Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 10:20:06 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t1211818882gw511xraai4axdh.htm/, Retrieved Tue, 14 May 2024 10:23:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13272, Retrieved Tue, 14 May 2024 10:23:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [triple exponentia...] [2008-05-26 16:20:06] [303435f2616c8b7fa1931e576f2293ac] [Current]
Feedback Forum

Post a new message
Dataseries X:
20.18
20.19
20.3
20.47
20.47
20.46
20.46
20.46
20.52
20.64
20.65
20.66
20.66
20.66
20.67
20.71
20.73
20.73
20.74
20.74
20.75
20.75
20.77
20.78
20.78
20.8
20.84
20.85
20.86
20.86
20.86
20.86
20.9
20.92
20.95
20.95
20.95
20.96
21.1
21.18
21.19
21.19
21.19
21.19
21.19
21.21
21.22
21.22
21.22
21.23
21.41
21.42
21.43
21.44
21.44
21.44
21.48
21.53
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.54
21.57
21.6
21.61
21.6
21.6
21.71
21.75
21.84
21.85
21.92
21.92
21.93
22
22
21.99
22.01
22.01
22.06
22.03
22.05
22.05
22.06
22.06
22.13
22.06
22.25
22.28
22.18




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13272&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13272&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13272&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.793474145780884
beta0.00479652073271958
gamma0.737741601640285

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.793474145780884 \tabularnewline
beta & 0.00479652073271958 \tabularnewline
gamma & 0.737741601640285 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13272&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]0.793474145780884[/C][/ROW]
[ROW][C]beta[/C][C]0.00479652073271958[/C][/ROW]
[ROW][C]gamma[/C][C]0.737741601640285[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13272&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13272&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
alpha0.793474145780884
beta0.00479652073271958
gamma0.737741601640285







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1320.6620.55183013384750.108169866152533
1420.6620.62977881181780.0302211881822245
1520.6720.65805643417930.0119435658206584
1620.7120.70895004201840.00104995798160701
1720.7320.7357954823498-0.00579548234976812
1820.7320.7367669411756-0.00676694117561283
1920.7420.7469423940709-0.00694239407087593
2020.7420.7461152430691-0.00611524306907185
2120.7520.7538380170145-0.00383801701451247
2220.7520.7533511954977-0.00335119549767526
2320.7720.7749058575943-0.00490585759431639
2420.7820.7856242723208-0.00562427232076601
2520.7820.8404518388369-0.0604518388369435
2620.820.77225595880800.0277440411920438
2720.8420.79545077647700.0445492235230347
2820.8520.8706296669005-0.0206296669004580
2920.8620.8790969409233-0.0190969409233368
3020.8620.8690517876523-0.00905178765234993
3120.8620.8771298462342-0.0171298462342016
3220.8620.8679856040254-0.00798560402539295
3320.920.87425323599580.0257467640042393
3420.9220.89703572848290.0229642715171323
3520.9520.93921169576620.0107883042338450
3620.9520.9622350050685-0.0122350050685149
3720.9521.0036805635178-0.0536805635177693
3820.9620.95407272219450.00592727780550817
3921.120.96230343508060.137696564919395
4021.1821.10186268055310.0781373194469275
