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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Jan 2010 05:42:30 -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/2010/Jan/26/t1264509794yorethu7fhcwsw0.htm/, Retrieved Thu, 02 May 2024 17:07:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72620, Retrieved Thu, 02 May 2024 17:07:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Gemiddelde consum...] [2010-01-14 19:07:55] [bf68df4edce3d2e638b253cf289b9d76]
- R PD    [Exponential Smoothing] [consumptieprijs r...] [2010-01-26 12:42:30] [6590c54be3d1f5d26c781440f79f0ebc] [Current]
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Dataseries X:
2.12
2.13
2.14
2.15
2.15
2.16
2.17
2.17
2.18
2.17
2.17
2.18
2.17
2.18
2.18
2.18
2.17
2.17
2.18
2.17
2.18
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.17
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.18
2.19
2.19
2.19
2.2
2.2
2.21
2.21
2.21
2.2
2.21
2.2
2.21
2.21
2.22
2.22
2.23
2.24
2.24
2.25
2.25
2.32
2.36
2.37
2.37
2.37
2.38
2.38
2.41
2.42
2.43
2.44
2.44
2.44
2.43
2.43
2.43
2.42
2.42
2.42
2.42
2.42




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=72620&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=72620&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72620&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
beta0.191978877192319
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.191978877192319 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72620&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]0.191978877192319[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72620&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72620&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
beta0.191978877192319
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32.142.144.44089209850063e-16
42.152.150
52.152.16-0.00999999999999979
62.162.158080211228080.00191978877192334
72.172.168448770120960.00155122987904299
82.172.17874657349140-0.00874657349140273
92.182.177067416133240.0029325838667571
102.172.18763041029126-0.0176304102912557
112.172.1742457439191-0.00424574391910015
122.182.173430650768670.00656934923133479
132.172.18469182705798-0.0146918270579817
142.182.171871306595490.00812869340451394
152.182.18343184402833-0.00343184402832541
162.182.18277300246507-0.00277300246506851
172.172.18224064456537-0.0122406445653733
182.172.169890699365600.000109300634397513
192.182.169911682778670.0100883172213297
202.172.18184842659158-0.0118484265915817
212.182.169573778958030.0104262210419663
222.172.18157539316703-0.0115753931670297
232.172.169353162183760.000646837816236534
242.172.169477341381450.000522658618550054
252.172.169577680796190.000422319203805976
262.172.169658757162760.000341242837242461
272.172.16972426857950.000275731420498637
282.172.169777203188020.000222796811984782
292.172.169819975469820.000180024530177736
302.172.169854536376990.000145463623007380
312.182.169882462320010.0101175376799900
322.182.18182481584377-0.00182481584376548
332.182.18147448974700-0.00147448974699671
342.182.18119141886094-0.00119141886093654
352.182.18096269160575-0.000962691605748134
362.182.18077787515219-0.000777875152194074
372.182.18062853955388-0.000628539553880092
382.182.18050787323606-0.000507873236055278
392.182.18041037230244-0.000410372302441342
402.182.18033158948859-0.000331589488587802
412.182.18026793131088-0.000267931310879987
422.182.18021649415865-0.000216494158652658
432.182.18017493185316-0.000174931853155869
442.192.18014134863240.009858651367598
452.192.19203400145258-0.00203400145258392
462.192.19164351613751-0.00164351613750924
472.22.191327995754780.00867200424521775
482.22.20299283739279-0.00299283739278655
