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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 08:41:39 -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/t1259941359er0owouh9lj8nb2.htm/, Retrieved Sun, 28 Apr 2024 11:28:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63790, Retrieved Sun, 28 Apr 2024 11:28:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
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] [] [2009-12-04 12:40:04] [1f74ef2f756548f1f3a7b6136ea56d7f]
-   PD        [Exponential Smoothing] [ws 9 Exponentiona...] [2009-12-04 15:41:39] [ac4f1d4b47349b2602192853b2bc5b72] [Current]
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Dataseries X:
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




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=63790&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=63790&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63790&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
beta0.916379251616883
gamma0.00180441050470130

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.916379251616883 \tabularnewline
gamma & 0.00180441050470130 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63790&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]0.916379251616883[/C][/ROW]
[ROW][C]gamma[/C][C]0.00180441050470130[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63790&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63790&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
beta0.916379251616883
gamma0.00180441050470130







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138.78.680990517871520.0190094821284745
148.78.7154941714524-0.0154941714523904
158.58.492909553007770.00709044699222972
168.48.395297855961760.0047021440382391
178.58.5079238029641-0.00792380296410578
188.78.7262674174135-0.0262674174135054
198.78.597953561376220.102046438623784
208.68.73231590394013-0.132315903940132
218.58.291874682797270.208125317202725
228.38.54770867588768-0.247708675887676
2388.00543315104749-0.00543315104748565
248.28.60627807175544-0.406278071755439
258.17.820752954263950.279247045736052
268.17.885792411302820.214207588697183
2787.888549394487310.111450605512690
287.97.977636400544-0.0776364005440007
297.98.00250399280299-0.102503992802985
3088.02218989935545-0.0221898993554515
3187.820898207545940.179101792454064
327.98.0226269351786-0.122626935178609
3387.609204325065050.390795674934951
347.78.21451830560136-0.514518305601364
357.27.3398493281955-0.139849328195498
367.57.51467812018654-0.0146781201865442
377.37.25146345826260.0485365417373931
3877.01303738473855-0.0130373847385457
3976.541182783833540.458817216166462
4077.03475850042076-0.03475850042076
417.27.176211410724290.0237885892757124
427.37.5084592509359-0.208459250935899
437.17.16101698409946-0.0610169840994583
446.86.94161668171015-0.141616681710153
456.46.346620046787880.053379953212116
466.16.13380440161523-0.0338044016152281
476.55.724322200972450.775677799027552
487.77.602517985621670.0974820143783273
497.98.41426891467136-0.514268914671362
507.58.05704408252355-0.557044082523548
516.96.97615247416296-0.0761524741629582
526.66.401066990655210.198933009344787
536.96.447739689750570.452260310249427
547.77.270998110095750.429001889904248
5588.20412774118276-0.204127741182761
