Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2016 21:36:01 +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/2016/Nov/28/t14803689794kmxq02di3ra3na.htm/, Retrieved Sat, 04 May 2024 13:55:56 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 13:55:56 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
94.94
96.24
95.77
94.41
95.09
95.37
95.17
95.05
95.33
95.42
95.95
96.12
96.94
98.73
98.03
97.42
98.39
98.77
98.46
98.3
98.25
98.33
98.61
98.99
98.8
100.26
100.85
98.87
99.81
100.44
100.07
99.8
99.77
99.9
100.58
100.86
101.05
101.3
101.45
101.13
101.38
101.03
100.79
100.84
101.17
101.36
101.14
101.24
100.98
102.23
99.96
101.43
101.72
101.51
101.29
101.55
101.6
101.88
102.11
102.24




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.619015238012146
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.619015238012146 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.619015238012146[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.619015238012146
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
296.2494.941.3
395.7795.74471980941580.0252801905842119
494.4195.7603686326073-1.35036863260726
595.0994.92446987208970.165530127910273
695.3795.02693554361630.343064456383715
795.1795.2392976697382-0.0692976697381624
895.0595.1964013562115-0.146401356211513
995.3395.10577668585090.224223314149057
1095.4295.24457433402680.175425665973208
1195.9595.35316549440260.596834505597357
1296.1295.72261514793890.397384852061151
1396.9495.96860242671990.971397573280086
1498.7396.56991232674832.16008767325171
1598.0397.90703951193330.122960488066695
1697.4297.98315392772-0.563153927719995
1798.3997.63455306511490.755446934885072
1898.7798.10218622931840.667813770681633
1998.4698.5155731295246-0.055573129524646
2098.398.4811725155249-0.181172515524864
2198.2598.369023967706-0.119023967705971
2298.3398.29534631800730.0346536819926797
2398.6198.3167974752140.293202524785983
2498.9998.49829430588020.491705694119815
2598.898.8026676231577-0.00266762315767721
26100.2698.80101632377381.45898367622621
27100.8599.70414945136881.1458505486312
2898.87100.413448401456-1.54344840145608
2999.8199.45803032186930.351969678130729
30100.4499.67590491595040.764095084049572
31100.07100.148891416267-0.0788914162672825
3299.8100.100056427449-0.300056427449462
3399.7799.9143169265948-0.144316926594755
3499.999.82498254992950.0750174500704901
35100.5899.871419494640.708580505360032
36100.86100.3100416248160.549958375183834
37101.05100.6504742393270.399525760672631
38101.3100.8977867731620.402213226837873
39101.45101.1467628895050.303237110495203
40101.13101.334471281632-0.204471281632109
41101.38101.2079004425660.172099557434038
42101.03101.314432691073-0.284432691072766
43100.79101.13836452111-0.348364521109914
44100.84100.92272157416-0.0827215741600753
45101.17100.8715156592430.298484340757355
46101.36101.0562820144790.303717985520535
47101.14101.244288075575-0.104288075575028
48101.24101.1797321676510.0602678323488846
49100.98101.217038874237-0.23703887423703
