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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 31 Dec 2011 07:42:07 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/31/t13253353890k6iw47nb63uxdf.htm/, Retrieved Sun, 05 May 2024 06:17:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160902, Retrieved Sun, 05 May 2024 06:17:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact177
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opdracht 10 Oefen...] [2011-12-31 12:42:07] [659094c92b72720b61457cd096818e91] [Current]
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Dataseries X:
31,5
31,29
31,3
31,06
31,09
31,11
31,13
31,1
31,03
30,74
30,83
30,82
30,8
30,74
30,71
30,58
30,71
30,7
30,7
30,72
30,68
30,78
30,84
30,8
30,8
30,88
30,87
30,92
30,82
30,75
30,75
30,75
30,63
30,52
30,58
30,6
30,6
30,63
30,56
30,61
30,53
30,6
30,6
30,63
30,66
30,34
30,32
30,3
30,3
30,08
29,96
29,91
29,83
29,89
29,85
30,06
29,83
29,95
30,02
30,03




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160902&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160902&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160902&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.758461231173782
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.758461231173782 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160902&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]0.758461231173782[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160902&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160902&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
alpha0.758461231173782
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1330.831.0295130932007-0.229513093200673
1430.7430.7985139390763-0.0585139390763416
1530.7130.7239286864673-0.0139286864672847
1630.5830.5657323396450.0142676603549496
1730.7130.67385691675360.0361430832464222
1830.730.66109798503710.038902014962936
1930.730.7657518124672-0.0657518124671554
2030.7230.70711501311680.0128849868831722
2130.6830.66408288728980.0159171127102091
2230.7830.4028415486590.377158451341039
2330.8430.78389664935060.0561033506493764
2430.830.8187395581557-0.0187395581556693
2530.830.73357939726930.0664206027307301
2630.8830.76830922848050.111690771519466
2730.8730.83362655419720.0363734458028233
2830.9230.71984837727030.200151622729749
2930.8230.975504980166-0.155504980166025
3030.7530.8180029448015-0.0680029448014778
3130.7530.8164439943423-0.0664439943422934
3230.7530.7763631436589-0.0263631436588625
3330.6330.7042683920392-0.0742683920392295
3430.5230.46119288390520.0588071160947905
3530.5830.52279708821210.057202911787865
3630.630.54035173680310.0596482631969124
3730.630.5353269484080.064673051591992
3830.6330.57941103620670.0505889637932775
3930.5630.5802445472788-0.0202445472787751
4030.6130.46355175975720.14644824024284
4130.5330.5918876859844-0.0618876859843915
4230.630.52639004641640.0736099535836203
4330.630.6321471087439-0.0321471087438852
4430.6330.62752151090210.00247848909789994
4530.6630.56582757968590.0941724203140559
4630.3430.4826006428311-0.14260064283113
4730.3230.3908126769674-0.0708126769673889
4830.330.3117993189941-0.0117993189941323
4930.330.25395244081270.0460475591873291
5030.0830.2802666352654-0.200266635265422
5129.9630.0741183941002-0.11411839410022
5229.9129.926934210457-0.0169342104570163
