Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 23 May 2012 08:20:56 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/23/t1337775895ic4gua4asimd0in.htm/, Retrieved Mon, 29 Apr 2024 00:25:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167175, Retrieved Mon, 29 Apr 2024 00:25:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [IKO opgave 10 opd...] [2012-05-23 12:20:56] [76c30f62b7052b57088120e90a652e05] [Current]
Feedback Forum

Post a new message
Dataseries X:
7.08				
7.08				
7.09				
7.07				
7.06				
6.99				
6.99				
6.99				
6.98				
6.96				
6.95				
6.91				
6.91				
6.87				
6.91				
6.89				
6.88				
6.9				
6.91				
6.85				
6.86				
6.82				
6.8				
6.83				
6.84				
6.89				
7.14				
7.21				
7.25				
7.31				
7.3				
7.48				
7.49				
7.4				
7.44				
7.42				
7.14				
7.24				
7.33				
7.61				
7.66				
7.69				
7.7				
7.68				
7.71				
7.71				
7.72				
7.68				
7.72				
7.74				
7.76				
7.9				
7.97				
7.96				
7.95				
7.97				
7.93				
7.99				
7.96				
7.92				
7.97				
7.98				
8				
8.04				
8.17				
8.29				
8.26				
8.3				
8.32				
8.28				
8.27				
8.32				
8.31				
8.34				
8.32				
8.36				
8.33				
8.35				
8.34				
8.37				
8.31				
8.33				
8.34				
8.25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167175&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167175&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167175&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0244318563534208
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0244318563534208 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167175&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]0.0244318563534208[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167175&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167175&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
beta0.0244318563534208
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
37.097.080.00999999999999979
47.077.09024431856353-0.0202443185635337
57.067.06974971228042-0.00974971228041799
66.997.05951150871049-0.0695115087104945
76.996.987813213514770.00218678648522985
86.996.987866640768050.00213335923194702
96.986.98791876269436-0.00791876269435843
106.966.97772529262171-0.0177252926217131
116.956.95729223081856-0.00729223081855679
126.916.9471140680827-0.037114068082702
136.916.906207302502610.00379269749738587
146.876.90629996514306-0.036299965143062
156.916.865413089609050.0445869103909473
166.896.90650243059897-0.0165024305989681
176.886.88609924558509-0.00609924558509078
186.96.875950229693090.0240497703069087
196.916.896537810226560.0134621897734366
206.856.90686671651331-0.0568667165133103
216.866.845477357064170.0145226429358347
226.826.85583217219025-0.0358321721902461
236.86.81495672570646-0.0149567257064636
246.836.794591305132490.035408694867515
256.846.825456405279150.0145435947208492
266.896.835811732296230.0541882677037666
277.146.887135652268810.252864347731188
287.217.143313597689480.066686402310518
297.257.214942870291460.0350571297085409
307.317.255799381048660.054200618951338
