188-2009.14614331885
394390841692.61958200562215.38041799444
404201341726.8798484619286.120151538118
413884641831.9212902576-2985.92129025756
423508738450.5794353890-3363.57943538904
433302634760.9677878567-1734.96778785666
443464636160.2960914411-1514.2960914411
453713536280.0830782005854.916921799471
463798536608.84067513561376.15932486445
474312138638.67529826094482.32470173906
484372241761.64956401741960.35043598259
494363046635.0397405614-3005.03974056143
504223444154.0741689972-1920.07416899723
513935141584.717002687-2233.71700268699
523932737366.23911777131960.76088222873
533570438298.1139580916-2594.11395809161
543046635073.6058965703-4607.60589657035
552815530405.1145719043-2250.11457190428
562925731234.1633517367-1977.16335173673
572999831129.2626216296-1131.26262162965
583252929620.19826459132908.80173540870
593478733228.97595257141558.02404742860
603385533241.4082660266613.5917339734
613455635970.9713958884-1414.97139588836
623134834767.7903853884-3419.7903853884
633080530598.767235971206.232764029002
642835328855.1744048542-502.174404854162
652451426749.3885697929-2235.38856979291
662110623276.0674204115-2170.0674204115
672134620821.8051312095524.194868790517
682333523911.3775826198-576.377582619753
692437925005.3223520738-626.322352073832
702629024401.91481585491888.0851841451
713008426809.43729239993274.56270760011
722942928057.65324022131371.34675977875
733063231062.4278767054-430.427876705362
742734930353.1093545012-3004.10935450122
752726427015.058976107248.941023893000
762747425157.22348805342316.77651194663
772448225224.2967310677-742.29673106769
782145323082.2401301385-1629.24013013846
791878821536.7925738898-2748.79257388979
801928221653.5015583878-2371.50155838779
811971321151.9046658262-1438.90466582622
822191720146.83142281221770.16857718777
832381222581.10752467911230.89247532091
842378521688.89265965242096.10734034764
852469624951.4291364799-255.429136479881
862456223921.7448591370640.255140862955
872358024152.3917831075-572.391783107512
882493921854.47436454583084.52563545419
892389922115.4065781821783.59342181799
902145422039.7401379344-585.740137934441
911976121281.6292132008-1520.62921320078
921981522586.6868569339-2771.68685693386
932078021952.3989437535-1172.39894375353
942346221719.98715337511742.01284662486
952500524131.9585396449873.041460355107
962472523130.93457042231594.06542957765
972619825685.0864539043512.913546095737
982754325519.99677655962023.00322344036
992647126865.5348163776-394.5348163776
1002655825360.33779335211197.66220664792
1012531723889.97108212151427.02891787852
1022289623229.6190197624-333.619019762369

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 38737 & 38442.7943376068 & 294.205662393157 \tabularnewline
14 & 38144 & 37937.7174870782 & 206.282512921782 \tabularnewline
15 & 37594 & 37283.4305493924 & 310.569450607611 \tabularnewline
16 & 36424 & 35777.8334969757 & 646.166503024266 \tabularnewline
17 & 36843 & 36054.1342913292 & 788.865708670812 \tabularnewline
18 & 37246 & 36599.1313824386 & 646.86861756137 \tabularnewline
19 & 38661 & 36911.4230970538 & 1749.57690294621 \tabularnewline
20 & 40454 & 40489.9969874451 & -35.9969874451199 \tabularnewline
21 & 44928 & 43103.8164084717 & 1824.18359152826 \tabularnewline
22 & 48441 & 43273.6965070294 & 5167.30349297063 \tabularnewline