50102.23101.0703081990831.15969180091695
5199.96101.788175095248-1.8281750952484
52101.43100.6565068535350.773493146464688
53101.72101.1353108976950.584689102305077
54101.51101.4972423615210.0127576384785897
55101.29101.505139534141-0.215139534140704
56101.55101.3719648842090.178035115791218
57101.6101.4821713337850.117828666215189
58101.88101.5551090736470.324890926353333
59102.11101.7562215077510.353778492248736
60102.24101.9752157853340.264784214665795

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 96.24 & 94.94 & 1.3 \tabularnewline
3 & 95.77 & 95.7447198094158 & 0.0252801905842119 \tabularnewline
4 & 94.41 & 95.7603686326073 & -1.35036863260726 \tabularnewline
5 & 95.09 & 94.9244698720897 & 0.165530127910273 \tabularnewline
6 & 95.37 & 95.0269355436163 & 0.343064456383715 \tabularnewline
7 & 95.17 & 95.2392976697382 & -0.0692976697381624 \tabularnewline
8 & 95.05 & 95.1964013562115 & -0.146401356211513 \tabularnewline
9 & 95.33 & 95.1057766858509 & 0.224223314149057 \tabularnewline
10 & 95.42 & 95.2445743340268 & 0.175425665973208 \tabularnewline
11 & 95.95 & 95.3531654944026 & 0.596834505597357 \tabularnewline
12 & 96.12 & 95.7226151479389 & 0.397384852061151 \tabularnewline
13 & 96.94 & 95.9686024267199 & 0.971397573280086 \tabularnewline
14 & 98.73 & 96.5699123267483 & 2.16008767325171 \tabularnewline
15 & 98.03 & 97.9070395119333 & 0.122960488066695 \tabularnewline
16 & 97.42 & 97.98315392772 & -0.563153927719995 \tabularnewline
17 & 98.39 & 97.6345530651149 & 0.755446934885072 \tabularnewline
18 & 98.77 & 98.1021862293184 & 0.667813770681633 \tabularnewline
19 & 98.46 & 98.5155731295246 & -0.055573129524646 \tabularnewline
20 & 98.3 & 98.4811725155249 & -0.181172515524864 \tabularnewline
21 & 98.25 & 98.369023967706 & -0.119023967705971 \tabularnewline
22 & 98.33 & 98.2953463180073 & 0.0346536819926797 \tabularnewline
23 & 98.61 & 98.316797475214 & 0.293202524785983 \tabularnewline
24 & 98.99 & 98.4982943058802 & 0.491705694119815 \tabularnewline
25 & 98.8 & 98.8026676231577 & -0.00266762315767721 \tabularnewline
26 & 100.26 & 98.8010163237738 & 1.45898367622621 \tabularnewline
27 & 100.85 & 99.7041494513688 & 1.1458505486312 \tabularnewline
28 & 98.87 & 100.413448401456 & -1.54344840145608 \tabularnewline
29 & 99.81 & 99.4580303218693 & 0.351969678130729 \tabularnewline
30 & 100.44 & 99.6759049159504 & 0.764095084049572 \tabularnewline
31 & 100.07 & 100.148891416267 & -0.0788914162672825 \tabularnewline
32 & 99.8 & 100.100056427449 & -0.300056427449462 \tabularnewline
33 & 99.77 & 99.9143169265948 & -0.144316926594755 \tabularnewline
34 & 99.9 & 99.8249825499295 & 0.0750174500704901 \tabularnewline
35 & 100.58 & 99.87141949464 & 0.708580505360032 \tabularnewline
36 & 100.86 & 100.310041624816 & 0.549958375183834 \tabularnewline
37 & 101.05 & 100.650474239327 & 0.399525760672631 \tabularnewline
38 & 101.3 & 100.897786773162 & 0.402213226837873 \tabularnewline
39 & 101.45 & 101.146762889505 & 0.303237110495203 \tabularnewline