317.37.31712360278515-0.0171236027851469
327.487.306705241381650.173294758618353
337.497.49093915403101-0.000939154031011746
347.47.50091620875463-0.100916208754632
357.447.408450638438610.0315493615613933
367.427.44922144790832-0.0292214479083173
377.147.42850751369058-0.288507513690583
387.247.141458739559210.0985412604407889
397.337.243866285479190.0861337145208143
407.617.335970692019540.274029307980456
417.667.622665736708750.0373342632912497
427.697.673577882066540.0164221179334572
437.77.70397910489291-0.00397910489291231
447.687.71388188797375-0.0338818879737541
457.717.69305409055380.0169459094462043
467.717.72346811057916-0.0134681105791641
477.727.72313905963614-0.00313905963614225
487.687.73306236658203-0.0530623665820267
497.727.691765954463920.0282340455360783
507.747.732455764608740.00754423539126492
517.767.752640084284110.00735991571588812
527.97.772819900687650.127180099312346
537.977.915927146605070.0540728533949313
547.967.98724824679183-0.0272482467918325
557.957.97658252154033-0.0265825215403321
567.977.965933061192550.00406693880745301
577.937.98603242405729-0.0560324240572889
587.997.944663447921590.045336552078413
597.968.00577110404953-0.0457711040495257
607.927.97465283101025-0.0546528310102508
617.977.93331756089370.0366824391062996
627.987.98421378097664-0.00421378097663805
6387.994110830485110.00588916951488727
648.048.014254713828740.0257452861712579
658.178.054883718962250.115116281037746
668.298.187696223404510.102303776595489
678.268.3101956945787-0.0501956945787025
688.38.27896932057920.0210306794208055
698.328.319483139117820.00051686088217906
708.288.33949576698865-0.0594957669886487
718.278.29804217495594-0.0280421749559441
728.328.287357052565580.0326429474344163
738.318.33815458036825-0.0281545803682537
748.348.327466711705010.0125332882949944
758.328.35777292320426-0.0377729232042636
768.368.336850060570490.0231499394295103
778.338.37741565656522-0.0474156565652208
788.358.346257204055120.00374279594488236
798.348.366348647508-0.0263486475080015
808.378.355704901136980.0142950988630197
818.318.38605415693896-0.0760541569389588
828.338.324196012701550.00580398729845299
838.348.3443378148855-0.00433781488549911
848.258.35423183401533-0.104231834015328

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 7.09 & 7.08 & 0.00999999999999979 \tabularnewline
4 & 7.07 & 7.09024431856353 & -0.0202443185635337 \tabularnewline
5 & 7.06 & 7.06974971228042 & -0.00974971228041799 \tabularnewline
6 & 6.99 & 7.05951150871049 & -0.0695115087104945 \tabularnewline
7 & 6.99 & 6.98781321351477 & 0.00218678648522985 \tabularnewline
8 & 6.99 & 6.98786664076805 & 0.00213335923194702 \tabularnewline
9 & 6.98 & 6.98791876269436 & -0.00791876269435843 \tabularnewline
10 & 6.96 & 6.97772529262171 & -0.0177252926217131 \tabularnewline
11 & 6.95 & 6.95729223081856 & -0.00729223081855679 \tabularnewline
12 & 6.91 & 6.9471140680827 & -0.037114068082702 \tabularnewline
13 & 6.91 & 6.90620730250261 & 0.00379269749738587 \tabularnewline
14 & 6.87 & 6.90629996514306 & -0.036299965143062 \tabularnewline