5329.8329.8810641465671-0.0510641465670787
5429.8929.85546350149110.0345364985089276
5529.8529.90474233412-0.0547423341199718
5630.0629.8899258870530.170074112947034
5729.8329.9776562967155-0.147656296715493
5829.9529.6583999156590.291600084341038
5930.0229.91227037281190.107729627188135
6030.0329.9827173217190.0472826782809577

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 30.8 & 31.0295130932007 & -0.229513093200673 \tabularnewline
14 & 30.74 & 30.7985139390763 & -0.0585139390763416 \tabularnewline
15 & 30.71 & 30.7239286864673 & -0.0139286864672847 \tabularnewline
16 & 30.58 & 30.565732339645 & 0.0142676603549496 \tabularnewline
17 & 30.71 & 30.6738569167536 & 0.0361430832464222 \tabularnewline
18 & 30.7 & 30.6610979850371 & 0.038902014962936 \tabularnewline
19 & 30.7 & 30.7657518124672 & -0.0657518124671554 \tabularnewline
20 & 30.72 & 30.7071150131168 & 0.0128849868831722 \tabularnewline
21 & 30.68 & 30.6640828872898 & 0.0159171127102091 \tabularnewline
22 & 30.78 & 30.402841548659 & 0.377158451341039 \tabularnewline
23 & 30.84 & 30.7838966493506 & 0.0561033506493764 \tabularnewline
24 & 30.8 & 30.8187395581557 & -0.0187395581556693 \tabularnewline
25 & 30.8 & 30.7335793972693 & 0.0664206027307301 \tabularnewline
26 & 30.88 & 30.7683092284805 & 0.111690771519466 \tabularnewline
27 & 30.87 & 30.8336265541972 & 0.0363734458028233 \tabularnewline
28 & 30.92 & 30.7198483772703 & 0.200151622729749 \tabularnewline
29 & 30.82 & 30.975504980166 & -0.155504980166025 \tabularnewline
30 & 30.75 & 30.8180029448015 & -0.0680029448014778 \tabularnewline
31 & 30.75 & 30.8164439943423 & -0.0664439943422934 \tabularnewline
32 & 30.75 & 30.7763631436589 & -0.0263631436588625 \tabularnewline
33 & 30.63 & 30.7042683920392 & -0.0742683920392295 \tabularnewline
34 & 30.52 & 30.4611928839052 & 0.0588071160947905 \tabularnewline
35 & 30.58 & 30.5227970882121 & 0.057202911787865 \tabularnewline
36 & 30.6 & 30.5403517368031 & 0.0596482631969124 \tabularnewline
37 & 30.6 & 30.535326948408 & 0.064673051591992 \tabularnewline
38 & 30.63 & 30.5794110362067 & 0.0505889637932775 \tabularnewline
39 & 30.56 & 30.5802445472788 & -0.0202445472787751 \tabularnewline
40 & 30.61 & 30.4635517597572 & 0.14644824024284 \tabularnewline
41 & 30.53 & 30.5918876859844 & -0.0618876859843915 \tabularnewline
42 & 30.6 & 30.5263900464164 & 0.0736099535836203 \tabularnewline
43 & 30.6 & 30.6321471087439 & -0.0321471087438852 \tabularnewline
44 & 30.63 & 30.6275215109021 & 0.00247848909789994 \tabularnewline
45 & 30.66 & 30.5658275796859 & 0.0941724203140559 \tabularnewline
46 & 30.34 & 30.4826006428311 & -0.14260064283113 \tabularnewline
47 & 30.32 & 30.3908126769674 & -0.0708126769673889 \tabularnewline
48 & 30.3 & 30.3117993189941 & -0.0117993189941323 \tabularnewline
49 & 30.3 & 30.2539524408127 & 0.0460475591873291 \tabularnewline
50 & 30.08 & 30.2802666352654 & -0.200266635265422 \tabularnewline
51 & 29.96 & 30.0741183941002 & -0.11411839410022 \tabularnewline
52 & 29.91 & 29.926934210457 & -0.0169342104570163 \tabularnewline
53 & 29.83 & 29.8810641465671 & -0.0510641465670787 \tabularnewline
54 & 29.89 & 29.8554635014911 & 0.0345364985089276 \tabularnewline
55 & 29.85 & 29.90474233412 & -0.0547423341199718 \tabularnewline
56 & 30.06 & 29.889925887053 & 0.170074112947034 \tabularnewline