40 & 101.13 & 101.334471281632 & -0.204471281632109 \tabularnewline
41 & 101.38 & 101.207900442566 & 0.172099557434038 \tabularnewline
42 & 101.03 & 101.314432691073 & -0.284432691072766 \tabularnewline
43 & 100.79 & 101.13836452111 & -0.348364521109914 \tabularnewline
44 & 100.84 & 100.92272157416 & -0.0827215741600753 \tabularnewline
45 & 101.17 & 100.871515659243 & 0.298484340757355 \tabularnewline
46 & 101.36 & 101.056282014479 & 0.303717985520535 \tabularnewline
47 & 101.14 & 101.244288075575 & -0.104288075575028 \tabularnewline
48 & 101.24 & 101.179732167651 & 0.0602678323488846 \tabularnewline
49 & 100.98 & 101.217038874237 & -0.23703887423703 \tabularnewline
50 & 102.23 & 101.070308199083 & 1.15969180091695 \tabularnewline
51 & 99.96 & 101.788175095248 & -1.8281750952484 \tabularnewline
52 & 101.43 & 100.656506853535 & 0.773493146464688 \tabularnewline
53 & 101.72 & 101.135310897695 & 0.584689102305077 \tabularnewline
54 & 101.51 & 101.497242361521 & 0.0127576384785897 \tabularnewline
55 & 101.29 & 101.505139534141 & -0.215139534140704 \tabularnewline
56 & 101.55 & 101.371964884209 & 0.178035115791218 \tabularnewline
57 & 101.6 & 101.482171333785 & 0.117828666215189 \tabularnewline
58 & 101.88 & 101.555109073647 & 0.324890926353333 \tabularnewline
59 & 102.11 & 101.756221507751 & 0.353778492248736 \tabularnewline
60 & 102.24 & 101.975215785334 & 0.264784214665795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2[/C][C]96.24[/C][C]94.94[/C][C]1.3[/C][/ROW]
[ROW][C]3[/C][C]95.77[/C][C]95.7447198094158[/C][C]0.0252801905842119[/C][/ROW]
[ROW][C]4[/C][C]94.41[/C][C]95.7603686326073[/C][C]-1.35036863260726[/C][/ROW]
[ROW][C]5[/C][C]95.09[/C][C]94.9244698720897[/C][C]0.165530127910273[/C][/ROW]
[ROW][C]6[/C][C]95.37[/C][C]95.0269355436163[/C][C]0.343064456383715[/C][/ROW]
[ROW][C]7[/C][C]95.17[/C][C]95.2392976697382[/C][C]-0.0692976697381624[/C][/ROW]
[ROW][C]8[/C][C]95.05[/C][C]95.1964013562115[/C][C]-0.146401356211513[/C][/ROW]
[ROW][C]9[/C][C]95.33[/C][C]95.1057766858509[/C][C]0.224223314149057[/C][/ROW]
[ROW][C]10[/C][C]95.42[/C][C]95.2445743340268[/C][C]0.175425665973208[/C][/ROW]
[ROW][C]11[/C][C]95.95[/C][C]95.3531654944026[/C][C]0.596834505597357[/C][/ROW]
[ROW][C]12[/C][C]96.12[/C][C]95.7226151479389[/C][C]0.397384852061151[/C][/ROW]
[ROW][C]13[/C][C]96.94[/C][C]95.9686024267199[/C][C]0.971397573280086[/C][/ROW]
[ROW][C]14[/C][C]98.73[/C][C]96.5699123267483[/C][C]2.16008767325171[/C][/ROW]
[ROW][C]15[/C][C]98.03[/C][C]97.9070395119333[/C][C]0.122960488066695[/C][/ROW]
[ROW][C]16[/C][C]97.42[/C][C]97.98315392772[/C][C]-0.563153927719995[/C][/ROW]
[ROW][C]17[/C][C]98.39[/C][C]97.6345530651149[/C][C]0.755446934885072[/C][/ROW]
[ROW][C]18[/C][C]98.77[/C][C]98.1021862293184[/C][C]0.667813770681633[/C][/ROW]
[ROW][C]19[/C][C]98.46[/C][C]98.5155731295246[/C][C]-0.055573129524646[/C][/ROW]
[ROW][C]20[/C][C]98.3[/C][C]98.4811725155249[/C][C]-0.181172515524864[/C][/ROW]
[ROW][C]21[/C][C]98.25[/C][C]98.369023967706[/C][C]-0.119023967705971[/C][/ROW]