15 & 6.91 & 6.86541308960905 & 0.0445869103909473 \tabularnewline
16 & 6.89 & 6.90650243059897 & -0.0165024305989681 \tabularnewline
17 & 6.88 & 6.88609924558509 & -0.00609924558509078 \tabularnewline
18 & 6.9 & 6.87595022969309 & 0.0240497703069087 \tabularnewline
19 & 6.91 & 6.89653781022656 & 0.0134621897734366 \tabularnewline
20 & 6.85 & 6.90686671651331 & -0.0568667165133103 \tabularnewline
21 & 6.86 & 6.84547735706417 & 0.0145226429358347 \tabularnewline
22 & 6.82 & 6.85583217219025 & -0.0358321721902461 \tabularnewline
23 & 6.8 & 6.81495672570646 & -0.0149567257064636 \tabularnewline
24 & 6.83 & 6.79459130513249 & 0.035408694867515 \tabularnewline
25 & 6.84 & 6.82545640527915 & 0.0145435947208492 \tabularnewline
26 & 6.89 & 6.83581173229623 & 0.0541882677037666 \tabularnewline
27 & 7.14 & 6.88713565226881 & 0.252864347731188 \tabularnewline
28 & 7.21 & 7.14331359768948 & 0.066686402310518 \tabularnewline
29 & 7.25 & 7.21494287029146 & 0.0350571297085409 \tabularnewline
30 & 7.31 & 7.25579938104866 & 0.054200618951338 \tabularnewline
31 & 7.3 & 7.31712360278515 & -0.0171236027851469 \tabularnewline
32 & 7.48 & 7.30670524138165 & 0.173294758618353 \tabularnewline
33 & 7.49 & 7.49093915403101 & -0.000939154031011746 \tabularnewline
34 & 7.4 & 7.50091620875463 & -0.100916208754632 \tabularnewline
35 & 7.44 & 7.40845063843861 & 0.0315493615613933 \tabularnewline
36 & 7.42 & 7.44922144790832 & -0.0292214479083173 \tabularnewline
37 & 7.14 & 7.42850751369058 & -0.288507513690583 \tabularnewline
38 & 7.24 & 7.14145873955921 & 0.0985412604407889 \tabularnewline
39 & 7.33 & 7.24386628547919 & 0.0861337145208143 \tabularnewline
40 & 7.61 & 7.33597069201954 & 0.274029307980456 \tabularnewline
41 & 7.66 & 7.62266573670875 & 0.0373342632912497 \tabularnewline
42 & 7.69 & 7.67357788206654 & 0.0164221179334572 \tabularnewline
43 & 7.7 & 7.70397910489291 & -0.00397910489291231 \tabularnewline
44 & 7.68 & 7.71388188797375 & -0.0338818879737541 \tabularnewline
45 & 7.71 & 7.6930540905538 & 0.0169459094462043 \tabularnewline
46 & 7.71 & 7.72346811057916 & -0.0134681105791641 \tabularnewline
47 & 7.72 & 7.72313905963614 & -0.00313905963614225 \tabularnewline
48 & 7.68 & 7.73306236658203 & -0.0530623665820267 \tabularnewline
49 & 7.72 & 7.69176595446392 & 0.0282340455360783 \tabularnewline
50 & 7.74 & 7.73245576460874 & 0.00754423539126492 \tabularnewline
51 & 7.76 & 7.75264008428411 & 0.00735991571588812 \tabularnewline
52 & 7.9 & 7.77281990068765 & 0.127180099312346 \tabularnewline
53 & 7.97 & 7.91592714660507 & 0.0540728533949313 \tabularnewline
54 & 7.96 & 7.98724824679183 & -0.0272482467918325 \tabularnewline
55 & 7.95 & 7.97658252154033 & -0.0265825215403321 \tabularnewline
56 & 7.97 & 7.96593306119255 & 0.00406693880745301 \tabularnewline
57 & 7.93 & 7.98603242405729 & -0.0560324240572889 \tabularnewline
58 & 7.99 & 7.94466344792159 & 0.045336552078413 \tabularnewline
59 & 7.96 & 8.00577110404953 & -0.0457711040495257 \tabularnewline
60 & 7.92 & 7.97465283101025 & -0.0546528310102508 \tabularnewline
61 & 7.97 & 7.9333175608937 & 0.0366824391062996 \tabularnewline