5688.34961669172671-0.349616691726709
577.77.82129410731772-0.121294107317724
587.37.5684626041225-0.268462604122502
597.46.829570930297140.570429069702856
608.18.30774672381223-0.207746723812228
618.38.260436866039040.0395631339609626

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8.7 & 8.68099051787152 & 0.0190094821284745 \tabularnewline
14 & 8.7 & 8.7154941714524 & -0.0154941714523904 \tabularnewline
15 & 8.5 & 8.49290955300777 & 0.00709044699222972 \tabularnewline
16 & 8.4 & 8.39529785596176 & 0.0047021440382391 \tabularnewline
17 & 8.5 & 8.5079238029641 & -0.00792380296410578 \tabularnewline
18 & 8.7 & 8.7262674174135 & -0.0262674174135054 \tabularnewline
19 & 8.7 & 8.59795356137622 & 0.102046438623784 \tabularnewline
20 & 8.6 & 8.73231590394013 & -0.132315903940132 \tabularnewline
21 & 8.5 & 8.29187468279727 & 0.208125317202725 \tabularnewline
22 & 8.3 & 8.54770867588768 & -0.247708675887676 \tabularnewline
23 & 8 & 8.00543315104749 & -0.00543315104748565 \tabularnewline
24 & 8.2 & 8.60627807175544 & -0.406278071755439 \tabularnewline
25 & 8.1 & 7.82075295426395 & 0.279247045736052 \tabularnewline
26 & 8.1 & 7.88579241130282 & 0.214207588697183 \tabularnewline
27 & 8 & 7.88854939448731 & 0.111450605512690 \tabularnewline
28 & 7.9 & 7.977636400544 & -0.0776364005440007 \tabularnewline
29 & 7.9 & 8.00250399280299 & -0.102503992802985 \tabularnewline
30 & 8 & 8.02218989935545 & -0.0221898993554515 \tabularnewline
31 & 8 & 7.82089820754594 & 0.179101792454064 \tabularnewline
32 & 7.9 & 8.0226269351786 & -0.122626935178609 \tabularnewline
33 & 8 & 7.60920432506505 & 0.390795674934951 \tabularnewline
34 & 7.7 & 8.21451830560136 & -0.514518305601364 \tabularnewline
35 & 7.2 & 7.3398493281955 & -0.139849328195498 \tabularnewline
36 & 7.5 & 7.51467812018654 & -0.0146781201865442 \tabularnewline
37 & 7.3 & 7.2514634582626 & 0.0485365417373931 \tabularnewline
38 & 7 & 7.01303738473855 & -0.0130373847385457 \tabularnewline
39 & 7 & 6.54118278383354 & 0.458817216166462 \tabularnewline
40 & 7 & 7.03475850042076 & -0.03475850042076 \tabularnewline
41 & 7.2 & 7.17621141072429 & 0.0237885892757124 \tabularnewline
42 & 7.3 & 7.5084592509359 & -0.208459250935899 \tabularnewline
43 & 7.1 & 7.16101698409946 & -0.0610169840994583 \tabularnewline
44 & 6.8 & 6.94161668171015 & -0.141616681710153 \tabularnewline
45 & 6.4 & 6.34662004678788 & 0.053379953212116 \tabularnewline
46 & 6.1 & 6.13380440161523 & -0.0338044016152281 \tabularnewline
47 & 6.5 & 5.72432220097245 & 0.775677799027552 \tabularnewline
48 & 7.7 & 7.60251798562167 & 0.0974820143783273 \tabularnewline
49 & 7.9 & 8.41426891467136 & -0.514268914671362 \tabularnewline
50 & 7.5 & 8.05704408252355 & -0.557044082523548 \tabularnewline
51 & 6.9 & 6.97615247416296 & -0.0761524741629582 \tabularnewline
52 & 6.6 & 6.40106699065521 & 0.198933009344787 \tabularnewline
53 & 6.9 & 6.44773968975057 & 0.452260310249427 \tabularnewline
54 & 7.7 & 7.27099811009575 & 0.429001889904248 \tabularnewline
55 & 8 & 8.20412774118276 & -0.204127741182761 \tabularnewline
56 & 8 & 8.34961669172671 & -0.349616691726709 \tabularnewline
57 & 7.7 & 7.82129410731772 & -0.121294107317724 \tabularnewline
58 & 7.3 & 7.5684626041225 & -0.268462604122502 \tabularnewline
59 & 7.4 & 6.82957093029714 & 0.570429069702856 \tabularnewline