57 & 29.83 & 29.9776562967155 & -0.147656296715493 \tabularnewline
58 & 29.95 & 29.658399915659 & 0.291600084341038 \tabularnewline
59 & 30.02 & 29.9122703728119 & 0.107729627188135 \tabularnewline
60 & 30.03 & 29.982717321719 & 0.0472826782809577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160902&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]30.8[/C][C]31.0295130932007[/C][C]-0.229513093200673[/C][/ROW]
[ROW][C]14[/C][C]30.74[/C][C]30.7985139390763[/C][C]-0.0585139390763416[/C][/ROW]
[ROW][C]15[/C][C]30.71[/C][C]30.7239286864673[/C][C]-0.0139286864672847[/C][/ROW]
[ROW][C]16[/C][C]30.58[/C][C]30.565732339645[/C][C]0.0142676603549496[/C][/ROW]
[ROW][C]17[/C][C]30.71[/C][C]30.6738569167536[/C][C]0.0361430832464222[/C][/ROW]
[ROW][C]18[/C][C]30.7[/C][C]30.6610979850371[/C][C]0.038902014962936[/C][/ROW]
[ROW][C]19[/C][C]30.7[/C][C]30.7657518124672[/C][C]-0.0657518124671554[/C][/ROW]
[ROW][C]20[/C][C]30.72[/C][C]30.7071150131168[/C][C]0.0128849868831722[/C][/ROW]
[ROW][C]21[/C][C]30.68[/C][C]30.6640828872898[/C][C]0.0159171127102091[/C][/ROW]
[ROW][C]22[/C][C]30.78[/C][C]30.402841548659[/C][C]0.377158451341039[/C][/ROW]
[ROW][C]23[/C][C]30.84[/C][C]30.7838966493506[/C][C]0.0561033506493764[/C][/ROW]
[ROW][C]24[/C][C]30.8[/C][C]30.8187395581557[/C][C]-0.0187395581556693[/C][/ROW]
[ROW][C]25[/C][C]30.8[/C][C]30.7335793972693[/C][C]0.0664206027307301[/C][/ROW]
[ROW][C]26[/C][C]30.88[/C][C]30.7683092284805[/C][C]0.111690771519466[/C][/ROW]
[ROW][C]27[/C][C]30.87[/C][C]30.8336265541972[/C][C]0.0363734458028233[/C][/ROW]
[ROW][C]28[/C][C]30.92[/C][C]30.7198483772703[/C][C]0.200151622729749[/C][/ROW]
[ROW][C]29[/C][C]30.82[/C][C]30.975504980166[/C][C]-0.155504980166025[/C][/ROW]
[ROW][C]30[/C][C]30.75[/C][C]30.8180029448015[/C][C]-0.0680029448014778[/C][/ROW]
[ROW][C]31[/C][C]30.75[/C][C]30.8164439943423[/C][C]-0.0664439943422934[/C][/ROW]
[ROW][C]32[/C][C]30.75[/C][C]30.7763631436589[/C][C]-0.0263631436588625[/C][/ROW]
[ROW][C]33[/C][C]30.63[/C][C]30.7042683920392[/C][C]-0.0742683920392295[/C][/ROW]
[ROW][C]34[/C][C]30.52[/C][C]30.4611928839052[/C][C]0.0588071160947905[/C][/ROW]
[ROW][C]35[/C][C]30.58[/C][C]30.5227970882121[/C][C]0.057202911787865[/C][/ROW]
[ROW][C]36[/C][C]30.6[/C][C]30.5403517368031[/C][C]0.0596482631969124[/C][/ROW]
[ROW][C]37[/C][C]30.6[/C][C]30.535326948408[/C][C]0.064673051591992[/C][/ROW]
[ROW][C]38[/C][C]30.63[/C][C]30.5794110362067[/C][C]0.0505889637932775[/C][/ROW]
[ROW][C]39[/C][C]30.56[/C][C]30.5802445472788[/C][C]-0.0202445472787751[/C][/ROW]
[ROW][C]40[/C][C]30.61[/C][C]30.4635517597572[/C][C]0.14644824024284[/C][/ROW]
[ROW][C]41[/C][C]30.53[/C][C]30.5918876859844[/C][C]-0.0618876859843915[/C][/ROW]
[ROW][C]42[/C][C]30.6[/C][C]30.5263900464164[/C][C]0.0736099535836203[/C][/ROW]
[ROW][C]43[/C][C]30.6[/C][C]30.6321471087439[/C][C]-0.0321471087438852[/C][/ROW]
[ROW][C]44[/C][C]30.63[/C][C]30.6275215109021[/C][C]0.00247848909789994[/C][/ROW]
[ROW][C]45[/C][C]30.66[/C][C]30.5658275796859[/C][C]0.0941724203140559[/C][/ROW]
[ROW][C]46[/C][C]30.34[/C][C]30.4826006428311[/C][C]-0.14260064283113[/C][/ROW]
[ROW][C]47[/C][C]30.32[/C][C]30.3908126769674[/C][C]-0.0708126769673889[/C][/ROW]
[ROW][C]48[/C][C]30.3[/C][C]30.3117993189941[/C][C]-0.0117993189941323[/C][/ROW]
[ROW][C]49[/C][C]30.3[/C][C]30.2539524408127[/C][C]0.0460475591873291[/C][/ROW]