62 & 7.98 & 7.98421378097664 & -0.00421378097663805 \tabularnewline
63 & 8 & 7.99411083048511 & 0.00588916951488727 \tabularnewline
64 & 8.04 & 8.01425471382874 & 0.0257452861712579 \tabularnewline
65 & 8.17 & 8.05488371896225 & 0.115116281037746 \tabularnewline
66 & 8.29 & 8.18769622340451 & 0.102303776595489 \tabularnewline
67 & 8.26 & 8.3101956945787 & -0.0501956945787025 \tabularnewline
68 & 8.3 & 8.2789693205792 & 0.0210306794208055 \tabularnewline
69 & 8.32 & 8.31948313911782 & 0.00051686088217906 \tabularnewline
70 & 8.28 & 8.33949576698865 & -0.0594957669886487 \tabularnewline
71 & 8.27 & 8.29804217495594 & -0.0280421749559441 \tabularnewline
72 & 8.32 & 8.28735705256558 & 0.0326429474344163 \tabularnewline
73 & 8.31 & 8.33815458036825 & -0.0281545803682537 \tabularnewline
74 & 8.34 & 8.32746671170501 & 0.0125332882949944 \tabularnewline
75 & 8.32 & 8.35777292320426 & -0.0377729232042636 \tabularnewline
76 & 8.36 & 8.33685006057049 & 0.0231499394295103 \tabularnewline
77 & 8.33 & 8.37741565656522 & -0.0474156565652208 \tabularnewline
78 & 8.35 & 8.34625720405512 & 0.00374279594488236 \tabularnewline
79 & 8.34 & 8.366348647508 & -0.0263486475080015 \tabularnewline
80 & 8.37 & 8.35570490113698 & 0.0142950988630197 \tabularnewline
81 & 8.31 & 8.38605415693896 & -0.0760541569389588 \tabularnewline
82 & 8.33 & 8.32419601270155 & 0.00580398729845299 \tabularnewline
83 & 8.34 & 8.3443378148855 & -0.00433781488549911 \tabularnewline
84 & 8.25 & 8.35423183401533 & -0.104231834015328 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167175&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]3[/C][C]7.09[/C][C]7.08[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]7.07[/C][C]7.09024431856353[/C][C]-0.0202443185635337[/C][/ROW]
[ROW][C]5[/C][C]7.06[/C][C]7.06974971228042[/C][C]-0.00974971228041799[/C][/ROW]
[ROW][C]6[/C][C]6.99[/C][C]7.05951150871049[/C][C]-0.0695115087104945[/C][/ROW]
[ROW][C]7[/C][C]6.99[/C][C]6.98781321351477[/C][C]0.00218678648522985[/C][/ROW]
[ROW][C]8[/C][C]6.99[/C][C]6.98786664076805[/C][C]0.00213335923194702[/C][/ROW]
[ROW][C]9[/C][C]6.98[/C][C]6.98791876269436[/C][C]-0.00791876269435843[/C][/ROW]
[ROW][C]10[/C][C]6.96[/C][C]6.97772529262171[/C][C]-0.0177252926217131[/C][/ROW]
[ROW][C]11[/C][C]6.95[/C][C]6.95729223081856[/C][C]-0.00729223081855679[/C][/ROW]
[ROW][C]12[/C][C]6.91[/C][C]6.9471140680827[/C][C]-0.037114068082702[/C][/ROW]
[ROW][C]13[/C][C]6.91[/C][C]6.90620730250261[/C][C]0.00379269749738587[/C][/ROW]
[ROW][C]14[/C][C]6.87[/C][C]6.90629996514306[/C][C]-0.036299965143062[/C][/ROW]
[ROW][C]15[/C][C]6.91[/C][C]6.86541308960905[/C][C]0.0445869103909473[/C][/ROW]
[ROW][C]16[/C][C]6.89[/C][C]6.90650243059897[/C][C]-0.0165024305989681[/C][/ROW]
[ROW][C]17[/C][C]6.88[/C][C]6.88609924558509[/C][C]-0.00609924558509078[/C][/ROW]
[ROW][C]18[/C][C]6.9[/C][C]6.87595022969309[/C][C]0.0240497703069087[/C][/ROW]
[ROW][C]19[/C][C]6.91[/C][C]6.89653781022656[/C][C]0.0134621897734366[/C][/ROW]
[ROW][C]20[/C][C]6.85[/C][C]6.90686671651331[/C][C]-0.0568667165133103[/C][/ROW]
