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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Jan 2010 13:15:08 -0700
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/Jan/25/t12644505589jw94c49ex8047m.htm/, Retrieved Sun, 05 May 2024 22:56:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72499, Retrieved Sun, 05 May 2024 22:56:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-01-25 20:15:08] [2a9ec9c0b57e4896ade7900b00318ff3] [Current]
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Dataseries X:
5789
6333
6901
5813
6504
5619
5867
6084
5258
5601
5081
4678
5463
5546
6810
6407
5985
5119
5904
5034
4922
6083
4365
4464
4557
5885
5286
6017
5376
5935
6276
5510
5998
5193
4602
5326
5307
5014
6153
6441
5584
6427
6062
5589
6216
5809
4989
6706
7174
6122
8075
6292
6337
8576
6077
5931
6288
7167
6054
6468
6403
6927
7914
7728
8701
8522
6481
7502
7778
7424
6941
8574
9171
7718
9083
7164
8213
8124
7075
7026
7390
7778
6203
6905
7087
6495
7664
6516
6322
7828
6708
6717
5707
8063
6315
5893
6914
7319
6615
7341
6210
7408
6168
5878
6834
6211
5982
6973




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72499&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72499&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72499&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.227226293087861
beta0.00400719516398090
gamma0.468268628242811

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.227226293087861 \tabularnewline
beta & 0.00400719516398090 \tabularnewline
gamma & 0.468268628242811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72499&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]0.227226293087861[/C][/ROW]
[ROW][C]beta[/C][C]0.00400719516398090[/C][/ROW]
[ROW][C]gamma[/C][C]0.468268628242811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72499&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72499&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
alpha0.227226293087861
beta0.00400719516398090
gamma0.468268628242811







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1354635564.62030934466-101.620309344661
1455465645.370230533-99.3702305330025
1568106947.82867380658-137.828673806577
1664076473.49533036791-66.4953303679094
1759856018.63991562603-33.6399156260304
1851195155.82803312001-36.8280331200131
1959045607.62182296341296.378177036587
2050345908.09839262955-874.098392629551
2149224944.12993792744-22.1299379274387
2260835218.77152118562864.228478814378
2343654889.35761956567-524.357619565667
2444644405.3657905315258.6342094684833
2545575120.96749380307-563.967493803075
2658855084.51720181596800.48279818404
2752866500.28623857647-1214.28623857647
2860175842.51903868147174.480961318528
2953765488.01101343521-112.011013435206
3059354680.04532826851254.9546717315
3162765525.22771223572750.772287764278
3255105497.8596827090212.1403172909777
3359985036.32253345798961.677466542022
3451935886.82285300407-693.82285300407
3546024696.88212709086-94.8821270908611
3653264519.87855823765806.121441762346
3753075206.21138924348100.78861075652
3850145862.86548180036-848.86548180036
3961536167.51037641228-14.5103764122814
4064416297.004497691143.995502309000
4155845803.71369864202-219.71369864202
4264275424.45265462471002.54734537530
4360626040.7731626340721.2268373659344
4455895575.8774611615713.1225388384264
4562165443.4791066912772.520893308798
4658095646.23803220823162.761967791771
4749894839.22847908395149.771520916050