23 & 48140 & 50920.4732504005 & -2780.4732504005 \tabularnewline
24 & 45998 & 47484.4140376552 & -1486.41403765516 \tabularnewline
25 & 47369 & 50644.3496980102 & -3275.34969801022 \tabularnewline
26 & 49554 & 47154.6081854782 & 2399.39181452175 \tabularnewline
27 & 47510 & 48519.6721805846 & -1009.67218058464 \tabularnewline
28 & 44873 & 46033.3897680229 & -1160.38976802291 \tabularnewline
29 & 45344 & 44846.1699821568 & 497.83001784324 \tabularnewline
30 & 42413 & 45176.4238107366 & -2763.42381073661 \tabularnewline
31 & 36912 & 42712.5442437365 & -5800.54424373655 \tabularnewline
32 & 43452 & 39393.3162490431 & 4058.68375095692 \tabularnewline
33 & 42142 & 45685.1287516123 & -3543.12875161225 \tabularnewline
34 & 44382 & 41538.7864982645 & 2843.21350173555 \tabularnewline
35 & 43636 & 45788.4906863834 & -2152.49068638339 \tabularnewline
36 & 44167 & 42831.0144843376 & 1335.98551566244 \tabularnewline
37 & 44423 & 47961.2759558062 & -3538.27595580615 \tabularnewline
38 & 42868 & 44877.1461433188 & -2009.14614331885 \tabularnewline
39 & 43908 & 41692.6195820056 & 2215.38041799444 \tabularnewline
40 & 42013 & 41726.8798484619 & 286.120151538118 \tabularnewline
41 & 38846 & 41831.9212902576 & -2985.92129025756 \tabularnewline
42 & 35087 & 38450.5794353890 & -3363.57943538904 \tabularnewline
43 & 33026 & 34760.9677878567 & -1734.96778785666 \tabularnewline
44 & 34646 & 36160.2960914411 & -1514.2960914411 \tabularnewline
45 & 37135 & 36280.0830782005 & 854.916921799471 \tabularnewline
46 & 37985 & 36608.8406751356 & 1376.15932486445 \tabularnewline
47 & 43121 & 38638.6752982609 & 4482.32470173906 \tabularnewline
48 & 43722 & 41761.6495640174 & 1960.35043598259 \tabularnewline
49 & 43630 & 46635.0397405614 & -3005.03974056143 \tabularnewline
50 & 42234 & 44154.0741689972 & -1920.07416899723 \tabularnewline
51 & 39351 & 41584.717002687 & -2233.71700268699 \tabularnewline
52 & 39327 & 37366.2391177713 & 1960.76088222873 \tabularnewline
53 & 35704 & 38298.1139580916 & -2594.11395809161 \tabularnewline
54 & 30466 & 35073.6058965703 & -4607.60589657035 \tabularnewline
55 & 28155 & 30405.1145719043 & -2250.11457190428 \tabularnewline
56 & 29257 & 31234.1633517367 & -1977.16335173673 \tabularnewline
57 & 29998 & 31129.2626216296 & -1131.26262162965 \tabularnewline
58 & 32529 & 29620.1982645913 & 2908.80173540870 \tabularnewline
59 & 34787 & 33228.9759525714 & 1558.02404742860 \tabularnewline
60 & 33855 & 33241.4082660266 & 613.5917339734 \tabularnewline
61 & 34556 & 35970.9713958884 & -1414.97139588836 \tabularnewline
62 & 31348 & 34767.7903853884 & -3419.7903853884 \tabularnewline
63 & 30805 & 30598.767235971 & 206.232764029002 \tabularnewline
64 & 28353 & 28855.1744048542 & -502.174404854162 \tabularnewline
65 & 24514 & 26749.3885697929 & -2235.38856979291 \tabularnewline
66 & 21106 & 23276.0674204115 & -2170.0674204115 \tabularnewline
67 & 21346 & 20821.8051312095 & 524.194868790517 \tabularnewline
68 & 23335 & 23911.3775826198 & -576.377582619753 \tabularnewline
69 & 24379 & 25005.3223520738 & -626.322352073832 \tabularnewline
70 & 26290 & 24401.9148158549 & 1888.0851841451 \tabularnewline
71 & 30084 & 26809.4372923999 & 3274.56270760011 \tabularnewline
72 & 29429 & 28057.6532402213 & 1371.34675977875 \tabularnewline
73 & 30632 & 31062.4278767054 & -430.427876705362 \tabularnewline
