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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 04 Dec 2009 07:22:33 -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/2009/Dec/04/t1259936588er729b825fjepko.htm/, Retrieved Sat, 27 Apr 2024 23:40:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63592, Retrieved Sat, 27 Apr 2024 23:40:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-    D      [Exponential Smoothing] [H] [2009-12-04 14:22:33] [b58cdc967a53abb3723a2bc8f9332128] [Current]
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Dataseries X:
7.2
7.4
8.8
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.2




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=63592&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=63592&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63592&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
alpha1
beta0.946034419946908
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.946034419946908 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63592&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.946034419946908[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63592&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63592&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
alpha1
beta0.946034419946908
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138.18.22384559327192-0.123845593271925
147.97.767123310102740.132876689897259
158.68.592209259828120.00779074017188108
168.78.70386313482342-0.00386313482342437
178.78.70449187515322-0.00449187515321725
188.58.49188256020620.00811743979380708
198.48.239990146036310.160009853963686
208.58.61217005966233-0.112170059662327
218.78.75533243442093-0.0553324344209294
228.78.8480082867998-0.148008286799808
238.68.521593982694850.078406017305154
248.58.277060449242630.222939550757374
258.38.5530156898059-0.253015689805892
2687.998561632423260.00143836757673910
278.28.60570013405751-0.405700134057511
288.17.808551130240750.291448869759249
298.17.893407544646550.206592455353447
3087.895144244739110.104855755260888
317.97.83345500888540.0665449911145988
327.98.0983050426575-0.198305042657497
3388.04695829630531-0.0469582963053128
3488.04873041837974-0.0487304183797423
357.97.831260785612020.0687392143879819
3687.59568005127990.404319948720105
377.78.22524514176846-0.525245141768457
387.27.32556085376415-0.125560853764153
397.57.5093345474902-0.00933454749020335
407.37.250732474993280.0492675250067167
4177.01443591757384-0.0144359175738371
4276.540879381120920.459120618879081
4376.9176434197420.0823565802580015
447.27.26062819528953-0.060628195289528
457.37.5329031591577-0.232903159157704
467.17.363972770967-0.263972770966996
476.86.760112366059540.039887633940463
486.46.333065802276340.066934197723656
496.16.134645545948-0.0346455459480026
506.55.723390596846690.776609403153308
517.77.627455008377240.072544991622765
527.98.41854842685904-0.518548426859036
537.58.04203908818125-0.542039088181253
546.96.95925513133752-0.0592551313375207
556.66.279469714975740.320530285024256
566.96.540765003084910.359234996915093
577.77.307365170162340.392634829837657
5888.4538790675717-0.453879067571698
5988.15596012961007-0.155960129610072
607.77.80113053625897-0.101130536258967
617.37.56383460394904-0.263834603949042
627.46.821578458364390.578421541635613
638.18.32565682809922-0.225656828099220
648.38.255190002355520.0448099976444816