4867065043.289379918821662.71062008118
4971745694.408430606071479.59156939393
5061226358.08576395324-236.085763953241
5180757254.01794292782820.98205707218
5262927681.66551547145-1389.66551547145
5363376614.10719025756-277.107190257564
5485766672.86387477271903.1361252273
5560777154.25202246334-1077.25202246334
5659316376.98248550287-445.982485502868
5762886428.93049316508-140.930493165078
5871676191.21066920885975.789330791152
5960545469.68382585193584.316174148069
6064686377.1189383678490.8810616321607
6164036589.49810437552-186.498104375516
6269276254.52454015845672.475459841549
6379147774.53806132073139.461938679266
6477287221.93899691618506.061003083815
6587016966.450530146641734.54946985336
6685228359.83831051347162.161689486527
6764817276.77058106426-795.770581064257
6875026766.5726491668735.427350833205
6977787238.94888090384539.051119096164
7074247585.31733620368-161.317336203680
7169416337.61620357216603.383796427842
7285747143.827379204311430.17262079569
7391717581.827942222581589.17205777742
7477187968.311187041-250.311187041008
7590839318.25292636613-235.252926366129
7671648737.87363004178-1573.87363004178
7782138431.35671139932-218.356711399318
7881248836.0324898033-712.032489803305
7970757163.79785863682-88.7978586368235
8070267375.32200042453-349.322000424528
8173907531.14629362274-141.146293622739
8277787469.69768740157308.302312598425
8362036595.34870468105-392.348704681050
8469057424.91832742048-519.918327420483
8570877435.72618656723-348.726186567232
8664956797.93282439275-302.932824392748
8776647937.71647368105-273.716473681052
8865166981.53634082563-465.536340825629
8963227347.30617119082-1025.30617119082
9078287340.32445446061487.675545539393
9167086309.53217276756398.467827232438
9267176519.05061806593197.949381934065
9357076845.19391198431-1138.19391198431
9480636699.156042761661363.84395723834
9563155907.39682102024407.60317897976
9658936818.06315412562-925.063154125619
9769146781.4279857217132.572014278303
9873196298.260547445641020.73945255436
9966157732.32433212231-1117.32433212231
10073416548.57837227765792.421627722353
10162106987.14737327979-777.147373279788
10274087590.3860097346-182.386009734596
10361686385.39907855026-217.399078550256
10458786379.84234581784-501.842345817840
10568346057.93455901892776.065440981076
10662117241.26909505805-1030.26909505805
10759825651.11627772225330.883722277754
10869736027.16018506365945.839814936346

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5463 & 5564.62030934466 & -101.620309344661 \tabularnewline
14 & 5546 & 5645.370230533 & -99.3702305330025 \tabularnewline
15 & 6810 & 6947.82867380658 & -137.828673806577 \tabularnewline
16 & 6407 & 6473.49533036791 & -66.4953303679094 \tabularnewline
17 & 5985 & 6018.63991562603 & -33.6399156260304 \tabularnewline
18 & 5119 & 5155.82803312001 & -36.8280331200131 \tabularnewline
19 & 5904 & 5607.62182296341 & 296.378177036587 \tabularnewline
20 & 5034 & 5908.09839262955 & -874.098392629551 \tabularnewline
21 & 4922 & 4944.12993792744 & -22.1299379274387 \tabularnewline
22 & 6083 & 5218.77152118562 & 864.228478814378 \tabularnewline
23 & 4365 & 4889.35761956567 & -524.357619565667 \tabularnewline
24 & 4464 & 4405.36579053152 & 58.6342094684833 \tabularnewline
25 & 4557 & 5120.96749380307 & -563.967493803075 \tabularnewline
26 & 5885 & 5084.51720181596 & 800.48279818404 \tabularnewline