4121.1921.18969325483650.000306745163527467
4221.1921.1971289285829-0.0071289285829117
4321.1921.2061789227885-0.0161789227885443
4421.1921.1997346735471-0.00973467354705448
4521.1921.2104861590069-0.0204861590069179
4621.2121.19648728836070.0135127116393505
4721.2221.2298839320915-0.00988393209154026
4821.2221.2333421756721-0.0133421756720722
4921.2221.268361062396-0.0483610623959976
5021.2321.2323034501463-0.00230345014628952
5121.4121.25446805103180.155531948968161
5221.4221.39960073809580.0203992619042452
5321.4321.42997308822712.69117729345680e-05
5421.4421.43617670580970.00382329419034022
5521.4421.4527830080177-0.0127830080177311
5621.4421.4502035593178-0.0102035593177519
5721.4821.45924243178150.0207575682184924
5821.5321.48348162354470.046518376455321
5921.5421.540120982806-0.000120982805999148
6021.5421.5513302409796-0.0113302409796461
6121.5421.5835841447035-0.0435841447034768
6221.5421.5588725350669-0.0188725350668868
6321.5421.592851032018-0.0528510320180118
6421.5421.551719275084-0.0117192750840189
6521.5421.5531290332296-0.0131290332296388
6621.5421.5490287564667-0.00902875646671575
6721.5421.5524391071715-0.0124391071714847
6821.5421.5500450030218-0.0100450030217978
6921.5721.56351119794050.0064888020595184
7021.621.57982775520760.0201722447924197
7121.6121.60784927288660.00215072711336362
7221.621.6185445899320-0.0185445899319525
7321.621.6395937379819-0.0395937379818747
7421.7121.62120494978240.088795050217648
7521.7521.73542594076910.0145740592308918
7621.8421.75404350857630.0859564914237474
7721.8521.83310879713210.0168912028678925
7821.9221.85387948901150.0661205109884762
7921.9221.91713922014920.00286077985083111
8021.9321.92800670572430.00199329427568173
812221.95463521774560.0453647822543672
822222.004923190723-0.00492319072300873
8321.9922.0111590373927-0.0211590373927102
8422.0122.00093141135100.00906858864895455
8522.0122.0420028126096-0.0320028126095586
8622.0622.05052069249410.00947930750593784
8722.0322.0915045060217-0.0615045060216524
8822.0522.0610659523722-0.0110659523721566
8922.0522.0525434402411-0.00254344024108377
9022.0622.0653620495792-0.00536204957916908
9122.0622.0618961530736-0.00189615307357016
9222.1322.06852112748550.0614788725145097
9322.0622.1490177600930-0.0890177600929754
9422.2522.08440883662120.165591163378789
9522.2822.22345832105710.0565416789429101
9622.1822.2797955253477-0.0997955253476555

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 20.66 & 20.5518301338475 & 0.108169866152533 \tabularnewline
14 & 20.66 & 20.6297788118178 & 0.0302211881822245 \tabularnewline
15 & 20.67 & 20.6580564341793 & 0.0119435658206584 \tabularnewline
16 & 20.71 & 20.7089500420184 & 0.00104995798160701 \tabularnewline
17 & 20.73 & 20.7357954823498 & -0.00579548234976812 \tabularnewline
18 & 20.73 & 20.7367669411756 & -0.00676694117561283 \tabularnewline
19 & 20.74 & 20.7469423940709 & -0.00694239407087593 \tabularnewline
20 & 20.74 & 20.7461152430691 & -0.00611524306907185 \tabularnewline
21 & 20.75 & 20.7538380170145 & -0.00383801701451247 \tabularnewline
22 & 20.75 & 20.7533511954977 & -0.00335119549767526 \tabularnewline
23 & 20.77 & 20.7749058575943 & -0.00490585759431639 \tabularnewline