60 & 8.1 & 8.30774672381223 & -0.207746723812228 \tabularnewline
61 & 8.3 & 8.26043686603904 & 0.0395631339609626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63790&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]8.7[/C][C]8.68099051787152[/C][C]0.0190094821284745[/C][/ROW]
[ROW][C]14[/C][C]8.7[/C][C]8.7154941714524[/C][C]-0.0154941714523904[/C][/ROW]
[ROW][C]15[/C][C]8.5[/C][C]8.49290955300777[/C][C]0.00709044699222972[/C][/ROW]
[ROW][C]16[/C][C]8.4[/C][C]8.39529785596176[/C][C]0.0047021440382391[/C][/ROW]
[ROW][C]17[/C][C]8.5[/C][C]8.5079238029641[/C][C]-0.00792380296410578[/C][/ROW]
[ROW][C]18[/C][C]8.7[/C][C]8.7262674174135[/C][C]-0.0262674174135054[/C][/ROW]
[ROW][C]19[/C][C]8.7[/C][C]8.59795356137622[/C][C]0.102046438623784[/C][/ROW]
[ROW][C]20[/C][C]8.6[/C][C]8.73231590394013[/C][C]-0.132315903940132[/C][/ROW]
[ROW][C]21[/C][C]8.5[/C][C]8.29187468279727[/C][C]0.208125317202725[/C][/ROW]
[ROW][C]22[/C][C]8.3[/C][C]8.54770867588768[/C][C]-0.247708675887676[/C][/ROW]
[ROW][C]23[/C][C]8[/C][C]8.00543315104749[/C][C]-0.00543315104748565[/C][/ROW]
[ROW][C]24[/C][C]8.2[/C][C]8.60627807175544[/C][C]-0.406278071755439[/C][/ROW]
[ROW][C]25[/C][C]8.1[/C][C]7.82075295426395[/C][C]0.279247045736052[/C][/ROW]
[ROW][C]26[/C][C]8.1[/C][C]7.88579241130282[/C][C]0.214207588697183[/C][/ROW]
[ROW][C]27[/C][C]8[/C][C]7.88854939448731[/C][C]0.111450605512690[/C][/ROW]
[ROW][C]28[/C][C]7.9[/C][C]7.977636400544[/C][C]-0.0776364005440007[/C][/ROW]
[ROW][C]29[/C][C]7.9[/C][C]8.00250399280299[/C][C]-0.102503992802985[/C][/ROW]
[ROW][C]30[/C][C]8[/C][C]8.02218989935545[/C][C]-0.0221898993554515[/C][/ROW]
[ROW][C]31[/C][C]8[/C][C]7.82089820754594[/C][C]0.179101792454064[/C][/ROW]
[ROW][C]32[/C][C]7.9[/C][C]8.0226269351786[/C][C]-0.122626935178609[/C][/ROW]
[ROW][C]33[/C][C]8[/C][C]7.60920432506505[/C][C]0.390795674934951[/C][/ROW]
[ROW][C]34[/C][C]7.7[/C][C]8.21451830560136[/C][C]-0.514518305601364[/C][/ROW]
[ROW][C]35[/C][C]7.2[/C][C]7.3398493281955[/C][C]-0.139849328195498[/C][/ROW]
[ROW][C]36[/C][C]7.5[/C][C]7.51467812018654[/C][C]-0.0146781201865442[/C][/ROW]
[ROW][C]37[/C][C]7.3[/C][C]7.2514634582626[/C][C]0.0485365417373931[/C][/ROW]
[ROW][C]38[/C][C]7[/C][C]7.01303738473855[/C][C]-0.0130373847385457[/C][/ROW]
[ROW][C]39[/C][C]7[/C][C]6.54118278383354[/C][C]0.458817216166462[/C][/ROW]
[ROW][C]40[/C][C]7[/C][C]7.03475850042076[/C][C]-0.03475850042076[/C][/ROW]
[ROW][C]41[/C][C]7.2[/C][C]7.17621141072429[/C][C]0.0237885892757124[/C][/ROW]
[ROW][C]42[/C][C]7.3[/C][C]7.5084592509359[/C][C]-0.208459250935899[/C][/ROW]
[ROW][C]43[/C][C]7.1[/C][C]7.16101698409946[/C][C]-0.0610169840994583[/C][/ROW]
[ROW][C]44[/C][C]6.8[/C][C]6.94161668171015[/C][C]-0.141616681710153[/C][/ROW]
[ROW][C]45[/C][C]6.4[/C][C]6.34662004678788[/C][C]0.053379953212116[/C][/ROW]
[ROW][C]46[/C][C]6.1[/C][C]6.13380440161523[/C][C]-0.0338044016152281[/C][/ROW]
[ROW][C]47[/C][C]6.5[/C][C]5.72432220097245[/C][C]0.775677799027552[/C][/ROW]
[ROW][C]48[/C][C]7.7[/C][C]7.60251798562167[/C][C]0.0974820143783273[/C][/ROW]
[ROW][C]49[/C][C]7.9[/C][C]8.41426891467136[/C][C]-0.514268914671362[/C][/ROW]
[ROW][C]50[/C][C]7.5[/C][C]8.05704408252355[/C][C]-0.557044082523548[/C][/ROW]
[ROW][C]51[/C][C]6.9[/C][C]6.97615247416296[/C][C]-0.0761524741629582[/C][/ROW]