[ROW][C]22[/C][C]98.33[/C][C]98.2953463180073[/C][C]0.0346536819926797[/C][/ROW]
[ROW][C]23[/C][C]98.61[/C][C]98.316797475214[/C][C]0.293202524785983[/C][/ROW]
[ROW][C]24[/C][C]98.99[/C][C]98.4982943058802[/C][C]0.491705694119815[/C][/ROW]
[ROW][C]25[/C][C]98.8[/C][C]98.8026676231577[/C][C]-0.00266762315767721[/C][/ROW]
[ROW][C]26[/C][C]100.26[/C][C]98.8010163237738[/C][C]1.45898367622621[/C][/ROW]
[ROW][C]27[/C][C]100.85[/C][C]99.7041494513688[/C][C]1.1458505486312[/C][/ROW]
[ROW][C]28[/C][C]98.87[/C][C]100.413448401456[/C][C]-1.54344840145608[/C][/ROW]
[ROW][C]29[/C][C]99.81[/C][C]99.4580303218693[/C][C]0.351969678130729[/C][/ROW]
[ROW][C]30[/C][C]100.44[/C][C]99.6759049159504[/C][C]0.764095084049572[/C][/ROW]
[ROW][C]31[/C][C]100.07[/C][C]100.148891416267[/C][C]-0.0788914162672825[/C][/ROW]
[ROW][C]32[/C][C]99.8[/C][C]100.100056427449[/C][C]-0.300056427449462[/C][/ROW]
[ROW][C]33[/C][C]99.77[/C][C]99.9143169265948[/C][C]-0.144316926594755[/C][/ROW]
[ROW][C]34[/C][C]99.9[/C][C]99.8249825499295[/C][C]0.0750174500704901[/C][/ROW]
[ROW][C]35[/C][C]100.58[/C][C]99.87141949464[/C][C]0.708580505360032[/C][/ROW]
[ROW][C]36[/C][C]100.86[/C][C]100.310041624816[/C][C]0.549958375183834[/C][/ROW]
[ROW][C]37[/C][C]101.05[/C][C]100.650474239327[/C][C]0.399525760672631[/C][/ROW]
[ROW][C]38[/C][C]101.3[/C][C]100.897786773162[/C][C]0.402213226837873[/C][/ROW]
[ROW][C]39[/C][C]101.45[/C][C]101.146762889505[/C][C]0.303237110495203[/C][/ROW]
[ROW][C]40[/C][C]101.13[/C][C]101.334471281632[/C][C]-0.204471281632109[/C][/ROW]
[ROW][C]41[/C][C]101.38[/C][C]101.207900442566[/C][C]0.172099557434038[/C][/ROW]
[ROW][C]42[/C][C]101.03[/C][C]101.314432691073[/C][C]-0.284432691072766[/C][/ROW]
[ROW][C]43[/C][C]100.79[/C][C]101.13836452111[/C][C]-0.348364521109914[/C][/ROW]
[ROW][C]44[/C][C]100.84[/C][C]100.92272157416[/C][C]-0.0827215741600753[/C][/ROW]
[ROW][C]45[/C][C]101.17[/C][C]100.871515659243[/C][C]0.298484340757355[/C][/ROW]
[ROW][C]46[/C][C]101.36[/C][C]101.056282014479[/C][C]0.303717985520535[/C][/ROW]
[ROW][C]47[/C][C]101.14[/C][C]101.244288075575[/C][C]-0.104288075575028[/C][/ROW]
[ROW][C]48[/C][C]101.24[/C][C]101.179732167651[/C][C]0.0602678323488846[/C][/ROW]
[ROW][C]49[/C][C]100.98[/C][C]101.217038874237[/C][C]-0.23703887423703[/C][/ROW]
[ROW][C]50[/C][C]102.23[/C][C]101.070308199083[/C][C]1.15969180091695[/C][/ROW]
[ROW][C]51[/C][C]99.96[/C][C]101.788175095248[/C][C]-1.8281750952484[/C][/ROW]
[ROW][C]52[/C][C]101.43[/C][C]100.656506853535[/C][C]0.773493146464688[/C][/ROW]
[ROW][C]53[/C][C]101.72[/C][C]101.135310897695[/C][C]0.584689102305077[/C][/ROW]
[ROW][C]54[/C][C]101.51[/C][C]101.497242361521[/C][C]0.0127576384785897[/C][/ROW]
[ROW][C]55[/C][C]101.29[/C][C]101.505139534141[/C][C]-0.215139534140704[/C][/ROW]
[ROW][C]56[/C][C]101.55[/C][C]101.371964884209[/C][C]0.178035115791218[/C][/ROW]
[ROW][C]57[/C][C]101.6[/C][C]101.482171333785[/C][C]0.117828666215189[/C][/ROW]
[ROW][C]58[/C][C]101.88[/C][C]101.555109073647[/C][C]0.324890926353333[/C][/ROW]
[ROW][C]59[/C][C]102.11[/C][C]101.756221507751[/C][C]0.353778492248736[/C][/ROW]