24 & 20.78 & 20.7856242723208 & -0.00562427232076601 \tabularnewline
25 & 20.78 & 20.8404518388369 & -0.0604518388369435 \tabularnewline
26 & 20.8 & 20.7722559588080 & 0.0277440411920438 \tabularnewline
27 & 20.84 & 20.7954507764770 & 0.0445492235230347 \tabularnewline
28 & 20.85 & 20.8706296669005 & -0.0206296669004580 \tabularnewline
29 & 20.86 & 20.8790969409233 & -0.0190969409233368 \tabularnewline
30 & 20.86 & 20.8690517876523 & -0.00905178765234993 \tabularnewline
31 & 20.86 & 20.8771298462342 & -0.0171298462342016 \tabularnewline
32 & 20.86 & 20.8679856040254 & -0.00798560402539295 \tabularnewline
33 & 20.9 & 20.8742532359958 & 0.0257467640042393 \tabularnewline
34 & 20.92 & 20.8970357284829 & 0.0229642715171323 \tabularnewline
35 & 20.95 & 20.9392116957662 & 0.0107883042338450 \tabularnewline
36 & 20.95 & 20.9622350050685 & -0.0122350050685149 \tabularnewline
37 & 20.95 & 21.0036805635178 & -0.0536805635177693 \tabularnewline
38 & 20.96 & 20.9540727221945 & 0.00592727780550817 \tabularnewline
39 & 21.1 & 20.9623034350806 & 0.137696564919395 \tabularnewline
40 & 21.18 & 21.1018626805531 & 0.0781373194469275 \tabularnewline
41 & 21.19 & 21.1896932548365 & 0.000306745163527467 \tabularnewline
42 & 21.19 & 21.1971289285829 & -0.0071289285829117 \tabularnewline
43 & 21.19 & 21.2061789227885 & -0.0161789227885443 \tabularnewline
44 & 21.19 & 21.1997346735471 & -0.00973467354705448 \tabularnewline
45 & 21.19 & 21.2104861590069 & -0.0204861590069179 \tabularnewline
46 & 21.21 & 21.1964872883607 & 0.0135127116393505 \tabularnewline
47 & 21.22 & 21.2298839320915 & -0.00988393209154026 \tabularnewline
48 & 21.22 & 21.2333421756721 & -0.0133421756720722 \tabularnewline
49 & 21.22 & 21.268361062396 & -0.0483610623959976 \tabularnewline
50 & 21.23 & 21.2323034501463 & -0.00230345014628952 \tabularnewline
51 & 21.41 & 21.2544680510318 & 0.155531948968161 \tabularnewline
52 & 21.42 & 21.3996007380958 & 0.0203992619042452 \tabularnewline
53 & 21.43 & 21.4299730882271 & 2.69117729345680e-05 \tabularnewline
54 & 21.44 & 21.4361767058097 & 0.00382329419034022 \tabularnewline
55 & 21.44 & 21.4527830080177 & -0.0127830080177311 \tabularnewline
56 & 21.44 & 21.4502035593178 & -0.0102035593177519 \tabularnewline
57 & 21.48 & 21.4592424317815 & 0.0207575682184924 \tabularnewline
58 & 21.53 & 21.4834816235447 & 0.046518376455321 \tabularnewline
59 & 21.54 & 21.540120982806 & -0.000120982805999148 \tabularnewline
60 & 21.54 & 21.5513302409796 & -0.0113302409796461 \tabularnewline
61 & 21.54 & 21.5835841447035 & -0.0435841447034768 \tabularnewline
62 & 21.54 & 21.5588725350669 & -0.0188725350668868 \tabularnewline
63 & 21.54 & 21.592851032018 & -0.0528510320180118 \tabularnewline
64 & 21.54 & 21.551719275084 & -0.0117192750840189 \tabularnewline
65 & 21.54 & 21.5531290332296 & -0.0131290332296388 \tabularnewline
66 & 21.54 & 21.5490287564667 & -0.00902875646671575 \tabularnewline
67 & 21.54 & 21.5524391071715 & -0.0124391071714847 \tabularnewline
68 & 21.54 & 21.5500450030218 & -0.0100450030217978 \tabularnewline
69 & 21.57 & 21.5635111979405 & 0.0064888020595184 \tabularnewline
70 & 21.6 & 21.5798277552076 & 0.0201722447924197 \tabularnewline
71 & 21.61 & 21.6078492728866 & 0.00215072711336362 \tabularnewline