658.28.4072242969027-0.207224296902703

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8.1 & 8.22384559327192 & -0.123845593271925 \tabularnewline
14 & 7.9 & 7.76712331010274 & 0.132876689897259 \tabularnewline
15 & 8.6 & 8.59220925982812 & 0.00779074017188108 \tabularnewline
16 & 8.7 & 8.70386313482342 & -0.00386313482342437 \tabularnewline
17 & 8.7 & 8.70449187515322 & -0.00449187515321725 \tabularnewline
18 & 8.5 & 8.4918825602062 & 0.00811743979380708 \tabularnewline
19 & 8.4 & 8.23999014603631 & 0.160009853963686 \tabularnewline
20 & 8.5 & 8.61217005966233 & -0.112170059662327 \tabularnewline
21 & 8.7 & 8.75533243442093 & -0.0553324344209294 \tabularnewline
22 & 8.7 & 8.8480082867998 & -0.148008286799808 \tabularnewline
23 & 8.6 & 8.52159398269485 & 0.078406017305154 \tabularnewline
24 & 8.5 & 8.27706044924263 & 0.222939550757374 \tabularnewline
25 & 8.3 & 8.5530156898059 & -0.253015689805892 \tabularnewline
26 & 8 & 7.99856163242326 & 0.00143836757673910 \tabularnewline
27 & 8.2 & 8.60570013405751 & -0.405700134057511 \tabularnewline
28 & 8.1 & 7.80855113024075 & 0.291448869759249 \tabularnewline
29 & 8.1 & 7.89340754464655 & 0.206592455353447 \tabularnewline
30 & 8 & 7.89514424473911 & 0.104855755260888 \tabularnewline
31 & 7.9 & 7.8334550088854 & 0.0665449911145988 \tabularnewline
32 & 7.9 & 8.0983050426575 & -0.198305042657497 \tabularnewline
33 & 8 & 8.04695829630531 & -0.0469582963053128 \tabularnewline
34 & 8 & 8.04873041837974 & -0.0487304183797423 \tabularnewline
35 & 7.9 & 7.83126078561202 & 0.0687392143879819 \tabularnewline
36 & 8 & 7.5956800512799 & 0.404319948720105 \tabularnewline
37 & 7.7 & 8.22524514176846 & -0.525245141768457 \tabularnewline
38 & 7.2 & 7.32556085376415 & -0.125560853764153 \tabularnewline
39 & 7.5 & 7.5093345474902 & -0.00933454749020335 \tabularnewline
40 & 7.3 & 7.25073247499328 & 0.0492675250067167 \tabularnewline
41 & 7 & 7.01443591757384 & -0.0144359175738371 \tabularnewline
42 & 7 & 6.54087938112092 & 0.459120618879081 \tabularnewline
43 & 7 & 6.917643419742 & 0.0823565802580015 \tabularnewline
44 & 7.2 & 7.26062819528953 & -0.060628195289528 \tabularnewline
45 & 7.3 & 7.5329031591577 & -0.232903159157704 \tabularnewline
46 & 7.1 & 7.363972770967 & -0.263972770966996 \tabularnewline
47 & 6.8 & 6.76011236605954 & 0.039887633940463 \tabularnewline
48 & 6.4 & 6.33306580227634 & 0.066934197723656 \tabularnewline
49 & 6.1 & 6.134645545948 & -0.0346455459480026 \tabularnewline
50 & 6.5 & 5.72339059684669 & 0.776609403153308 \tabularnewline
51 & 7.7 & 7.62745500837724 & 0.072544991622765 \tabularnewline
52 & 7.9 & 8.41854842685904 & -0.518548426859036 \tabularnewline
53 & 7.5 & 8.04203908818125 & -0.542039088181253 \tabularnewline
54 & 6.9 & 6.95925513133752 & -0.0592551313375207 \tabularnewline
55 & 6.6 & 6.27946971497574 & 0.320530285024256 \tabularnewline
56 & 6.9 & 6.54076500308491 & 0.359234996915093 \tabularnewline
57 & 7.7 & 7.30736517016234 & 0.392634829837657 \tabularnewline
58 & 8 & 8.4538790675717 & -0.453879067571698 \tabularnewline
59 & 8 & 8.15596012961007 & -0.155960129610072 \tabularnewline
60 & 7.7 & 7.80113053625897 & -0.101130536258967 \tabularnewline
61 & 7.3 & 7.56383460394904 & -0.263834603949042 \tabularnewline
62 & 7.4 & 6.82157845836439 & 0.578421541635613 \tabularnewline
63 & 8.1 & 8.32565682809922 & -0.225656828099220 \tabularnewline
64 & 8.3 & 8.25519000235552 & 0.0448099976444816 \tabularnewline