27 & 5286 & 6500.28623857647 & -1214.28623857647 \tabularnewline
28 & 6017 & 5842.51903868147 & 174.480961318528 \tabularnewline
29 & 5376 & 5488.01101343521 & -112.011013435206 \tabularnewline
30 & 5935 & 4680.0453282685 & 1254.9546717315 \tabularnewline
31 & 6276 & 5525.22771223572 & 750.772287764278 \tabularnewline
32 & 5510 & 5497.85968270902 & 12.1403172909777 \tabularnewline
33 & 5998 & 5036.32253345798 & 961.677466542022 \tabularnewline
34 & 5193 & 5886.82285300407 & -693.82285300407 \tabularnewline
35 & 4602 & 4696.88212709086 & -94.8821270908611 \tabularnewline
36 & 5326 & 4519.87855823765 & 806.121441762346 \tabularnewline
37 & 5307 & 5206.21138924348 & 100.78861075652 \tabularnewline
38 & 5014 & 5862.86548180036 & -848.86548180036 \tabularnewline
39 & 6153 & 6167.51037641228 & -14.5103764122814 \tabularnewline
40 & 6441 & 6297.004497691 & 143.995502309000 \tabularnewline
41 & 5584 & 5803.71369864202 & -219.71369864202 \tabularnewline
42 & 6427 & 5424.4526546247 & 1002.54734537530 \tabularnewline
43 & 6062 & 6040.77316263407 & 21.2268373659344 \tabularnewline
44 & 5589 & 5575.87746116157 & 13.1225388384264 \tabularnewline
45 & 6216 & 5443.4791066912 & 772.520893308798 \tabularnewline
46 & 5809 & 5646.23803220823 & 162.761967791771 \tabularnewline
47 & 4989 & 4839.22847908395 & 149.771520916050 \tabularnewline
48 & 6706 & 5043.28937991882 & 1662.71062008118 \tabularnewline
49 & 7174 & 5694.40843060607 & 1479.59156939393 \tabularnewline
50 & 6122 & 6358.08576395324 & -236.085763953241 \tabularnewline
51 & 8075 & 7254.01794292782 & 820.98205707218 \tabularnewline
52 & 6292 & 7681.66551547145 & -1389.66551547145 \tabularnewline
53 & 6337 & 6614.10719025756 & -277.107190257564 \tabularnewline
54 & 8576 & 6672.8638747727 & 1903.1361252273 \tabularnewline
55 & 6077 & 7154.25202246334 & -1077.25202246334 \tabularnewline
56 & 5931 & 6376.98248550287 & -445.982485502868 \tabularnewline
57 & 6288 & 6428.93049316508 & -140.930493165078 \tabularnewline
58 & 7167 & 6191.21066920885 & 975.789330791152 \tabularnewline
59 & 6054 & 5469.68382585193 & 584.316174148069 \tabularnewline
60 & 6468 & 6377.11893836784 & 90.8810616321607 \tabularnewline
61 & 6403 & 6589.49810437552 & -186.498104375516 \tabularnewline
62 & 6927 & 6254.52454015845 & 672.475459841549 \tabularnewline
63 & 7914 & 7774.53806132073 & 139.461938679266 \tabularnewline
64 & 7728 & 7221.93899691618 & 506.061003083815 \tabularnewline
65 & 8701 & 6966.45053014664 & 1734.54946985336 \tabularnewline
66 & 8522 & 8359.83831051347 & 162.161689486527 \tabularnewline
67 & 6481 & 7276.77058106426 & -795.770581064257 \tabularnewline
68 & 7502 & 6766.5726491668 & 735.427350833205 \tabularnewline
69 & 7778 & 7238.94888090384 & 539.051119096164 \tabularnewline
70 & 7424 & 7585.31733620368 & -161.317336203680 \tabularnewline
71 & 6941 & 6337.61620357216 & 603.383796427842 \tabularnewline
72 & 8574 & 7143.82737920431 & 1430.17262079569 \tabularnewline
73 & 9171 & 7581.82794222258 & 1589.17205777742 \tabularnewline
74 & 7718 & 7968.311187041 & -250.311187041008 \tabularnewline
75 & 9083 & 9318.25292636613 & -235.252926366129 \tabularnewline
76 & 7164 & 8737.87363004178 & -1573.87363004178 \tabularnewline
77 & 8213 & 8431.35671139932 & -218.356711399318 \tabularnewline
78 & 8124 & 8836.0324898033 & -712.032489803305 \tabularnewline
79 & 7075 & 7163.79785863682 & -88.7978586368235 \tabularnewline
80 & 7026 & 7375.32200042453 & -349.322000424528 \tabularnewline