74 & 27349 & 30353.1093545012 & -3004.10935450122 \tabularnewline
75 & 27264 & 27015.058976107 & 248.941023893000 \tabularnewline
76 & 27474 & 25157.2234880534 & 2316.77651194663 \tabularnewline
77 & 24482 & 25224.2967310677 & -742.29673106769 \tabularnewline
78 & 21453 & 23082.2401301385 & -1629.24013013846 \tabularnewline
79 & 18788 & 21536.7925738898 & -2748.79257388979 \tabularnewline
80 & 19282 & 21653.5015583878 & -2371.50155838779 \tabularnewline
81 & 19713 & 21151.9046658262 & -1438.90466582622 \tabularnewline
82 & 21917 & 20146.8314228122 & 1770.16857718777 \tabularnewline
83 & 23812 & 22581.1075246791 & 1230.89247532091 \tabularnewline
84 & 23785 & 21688.8926596524 & 2096.10734034764 \tabularnewline
85 & 24696 & 24951.4291364799 & -255.429136479881 \tabularnewline
86 & 24562 & 23921.7448591370 & 640.255140862955 \tabularnewline
87 & 23580 & 24152.3917831075 & -572.391783107512 \tabularnewline
88 & 24939 & 21854.4743645458 & 3084.52563545419 \tabularnewline
89 & 23899 & 22115.406578182 & 1783.59342181799 \tabularnewline
90 & 21454 & 22039.7401379344 & -585.740137934441 \tabularnewline
91 & 19761 & 21281.6292132008 & -1520.62921320078 \tabularnewline
92 & 19815 & 22586.6868569339 & -2771.68685693386 \tabularnewline
93 & 20780 & 21952.3989437535 & -1172.39894375353 \tabularnewline
94 & 23462 & 21719.9871533751 & 1742.01284662486 \tabularnewline
95 & 25005 & 24131.9585396449 & 873.041460355107 \tabularnewline
96 & 24725 & 23130.9345704223 & 1594.06542957765 \tabularnewline
97 & 26198 & 25685.0864539043 & 512.913546095737 \tabularnewline
98 & 27543 & 25519.9967765596 & 2023.00322344036 \tabularnewline
99 & 26471 & 26865.5348163776 & -394.5348163776 \tabularnewline
100 & 26558 & 25360.3377933521 & 1197.66220664792 \tabularnewline
101 & 25317 & 23889.9710821215 & 1427.02891787852 \tabularnewline
102 & 22896 & 23229.6190197624 & -333.619019762369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115014&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]38737[/C][C]38442.7943376068[/C][C]294.205662393157[/C][/ROW]
[ROW][C]14[/C][C]38144[/C][C]37937.7174870782[/C][C]206.282512921782[/C][/ROW]
[ROW][C]15[/C][C]37594[/C][C]37283.4305493924[/C][C]310.569450607611[/C][/ROW]
[ROW][C]16[/C][C]36424[/C][C]35777.8334969757[/C][C]646.166503024266[/C][/ROW]
[ROW][C]17[/C][C]36843[/C][C]36054.1342913292[/C][C]788.865708670812[/C][/ROW]
[ROW][C]18[/C][C]37246[/C][C]36599.1313824386[/C][C]646.86861756137[/C][/ROW]
[ROW][C]19[/C][C]38661[/C][C]36911.4230970538[/C][C]1749.57690294621[/C][/ROW]
[ROW][C]20[/C][C]40454[/C][C]40489.9969874451[/C][C]-35.9969874451199[/C][/ROW]
[ROW][C]21[/C][C]44928[/C][C]43103.8164084717[/C][C]1824.18359152826[/C][/ROW]
[ROW][C]22[/C][C]48441[/C][C]43273.6965070294[/C][C]5167.30349297063[/C][/ROW]
[ROW][C]23[/C][C]48140[/C][C]50920.4732504005[/C][C]-2780.4732504005[/C][/ROW]
[ROW][C]24[/C][C]45998[/C][C]47484.4140376552[/C][C]-1486.41403765516[/C][/ROW]
[ROW][C]25[/C][C]47369[/C][C]50644.3496980102[/C][C]-3275.34969801022[/C][/ROW]
[ROW][C]26[/C][C]49554[/C][C]47154.6081854782[/C][C]2399.39181452175[/C][/ROW]
[ROW][C]27[/C][C]47510[/C][C]48519.6721805846[/C][C]-1009.67218058464[/C][/ROW]
[ROW][C]28[/C][C]44873[/C][C]46033.3897680229[/C][C]-1160.38976802291[/C][/ROW]
[ROW][C]29[/C][C]45344[/C][C]44846.1699821568[/C][C]497.83001784324[/C][/ROW]