65 & 8.2 & 8.4072242969027 & -0.207224296902703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63592&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]8.1[/C][C]8.22384559327192[/C][C]-0.123845593271925[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]7.76712331010274[/C][C]0.132876689897259[/C][/ROW]
[ROW][C]15[/C][C]8.6[/C][C]8.59220925982812[/C][C]0.00779074017188108[/C][/ROW]
[ROW][C]16[/C][C]8.7[/C][C]8.70386313482342[/C][C]-0.00386313482342437[/C][/ROW]
[ROW][C]17[/C][C]8.7[/C][C]8.70449187515322[/C][C]-0.00449187515321725[/C][/ROW]
[ROW][C]18[/C][C]8.5[/C][C]8.4918825602062[/C][C]0.00811743979380708[/C][/ROW]
[ROW][C]19[/C][C]8.4[/C][C]8.23999014603631[/C][C]0.160009853963686[/C][/ROW]
[ROW][C]20[/C][C]8.5[/C][C]8.61217005966233[/C][C]-0.112170059662327[/C][/ROW]
[ROW][C]21[/C][C]8.7[/C][C]8.75533243442093[/C][C]-0.0553324344209294[/C][/ROW]
[ROW][C]22[/C][C]8.7[/C][C]8.8480082867998[/C][C]-0.148008286799808[/C][/ROW]
[ROW][C]23[/C][C]8.6[/C][C]8.52159398269485[/C][C]0.078406017305154[/C][/ROW]
[ROW][C]24[/C][C]8.5[/C][C]8.27706044924263[/C][C]0.222939550757374[/C][/ROW]
[ROW][C]25[/C][C]8.3[/C][C]8.5530156898059[/C][C]-0.253015689805892[/C][/ROW]
[ROW][C]26[/C][C]8[/C][C]7.99856163242326[/C][C]0.00143836757673910[/C][/ROW]
[ROW][C]27[/C][C]8.2[/C][C]8.60570013405751[/C][C]-0.405700134057511[/C][/ROW]
[ROW][C]28[/C][C]8.1[/C][C]7.80855113024075[/C][C]0.291448869759249[/C][/ROW]
[ROW][C]29[/C][C]8.1[/C][C]7.89340754464655[/C][C]0.206592455353447[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]7.89514424473911[/C][C]0.104855755260888[/C][/ROW]
[ROW][C]31[/C][C]7.9[/C][C]7.8334550088854[/C][C]0.0665449911145988[/C][/ROW]
[ROW][C]32[/C][C]7.9[/C][C]8.0983050426575[/C][C]-0.198305042657497[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]8.04695829630531[/C][C]-0.0469582963053128[/C][/ROW]
[ROW][C]34[/C][C]8[/C][C]8.04873041837974[/C][C]-0.0487304183797423[/C][/ROW]
[ROW][C]35[/C][C]7.9[/C][C]7.83126078561202[/C][C]0.0687392143879819[/C][/ROW]
[ROW][C]36[/C][C]8[/C][C]7.5956800512799[/C][C]0.404319948720105[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]8.22524514176846[/C][C]-0.525245141768457[/C][/ROW]
[ROW][C]38[/C][C]7.2[/C][C]7.32556085376415[/C][C]-0.125560853764153[/C][/ROW]
[ROW][C]39[/C][C]7.5[/C][C]7.5093345474902[/C][C]-0.00933454749020335[/C][/ROW]
[ROW][C]40[/C][C]7.3[/C][C]7.25073247499328[/C][C]0.0492675250067167[/C][/ROW]
[ROW][C]41[/C][C]7[/C][C]7.01443591757384[/C][C]-0.0144359175738371[/C][/ROW]
[ROW][C]42[/C][C]7[/C][C]6.54087938112092[/C][C]0.459120618879081[/C][/ROW]
[ROW][C]43[/C][C]7[/C][C]6.917643419742[/C][C]0.0823565802580015[/C][/ROW]
[ROW][C]44[/C][C]7.2[/C][C]7.26062819528953[/C][C]-0.060628195289528[/C][/ROW]
[ROW][C]45[/C][C]7.3[/C][C]7.5329031591577[/C][C]-0.232903159157704[/C][/ROW]
[ROW][C]46[/C][C]7.1[/C][C]7.363972770967[/C][C]-0.263972770966996[/C][/ROW]
[ROW][C]47[/C][C]6.8[/C][C]6.76011236605954[/C][C]0.039887633940463[/C][/ROW]
[ROW][C]48[/C][C]6.4[/C][C]6.33306580227634[/C][C]0.066934197723656[/C][/ROW]
[ROW][C]49[/C][C]6.1[/C][C]6.134645545948[/C][C]-0.0346455459480026[/C][/ROW]
[ROW][C]50[/C][C]6.5[/C][C]5.72339059684669[/C][C]0.776609403153308[/C][/ROW]
[ROW][C]51[/C][C]7.7[/C][C]7.62745500837724[/C][C]0.072544991622765[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]8.41854842685904[/C][C]-0.518548426859036[/C][/ROW]
[ROW][C]53[/C][C]7.5[/C][C]8.04203908818125[/C][C]-0.542039088181253[/C][/ROW]