72 & 21.6 & 21.6185445899320 & -0.0185445899319525 \tabularnewline
73 & 21.6 & 21.6395937379819 & -0.0395937379818747 \tabularnewline
74 & 21.71 & 21.6212049497824 & 0.088795050217648 \tabularnewline
75 & 21.75 & 21.7354259407691 & 0.0145740592308918 \tabularnewline
76 & 21.84 & 21.7540435085763 & 0.0859564914237474 \tabularnewline
77 & 21.85 & 21.8331087971321 & 0.0168912028678925 \tabularnewline
78 & 21.92 & 21.8538794890115 & 0.0661205109884762 \tabularnewline
79 & 21.92 & 21.9171392201492 & 0.00286077985083111 \tabularnewline
80 & 21.93 & 21.9280067057243 & 0.00199329427568173 \tabularnewline
81 & 22 & 21.9546352177456 & 0.0453647822543672 \tabularnewline
82 & 22 & 22.004923190723 & -0.00492319072300873 \tabularnewline
83 & 21.99 & 22.0111590373927 & -0.0211590373927102 \tabularnewline
84 & 22.01 & 22.0009314113510 & 0.00906858864895455 \tabularnewline
85 & 22.01 & 22.0420028126096 & -0.0320028126095586 \tabularnewline
86 & 22.06 & 22.0505206924941 & 0.00947930750593784 \tabularnewline
87 & 22.03 & 22.0915045060217 & -0.0615045060216524 \tabularnewline
88 & 22.05 & 22.0610659523722 & -0.0110659523721566 \tabularnewline
89 & 22.05 & 22.0525434402411 & -0.00254344024108377 \tabularnewline
90 & 22.06 & 22.0653620495792 & -0.00536204957916908 \tabularnewline
91 & 22.06 & 22.0618961530736 & -0.00189615307357016 \tabularnewline
92 & 22.13 & 22.0685211274855 & 0.0614788725145097 \tabularnewline
93 & 22.06 & 22.1490177600930 & -0.0890177600929754 \tabularnewline
94 & 22.25 & 22.0844088366212 & 0.165591163378789 \tabularnewline
95 & 22.28 & 22.2234583210571 & 0.0565416789429101 \tabularnewline
96 & 22.18 & 22.2797955253477 & -0.0997955253476555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13272&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]20.66[/C][C]20.5518301338475[/C][C]0.108169866152533[/C][/ROW]
[ROW][C]14[/C][C]20.66[/C][C]20.6297788118178[/C][C]0.0302211881822245[/C][/ROW]
[ROW][C]15[/C][C]20.67[/C][C]20.6580564341793[/C][C]0.0119435658206584[/C][/ROW]
[ROW][C]16[/C][C]20.71[/C][C]20.7089500420184[/C][C]0.00104995798160701[/C][/ROW]
[ROW][C]17[/C][C]20.73[/C][C]20.7357954823498[/C][C]-0.00579548234976812[/C][/ROW]
[ROW][C]18[/C][C]20.73[/C][C]20.7367669411756[/C][C]-0.00676694117561283[/C][/ROW]
[ROW][C]19[/C][C]20.74[/C][C]20.7469423940709[/C][C]-0.00694239407087593[/C][/ROW]
[ROW][C]20[/C][C]20.74[/C][C]20.7461152430691[/C][C]-0.00611524306907185[/C][/ROW]
[ROW][C]21[/C][C]20.75[/C][C]20.7538380170145[/C][C]-0.00383801701451247[/C][/ROW]
[ROW][C]22[/C][C]20.75[/C][C]20.7533511954977[/C][C]-0.00335119549767526[/C][/ROW]
[ROW][C]23[/C][C]20.77[/C][C]20.7749058575943[/C][C]-0.00490585759431639[/C][/ROW]
[ROW][C]24[/C][C]20.78[/C][C]20.7856242723208[/C][C]-0.00562427232076601[/C][/ROW]
[ROW][C]25[/C][C]20.78[/C][C]20.8404518388369[/C][C]-0.0604518388369435[/C][/ROW]
[ROW][C]26[/C][C]20.8[/C][C]20.7722559588080[/C][C]0.0277440411920438[/C][/ROW]
[ROW][C]27[/C][C]20.84[/C][C]20.7954507764770[/C][C]0.0445492235230347[/C][/ROW]
[ROW][C]28[/C][C]20.85[/C][C]20.8706296669005[/C][C]-0.0206296669004580[/C][/ROW]
[ROW][C]29[/C][C]20.86[/C][C]20.8790969409233[/C][C]-0.0190969409233368[/C][/ROW]