[ROW][C]30[/C][C]42413[/C][C]45176.4238107366[/C][C]-2763.42381073661[/C][/ROW]
[ROW][C]31[/C][C]36912[/C][C]42712.5442437365[/C][C]-5800.54424373655[/C][/ROW]
[ROW][C]32[/C][C]43452[/C][C]39393.3162490431[/C][C]4058.68375095692[/C][/ROW]
[ROW][C]33[/C][C]42142[/C][C]45685.1287516123[/C][C]-3543.12875161225[/C][/ROW]
[ROW][C]34[/C][C]44382[/C][C]41538.7864982645[/C][C]2843.21350173555[/C][/ROW]
[ROW][C]35[/C][C]43636[/C][C]45788.4906863834[/C][C]-2152.49068638339[/C][/ROW]
[ROW][C]36[/C][C]44167[/C][C]42831.0144843376[/C][C]1335.98551566244[/C][/ROW]
[ROW][C]37[/C][C]44423[/C][C]47961.2759558062[/C][C]-3538.27595580615[/C][/ROW]
[ROW][C]38[/C][C]42868[/C][C]44877.1461433188[/C][C]-2009.14614331885[/C][/ROW]
[ROW][C]39[/C][C]43908[/C][C]41692.6195820056[/C][C]2215.38041799444[/C][/ROW]
[ROW][C]40[/C][C]42013[/C][C]41726.8798484619[/C][C]286.120151538118[/C][/ROW]
[ROW][C]41[/C][C]38846[/C][C]41831.9212902576[/C][C]-2985.92129025756[/C][/ROW]
[ROW][C]42[/C][C]35087[/C][C]38450.5794353890[/C][C]-3363.57943538904[/C][/ROW]
[ROW][C]43[/C][C]33026[/C][C]34760.9677878567[/C][C]-1734.96778785666[/C][/ROW]
[ROW][C]44[/C][C]34646[/C][C]36160.2960914411[/C][C]-1514.2960914411[/C][/ROW]
[ROW][C]45[/C][C]37135[/C][C]36280.0830782005[/C][C]854.916921799471[/C][/ROW]
[ROW][C]46[/C][C]37985[/C][C]36608.8406751356[/C][C]1376.15932486445[/C][/ROW]
[ROW][C]47[/C][C]43121[/C][C]38638.6752982609[/C][C]4482.32470173906[/C][/ROW]
[ROW][C]48[/C][C]43722[/C][C]41761.6495640174[/C][C]1960.35043598259[/C][/ROW]
[ROW][C]49[/C][C]43630[/C][C]46635.0397405614[/C][C]-3005.03974056143[/C][/ROW]
[ROW][C]50[/C][C]42234[/C][C]44154.0741689972[/C][C]-1920.07416899723[/C][/ROW]
[ROW][C]51[/C][C]39351[/C][C]41584.717002687[/C][C]-2233.71700268699[/C][/ROW]
[ROW][C]52[/C][C]39327[/C][C]37366.2391177713[/C][C]1960.76088222873[/C][/ROW]
[ROW][C]53[/C][C]35704[/C][C]38298.1139580916[/C][C]-2594.11395809161[/C][/ROW]
[ROW][C]54[/C][C]30466[/C][C]35073.6058965703[/C][C]-4607.60589657035[/C][/ROW]
[ROW][C]55[/C][C]28155[/C][C]30405.1145719043[/C][C]-2250.11457190428[/C][/ROW]
[ROW][C]56[/C][C]29257[/C][C]31234.1633517367[/C][C]-1977.16335173673[/C][/ROW]
[ROW][C]57[/C][C]29998[/C][C]31129.2626216296[/C][C]-1131.26262162965[/C][/ROW]
[ROW][C]58[/C][C]32529[/C][C]29620.1982645913[/C][C]2908.80173540870[/C][/ROW]
[ROW][C]59[/C][C]34787[/C][C]33228.9759525714[/C][C]1558.02404742860[/C][/ROW]
[ROW][C]60[/C][C]33855[/C][C]33241.4082660266[/C][C]613.5917339734[/C][/ROW]
[ROW][C]61[/C][C]34556[/C][C]35970.9713958884[/C][C]-1414.97139588836[/C][/ROW]
[ROW][C]62[/C][C]31348[/C][C]34767.7903853884[/C][C]-3419.7903853884[/C][/ROW]
[ROW][C]63[/C][C]30805[/C][C]30598.767235971[/C][C]206.232764029002[/C][/ROW]
[ROW][C]64[/C][C]28353[/C][C]28855.1744048542[/C][C]-502.174404854162[/C][/ROW]
[ROW][C]65[/C][C]24514[/C][C]26749.3885697929[/C][C]-2235.38856979291[/C][/ROW]
[ROW][C]66[/C][C]21106[/C][C]23276.0674204115[/C][C]-2170.0674204115[/C][/ROW]
[ROW][C]67[/C][C]21346[/C][C]20821.8051312095[/C][C]524.194868790517[/C][/ROW]
[ROW][C]68[/C][C]23335[/C][C]23911.3775826198[/C][C]-576.377582619753[/C][/ROW]
[ROW][C]69[/C][C]24379[/C][C]25005.3223520738[/C][C]-626.322352073832[/C][/ROW]
[ROW][C]70[/C][C]26290[/C][C]24401.9148158549[/C][C]1888.0851841451[/C][/ROW]
[ROW][C]71[/C][C]30084[/C][C]26809.4372923999[/C][C]3274.56270760011[/C][/ROW]