81 & 7390 & 7531.14629362274 & -141.146293622739 \tabularnewline
82 & 7778 & 7469.69768740157 & 308.302312598425 \tabularnewline
83 & 6203 & 6595.34870468105 & -392.348704681050 \tabularnewline
84 & 6905 & 7424.91832742048 & -519.918327420483 \tabularnewline
85 & 7087 & 7435.72618656723 & -348.726186567232 \tabularnewline
86 & 6495 & 6797.93282439275 & -302.932824392748 \tabularnewline
87 & 7664 & 7937.71647368105 & -273.716473681052 \tabularnewline
88 & 6516 & 6981.53634082563 & -465.536340825629 \tabularnewline
89 & 6322 & 7347.30617119082 & -1025.30617119082 \tabularnewline
90 & 7828 & 7340.32445446061 & 487.675545539393 \tabularnewline
91 & 6708 & 6309.53217276756 & 398.467827232438 \tabularnewline
92 & 6717 & 6519.05061806593 & 197.949381934065 \tabularnewline
93 & 5707 & 6845.19391198431 & -1138.19391198431 \tabularnewline
94 & 8063 & 6699.15604276166 & 1363.84395723834 \tabularnewline
95 & 6315 & 5907.39682102024 & 407.60317897976 \tabularnewline
96 & 5893 & 6818.06315412562 & -925.063154125619 \tabularnewline
97 & 6914 & 6781.4279857217 & 132.572014278303 \tabularnewline
98 & 7319 & 6298.26054744564 & 1020.73945255436 \tabularnewline
99 & 6615 & 7732.32433212231 & -1117.32433212231 \tabularnewline
100 & 7341 & 6548.57837227765 & 792.421627722353 \tabularnewline
101 & 6210 & 6987.14737327979 & -777.147373279788 \tabularnewline
102 & 7408 & 7590.3860097346 & -182.386009734596 \tabularnewline
103 & 6168 & 6385.39907855026 & -217.399078550256 \tabularnewline
104 & 5878 & 6379.84234581784 & -501.842345817840 \tabularnewline
105 & 6834 & 6057.93455901892 & 776.065440981076 \tabularnewline
106 & 6211 & 7241.26909505805 & -1030.26909505805 \tabularnewline
107 & 5982 & 5651.11627772225 & 330.883722277754 \tabularnewline
108 & 6973 & 6027.16018506365 & 945.839814936346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72499&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]5463[/C][C]5564.62030934466[/C][C]-101.620309344661[/C][/ROW]
[ROW][C]14[/C][C]5546[/C][C]5645.370230533[/C][C]-99.3702305330025[/C][/ROW]
[ROW][C]15[/C][C]6810[/C][C]6947.82867380658[/C][C]-137.828673806577[/C][/ROW]
[ROW][C]16[/C][C]6407[/C][C]6473.49533036791[/C][C]-66.4953303679094[/C][/ROW]
[ROW][C]17[/C][C]5985[/C][C]6018.63991562603[/C][C]-33.6399156260304[/C][/ROW]
[ROW][C]18[/C][C]5119[/C][C]5155.82803312001[/C][C]-36.8280331200131[/C][/ROW]
[ROW][C]19[/C][C]5904[/C][C]5607.62182296341[/C][C]296.378177036587[/C][/ROW]
[ROW][C]20[/C][C]5034[/C][C]5908.09839262955[/C][C]-874.098392629551[/C][/ROW]
[ROW][C]21[/C][C]4922[/C][C]4944.12993792744[/C][C]-22.1299379274387[/C][/ROW]
[ROW][C]22[/C][C]6083[/C][C]5218.77152118562[/C][C]864.228478814378[/C][/ROW]
[ROW][C]23[/C][C]4365[/C][C]4889.35761956567[/C][C]-524.357619565667[/C][/ROW]
[ROW][C]24[/C][C]4464[/C][C]4405.36579053152[/C][C]58.6342094684833[/C][/ROW]
[ROW][C]25[/C][C]4557[/C][C]5120.96749380307[/C][C]-563.967493803075[/C][/ROW]
[ROW][C]26[/C][C]5885[/C][C]5084.51720181596[/C][C]800.48279818404[/C][/ROW]
[ROW][C]27[/C][C]5286[/C][C]6500.28623857647[/C][C]-1214.28623857647[/C][/ROW]
[ROW][C]28[/C][C]6017[/C][C]5842.51903868147[/C][C]174.480961318528[/C][/ROW]
[ROW][C]29[/C][C]5376[/C][C]5488.01101343521[/C][C]-112.011013435206[/C][/ROW]
[ROW][C]30[/C][C]5935[/C][C]4680.0453282685[/C][C]1254.9546717315[/C][/ROW]
[ROW][C]31[/C][C]6276[/C][C]5525.22771223572[/C][C]750.772287764278[/C][/ROW]