[ROW][C]52[/C][C]6.6[/C][C]6.40106699065521[/C][C]0.198933009344787[/C][/ROW]
[ROW][C]53[/C][C]6.9[/C][C]6.44773968975057[/C][C]0.452260310249427[/C][/ROW]
[ROW][C]54[/C][C]7.7[/C][C]7.27099811009575[/C][C]0.429001889904248[/C][/ROW]
[ROW][C]55[/C][C]8[/C][C]8.20412774118276[/C][C]-0.204127741182761[/C][/ROW]
[ROW][C]56[/C][C]8[/C][C]8.34961669172671[/C][C]-0.349616691726709[/C][/ROW]
[ROW][C]57[/C][C]7.7[/C][C]7.82129410731772[/C][C]-0.121294107317724[/C][/ROW]
[ROW][C]58[/C][C]7.3[/C][C]7.5684626041225[/C][C]-0.268462604122502[/C][/ROW]
[ROW][C]59[/C][C]7.4[/C][C]6.82957093029714[/C][C]0.570429069702856[/C][/ROW]
[ROW][C]60[/C][C]8.1[/C][C]8.30774672381223[/C][C]-0.207746723812228[/C][/ROW]
[ROW][C]61[/C][C]8.3[/C][C]8.26043686603904[/C][C]0.0395631339609626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63790&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63790&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
138.78.680990517871520.0190094821284745
148.78.7154941714524-0.0154941714523904
158.58.492909553007770.00709044699222972
168.48.395297855961760.0047021440382391
178.58.5079238029641-0.00792380296410578
188.78.7262674174135-0.0262674174135054
198.78.597953561376220.102046438623784
208.68.73231590394013-0.132315903940132
218.58.291874682797270.208125317202725
228.38.54770867588768-0.247708675887676
2388.00543315104749-0.00543315104748565
248.28.60627807175544-0.406278071755439
258.17.820752954263950.279247045736052
268.17.885792411302820.214207588697183
2787.888549394487310.111450605512690
287.97.977636400544-0.0776364005440007
297.98.00250399280299-0.102503992802985
3088.02218989935545-0.0221898993554515
3187.820898207545940.179101792454064
327.98.0226269351786-0.122626935178609
3387.609204325065050.390795674934951
347.78.21451830560136-0.514518305601364
357.27.3398493281955-0.139849328195498
367.57.51467812018654-0.0146781201865442
377.37.25146345826260.0485365417373931
3877.01303738473855-0.0130373847385457
3976.541182783833540.458817216166462
4077.03475850042076-0.03475850042076
417.27.176211410724290.0237885892757124
427.37.5084592509359-0.208459250935899
437.17.16101698409946-0.0610169840994583
446.86.94161668171015-0.141616681710153
456.46.346620046787880.053379953212116
466.16.13380440161523-0.0338044016152281
476.55.724322200972450.775677799027552
487.77.602517985621670.0974820143783273
497.98.41426891467136-0.514268914671362
507.58.05704408252355-0.557044082523548
516.96.97615247416296-0.0761524741629582
526.66.401066990655210.198933009344787
536.96.447739689750570.452260310249427
547.77.270998110095750.429001889904248
5588.20412774118276-0.204127741182761
5688.34961669172671-0.349616691726709
577.77.82129410731772-0.121294107317724
587.37.5684626041225-0.268462604122502
597.46.829570930297140.570429069702856
608.18.30774672381223-0.207746723812228
618.38.260436866039040.0395631339609626







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
628.406335072062947.879852812732718.93281733139316
638.308598437296567.192775016882139.42442185771099
648.300797644256686.478238566695410.1233567218179
658.498501306183375.8154407644469411.1815618479198
668.825261106274075.1138330455662512.5366891669819
678.845185894338974.1342436157612313.5561281729167
688.90626786351623.1094788002275014.7030569268049