[ROW][C]30[/C][C]20.86[/C][C]20.8690517876523[/C][C]-0.00905178765234993[/C][/ROW]
[ROW][C]31[/C][C]20.86[/C][C]20.8771298462342[/C][C]-0.0171298462342016[/C][/ROW]
[ROW][C]32[/C][C]20.86[/C][C]20.8679856040254[/C][C]-0.00798560402539295[/C][/ROW]
[ROW][C]33[/C][C]20.9[/C][C]20.8742532359958[/C][C]0.0257467640042393[/C][/ROW]
[ROW][C]34[/C][C]20.92[/C][C]20.8970357284829[/C][C]0.0229642715171323[/C][/ROW]
[ROW][C]35[/C][C]20.95[/C][C]20.9392116957662[/C][C]0.0107883042338450[/C][/ROW]
[ROW][C]36[/C][C]20.95[/C][C]20.9622350050685[/C][C]-0.0122350050685149[/C][/ROW]
[ROW][C]37[/C][C]20.95[/C][C]21.0036805635178[/C][C]-0.0536805635177693[/C][/ROW]
[ROW][C]38[/C][C]20.96[/C][C]20.9540727221945[/C][C]0.00592727780550817[/C][/ROW]
[ROW][C]39[/C][C]21.1[/C][C]20.9623034350806[/C][C]0.137696564919395[/C][/ROW]
[ROW][C]40[/C][C]21.18[/C][C]21.1018626805531[/C][C]0.0781373194469275[/C][/ROW]
[ROW][C]41[/C][C]21.19[/C][C]21.1896932548365[/C][C]0.000306745163527467[/C][/ROW]
[ROW][C]42[/C][C]21.19[/C][C]21.1971289285829[/C][C]-0.0071289285829117[/C][/ROW]
[ROW][C]43[/C][C]21.19[/C][C]21.2061789227885[/C][C]-0.0161789227885443[/C][/ROW]
[ROW][C]44[/C][C]21.19[/C][C]21.1997346735471[/C][C]-0.00973467354705448[/C][/ROW]
[ROW][C]45[/C][C]21.19[/C][C]21.2104861590069[/C][C]-0.0204861590069179[/C][/ROW]
[ROW][C]46[/C][C]21.21[/C][C]21.1964872883607[/C][C]0.0135127116393505[/C][/ROW]
[ROW][C]47[/C][C]21.22[/C][C]21.2298839320915[/C][C]-0.00988393209154026[/C][/ROW]
[ROW][C]48[/C][C]21.22[/C][C]21.2333421756721[/C][C]-0.0133421756720722[/C][/ROW]
[ROW][C]49[/C][C]21.22[/C][C]21.268361062396[/C][C]-0.0483610623959976[/C][/ROW]
[ROW][C]50[/C][C]21.23[/C][C]21.2323034501463[/C][C]-0.00230345014628952[/C][/ROW]
[ROW][C]51[/C][C]21.41[/C][C]21.2544680510318[/C][C]0.155531948968161[/C][/ROW]
[ROW][C]52[/C][C]21.42[/C][C]21.3996007380958[/C][C]0.0203992619042452[/C][/ROW]
[ROW][C]53[/C][C]21.43[/C][C]21.4299730882271[/C][C]2.69117729345680e-05[/C][/ROW]
[ROW][C]54[/C][C]21.44[/C][C]21.4361767058097[/C][C]0.00382329419034022[/C][/ROW]
[ROW][C]55[/C][C]21.44[/C][C]21.4527830080177[/C][C]-0.0127830080177311[/C][/ROW]
[ROW][C]56[/C][C]21.44[/C][C]21.4502035593178[/C][C]-0.0102035593177519[/C][/ROW]
[ROW][C]57[/C][C]21.48[/C][C]21.4592424317815[/C][C]0.0207575682184924[/C][/ROW]
[ROW][C]58[/C][C]21.53[/C][C]21.4834816235447[/C][C]0.046518376455321[/C][/ROW]
[ROW][C]59[/C][C]21.54[/C][C]21.540120982806[/C][C]-0.000120982805999148[/C][/ROW]
[ROW][C]60[/C][C]21.54[/C][C]21.5513302409796[/C][C]-0.0113302409796461[/C][/ROW]
[ROW][C]61[/C][C]21.54[/C][C]21.5835841447035[/C][C]-0.0435841447034768[/C][/ROW]
[ROW][C]62[/C][C]21.54[/C][C]21.5588725350669[/C][C]-0.0188725350668868[/C][/ROW]
[ROW][C]63[/C][C]21.54[/C][C]21.592851032018[/C][C]-0.0528510320180118[/C][/ROW]
[ROW][C]64[/C][C]21.54[/C][C]21.551719275084[/C][C]-0.0117192750840189[/C][/ROW]
[ROW][C]65[/C][C]21.54[/C][C]21.5531290332296[/C][C]-0.0131290332296388[/C][/ROW]
[ROW][C]66[/C][C]21.54[/C][C]21.5490287564667[/C][C]-0.00902875646671575[/C][/ROW]
[ROW][C]67[/C][C]21.54[/C][C]21.5524391071715[/C][C]-0.0124391071714847[/C][/ROW]
[ROW][C]68[/C][C]21.54[/C][C]21.5500450030218[/C][C]-0.0100450030217978[/C][/ROW]
[ROW][C]69[/C][C]21.57[/C][C]21.5635111979405[/C][C]0.0064888020595184[/C][/ROW]