[ROW][C]32[/C][C]5510[/C][C]5497.85968270902[/C][C]12.1403172909777[/C][/ROW]
[ROW][C]33[/C][C]5998[/C][C]5036.32253345798[/C][C]961.677466542022[/C][/ROW]
[ROW][C]34[/C][C]5193[/C][C]5886.82285300407[/C][C]-693.82285300407[/C][/ROW]
[ROW][C]35[/C][C]4602[/C][C]4696.88212709086[/C][C]-94.8821270908611[/C][/ROW]
[ROW][C]36[/C][C]5326[/C][C]4519.87855823765[/C][C]806.121441762346[/C][/ROW]
[ROW][C]37[/C][C]5307[/C][C]5206.21138924348[/C][C]100.78861075652[/C][/ROW]
[ROW][C]38[/C][C]5014[/C][C]5862.86548180036[/C][C]-848.86548180036[/C][/ROW]
[ROW][C]39[/C][C]6153[/C][C]6167.51037641228[/C][C]-14.5103764122814[/C][/ROW]
[ROW][C]40[/C][C]6441[/C][C]6297.004497691[/C][C]143.995502309000[/C][/ROW]
[ROW][C]41[/C][C]5584[/C][C]5803.71369864202[/C][C]-219.71369864202[/C][/ROW]
[ROW][C]42[/C][C]6427[/C][C]5424.4526546247[/C][C]1002.54734537530[/C][/ROW]
[ROW][C]43[/C][C]6062[/C][C]6040.77316263407[/C][C]21.2268373659344[/C][/ROW]
[ROW][C]44[/C][C]5589[/C][C]5575.87746116157[/C][C]13.1225388384264[/C][/ROW]
[ROW][C]45[/C][C]6216[/C][C]5443.4791066912[/C][C]772.520893308798[/C][/ROW]
[ROW][C]46[/C][C]5809[/C][C]5646.23803220823[/C][C]162.761967791771[/C][/ROW]
[ROW][C]47[/C][C]4989[/C][C]4839.22847908395[/C][C]149.771520916050[/C][/ROW]
[ROW][C]48[/C][C]6706[/C][C]5043.28937991882[/C][C]1662.71062008118[/C][/ROW]
[ROW][C]49[/C][C]7174[/C][C]5694.40843060607[/C][C]1479.59156939393[/C][/ROW]
[ROW][C]50[/C][C]6122[/C][C]6358.08576395324[/C][C]-236.085763953241[/C][/ROW]
[ROW][C]51[/C][C]8075[/C][C]7254.01794292782[/C][C]820.98205707218[/C][/ROW]
[ROW][C]52[/C][C]6292[/C][C]7681.66551547145[/C][C]-1389.66551547145[/C][/ROW]
[ROW][C]53[/C][C]6337[/C][C]6614.10719025756[/C][C]-277.107190257564[/C][/ROW]
[ROW][C]54[/C][C]8576[/C][C]6672.8638747727[/C][C]1903.1361252273[/C][/ROW]
[ROW][C]55[/C][C]6077[/C][C]7154.25202246334[/C][C]-1077.25202246334[/C][/ROW]
[ROW][C]56[/C][C]5931[/C][C]6376.98248550287[/C][C]-445.982485502868[/C][/ROW]
[ROW][C]57[/C][C]6288[/C][C]6428.93049316508[/C][C]-140.930493165078[/C][/ROW]
[ROW][C]58[/C][C]7167[/C][C]6191.21066920885[/C][C]975.789330791152[/C][/ROW]
[ROW][C]59[/C][C]6054[/C][C]5469.68382585193[/C][C]584.316174148069[/C][/ROW]
[ROW][C]60[/C][C]6468[/C][C]6377.11893836784[/C][C]90.8810616321607[/C][/ROW]
[ROW][C]61[/C][C]6403[/C][C]6589.49810437552[/C][C]-186.498104375516[/C][/ROW]
[ROW][C]62[/C][C]6927[/C][C]6254.52454015845[/C][C]672.475459841549[/C][/ROW]
[ROW][C]63[/C][C]7914[/C][C]7774.53806132073[/C][C]139.461938679266[/C][/ROW]
[ROW][C]64[/C][C]7728[/C][C]7221.93899691618[/C][C]506.061003083815[/C][/ROW]
[ROW][C]65[/C][C]8701[/C][C]6966.45053014664[/C][C]1734.54946985336[/C][/ROW]
[ROW][C]66[/C][C]8522[/C][C]8359.83831051347[/C][C]162.161689486527[/C][/ROW]
[ROW][C]67[/C][C]6481[/C][C]7276.77058106426[/C][C]-795.770581064257[/C][/ROW]
[ROW][C]68[/C][C]7502[/C][C]6766.5726491668[/C][C]735.427350833205[/C][/ROW]
[ROW][C]69[/C][C]7778[/C][C]7238.94888090384[/C][C]539.051119096164[/C][/ROW]
[ROW][C]70[/C][C]7424[/C][C]7585.31733620368[/C][C]-161.317336203680[/C][/ROW]
[ROW][C]71[/C][C]6941[/C][C]6337.61620357216[/C][C]603.383796427842[/C][/ROW]
[ROW][C]72[/C][C]8574[/C][C]7143.82737920431[/C][C]1430.17262079569[/C][/ROW]
[ROW][C]73[/C][C]9171[/C][C]7581.82794222258[/C][C]1589.17205777742[/C][/ROW]
[ROW][C]74[/C][C]7718[/C][C]7968.311187041[/C][C]-250.311187041008[/C][/ROW]
[ROW][C]75[/C][C]9083[/C][C]9318.25292636613[/C][C]-235.252926366129[/C][/ROW]