698.734612878188491.9680038016963615.5012219546806
708.735391256628880.84231596156962216.6284665516881
718.60729026555166-0.31964255395744217.5342230850608
729.4649336707083-1.6541629424861820.5840302839028
739.67545508936314-3.9474493448253523.2983595235516

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 8.40633507206294 & 7.87985281273271 & 8.93281733139316 \tabularnewline
63 & 8.30859843729656 & 7.19277501688213 & 9.42442185771099 \tabularnewline
64 & 8.30079764425668 & 6.4782385666954 & 10.1233567218179 \tabularnewline
65 & 8.49850130618337 & 5.81544076444694 & 11.1815618479198 \tabularnewline
66 & 8.82526110627407 & 5.11383304556625 & 12.5366891669819 \tabularnewline
67 & 8.84518589433897 & 4.13424361576123 & 13.5561281729167 \tabularnewline
68 & 8.9062678635162 & 3.10947880022750 & 14.7030569268049 \tabularnewline
69 & 8.73461287818849 & 1.96800380169636 & 15.5012219546806 \tabularnewline
70 & 8.73539125662888 & 0.842315961569622 & 16.6284665516881 \tabularnewline
71 & 8.60729026555166 & -0.319642553957442 & 17.5342230850608 \tabularnewline
72 & 9.4649336707083 & -1.65416294248618 & 20.5840302839028 \tabularnewline
73 & 9.67545508936314 & -3.94744934482535 & 23.2983595235516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63790&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]62[/C][C]8.40633507206294[/C][C]7.87985281273271[/C][C]8.93281733139316[/C][/ROW]
[ROW][C]63[/C][C]8.30859843729656[/C][C]7.19277501688213[/C][C]9.42442185771099[/C][/ROW]
[ROW][C]64[/C][C]8.30079764425668[/C][C]6.4782385666954[/C][C]10.1233567218179[/C][/ROW]
[ROW][C]65[/C][C]8.49850130618337[/C][C]5.81544076444694[/C][C]11.1815618479198[/C][/ROW]
[ROW][C]66[/C][C]8.82526110627407[/C][C]5.11383304556625[/C][C]12.5366891669819[/C][/ROW]
[ROW][C]67[/C][C]8.84518589433897[/C][C]4.13424361576123[/C][C]13.5561281729167[/C][/ROW]
[ROW][C]68[/C][C]8.9062678635162[/C][C]3.10947880022750[/C][C]14.7030569268049[/C][/ROW]
[ROW][C]69[/C][C]8.73461287818849[/C][C]1.96800380169636[/C][C]15.5012219546806[/C][/ROW]
[ROW][C]70[/C][C]8.73539125662888[/C][C]0.842315961569622[/C][C]16.6284665516881[/C][/ROW]
[ROW][C]71[/C][C]8.60729026555166[/C][C]-0.319642553957442[/C][C]17.5342230850608[/C][/ROW]
[ROW][C]72[/C][C]9.4649336707083[/C][C]-1.65416294248618[/C][C]20.5840302839028[/C][/ROW]
[ROW][C]73[/C][C]9.67545508936314[/C][C]-3.94744934482535[/C][C]23.2983595235516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63790&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63790&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
628.406335072062947.879852812732718.93281733139316
638.308598437296567.192775016882139.42442185771099
648.300797644256686.478238566695410.1233567218179
658.498501306183375.8154407644469411.1815618479198
668.825261106274075.1138330455662512.5366891669819
678.845185894338974.1342436157612313.5561281729167
688.90626786351623.1094788002275014.7030569268049
698.734612878188491.9680038016963615.5012219546806
708.735391256628880.84231596156962216.6284665516881
718.60729026555166-0.31964255395744217.5342230850608
729.4649336707083-1.6541629424861820.5840302839028
739.67545508936314-3.9474493448253523.2983595235516



Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
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')