[ROW][C]60[/C][C]102.24[/C][C]101.975215785334[/C][C]0.264784214665795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
296.2494.941.3
395.7795.74471980941580.0252801905842119
494.4195.7603686326073-1.35036863260726
595.0994.92446987208970.165530127910273
695.3795.02693554361630.343064456383715
795.1795.2392976697382-0.0692976697381624
895.0595.1964013562115-0.146401356211513
995.3395.10577668585090.224223314149057
1095.4295.24457433402680.175425665973208
1195.9595.35316549440260.596834505597357
1296.1295.72261514793890.397384852061151
1396.9495.96860242671990.971397573280086
1498.7396.56991232674832.16008767325171
1598.0397.90703951193330.122960488066695
1697.4297.98315392772-0.563153927719995
1798.3997.63455306511490.755446934885072
1898.7798.10218622931840.667813770681633
1998.4698.5155731295246-0.055573129524646
2098.398.4811725155249-0.181172515524864
2198.2598.369023967706-0.119023967705971
2298.3398.29534631800730.0346536819926797
2398.6198.3167974752140.293202524785983
2498.9998.49829430588020.491705694119815
2598.898.8026676231577-0.00266762315767721
26100.2698.80101632377381.45898367622621
27100.8599.70414945136881.1458505486312
2898.87100.413448401456-1.54344840145608
2999.8199.45803032186930.351969678130729
30100.4499.67590491595040.764095084049572
31100.07100.148891416267-0.0788914162672825
3299.8100.100056427449-0.300056427449462
3399.7799.9143169265948-0.144316926594755
3499.999.82498254992950.0750174500704901
35100.5899.871419494640.708580505360032
36100.86100.3100416248160.549958375183834
37101.05100.6504742393270.399525760672631
38101.3100.8977867731620.402213226837873
39101.45101.1467628895050.303237110495203
40101.13101.334471281632-0.204471281632109
41101.38101.2079004425660.172099557434038
42101.03101.314432691073-0.284432691072766
43100.79101.13836452111-0.348364521109914
44100.84100.92272157416-0.0827215741600753
45101.17100.8715156592430.298484340757355
46101.36101.0562820144790.303717985520535
47101.14101.244288075575-0.104288075575028
48101.24101.1797321676510.0602678323488846
49100.98101.217038874237-0.23703887423703
50102.23101.0703081990831.15969180091695
5199.96101.788175095248-1.8281750952484
52101.43100.6565068535350.773493146464688
53101.72101.1353108976950.584689102305077
54101.51101.4972423615210.0127576384785897
55101.29101.505139534141-0.215139534140704
56101.55101.3719648842090.178035115791218
57101.6101.4821713337850.117828666215189
58101.88101.5551090736470.324890926353333
59102.11101.7562215077510.353778492248736
60102.24101.9752157853340.264784214665795







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61102.139121248997100.884908860522103.393333637473
62102.139121248997100.664058772476103.614183725519
63102.139121248997100.47221696144103.806025536555
64102.139121248997100.300281805731103.977960692264
65102.139121248997100.143102438377104.135140059618
66102.13912124899799.9974275998996104.280814898095
67102.13912124899799.8610491955228104.417193302472