[ROW][C]50[/C][C]30.08[/C][C]30.2802666352654[/C][C]-0.200266635265422[/C][/ROW]
[ROW][C]51[/C][C]29.96[/C][C]30.0741183941002[/C][C]-0.11411839410022[/C][/ROW]
[ROW][C]52[/C][C]29.91[/C][C]29.926934210457[/C][C]-0.0169342104570163[/C][/ROW]
[ROW][C]53[/C][C]29.83[/C][C]29.8810641465671[/C][C]-0.0510641465670787[/C][/ROW]
[ROW][C]54[/C][C]29.89[/C][C]29.8554635014911[/C][C]0.0345364985089276[/C][/ROW]
[ROW][C]55[/C][C]29.85[/C][C]29.90474233412[/C][C]-0.0547423341199718[/C][/ROW]
[ROW][C]56[/C][C]30.06[/C][C]29.889925887053[/C][C]0.170074112947034[/C][/ROW]
[ROW][C]57[/C][C]29.83[/C][C]29.9776562967155[/C][C]-0.147656296715493[/C][/ROW]
[ROW][C]58[/C][C]29.95[/C][C]29.658399915659[/C][C]0.291600084341038[/C][/ROW]
[ROW][C]59[/C][C]30.02[/C][C]29.9122703728119[/C][C]0.107729627188135[/C][/ROW]
[ROW][C]60[/C][C]30.03[/C][C]29.982717321719[/C][C]0.0472826782809577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160902&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160902&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
1330.831.0295130932007-0.229513093200673
1430.7430.7985139390763-0.0585139390763416
1530.7130.7239286864673-0.0139286864672847
1630.5830.5657323396450.0142676603549496
1730.7130.67385691675360.0361430832464222
1830.730.66109798503710.038902014962936
1930.730.7657518124672-0.0657518124671554
2030.7230.70711501311680.0128849868831722
2130.6830.66408288728980.0159171127102091
2230.7830.4028415486590.377158451341039
2330.8430.78389664935060.0561033506493764
2430.830.8187395581557-0.0187395581556693
2530.830.73357939726930.0664206027307301
2630.8830.76830922848050.111690771519466
2730.8730.83362655419720.0363734458028233
2830.9230.71984837727030.200151622729749
2930.8230.975504980166-0.155504980166025
3030.7530.8180029448015-0.0680029448014778
3130.7530.8164439943423-0.0664439943422934
3230.7530.7763631436589-0.0263631436588625
3330.6330.7042683920392-0.0742683920392295
3430.5230.46119288390520.0588071160947905
3530.5830.52279708821210.057202911787865
3630.630.54035173680310.0596482631969124
3730.630.5353269484080.064673051591992
3830.6330.57941103620670.0505889637932775
3930.5630.5802445472788-0.0202445472787751
4030.6130.46355175975720.14644824024284
4130.5330.5918876859844-0.0618876859843915
4230.630.52639004641640.0736099535836203
4330.630.6321471087439-0.0321471087438852
4430.6330.62752151090210.00247848909789994
4530.6630.56582757968590.0941724203140559
4630.3430.4826006428311-0.14260064283113
4730.3230.3908126769674-0.0708126769673889
4830.330.3117993189941-0.0117993189941323
4930.330.25395244081270.0460475591873291
5030.0830.2802666352654-0.200266635265422
5129.9630.0741183941002-0.11411839410022
5229.9129.926934210457-0.0169342104570163
5329.8329.8810641465671-0.0510641465670787
5429.8929.85546350149110.0345364985089276
5529.8529.90474233412-0.0547423341199718
5630.0629.8899258870530.170074112947034
5729.8329.9776562967155-0.147656296715493
5829.9529.6583999156590.291600084341038
5930.0229.91227037281190.107729627188135
6030.0329.9827173217190.0472826782809577







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6129.983681547648629.762931481441330.2044316138559
6229.915726605063829.63879042336530.1926627867625
6329.882217605362729.558619791297430.205815419428
6429.84507693249629.480781109823430.2093727551686