[ROW][C]21[/C][C]6.86[/C][C]6.84547735706417[/C][C]0.0145226429358347[/C][/ROW]
[ROW][C]22[/C][C]6.82[/C][C]6.85583217219025[/C][C]-0.0358321721902461[/C][/ROW]
[ROW][C]23[/C][C]6.8[/C][C]6.81495672570646[/C][C]-0.0149567257064636[/C][/ROW]
[ROW][C]24[/C][C]6.83[/C][C]6.79459130513249[/C][C]0.035408694867515[/C][/ROW]
[ROW][C]25[/C][C]6.84[/C][C]6.82545640527915[/C][C]0.0145435947208492[/C][/ROW]
[ROW][C]26[/C][C]6.89[/C][C]6.83581173229623[/C][C]0.0541882677037666[/C][/ROW]
[ROW][C]27[/C][C]7.14[/C][C]6.88713565226881[/C][C]0.252864347731188[/C][/ROW]
[ROW][C]28[/C][C]7.21[/C][C]7.14331359768948[/C][C]0.066686402310518[/C][/ROW]
[ROW][C]29[/C][C]7.25[/C][C]7.21494287029146[/C][C]0.0350571297085409[/C][/ROW]
[ROW][C]30[/C][C]7.31[/C][C]7.25579938104866[/C][C]0.054200618951338[/C][/ROW]
[ROW][C]31[/C][C]7.3[/C][C]7.31712360278515[/C][C]-0.0171236027851469[/C][/ROW]
[ROW][C]32[/C][C]7.48[/C][C]7.30670524138165[/C][C]0.173294758618353[/C][/ROW]
[ROW][C]33[/C][C]7.49[/C][C]7.49093915403101[/C][C]-0.000939154031011746[/C][/ROW]
[ROW][C]34[/C][C]7.4[/C][C]7.50091620875463[/C][C]-0.100916208754632[/C][/ROW]
[ROW][C]35[/C][C]7.44[/C][C]7.40845063843861[/C][C]0.0315493615613933[/C][/ROW]
[ROW][C]36[/C][C]7.42[/C][C]7.44922144790832[/C][C]-0.0292214479083173[/C][/ROW]
[ROW][C]37[/C][C]7.14[/C][C]7.42850751369058[/C][C]-0.288507513690583[/C][/ROW]
[ROW][C]38[/C][C]7.24[/C][C]7.14145873955921[/C][C]0.0985412604407889[/C][/ROW]
[ROW][C]39[/C][C]7.33[/C][C]7.24386628547919[/C][C]0.0861337145208143[/C][/ROW]
[ROW][C]40[/C][C]7.61[/C][C]7.33597069201954[/C][C]0.274029307980456[/C][/ROW]
[ROW][C]41[/C][C]7.66[/C][C]7.62266573670875[/C][C]0.0373342632912497[/C][/ROW]
[ROW][C]42[/C][C]7.69[/C][C]7.67357788206654[/C][C]0.0164221179334572[/C][/ROW]
[ROW][C]43[/C][C]7.7[/C][C]7.70397910489291[/C][C]-0.00397910489291231[/C][/ROW]
[ROW][C]44[/C][C]7.68[/C][C]7.71388188797375[/C][C]-0.0338818879737541[/C][/ROW]
[ROW][C]45[/C][C]7.71[/C][C]7.6930540905538[/C][C]0.0169459094462043[/C][/ROW]
[ROW][C]46[/C][C]7.71[/C][C]7.72346811057916[/C][C]-0.0134681105791641[/C][/ROW]
[ROW][C]47[/C][C]7.72[/C][C]7.72313905963614[/C][C]-0.00313905963614225[/C][/ROW]
[ROW][C]48[/C][C]7.68[/C][C]7.73306236658203[/C][C]-0.0530623665820267[/C][/ROW]
[ROW][C]49[/C][C]7.72[/C][C]7.69176595446392[/C][C]0.0282340455360783[/C][/ROW]
[ROW][C]50[/C][C]7.74[/C][C]7.73245576460874[/C][C]0.00754423539126492[/C][/ROW]
[ROW][C]51[/C][C]7.76[/C][C]7.75264008428411[/C][C]0.00735991571588812[/C][/ROW]
[ROW][C]52[/C][C]7.9[/C][C]7.77281990068765[/C][C]0.127180099312346[/C][/ROW]
[ROW][C]53[/C][C]7.97[/C][C]7.91592714660507[/C][C]0.0540728533949313[/C][/ROW]
[ROW][C]54[/C][C]7.96[/C][C]7.98724824679183[/C][C]-0.0272482467918325[/C][/ROW]
[ROW][C]55[/C][C]7.95[/C][C]7.97658252154033[/C][C]-0.0265825215403321[/C][/ROW]
[ROW][C]56[/C][C]7.97[/C][C]7.96593306119255[/C][C]0.00406693880745301[/C][/ROW]
[ROW][C]57[/C][C]7.93[/C][C]7.98603242405729[/C][C]-0.0560324240572889[/C][/ROW]
[ROW][C]58[/C][C]7.99[/C][C]7.94466344792159[/C][C]0.045336552078413[/C][/ROW]