[ROW][C]54[/C][C]6.9[/C][C]6.95925513133752[/C][C]-0.0592551313375207[/C][/ROW]
[ROW][C]55[/C][C]6.6[/C][C]6.27946971497574[/C][C]0.320530285024256[/C][/ROW]
[ROW][C]56[/C][C]6.9[/C][C]6.54076500308491[/C][C]0.359234996915093[/C][/ROW]
[ROW][C]57[/C][C]7.7[/C][C]7.30736517016234[/C][C]0.392634829837657[/C][/ROW]
[ROW][C]58[/C][C]8[/C][C]8.4538790675717[/C][C]-0.453879067571698[/C][/ROW]
[ROW][C]59[/C][C]8[/C][C]8.15596012961007[/C][C]-0.155960129610072[/C][/ROW]
[ROW][C]60[/C][C]7.7[/C][C]7.80113053625897[/C][C]-0.101130536258967[/C][/ROW]
[ROW][C]61[/C][C]7.3[/C][C]7.56383460394904[/C][C]-0.263834603949042[/C][/ROW]
[ROW][C]62[/C][C]7.4[/C][C]6.82157845836439[/C][C]0.578421541635613[/C][/ROW]
[ROW][C]63[/C][C]8.1[/C][C]8.32565682809922[/C][C]-0.225656828099220[/C][/ROW]
[ROW][C]64[/C][C]8.3[/C][C]8.25519000235552[/C][C]0.0448099976444816[/C][/ROW]
[ROW][C]65[/C][C]8.2[/C][C]8.4072242969027[/C][C]-0.207224296902703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63592&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63592&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
138.18.22384559327192-0.123845593271925
147.97.767123310102740.132876689897259
158.68.592209259828120.00779074017188108
168.78.70386313482342-0.00386313482342437
178.78.70449187515322-0.00449187515321725
188.58.49188256020620.00811743979380708
198.48.239990146036310.160009853963686
208.58.61217005966233-0.112170059662327
218.78.75533243442093-0.0553324344209294
228.78.8480082867998-0.148008286799808
238.68.521593982694850.078406017305154
248.58.277060449242630.222939550757374
258.38.5530156898059-0.253015689805892
2687.998561632423260.00143836757673910
278.28.60570013405751-0.405700134057511
288.17.808551130240750.291448869759249
298.17.893407544646550.206592455353447
3087.895144244739110.104855755260888
317.97.83345500888540.0665449911145988
327.98.0983050426575-0.198305042657497
3388.04695829630531-0.0469582963053128
3488.04873041837974-0.0487304183797423
357.97.831260785612020.0687392143879819
3687.59568005127990.404319948720105
377.78.22524514176846-0.525245141768457
387.27.32556085376415-0.125560853764153
397.57.5093345474902-0.00933454749020335
407.37.250732474993280.0492675250067167
4177.01443591757384-0.0144359175738371
4276.540879381120920.459120618879081
4376.9176434197420.0823565802580015
447.27.26062819528953-0.060628195289528
457.37.5329031591577-0.232903159157704
467.17.363972770967-0.263972770966996
476.86.760112366059540.039887633940463
486.46.333065802276340.066934197723656
496.16.134645545948-0.0346455459480026
506.55.723390596846690.776609403153308
517.77.627455008377240.072544991622765
527.98.41854842685904-0.518548426859036
537.58.04203908818125-0.542039088181253
546.96.95925513133752-0.0592551313375207
556.66.279469714975740.320530285024256
566.96.540765003084910.359234996915093
577.77.307365170162340.392634829837657
5888.4538790675717-0.453879067571698
5988.15596012961007-0.155960129610072
607.77.80113053625897-0.101130536258967
617.37.56383460394904-0.263834603949042
627.46.821578458364390.578421541635613
638.18.32565682809922-0.225656828099220
648.38.255190002355520.0448099976444816
658.28.4072242969027-0.207224296902703







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
667.917111884808167.395489510324758.43873425929157
677.58418603527566.472099675003778.69627239554743
687.547586348399175.685771458300189.40940123849816