492.212.20241827583050.00758172416949954
502.212.21387380672374-0.00387380672374249
512.212.21313011765846-0.00313011765845861
522.22.21252920118491-0.0125292011849076
532.212.200123859209310.00987614079068733
542.22.21201986962930-0.0120198696293019
552.212.199712308553870.0102876914461292
562.212.2116873280066-0.00168732800659965
572.222.211363396670440.00863660332956284
582.222.22302144208040-0.00302144208040245
592.232.222441389022310.00755861097769461
602.242.233892482670940.00610751732906367
612.242.24506499699020-0.0050649969902028
622.252.244092624555040.00590737544495878
632.252.25522671586012-0.0052267158601178
642.322.254223296817890.0657767031821108
652.362.336851034440200.0231489655597970
662.372.38129514685654-0.0112951468565363
672.372.38912671724530-0.0191267172452965
682.372.38545479154417-0.0154547915441694
692.382.38248779801628-0.00248779801627874
702.382.39201019334643-0.0120101933464318
712.412.389704489912920.0202955100870787
722.422.42360079915148-0.00360079915148415
732.432.43290952177339-0.00290952177338699
742.442.44235095505017-0.00235095505016591
752.442.45189962133931-0.0118996213393054
762.442.44961514539557-0.00961514539557173
772.432.44776924057849-0.0177692405784886
782.432.43435792172367-0.00435792172367044
792.432.43352129280427-0.00352129280426805
802.422.43284527896544-0.0128452789654396
812.422.42037925673243-0.000379256732432331
822.422.42030644745077-0.000306447450772129
832.422.42024761601325-0.000247616013254515
842.422.42020007896906-0.000200078969055273

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2.14 & 2.14 & 4.44089209850063e-16 \tabularnewline
4 & 2.15 & 2.15 & 0 \tabularnewline
5 & 2.15 & 2.16 & -0.00999999999999979 \tabularnewline
6 & 2.16 & 2.15808021122808 & 0.00191978877192334 \tabularnewline
7 & 2.17 & 2.16844877012096 & 0.00155122987904299 \tabularnewline
8 & 2.17 & 2.17874657349140 & -0.00874657349140273 \tabularnewline
9 & 2.18 & 2.17706741613324 & 0.0029325838667571 \tabularnewline
10 & 2.17 & 2.18763041029126 & -0.0176304102912557 \tabularnewline
11 & 2.17 & 2.1742457439191 & -0.00424574391910015 \tabularnewline
12 & 2.18 & 2.17343065076867 & 0.00656934923133479 \tabularnewline
13 & 2.17 & 2.18469182705798 & -0.0146918270579817 \tabularnewline
14 & 2.18 & 2.17187130659549 & 0.00812869340451394 \tabularnewline
15 & 2.18 & 2.18343184402833 & -0.00343184402832541 \tabularnewline
16 & 2.18 & 2.18277300246507 & -0.00277300246506851 \tabularnewline
17 & 2.17 & 2.18224064456537 & -0.0122406445653733 \tabularnewline
18 & 2.17 & 2.16989069936560 & 0.000109300634397513 \tabularnewline
19 & 2.18 & 2.16991168277867 & 0.0100883172213297 \tabularnewline
20 & 2.17 & 2.18184842659158 & -0.0118484265915817 \tabularnewline
21 & 2.18 & 2.16957377895803 & 0.0104262210419663 \tabularnewline
22 & 2.17 & 2.18157539316703 & -0.0115753931670297 \tabularnewline
23 & 2.17 & 2.16935316218376 & 0.000646837816236534 \tabularnewline
24 & 2.17 & 2.16947734138145 & 0.000522658618550054 \tabularnewline
25 & 2.17 & 2.16957768079619 & 0.000422319203805976 \tabularnewline
26 & 2.17 & 2.16965875716276 & 0.000341242837242461 \tabularnewline
27 & 2.17 & 2.1697242685795 & 0.000275731420498637 \tabularnewline
28 & 2.17 & 2.16977720318802 & 0.000222796811984782 \tabularnewline
29 & 2.17 & 2.16981997546982 & 0.000180024530177736 \tabularnewline
30 & 2.17 & 2.16985453637699 & 0.000145463623007380 \tabularnewline
31 & 2.18 & 2.16988246232001 & 0.0101175376799900 \tabularnewline
32 & 2.18 & 2.18182481584377 & -0.00182481584376548 \tabularnewline
33 & 2.18 & 2.18147448974700 & -0.00147448974699671 \tabularnewline
34 & 2.18 & 2.18119141886094 & -0.00119141886093654 \tabularnewline
35 & 2.18 & 2.18096269160575 & -0.000962691605748134 \tabularnewline