[ROW][C]72[/C][C]29429[/C][C]28057.6532402213[/C][C]1371.34675977875[/C][/ROW]
[ROW][C]73[/C][C]30632[/C][C]31062.4278767054[/C][C]-430.427876705362[/C][/ROW]
[ROW][C]74[/C][C]27349[/C][C]30353.1093545012[/C][C]-3004.10935450122[/C][/ROW]
[ROW][C]75[/C][C]27264[/C][C]27015.058976107[/C][C]248.941023893000[/C][/ROW]
[ROW][C]76[/C][C]27474[/C][C]25157.2234880534[/C][C]2316.77651194663[/C][/ROW]
[ROW][C]77[/C][C]24482[/C][C]25224.2967310677[/C][C]-742.29673106769[/C][/ROW]
[ROW][C]78[/C][C]21453[/C][C]23082.2401301385[/C][C]-1629.24013013846[/C][/ROW]
[ROW][C]79[/C][C]18788[/C][C]21536.7925738898[/C][C]-2748.79257388979[/C][/ROW]
[ROW][C]80[/C][C]19282[/C][C]21653.5015583878[/C][C]-2371.50155838779[/C][/ROW]
[ROW][C]81[/C][C]19713[/C][C]21151.9046658262[/C][C]-1438.90466582622[/C][/ROW]
[ROW][C]82[/C][C]21917[/C][C]20146.8314228122[/C][C]1770.16857718777[/C][/ROW]
[ROW][C]83[/C][C]23812[/C][C]22581.1075246791[/C][C]1230.89247532091[/C][/ROW]
[ROW][C]84[/C][C]23785[/C][C]21688.8926596524[/C][C]2096.10734034764[/C][/ROW]
[ROW][C]85[/C][C]24696[/C][C]24951.4291364799[/C][C]-255.429136479881[/C][/ROW]
[ROW][C]86[/C][C]24562[/C][C]23921.7448591370[/C][C]640.255140862955[/C][/ROW]
[ROW][C]87[/C][C]23580[/C][C]24152.3917831075[/C][C]-572.391783107512[/C][/ROW]
[ROW][C]88[/C][C]24939[/C][C]21854.4743645458[/C][C]3084.52563545419[/C][/ROW]
[ROW][C]89[/C][C]23899[/C][C]22115.406578182[/C][C]1783.59342181799[/C][/ROW]
[ROW][C]90[/C][C]21454[/C][C]22039.7401379344[/C][C]-585.740137934441[/C][/ROW]
[ROW][C]91[/C][C]19761[/C][C]21281.6292132008[/C][C]-1520.62921320078[/C][/ROW]
[ROW][C]92[/C][C]19815[/C][C]22586.6868569339[/C][C]-2771.68685693386[/C][/ROW]
[ROW][C]93[/C][C]20780[/C][C]21952.3989437535[/C][C]-1172.39894375353[/C][/ROW]
[ROW][C]94[/C][C]23462[/C][C]21719.9871533751[/C][C]1742.01284662486[/C][/ROW]
[ROW][C]95[/C][C]25005[/C][C]24131.9585396449[/C][C]873.041460355107[/C][/ROW]
[ROW][C]96[/C][C]24725[/C][C]23130.9345704223[/C][C]1594.06542957765[/C][/ROW]
[ROW][C]97[/C][C]26198[/C][C]25685.0864539043[/C][C]512.913546095737[/C][/ROW]
[ROW][C]98[/C][C]27543[/C][C]25519.9967765596[/C][C]2023.00322344036[/C][/ROW]
[ROW][C]99[/C][C]26471[/C][C]26865.5348163776[/C][C]-394.5348163776[/C][/ROW]
[ROW][C]100[/C][C]26558[/C][C]25360.3377933521[/C][C]1197.66220664792[/C][/ROW]
[ROW][C]101[/C][C]25317[/C][C]23889.9710821215[/C][C]1427.02891787852[/C][/ROW]
[ROW][C]102[/C][C]22896[/C][C]23229.6190197624[/C][C]-333.619019762369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115014&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115014&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
133873738442.7943376068294.205662393157
143814437937.7174870782206.282512921782
153759437283.4305493924310.569450607611
163642435777.8334969757646.166503024266
173684336054.1342913292788.865708670812
183724636599.1313824386646.86861756137
193866136911.42309705381749.57690294621
204045440489.9969874451-35.9969874451199
214492843103.81640847171824.18359152826
224844143273.69650702945167.30349297063
234814050920.4732504005-2780.4732504005
244599847484.4140376552-1486.41403765516
254736950644.3496980102-3275.34969801022
264955447154.60818547822399.39181452175
274751048519.6721805846-1009.67218058464
284487346033.3897680229-1160.38976802291
294534444846.1699821568497.83001784324