697.639910195298054.8614830188918410.4183373717043
707.680691185774563.8706285631115911.4907538084375
717.557360303838412.6982357260540412.4164848816228
727.243033675468741.4187273216562613.0673400292812
737.079138244140660.14501167037531314.0132648179060
746.81713212553776-1.1538452541830814.7881095052586
757.3266164163001-2.7339844768392817.3872173094395
767.32012762070259-4.3253074083401418.9655626497453
777.23227551626457-7.6498798524406222.1144308849698

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
66 & 7.91711188480816 & 7.39548951032475 & 8.43873425929157 \tabularnewline
67 & 7.5841860352756 & 6.47209967500377 & 8.69627239554743 \tabularnewline
68 & 7.54758634839917 & 5.68577145830018 & 9.40940123849816 \tabularnewline
69 & 7.63991019529805 & 4.86148301889184 & 10.4183373717043 \tabularnewline
70 & 7.68069118577456 & 3.87062856311159 & 11.4907538084375 \tabularnewline
71 & 7.55736030383841 & 2.69823572605404 & 12.4164848816228 \tabularnewline
72 & 7.24303367546874 & 1.41872732165626 & 13.0673400292812 \tabularnewline
73 & 7.07913824414066 & 0.145011670375313 & 14.0132648179060 \tabularnewline
74 & 6.81713212553776 & -1.15384525418308 & 14.7881095052586 \tabularnewline
75 & 7.3266164163001 & -2.73398447683928 & 17.3872173094395 \tabularnewline
76 & 7.32012762070259 & -4.32530740834014 & 18.9655626497453 \tabularnewline
77 & 7.23227551626457 & -7.64987985244062 & 22.1144308849698 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63592&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]66[/C][C]7.91711188480816[/C][C]7.39548951032475[/C][C]8.43873425929157[/C][/ROW]
[ROW][C]67[/C][C]7.5841860352756[/C][C]6.47209967500377[/C][C]8.69627239554743[/C][/ROW]
[ROW][C]68[/C][C]7.54758634839917[/C][C]5.68577145830018[/C][C]9.40940123849816[/C][/ROW]
[ROW][C]69[/C][C]7.63991019529805[/C][C]4.86148301889184[/C][C]10.4183373717043[/C][/ROW]
[ROW][C]70[/C][C]7.68069118577456[/C][C]3.87062856311159[/C][C]11.4907538084375[/C][/ROW]
[ROW][C]71[/C][C]7.55736030383841[/C][C]2.69823572605404[/C][C]12.4164848816228[/C][/ROW]
[ROW][C]72[/C][C]7.24303367546874[/C][C]1.41872732165626[/C][C]13.0673400292812[/C][/ROW]
[ROW][C]73[/C][C]7.07913824414066[/C][C]0.145011670375313[/C][C]14.0132648179060[/C][/ROW]
[ROW][C]74[/C][C]6.81713212553776[/C][C]-1.15384525418308[/C][C]14.7881095052586[/C][/ROW]
[ROW][C]75[/C][C]7.3266164163001[/C][C]-2.73398447683928[/C][C]17.3872173094395[/C][/ROW]
[ROW][C]76[/C][C]7.32012762070259[/C][C]-4.32530740834014[/C][C]18.9655626497453[/C][/ROW]
[ROW][C]77[/C][C]7.23227551626457[/C][C]-7.64987985244062[/C][C]22.1144308849698[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63592&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63592&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
667.917111884808167.395489510324758.43873425929157
677.58418603527566.472099675003778.69627239554743
687.547586348399175.685771458300189.40940123849816
697.639910195298054.8614830188918410.4183373717043
707.680691185774563.8706285631115911.4907538084375
717.557360303838412.6982357260540412.4164848816228
727.243033675468741.4187273216562613.0673400292812
737.079138244140660.14501167037531314.0132648179060
746.81713212553776-1.1538452541830814.7881095052586
757.3266164163001-2.7339844768392817.3872173094395
767.32012762070259-4.3253074083401418.9655626497453
777.23227551626457-7.6498798524406222.1144308849698



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')