[ROW][C]76[/C][C]7164[/C][C]8737.87363004178[/C][C]-1573.87363004178[/C][/ROW]
[ROW][C]77[/C][C]8213[/C][C]8431.35671139932[/C][C]-218.356711399318[/C][/ROW]
[ROW][C]78[/C][C]8124[/C][C]8836.0324898033[/C][C]-712.032489803305[/C][/ROW]
[ROW][C]79[/C][C]7075[/C][C]7163.79785863682[/C][C]-88.7978586368235[/C][/ROW]
[ROW][C]80[/C][C]7026[/C][C]7375.32200042453[/C][C]-349.322000424528[/C][/ROW]
[ROW][C]81[/C][C]7390[/C][C]7531.14629362274[/C][C]-141.146293622739[/C][/ROW]
[ROW][C]82[/C][C]7778[/C][C]7469.69768740157[/C][C]308.302312598425[/C][/ROW]
[ROW][C]83[/C][C]6203[/C][C]6595.34870468105[/C][C]-392.348704681050[/C][/ROW]
[ROW][C]84[/C][C]6905[/C][C]7424.91832742048[/C][C]-519.918327420483[/C][/ROW]
[ROW][C]85[/C][C]7087[/C][C]7435.72618656723[/C][C]-348.726186567232[/C][/ROW]
[ROW][C]86[/C][C]6495[/C][C]6797.93282439275[/C][C]-302.932824392748[/C][/ROW]
[ROW][C]87[/C][C]7664[/C][C]7937.71647368105[/C][C]-273.716473681052[/C][/ROW]
[ROW][C]88[/C][C]6516[/C][C]6981.53634082563[/C][C]-465.536340825629[/C][/ROW]
[ROW][C]89[/C][C]6322[/C][C]7347.30617119082[/C][C]-1025.30617119082[/C][/ROW]
[ROW][C]90[/C][C]7828[/C][C]7340.32445446061[/C][C]487.675545539393[/C][/ROW]
[ROW][C]91[/C][C]6708[/C][C]6309.53217276756[/C][C]398.467827232438[/C][/ROW]
[ROW][C]92[/C][C]6717[/C][C]6519.05061806593[/C][C]197.949381934065[/C][/ROW]
[ROW][C]93[/C][C]5707[/C][C]6845.19391198431[/C][C]-1138.19391198431[/C][/ROW]
[ROW][C]94[/C][C]8063[/C][C]6699.15604276166[/C][C]1363.84395723834[/C][/ROW]
[ROW][C]95[/C][C]6315[/C][C]5907.39682102024[/C][C]407.60317897976[/C][/ROW]
[ROW][C]96[/C][C]5893[/C][C]6818.06315412562[/C][C]-925.063154125619[/C][/ROW]
[ROW][C]97[/C][C]6914[/C][C]6781.4279857217[/C][C]132.572014278303[/C][/ROW]
[ROW][C]98[/C][C]7319[/C][C]6298.26054744564[/C][C]1020.73945255436[/C][/ROW]
[ROW][C]99[/C][C]6615[/C][C]7732.32433212231[/C][C]-1117.32433212231[/C][/ROW]
[ROW][C]100[/C][C]7341[/C][C]6548.57837227765[/C][C]792.421627722353[/C][/ROW]
[ROW][C]101[/C][C]6210[/C][C]6987.14737327979[/C][C]-777.147373279788[/C][/ROW]
[ROW][C]102[/C][C]7408[/C][C]7590.3860097346[/C][C]-182.386009734596[/C][/ROW]
[ROW][C]103[/C][C]6168[/C][C]6385.39907855026[/C][C]-217.399078550256[/C][/ROW]
[ROW][C]104[/C][C]5878[/C][C]6379.84234581784[/C][C]-501.842345817840[/C][/ROW]
[ROW][C]105[/C][C]6834[/C][C]6057.93455901892[/C][C]776.065440981076[/C][/ROW]
[ROW][C]106[/C][C]6211[/C][C]7241.26909505805[/C][C]-1030.26909505805[/C][/ROW]
[ROW][C]107[/C][C]5982[/C][C]5651.11627772225[/C][C]330.883722277754[/C][/ROW]
[ROW][C]108[/C][C]6973[/C][C]6027.16018506365[/C][C]945.839814936346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72499&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72499&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
1354635564.62030934466-101.620309344661
1455465645.370230533-99.3702305330025
1568106947.82867380658-137.828673806577
1664076473.49533036791-66.4953303679094
1759856018.63991562603-33.6399156260304
1851195155.82803312001-36.8280331200131
1959045607.62182296341296.378177036587
2050345908.09839262955-874.098392629551
2149224944.12993792744-22.1299379274387
2260835218.77152118562864.228478814378
2343654889.35761956567-524.357619565667
2444644405.3657905315258.6342094684833
2545575120.96749380307-563.967493803075
2658855084.51720181596800.48279818404
2752866500.28623857647-1214.28623857647
2860175842.51903868147174.480961318528