[ROW][C]59[/C][C]7.96[/C][C]8.00577110404953[/C][C]-0.0457711040495257[/C][/ROW]
[ROW][C]60[/C][C]7.92[/C][C]7.97465283101025[/C][C]-0.0546528310102508[/C][/ROW]
[ROW][C]61[/C][C]7.97[/C][C]7.9333175608937[/C][C]0.0366824391062996[/C][/ROW]
[ROW][C]62[/C][C]7.98[/C][C]7.98421378097664[/C][C]-0.00421378097663805[/C][/ROW]
[ROW][C]63[/C][C]8[/C][C]7.99411083048511[/C][C]0.00588916951488727[/C][/ROW]
[ROW][C]64[/C][C]8.04[/C][C]8.01425471382874[/C][C]0.0257452861712579[/C][/ROW]
[ROW][C]65[/C][C]8.17[/C][C]8.05488371896225[/C][C]0.115116281037746[/C][/ROW]
[ROW][C]66[/C][C]8.29[/C][C]8.18769622340451[/C][C]0.102303776595489[/C][/ROW]
[ROW][C]67[/C][C]8.26[/C][C]8.3101956945787[/C][C]-0.0501956945787025[/C][/ROW]
[ROW][C]68[/C][C]8.3[/C][C]8.2789693205792[/C][C]0.0210306794208055[/C][/ROW]
[ROW][C]69[/C][C]8.32[/C][C]8.31948313911782[/C][C]0.00051686088217906[/C][/ROW]
[ROW][C]70[/C][C]8.28[/C][C]8.33949576698865[/C][C]-0.0594957669886487[/C][/ROW]
[ROW][C]71[/C][C]8.27[/C][C]8.29804217495594[/C][C]-0.0280421749559441[/C][/ROW]
[ROW][C]72[/C][C]8.32[/C][C]8.28735705256558[/C][C]0.0326429474344163[/C][/ROW]
[ROW][C]73[/C][C]8.31[/C][C]8.33815458036825[/C][C]-0.0281545803682537[/C][/ROW]
[ROW][C]74[/C][C]8.34[/C][C]8.32746671170501[/C][C]0.0125332882949944[/C][/ROW]
[ROW][C]75[/C][C]8.32[/C][C]8.35777292320426[/C][C]-0.0377729232042636[/C][/ROW]
[ROW][C]76[/C][C]8.36[/C][C]8.33685006057049[/C][C]0.0231499394295103[/C][/ROW]
[ROW][C]77[/C][C]8.33[/C][C]8.37741565656522[/C][C]-0.0474156565652208[/C][/ROW]
[ROW][C]78[/C][C]8.35[/C][C]8.34625720405512[/C][C]0.00374279594488236[/C][/ROW]
[ROW][C]79[/C][C]8.34[/C][C]8.366348647508[/C][C]-0.0263486475080015[/C][/ROW]
[ROW][C]80[/C][C]8.37[/C][C]8.35570490113698[/C][C]0.0142950988630197[/C][/ROW]
[ROW][C]81[/C][C]8.31[/C][C]8.38605415693896[/C][C]-0.0760541569389588[/C][/ROW]
[ROW][C]82[/C][C]8.33[/C][C]8.32419601270155[/C][C]0.00580398729845299[/C][/ROW]
[ROW][C]83[/C][C]8.34[/C][C]8.3443378148855[/C][C]-0.00433781488549911[/C][/ROW]
[ROW][C]84[/C][C]8.25[/C][C]8.35423183401533[/C][C]-0.104231834015328[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167175&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167175&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
37.097.080.00999999999999979
47.077.09024431856353-0.0202443185635337
57.067.06974971228042-0.00974971228041799
66.997.05951150871049-0.0695115087104945
76.996.987813213514770.00218678648522985
86.996.987866640768050.00213335923194702
96.986.98791876269436-0.00791876269435843
106.966.97772529262171-0.0177252926217131
116.956.95729223081856-0.00729223081855679
126.916.9471140680827-0.037114068082702
136.916.906207302502610.00379269749738587
146.876.90629996514306-0.036299965143062
156.916.865413089609050.0445869103909473
166.896.90650243059897-0.0165024305989681
176.886.88609924558509-0.00609924558509078
186.96.875950229693090.0240497703069087
196.916.896537810226560.0134621897734366
206.856.90686671651331-0.0568667165133103
216.866.845477357064170.0145226429358347
226.826.85583217219025-0.0358321721902461
236.86.81495672570646-0.0149567257064636