6529.803814416043929.402985356484830.2046434756031
6629.837555968748729.402467539400430.272644398097
6729.839001122964129.372420249763530.3055819961646
6829.919788862214529.422590448900630.4169872755283
6929.802054712401529.278678327810630.3254310969924
7029.700432614841329.152025658511630.2488395711709
7129.688496036599929.114792746069530.2621993271304
7229.662567931781222.422724621506436.902411242056

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 29.9836815476486 & 29.7629314814413 & 30.2044316138559 \tabularnewline
62 & 29.9157266050638 & 29.638790423365 & 30.1926627867625 \tabularnewline
63 & 29.8822176053627 & 29.5586197912974 & 30.205815419428 \tabularnewline
64 & 29.845076932496 & 29.4807811098234 & 30.2093727551686 \tabularnewline
65 & 29.8038144160439 & 29.4029853564848 & 30.2046434756031 \tabularnewline
66 & 29.8375559687487 & 29.4024675394004 & 30.272644398097 \tabularnewline
67 & 29.8390011229641 & 29.3724202497635 & 30.3055819961646 \tabularnewline
68 & 29.9197888622145 & 29.4225904489006 & 30.4169872755283 \tabularnewline
69 & 29.8020547124015 & 29.2786783278106 & 30.3254310969924 \tabularnewline
70 & 29.7004326148413 & 29.1520256585116 & 30.2488395711709 \tabularnewline
71 & 29.6884960365999 & 29.1147927460695 & 30.2621993271304 \tabularnewline
72 & 29.6625679317812 & 22.4227246215064 & 36.902411242056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160902&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]29.9836815476486[/C][C]29.7629314814413[/C][C]30.2044316138559[/C][/ROW]
[ROW][C]62[/C][C]29.9157266050638[/C][C]29.638790423365[/C][C]30.1926627867625[/C][/ROW]
[ROW][C]63[/C][C]29.8822176053627[/C][C]29.5586197912974[/C][C]30.205815419428[/C][/ROW]
[ROW][C]64[/C][C]29.845076932496[/C][C]29.4807811098234[/C][C]30.2093727551686[/C][/ROW]
[ROW][C]65[/C][C]29.8038144160439[/C][C]29.4029853564848[/C][C]30.2046434756031[/C][/ROW]
[ROW][C]66[/C][C]29.8375559687487[/C][C]29.4024675394004[/C][C]30.272644398097[/C][/ROW]
[ROW][C]67[/C][C]29.8390011229641[/C][C]29.3724202497635[/C][C]30.3055819961646[/C][/ROW]
[ROW][C]68[/C][C]29.9197888622145[/C][C]29.4225904489006[/C][C]30.4169872755283[/C][/ROW]
[ROW][C]69[/C][C]29.8020547124015[/C][C]29.2786783278106[/C][C]30.3254310969924[/C][/ROW]
[ROW][C]70[/C][C]29.7004326148413[/C][C]29.1520256585116[/C][C]30.2488395711709[/C][/ROW]
[ROW][C]71[/C][C]29.6884960365999[/C][C]29.1147927460695[/C][C]30.2621993271304[/C][/ROW]
[ROW][C]72[/C][C]29.6625679317812[/C][C]22.4227246215064[/C][C]36.902411242056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160902&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160902&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
6129.983681547648629.762931481441330.2044316138559
6229.915726605063829.63879042336530.1926627867625
6329.882217605362729.558619791297430.205815419428
6429.84507693249629.480781109823430.2093727551686
6529.803814416043929.402985356484830.2046434756031
6629.837555968748729.402467539400430.272644398097
6729.839001122964129.372420249763530.3055819961646
6829.919788862214529.422590448900630.4169872755283
6929.802054712401529.278678327810630.3254310969924
7029.700432614841329.152025658511630.2488395711709
7129.688496036599929.114792746069530.2621993271304
7229.662567931781222.422724621506436.902411242056



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')