68102.13912124899799.7323863497909104.545856148204
69102.13912124899799.6102611363588104.667981361636
70102.13912124899799.4937679524544104.78447454554
71102.13912124899799.3821927664707104.896049731524
72102.13912124899799.2749607695544105.00328172844

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 102.139121248997 & 100.884908860522 & 103.393333637473 \tabularnewline
62 & 102.139121248997 & 100.664058772476 & 103.614183725519 \tabularnewline
63 & 102.139121248997 & 100.47221696144 & 103.806025536555 \tabularnewline
64 & 102.139121248997 & 100.300281805731 & 103.977960692264 \tabularnewline
65 & 102.139121248997 & 100.143102438377 & 104.135140059618 \tabularnewline
66 & 102.139121248997 & 99.9974275998996 & 104.280814898095 \tabularnewline
67 & 102.139121248997 & 99.8610491955228 & 104.417193302472 \tabularnewline
68 & 102.139121248997 & 99.7323863497909 & 104.545856148204 \tabularnewline
69 & 102.139121248997 & 99.6102611363588 & 104.667981361636 \tabularnewline
70 & 102.139121248997 & 99.4937679524544 & 104.78447454554 \tabularnewline
71 & 102.139121248997 & 99.3821927664707 & 104.896049731524 \tabularnewline
72 & 102.139121248997 & 99.2749607695544 & 105.00328172844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]102.139121248997[/C][C]100.884908860522[/C][C]103.393333637473[/C][/ROW]
[ROW][C]62[/C][C]102.139121248997[/C][C]100.664058772476[/C][C]103.614183725519[/C][/ROW]
[ROW][C]63[/C][C]102.139121248997[/C][C]100.47221696144[/C][C]103.806025536555[/C][/ROW]
[ROW][C]64[/C][C]102.139121248997[/C][C]100.300281805731[/C][C]103.977960692264[/C][/ROW]
[ROW][C]65[/C][C]102.139121248997[/C][C]100.143102438377[/C][C]104.135140059618[/C][/ROW]
[ROW][C]66[/C][C]102.139121248997[/C][C]99.9974275998996[/C][C]104.280814898095[/C][/ROW]
[ROW][C]67[/C][C]102.139121248997[/C][C]99.8610491955228[/C][C]104.417193302472[/C][/ROW]
[ROW][C]68[/C][C]102.139121248997[/C][C]99.7323863497909[/C][C]104.545856148204[/C][/ROW]
[ROW][C]69[/C][C]102.139121248997[/C][C]99.6102611363588[/C][C]104.667981361636[/C][/ROW]
[ROW][C]70[/C][C]102.139121248997[/C][C]99.4937679524544[/C][C]104.78447454554[/C][/ROW]
[ROW][C]71[/C][C]102.139121248997[/C][C]99.3821927664707[/C][C]104.896049731524[/C][/ROW]
[ROW][C]72[/C][C]102.139121248997[/C][C]99.2749607695544[/C][C]105.00328172844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61102.139121248997100.884908860522103.393333637473
62102.139121248997100.664058772476103.614183725519
63102.139121248997100.47221696144103.806025536555
64102.139121248997100.300281805731103.977960692264
65102.139121248997100.143102438377104.135140059618
66102.13912124899799.9974275998996104.280814898095
67102.13912124899799.8610491955228104.417193302472
68102.13912124899799.7323863497909104.545856148204
69102.13912124899799.6102611363588104.667981361636
70102.13912124899799.4937679524544104.78447454554
71102.13912124899799.3821927664707104.896049731524
72102.13912124899799.2749607695544105.00328172844



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')