246.836.794591305132490.035408694867515
256.846.825456405279150.0145435947208492
266.896.835811732296230.0541882677037666
277.146.887135652268810.252864347731188
287.217.143313597689480.066686402310518
297.257.214942870291460.0350571297085409
307.317.255799381048660.054200618951338
317.37.31712360278515-0.0171236027851469
327.487.306705241381650.173294758618353
337.497.49093915403101-0.000939154031011746
347.47.50091620875463-0.100916208754632
357.447.408450638438610.0315493615613933
367.427.44922144790832-0.0292214479083173
377.147.42850751369058-0.288507513690583
387.247.141458739559210.0985412604407889
397.337.243866285479190.0861337145208143
407.617.335970692019540.274029307980456
417.667.622665736708750.0373342632912497
427.697.673577882066540.0164221179334572
437.77.70397910489291-0.00397910489291231
447.687.71388188797375-0.0338818879737541
457.717.69305409055380.0169459094462043
467.717.72346811057916-0.0134681105791641
477.727.72313905963614-0.00313905963614225
487.687.73306236658203-0.0530623665820267
497.727.691765954463920.0282340455360783
507.747.732455764608740.00754423539126492
517.767.752640084284110.00735991571588812
527.97.772819900687650.127180099312346
537.977.915927146605070.0540728533949313
547.967.98724824679183-0.0272482467918325
557.957.97658252154033-0.0265825215403321
567.977.965933061192550.00406693880745301
577.937.98603242405729-0.0560324240572889
587.997.944663447921590.045336552078413
597.968.00577110404953-0.0457711040495257
607.927.97465283101025-0.0546528310102508
617.977.93331756089370.0366824391062996
627.987.98421378097664-0.00421378097663805
6387.994110830485110.00588916951488727
648.048.014254713828740.0257452861712579
658.178.054883718962250.115116281037746
668.298.187696223404510.102303776595489
678.268.3101956945787-0.0501956945787025
688.38.27896932057920.0210306794208055
698.328.319483139117820.00051686088217906
708.288.33949576698865-0.0594957669886487
718.278.29804217495594-0.0280421749559441
728.328.287357052565580.0326429474344163
738.318.33815458036825-0.0281545803682537
748.348.327466711705010.0125332882949944
758.328.35777292320426-0.0377729232042636
768.368.336850060570490.0231499394295103
778.338.37741565656522-0.0474156565652208
788.358.346257204055120.00374279594488236
798.348.366348647508-0.0263486475080015
808.378.355704901136980.0142950988630197
818.318.38605415693896-0.0760541569389588
828.338.324196012701550.00580398729845299
838.348.3443378148855-0.00433781488549911
848.258.35423183401533-0.104231834015328







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
858.261685256819218.123376508141298.39999400549714
868.273370513638438.075368575234938.47137245204192
878.285055770457648.039598625278868.53051291563641
888.296741027276858.009886578729468.58359547582424
898.308426284096067.983870590300498.63298197789164
908.320111540915287.96035493088898.67986815094165
918.331796797734497.938638341045198.72495525442378
928.34348205455377.918269758907998.76869435019941
938.355167311372917.898939924502218.81139469824362
948.366852568192137.880426617279448.85327851910481