304241345176.4238107366-2763.42381073661
313691242712.5442437365-5800.54424373655
324345239393.31624904314058.68375095692
334214245685.1287516123-3543.12875161225
344438241538.78649826452843.21350173555
354363645788.4906863834-2152.49068638339
364416742831.01448433761335.98551566244
374442347961.2759558062-3538.27595580615
384286844877.1461433188-2009.14614331885
394390841692.61958200562215.38041799444
404201341726.8798484619286.120151538118
413884641831.9212902576-2985.92129025756
423508738450.5794353890-3363.57943538904
433302634760.9677878567-1734.96778785666
443464636160.2960914411-1514.2960914411
453713536280.0830782005854.916921799471
463798536608.84067513561376.15932486445
474312138638.67529826094482.32470173906
484372241761.64956401741960.35043598259
494363046635.0397405614-3005.03974056143
504223444154.0741689972-1920.07416899723
513935141584.717002687-2233.71700268699
523932737366.23911777131960.76088222873
533570438298.1139580916-2594.11395809161
543046635073.6058965703-4607.60589657035
552815530405.1145719043-2250.11457190428
562925731234.1633517367-1977.16335173673
572999831129.2626216296-1131.26262162965
583252929620.19826459132908.80173540870
593478733228.97595257141558.02404742860
603385533241.4082660266613.5917339734
613455635970.9713958884-1414.97139588836
623134834767.7903853884-3419.7903853884
633080530598.767235971206.232764029002
642835328855.1744048542-502.174404854162
652451426749.3885697929-2235.38856979291
662110623276.0674204115-2170.0674204115
672134620821.8051312095524.194868790517
682333523911.3775826198-576.377582619753
692437925005.3223520738-626.322352073832
702629024401.91481585491888.0851841451
713008426809.43729239993274.56270760011
722942928057.65324022131371.34675977875
733063231062.4278767054-430.427876705362
742734930353.1093545012-3004.10935450122
752726427015.058976107248.941023893000
762747425157.22348805342316.77651194663
772448225224.2967310677-742.29673106769
782145323082.2401301385-1629.24013013846
791878821536.7925738898-2748.79257388979
801928221653.5015583878-2371.50155838779
811971321151.9046658262-1438.90466582622
822191720146.83142281221770.16857718777
832381222581.10752467911230.89247532091
842378521688.89265965242096.10734034764
852469624951.4291364799-255.429136479881
862456223921.7448591370640.255140862955
872358024152.3917831075-572.391783107512
882493921854.47436454583084.52563545419
892389922115.4065781821783.59342181799
902145422039.7401379344-585.740137934441
911976121281.6292132008-1520.62921320078
921981522586.6868569339-2771.68685693386
932078021952.3989437535-1172.39894375353
942346221719.98715337511742.01284662486
952500524131.9585396449873.041460355107
962472523130.93457042231594.06542957765
972619825685.0864539043512.913546095737
982754325519.99677655962023.00322344036
992647126865.5348163776-394.5348163776
1002655825360.33779335211197.66220664792
1012531723889.97108212151427.02891787852
1022289623229.6190197624-333.619019762369







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10322620.422246850218403.82861411526837.0158795853
10425146.428179214619538.306187035230754.5501713939
10527275.334199248120507.515428865634043.1529696305
10628653.793168097220852.945295524436454.64104067
10729598.915075610920845.792665597138352.0374856247
10828085.499959104718436.059878540237734.9400396691