36 & 2.18 & 2.18077787515219 & -0.000777875152194074 \tabularnewline
37 & 2.18 & 2.18062853955388 & -0.000628539553880092 \tabularnewline
38 & 2.18 & 2.18050787323606 & -0.000507873236055278 \tabularnewline
39 & 2.18 & 2.18041037230244 & -0.000410372302441342 \tabularnewline
40 & 2.18 & 2.18033158948859 & -0.000331589488587802 \tabularnewline
41 & 2.18 & 2.18026793131088 & -0.000267931310879987 \tabularnewline
42 & 2.18 & 2.18021649415865 & -0.000216494158652658 \tabularnewline
43 & 2.18 & 2.18017493185316 & -0.000174931853155869 \tabularnewline
44 & 2.19 & 2.1801413486324 & 0.009858651367598 \tabularnewline
45 & 2.19 & 2.19203400145258 & -0.00203400145258392 \tabularnewline
46 & 2.19 & 2.19164351613751 & -0.00164351613750924 \tabularnewline
47 & 2.2 & 2.19132799575478 & 0.00867200424521775 \tabularnewline
48 & 2.2 & 2.20299283739279 & -0.00299283739278655 \tabularnewline
49 & 2.21 & 2.2024182758305 & 0.00758172416949954 \tabularnewline
50 & 2.21 & 2.21387380672374 & -0.00387380672374249 \tabularnewline
51 & 2.21 & 2.21313011765846 & -0.00313011765845861 \tabularnewline
52 & 2.2 & 2.21252920118491 & -0.0125292011849076 \tabularnewline
53 & 2.21 & 2.20012385920931 & 0.00987614079068733 \tabularnewline
54 & 2.2 & 2.21201986962930 & -0.0120198696293019 \tabularnewline
55 & 2.21 & 2.19971230855387 & 0.0102876914461292 \tabularnewline
56 & 2.21 & 2.2116873280066 & -0.00168732800659965 \tabularnewline
57 & 2.22 & 2.21136339667044 & 0.00863660332956284 \tabularnewline
58 & 2.22 & 2.22302144208040 & -0.00302144208040245 \tabularnewline
59 & 2.23 & 2.22244138902231 & 0.00755861097769461 \tabularnewline
60 & 2.24 & 2.23389248267094 & 0.00610751732906367 \tabularnewline
61 & 2.24 & 2.24506499699020 & -0.0050649969902028 \tabularnewline
62 & 2.25 & 2.24409262455504 & 0.00590737544495878 \tabularnewline
63 & 2.25 & 2.25522671586012 & -0.0052267158601178 \tabularnewline
64 & 2.32 & 2.25422329681789 & 0.0657767031821108 \tabularnewline
65 & 2.36 & 2.33685103444020 & 0.0231489655597970 \tabularnewline
66 & 2.37 & 2.38129514685654 & -0.0112951468565363 \tabularnewline
67 & 2.37 & 2.38912671724530 & -0.0191267172452965 \tabularnewline
68 & 2.37 & 2.38545479154417 & -0.0154547915441694 \tabularnewline
69 & 2.38 & 2.38248779801628 & -0.00248779801627874 \tabularnewline
70 & 2.38 & 2.39201019334643 & -0.0120101933464318 \tabularnewline
71 & 2.41 & 2.38970448991292 & 0.0202955100870787 \tabularnewline
72 & 2.42 & 2.42360079915148 & -0.00360079915148415 \tabularnewline
73 & 2.43 & 2.43290952177339 & -0.00290952177338699 \tabularnewline
74 & 2.44 & 2.44235095505017 & -0.00235095505016591 \tabularnewline
75 & 2.44 & 2.45189962133931 & -0.0118996213393054 \tabularnewline
76 & 2.44 & 2.44961514539557 & -0.00961514539557173 \tabularnewline
77 & 2.43 & 2.44776924057849 & -0.0177692405784886 \tabularnewline
78 & 2.43 & 2.43435792172367 & -0.00435792172367044 \tabularnewline
79 & 2.43 & 2.43352129280427 & -0.00352129280426805 \tabularnewline
80 & 2.42 & 2.43284527896544 & -0.0128452789654396 \tabularnewline
81 & 2.42 & 2.42037925673243 & -0.000379256732432331 \tabularnewline
82 & 2.42 & 2.42030644745077 & -0.000306447450772129 \tabularnewline
83 & 2.42 & 2.42024761601325 & -0.000247616013254515 \tabularnewline
84 & 2.42 & 2.42020007896906 & -0.000200078969055273 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72620&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]2.14[/C][C]2.14[/C][C]4.44089209850063e-16[/C][/ROW]
[ROW][C]4[/C][C]2.15[/C][C]2.15[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]2.15[/C][C]2.16[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]6[/C][C]2.16[/C][C]2.15808021122808[/C][C]0.00191978877192334[/C][/ROW]