2953765488.01101343521-112.011013435206
3059354680.04532826851254.9546717315
3162765525.22771223572750.772287764278
3255105497.8596827090212.1403172909777
3359985036.32253345798961.677466542022
3451935886.82285300407-693.82285300407
3546024696.88212709086-94.8821270908611
3653264519.87855823765806.121441762346
3753075206.21138924348100.78861075652
3850145862.86548180036-848.86548180036
3961536167.51037641228-14.5103764122814
4064416297.004497691143.995502309000
4155845803.71369864202-219.71369864202
4264275424.45265462471002.54734537530
4360626040.7731626340721.2268373659344
4455895575.8774611615713.1225388384264
4562165443.4791066912772.520893308798
4658095646.23803220823162.761967791771
4749894839.22847908395149.771520916050
4867065043.289379918821662.71062008118
4971745694.408430606071479.59156939393
5061226358.08576395324-236.085763953241
5180757254.01794292782820.98205707218
5262927681.66551547145-1389.66551547145
5363376614.10719025756-277.107190257564
5485766672.86387477271903.1361252273
5560777154.25202246334-1077.25202246334
5659316376.98248550287-445.982485502868
5762886428.93049316508-140.930493165078
5871676191.21066920885975.789330791152
5960545469.68382585193584.316174148069
6064686377.1189383678490.8810616321607
6164036589.49810437552-186.498104375516
6269276254.52454015845672.475459841549
6379147774.53806132073139.461938679266
6477287221.93899691618506.061003083815
6587016966.450530146641734.54946985336
6685228359.83831051347162.161689486527
6764817276.77058106426-795.770581064257
6875026766.5726491668735.427350833205
6977787238.94888090384539.051119096164
7074247585.31733620368-161.317336203680
7169416337.61620357216603.383796427842
7285747143.827379204311430.17262079569
7391717581.827942222581589.17205777742
7477187968.311187041-250.311187041008
7590839318.25292636613-235.252926366129
7671648737.87363004178-1573.87363004178
7782138431.35671139932-218.356711399318
7881248836.0324898033-712.032489803305
7970757163.79785863682-88.7978586368235
8070267375.32200042453-349.322000424528
8173907531.14629362274-141.146293622739
8277787469.69768740157308.302312598425
8362036595.34870468105-392.348704681050
8469057424.91832742048-519.918327420483
8570877435.72618656723-348.726186567232
8664956797.93282439275-302.932824392748
8776647937.71647368105-273.716473681052
8865166981.53634082563-465.536340825629
8963227347.30617119082-1025.30617119082
9078287340.32445446061487.675545539393
9167086309.53217276756398.467827232438
9267176519.05061806593197.949381934065
9357076845.19391198431-1138.19391198431
9480636699.156042761661363.84395723834
9563155907.39682102024407.60317897976
9658936818.06315412562-925.063154125619
9769146781.4279857217132.572014278303
9873196298.260547445641020.73945255436
9966157732.32433212231-1117.32433212231
10073416548.57837227765792.421627722353
10162106987.14737327979-777.147373279788
10274087590.3860097346-182.386009734596
10361686385.39907855026-217.399078550256
10458786379.84234581784-501.842345817840
10568346057.93455901892776.065440981076
10662117241.26909505805-1030.26909505805
10759825651.11627772225330.883722277754
10869736027.16018506365945.839814936346







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1096795.910815267215948.801380450657643.02025008377
1106593.113223027135687.948987247897498.27745880638
1116988.195488464076011.102227878227965.28874904992
1126744.929640290365724.195339301527765.6639412792