10929215.420648882918710.497843795339720.3434539705
11028914.673882208917585.118307487640244.2294569301
11128221.040203776316090.725995701440351.3544118511
11227333.088216054914420.805973271640245.3704588382
11324895.117780104311215.830185664538574.4053745441
11422752.26977784478317.9806825137537186.5588731757

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
103 & 22620.4222468502 & 18403.828614115 & 26837.0158795853 \tabularnewline
104 & 25146.4281792146 & 19538.3061870352 & 30754.5501713939 \tabularnewline
105 & 27275.3341992481 & 20507.5154288656 & 34043.1529696305 \tabularnewline
106 & 28653.7931680972 & 20852.9452955244 & 36454.64104067 \tabularnewline
107 & 29598.9150756109 & 20845.7926655971 & 38352.0374856247 \tabularnewline
108 & 28085.4999591047 & 18436.0598785402 & 37734.9400396691 \tabularnewline
109 & 29215.4206488829 & 18710.4978437953 & 39720.3434539705 \tabularnewline
110 & 28914.6738822089 & 17585.1183074876 & 40244.2294569301 \tabularnewline
111 & 28221.0402037763 & 16090.7259957014 & 40351.3544118511 \tabularnewline
112 & 27333.0882160549 & 14420.8059732716 & 40245.3704588382 \tabularnewline
113 & 24895.1177801043 & 11215.8301856645 & 38574.4053745441 \tabularnewline
114 & 22752.2697778447 & 8317.98068251375 & 37186.5588731757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115014&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]103[/C][C]22620.4222468502[/C][C]18403.828614115[/C][C]26837.0158795853[/C][/ROW]
[ROW][C]104[/C][C]25146.4281792146[/C][C]19538.3061870352[/C][C]30754.5501713939[/C][/ROW]
[ROW][C]105[/C][C]27275.3341992481[/C][C]20507.5154288656[/C][C]34043.1529696305[/C][/ROW]
[ROW][C]106[/C][C]28653.7931680972[/C][C]20852.9452955244[/C][C]36454.64104067[/C][/ROW]
[ROW][C]107[/C][C]29598.9150756109[/C][C]20845.7926655971[/C][C]38352.0374856247[/C][/ROW]
[ROW][C]108[/C][C]28085.4999591047[/C][C]18436.0598785402[/C][C]37734.9400396691[/C][/ROW]
[ROW][C]109[/C][C]29215.4206488829[/C][C]18710.4978437953[/C][C]39720.3434539705[/C][/ROW]
[ROW][C]110[/C][C]28914.6738822089[/C][C]17585.1183074876[/C][C]40244.2294569301[/C][/ROW]
[ROW][C]111[/C][C]28221.0402037763[/C][C]16090.7259957014[/C][C]40351.3544118511[/C][/ROW]
[ROW][C]112[/C][C]27333.0882160549[/C][C]14420.8059732716[/C][C]40245.3704588382[/C][/ROW]
[ROW][C]113[/C][C]24895.1177801043[/C][C]11215.8301856645[/C][C]38574.4053745441[/C][/ROW]
[ROW][C]114[/C][C]22752.2697778447[/C][C]8317.98068251375[/C][C]37186.5588731757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115014&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115014&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
10322620.422246850218403.82861411526837.0158795853
10425146.428179214619538.306187035230754.5501713939
10527275.334199248120507.515428865634043.1529696305
10628653.793168097220852.945295524436454.64104067
10729598.915075610920845.792665597138352.0374856247
10828085.499959104718436.059878540237734.9400396691
10929215.420648882918710.497843795339720.3434539705
11028914.673882208917585.118307487640244.2294569301
11128221.040203776316090.725995701440351.3544118511
11227333.088216054914420.805973271640245.3704588382
11324895.117780104311215.830185664538574.4053745441
11422752.26977784478317.9806825137537186.5588731757



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