[ROW][C]70[/C][C]21.6[/C][C]21.5798277552076[/C][C]0.0201722447924197[/C][/ROW]
[ROW][C]71[/C][C]21.61[/C][C]21.6078492728866[/C][C]0.00215072711336362[/C][/ROW]
[ROW][C]72[/C][C]21.6[/C][C]21.6185445899320[/C][C]-0.0185445899319525[/C][/ROW]
[ROW][C]73[/C][C]21.6[/C][C]21.6395937379819[/C][C]-0.0395937379818747[/C][/ROW]
[ROW][C]74[/C][C]21.71[/C][C]21.6212049497824[/C][C]0.088795050217648[/C][/ROW]
[ROW][C]75[/C][C]21.75[/C][C]21.7354259407691[/C][C]0.0145740592308918[/C][/ROW]
[ROW][C]76[/C][C]21.84[/C][C]21.7540435085763[/C][C]0.0859564914237474[/C][/ROW]
[ROW][C]77[/C][C]21.85[/C][C]21.8331087971321[/C][C]0.0168912028678925[/C][/ROW]
[ROW][C]78[/C][C]21.92[/C][C]21.8538794890115[/C][C]0.0661205109884762[/C][/ROW]
[ROW][C]79[/C][C]21.92[/C][C]21.9171392201492[/C][C]0.00286077985083111[/C][/ROW]
[ROW][C]80[/C][C]21.93[/C][C]21.9280067057243[/C][C]0.00199329427568173[/C][/ROW]
[ROW][C]81[/C][C]22[/C][C]21.9546352177456[/C][C]0.0453647822543672[/C][/ROW]
[ROW][C]82[/C][C]22[/C][C]22.004923190723[/C][C]-0.00492319072300873[/C][/ROW]
[ROW][C]83[/C][C]21.99[/C][C]22.0111590373927[/C][C]-0.0211590373927102[/C][/ROW]
[ROW][C]84[/C][C]22.01[/C][C]22.0009314113510[/C][C]0.00906858864895455[/C][/ROW]
[ROW][C]85[/C][C]22.01[/C][C]22.0420028126096[/C][C]-0.0320028126095586[/C][/ROW]
[ROW][C]86[/C][C]22.06[/C][C]22.0505206924941[/C][C]0.00947930750593784[/C][/ROW]
[ROW][C]87[/C][C]22.03[/C][C]22.0915045060217[/C][C]-0.0615045060216524[/C][/ROW]
[ROW][C]88[/C][C]22.05[/C][C]22.0610659523722[/C][C]-0.0110659523721566[/C][/ROW]
[ROW][C]89[/C][C]22.05[/C][C]22.0525434402411[/C][C]-0.00254344024108377[/C][/ROW]
[ROW][C]90[/C][C]22.06[/C][C]22.0653620495792[/C][C]-0.00536204957916908[/C][/ROW]
[ROW][C]91[/C][C]22.06[/C][C]22.0618961530736[/C][C]-0.00189615307357016[/C][/ROW]
[ROW][C]92[/C][C]22.13[/C][C]22.0685211274855[/C][C]0.0614788725145097[/C][/ROW]
[ROW][C]93[/C][C]22.06[/C][C]22.1490177600930[/C][C]-0.0890177600929754[/C][/ROW]
[ROW][C]94[/C][C]22.25[/C][C]22.0844088366212[/C][C]0.165591163378789[/C][/ROW]
[ROW][C]95[/C][C]22.28[/C][C]22.2234583210571[/C][C]0.0565416789429101[/C][/ROW]
[ROW][C]96[/C][C]22.18[/C][C]22.2797955253477[/C][C]-0.0997955253476555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13272&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13272&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
1320.6620.55183013384750.108169866152533
1420.6620.62977881181780.0302211881822245
1520.6720.65805643417930.0119435658206584
1620.7120.70895004201840.00104995798160701
1720.7320.7357954823498-0.00579548234976812
1820.7320.7367669411756-0.00676694117561283
1920.7420.7469423940709-0.00694239407087593
2020.7420.7461152430691-0.00611524306907185
2120.7520.7538380170145-0.00383801701451247
2220.7520.7533511954977-0.00335119549767526
2320.7720.7749058575943-0.00490585759431639
2420.7820.7856242723208-0.00562427232076601
2520.7820.8404518388369-0.0604518388369435
2620.820.77225595880800.0277440411920438
2720.8420.79545077647700.0445492235230347
2820.8520.8706296669005-0.0206296669004580
2920.8620.8790969409233-0.0190969409233368
3020.8620.8690517876523-0.00905178765234993
3120.8620.8771298462342-0.0171298462342016