958.378537825011347.862564312990768.89451133703191
968.390223081830557.84522616087168.93522000278951

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 8.26168525681921 & 8.12337650814129 & 8.39999400549714 \tabularnewline
86 & 8.27337051363843 & 8.07536857523493 & 8.47137245204192 \tabularnewline
87 & 8.28505577045764 & 8.03959862527886 & 8.53051291563641 \tabularnewline
88 & 8.29674102727685 & 8.00988657872946 & 8.58359547582424 \tabularnewline
89 & 8.30842628409606 & 7.98387059030049 & 8.63298197789164 \tabularnewline
90 & 8.32011154091528 & 7.9603549308889 & 8.67986815094165 \tabularnewline
91 & 8.33179679773449 & 7.93863834104519 & 8.72495525442378 \tabularnewline
92 & 8.3434820545537 & 7.91826975890799 & 8.76869435019941 \tabularnewline
93 & 8.35516731137291 & 7.89893992450221 & 8.81139469824362 \tabularnewline
94 & 8.36685256819213 & 7.88042661727944 & 8.85327851910481 \tabularnewline
95 & 8.37853782501134 & 7.86256431299076 & 8.89451133703191 \tabularnewline
96 & 8.39022308183055 & 7.8452261608716 & 8.93522000278951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167175&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]85[/C][C]8.26168525681921[/C][C]8.12337650814129[/C][C]8.39999400549714[/C][/ROW]
[ROW][C]86[/C][C]8.27337051363843[/C][C]8.07536857523493[/C][C]8.47137245204192[/C][/ROW]
[ROW][C]87[/C][C]8.28505577045764[/C][C]8.03959862527886[/C][C]8.53051291563641[/C][/ROW]
[ROW][C]88[/C][C]8.29674102727685[/C][C]8.00988657872946[/C][C]8.58359547582424[/C][/ROW]
[ROW][C]89[/C][C]8.30842628409606[/C][C]7.98387059030049[/C][C]8.63298197789164[/C][/ROW]
[ROW][C]90[/C][C]8.32011154091528[/C][C]7.9603549308889[/C][C]8.67986815094165[/C][/ROW]
[ROW][C]91[/C][C]8.33179679773449[/C][C]7.93863834104519[/C][C]8.72495525442378[/C][/ROW]
[ROW][C]92[/C][C]8.3434820545537[/C][C]7.91826975890799[/C][C]8.76869435019941[/C][/ROW]
[ROW][C]93[/C][C]8.35516731137291[/C][C]7.89893992450221[/C][C]8.81139469824362[/C][/ROW]
[ROW][C]94[/C][C]8.36685256819213[/C][C]7.88042661727944[/C][C]8.85327851910481[/C][/ROW]
[ROW][C]95[/C][C]8.37853782501134[/C][C]7.86256431299076[/C][C]8.89451133703191[/C][/ROW]
[ROW][C]96[/C][C]8.39022308183055[/C][C]7.8452261608716[/C][C]8.93522000278951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167175&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167175&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
858.261685256819218.123376508141298.39999400549714
868.273370513638438.075368575234938.47137245204192
878.285055770457648.039598625278868.53051291563641
888.296741027276858.009886578729468.58359547582424
898.308426284096067.983870590300498.63298197789164
908.320111540915287.96035493088898.67986815094165
918.331796797734497.938638341045198.72495525442378
928.34348205455377.918269758907998.76869435019941
938.355167311372917.898939924502218.81139469824362
948.366852568192137.880426617279448.85327851910481
958.378537825011347.862564312990768.89451133703191
968.390223081830557.84522616087168.93522000278951



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