1136439.513853707965383.413626369487495.61408104644
1147420.669422082646239.223848969218602.11499519606
1156253.97608712945121.718854009417386.23332024938
1166192.255639192125015.956533941467368.55474444279
1176444.651767320625193.643921009217695.65961363203
1186782.108266145385445.20475346348119.01177882736
1195899.227134356044626.970348887777171.4839198243
1206416.531319447435316.101837863787516.96080103108

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 6795.91081526721 & 5948.80138045065 & 7643.02025008377 \tabularnewline
110 & 6593.11322302713 & 5687.94898724789 & 7498.27745880638 \tabularnewline
111 & 6988.19548846407 & 6011.10222787822 & 7965.28874904992 \tabularnewline
112 & 6744.92964029036 & 5724.19533930152 & 7765.6639412792 \tabularnewline
113 & 6439.51385370796 & 5383.41362636948 & 7495.61408104644 \tabularnewline
114 & 7420.66942208264 & 6239.22384896921 & 8602.11499519606 \tabularnewline
115 & 6253.9760871294 & 5121.71885400941 & 7386.23332024938 \tabularnewline
116 & 6192.25563919212 & 5015.95653394146 & 7368.55474444279 \tabularnewline
117 & 6444.65176732062 & 5193.64392100921 & 7695.65961363203 \tabularnewline
118 & 6782.10826614538 & 5445.2047534634 & 8119.01177882736 \tabularnewline
119 & 5899.22713435604 & 4626.97034888777 & 7171.4839198243 \tabularnewline
120 & 6416.53131944743 & 5316.10183786378 & 7516.96080103108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72499&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]109[/C][C]6795.91081526721[/C][C]5948.80138045065[/C][C]7643.02025008377[/C][/ROW]
[ROW][C]110[/C][C]6593.11322302713[/C][C]5687.94898724789[/C][C]7498.27745880638[/C][/ROW]
[ROW][C]111[/C][C]6988.19548846407[/C][C]6011.10222787822[/C][C]7965.28874904992[/C][/ROW]
[ROW][C]112[/C][C]6744.92964029036[/C][C]5724.19533930152[/C][C]7765.6639412792[/C][/ROW]
[ROW][C]113[/C][C]6439.51385370796[/C][C]5383.41362636948[/C][C]7495.61408104644[/C][/ROW]
[ROW][C]114[/C][C]7420.66942208264[/C][C]6239.22384896921[/C][C]8602.11499519606[/C][/ROW]
[ROW][C]115[/C][C]6253.9760871294[/C][C]5121.71885400941[/C][C]7386.23332024938[/C][/ROW]
[ROW][C]116[/C][C]6192.25563919212[/C][C]5015.95653394146[/C][C]7368.55474444279[/C][/ROW]
[ROW][C]117[/C][C]6444.65176732062[/C][C]5193.64392100921[/C][C]7695.65961363203[/C][/ROW]
[ROW][C]118[/C][C]6782.10826614538[/C][C]5445.2047534634[/C][C]8119.01177882736[/C][/ROW]
[ROW][C]119[/C][C]5899.22713435604[/C][C]4626.97034888777[/C][C]7171.4839198243[/C][/ROW]
[ROW][C]120[/C][C]6416.53131944743[/C][C]5316.10183786378[/C][C]7516.96080103108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72499&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72499&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
1096795.910815267215948.801380450657643.02025008377
1106593.113223027135687.948987247897498.27745880638
1116988.195488464076011.102227878227965.28874904992
1126744.929640290365724.195339301527765.6639412792
1136439.513853707965383.413626369487495.61408104644
1147420.669422082646239.223848969218602.11499519606
1156253.97608712945121.718854009417386.23332024938
1166192.255639192125015.956533941467368.55474444279
1176444.651767320625193.643921009217695.65961363203
1186782.108266145385445.20475346348119.01177882736
1195899.227134356044626.970348887777171.4839198243
1206416.531319447435316.101837863787516.96080103108



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')