3220.8620.8679856040254-0.00798560402539295
3320.920.87425323599580.0257467640042393
3420.9220.89703572848290.0229642715171323
3520.9520.93921169576620.0107883042338450
3620.9520.9622350050685-0.0122350050685149
3720.9521.0036805635178-0.0536805635177693
3820.9620.95407272219450.00592727780550817
3921.120.96230343508060.137696564919395
4021.1821.10186268055310.0781373194469275
4121.1921.18969325483650.000306745163527467
4221.1921.1971289285829-0.0071289285829117
4321.1921.2061789227885-0.0161789227885443
4421.1921.1997346735471-0.00973467354705448
4521.1921.2104861590069-0.0204861590069179
4621.2121.19648728836070.0135127116393505
4721.2221.2298839320915-0.00988393209154026
4821.2221.2333421756721-0.0133421756720722
4921.2221.268361062396-0.0483610623959976
5021.2321.2323034501463-0.00230345014628952
5121.4121.25446805103180.155531948968161
5221.4221.39960073809580.0203992619042452
5321.4321.42997308822712.69117729345680e-05
5421.4421.43617670580970.00382329419034022
5521.4421.4527830080177-0.0127830080177311
5621.4421.4502035593178-0.0102035593177519
5721.4821.45924243178150.0207575682184924
5821.5321.48348162354470.046518376455321
5921.5421.540120982806-0.000120982805999148
6021.5421.5513302409796-0.0113302409796461
6121.5421.5835841447035-0.0435841447034768
6221.5421.5588725350669-0.0188725350668868
6321.5421.592851032018-0.0528510320180118
6421.5421.551719275084-0.0117192750840189
6521.5421.5531290332296-0.0131290332296388
6621.5421.5490287564667-0.00902875646671575
6721.5421.5524391071715-0.0124391071714847
6821.5421.5500450030218-0.0100450030217978
6921.5721.56351119794050.0064888020595184
7021.621.57982775520760.0201722447924197
7121.6121.60784927288660.00215072711336362
7221.621.6185445899320-0.0185445899319525
7321.621.6395937379819-0.0395937379818747
7421.7121.62120494978240.088795050217648
7521.7521.73542594076910.0145740592308918
7621.8421.75404350857630.0859564914237474
7721.8521.83310879713210.0168912028678925
7821.9221.85387948901150.0661205109884762
7921.9221.91713922014920.00286077985083111
8021.9321.92800670572430.00199329427568173
812221.95463521774560.0453647822543672
822222.004923190723-0.00492319072300873
8321.9922.0111590373927-0.0211590373927102
8422.0122.00093141135100.00906858864895455
8522.0122.0420028126096-0.0320028126095586
8622.0622.05052069249410.00947930750593784
8722.0322.0915045060217-0.0615045060216524
8822.0522.0610659523722-0.0110659523721566
8922.0522.0525434402411-0.00254344024108377
9022.0622.0653620495792-0.00536204957916908
9122.0622.0618961530736-0.00189615307357016
9222.1322.06852112748550.0614788725145097
9322.0622.1490177600930-0.0890177600929754
9422.2522.08440883662120.165591163378789
9522.2822.22345832105710.0565416789429101
9622.1822.2797955253477-0.0997955253476555







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9722.228278816968922.145118090854522.3114395430833
9822.268825599506122.160013264657222.377637934355
9922.291555741123722.161916071727922.4211954105196
10022.31799769750122.170255702198022.4657396928041
10122.319697632100522.155817556769522.4835777074314
10222.334413630057722.155652727134722.5131745329807
10322.335896767885822.143372869652622.5284206661189
10422.354039760035722.148445825500922.5596336945705
10522.362826904760422.144910903876922.5807429056439
10622.408344099441822.178341624183622.6383465747000
10722.399009346513322.157913138125422.6401055549011
10822.386066775666717.422240424249127.3498931270843

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 22.2282788169689 & 22.1451180908545 & 22.3114395430833 \tabularnewline
98 & 22.2688255995061 & 22.1600132646572 & 22.377637934355 \tabularnewline
99 & 22.2915557411237 & 22.1619160717279 & 22.4211954105196 \tabularnewline
100 & 22.317997697501 & 22.1702557021980 & 22.4657396928041 \tabularnewline
101 & 22.3196976321005 & 22.1558175567695 & 22.4835777074314 \tabularnewline
102 & 22.3344136300577 & 22.1556527271347 & 22.5131745329807 \tabularnewline
103 & 22.3358967678858 & 22.1433728696526 & 22.5284206661189 \tabularnewline
104 & 22.3540397600357 & 22.1484458255009 & 22.5596336945705 \tabularnewline
105 & 22.3628269047604 & 22.1449109038769 & 22.5807429056439 \tabularnewline
106 & 22.4083440994418 & 22.1783416241836 & 22.6383465747000 \tabularnewline
107 & 22.3990093465133 & 22.1579131381254 & 22.6401055549011 \tabularnewline
108 & 22.3860667756667 & 17.4222404242491 & 27.3498931270843 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13272&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]22.2282788169689[/C][C]22.1451180908545[/C][C]22.3114395430833[/C][/ROW]
[ROW][C]98[/C][C]22.2688255995061[/C][C]22.1600132646572[/C][C]22.377637934355[/C][/ROW]
[ROW][C]99[/C][C]22.2915557411237[/C][C]22.1619160717279[/C][C]22.4211954105196[/C][/ROW]
[ROW][C]100[/C][C]22.317997697501[/C][C]22.1702557021980[/C][C]22.4657396928041[/C][/ROW]
[ROW][C]101[/C][C]22.3196976321005[/C][C]22.1558175567695[/C][C]22.4835777074314[/C][/ROW]
[ROW][C]102[/C][C]22.3344136300577[/C][C]22.1556527271347[/C][C]22.5131745329807[/C][/ROW]
[ROW][C]103[/C][C]22.3358967678858[/C][C]22.1433728696526[/C][C]22.5284206661189[/C][/ROW]
[ROW][C]104[/C][C]22.3540397600357[/C][C]22.1484458255009[/C][C]22.5596336945705[/C][/ROW]
[ROW][C]105[/C][C]22.3628269047604[/C][C]22.1449109038769[/C][C]22.5807429056439[/C][/ROW]
[ROW][C]106[/C][C]22.4083440994418[/C][C]22.1783416241836[/C][C]22.6383465747000[/C][/ROW]
[ROW][C]107[/C][C]22.3990093465133[/C][C]22.1579131381254[/C][C]22.6401055549011[/C][/ROW]
[ROW][C]108[/C][C]22.3860667756667[/C][C]17.4222404242491[/C][C]27.3498931270843[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13272&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13272&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
9722.228278816968922.145118090854522.3114395430833
9822.268825599506122.160013264657222.377637934355
9922.291555741123722.161916071727922.4211954105196
10022.31799769750122.170255702198022.4657396928041
10122.319697632100522.155817556769522.4835777074314
10222.334413630057722.155652727134722.5131745329807
10322.335896767885822.143372869652622.5284206661189
10422.354039760035722.148445825500922.5596336945705
10522.362826904760422.144910903876922.5807429056439
10622.408344099441822.178341624183622.6383465747000
10722.399009346513322.157913138125422.6401055549011
10822.386066775666717.422240424249127.3498931270843



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')