[ROW][C]7[/C][C]2.17[/C][C]2.16844877012096[/C][C]0.00155122987904299[/C][/ROW]
[ROW][C]8[/C][C]2.17[/C][C]2.17874657349140[/C][C]-0.00874657349140273[/C][/ROW]
[ROW][C]9[/C][C]2.18[/C][C]2.17706741613324[/C][C]0.0029325838667571[/C][/ROW]
[ROW][C]10[/C][C]2.17[/C][C]2.18763041029126[/C][C]-0.0176304102912557[/C][/ROW]
[ROW][C]11[/C][C]2.17[/C][C]2.1742457439191[/C][C]-0.00424574391910015[/C][/ROW]
[ROW][C]12[/C][C]2.18[/C][C]2.17343065076867[/C][C]0.00656934923133479[/C][/ROW]
[ROW][C]13[/C][C]2.17[/C][C]2.18469182705798[/C][C]-0.0146918270579817[/C][/ROW]
[ROW][C]14[/C][C]2.18[/C][C]2.17187130659549[/C][C]0.00812869340451394[/C][/ROW]
[ROW][C]15[/C][C]2.18[/C][C]2.18343184402833[/C][C]-0.00343184402832541[/C][/ROW]
[ROW][C]16[/C][C]2.18[/C][C]2.18277300246507[/C][C]-0.00277300246506851[/C][/ROW]
[ROW][C]17[/C][C]2.17[/C][C]2.18224064456537[/C][C]-0.0122406445653733[/C][/ROW]
[ROW][C]18[/C][C]2.17[/C][C]2.16989069936560[/C][C]0.000109300634397513[/C][/ROW]
[ROW][C]19[/C][C]2.18[/C][C]2.16991168277867[/C][C]0.0100883172213297[/C][/ROW]
[ROW][C]20[/C][C]2.17[/C][C]2.18184842659158[/C][C]-0.0118484265915817[/C][/ROW]
[ROW][C]21[/C][C]2.18[/C][C]2.16957377895803[/C][C]0.0104262210419663[/C][/ROW]
[ROW][C]22[/C][C]2.17[/C][C]2.18157539316703[/C][C]-0.0115753931670297[/C][/ROW]
[ROW][C]23[/C][C]2.17[/C][C]2.16935316218376[/C][C]0.000646837816236534[/C][/ROW]
[ROW][C]24[/C][C]2.17[/C][C]2.16947734138145[/C][C]0.000522658618550054[/C][/ROW]
[ROW][C]25[/C][C]2.17[/C][C]2.16957768079619[/C][C]0.000422319203805976[/C][/ROW]
[ROW][C]26[/C][C]2.17[/C][C]2.16965875716276[/C][C]0.000341242837242461[/C][/ROW]
[ROW][C]27[/C][C]2.17[/C][C]2.1697242685795[/C][C]0.000275731420498637[/C][/ROW]
[ROW][C]28[/C][C]2.17[/C][C]2.16977720318802[/C][C]0.000222796811984782[/C][/ROW]
[ROW][C]29[/C][C]2.17[/C][C]2.16981997546982[/C][C]0.000180024530177736[/C][/ROW]
[ROW][C]30[/C][C]2.17[/C][C]2.16985453637699[/C][C]0.000145463623007380[/C][/ROW]
[ROW][C]31[/C][C]2.18[/C][C]2.16988246232001[/C][C]0.0101175376799900[/C][/ROW]
[ROW][C]32[/C][C]2.18[/C][C]2.18182481584377[/C][C]-0.00182481584376548[/C][/ROW]
[ROW][C]33[/C][C]2.18[/C][C]2.18147448974700[/C][C]-0.00147448974699671[/C][/ROW]
[ROW][C]34[/C][C]2.18[/C][C]2.18119141886094[/C][C]-0.00119141886093654[/C][/ROW]
[ROW][C]35[/C][C]2.18[/C][C]2.18096269160575[/C][C]-0.000962691605748134[/C][/ROW]
[ROW][C]36[/C][C]2.18[/C][C]2.18077787515219[/C][C]-0.000777875152194074[/C][/ROW]
[ROW][C]37[/C][C]2.18[/C][C]2.18062853955388[/C][C]-0.000628539553880092[/C][/ROW]
[ROW][C]38[/C][C]2.18[/C][C]2.18050787323606[/C][C]-0.000507873236055278[/C][/ROW]
[ROW][C]39[/C][C]2.18[/C][C]2.18041037230244[/C][C]-0.000410372302441342[/C][/ROW]
[ROW][C]40[/C][C]2.18[/C][C]2.18033158948859[/C][C]-0.000331589488587802[/C][/ROW]
[ROW][C]41[/C][C]2.18[/C][C]2.18026793131088[/C][C]-0.000267931310879987[/C][/ROW]
[ROW][C]42[/C][C]2.18[/C][C]2.18021649415865[/C][C]-0.000216494158652658[/C][/ROW]
[ROW][C]43[/C][C]2.18[/C][C]2.18017493185316[/C][C]-0.000174931853155869[/C][/ROW]
[ROW][C]44[/C][C]2.19[/C][C]2.1801413486324[/C][C]0.009858651367598[/C][/ROW]
[ROW][C]45[/C][C]2.19[/C][C]2.19203400145258[/C][C]-0.00203400145258392[/C][/ROW]
[ROW][C]46[/C][C]2.19[/C][C]2.19164351613751[/C][C]-0.00164351613750924[/C][/ROW]
[ROW][C]47[/C][C]2.2[/C][C]2.19132799575478[/C][C]0.00867200424521775[/C][/ROW]
[ROW][C]48[/C][C]2.2[/C][C]2.20299283739279[/C][C]-0.00299283739278655[/C][/ROW]
[ROW][C]49[/C][C]2.21[/C][C]2.2024182758305[/C][C]0.00758172416949954[/C][/ROW]
[ROW][C]50[/C][C]2.21[/C][C]2.21387380672374[/C][C]-0.00387380672374249[/C][/ROW]
[ROW][C]51[/C][C]2.21[/C][C]2.21313011765846[/C][C]-0.00313011765845861[/C][/ROW]
[ROW][C]52[/C][C]2.2[/C][C]2.21252920118491[/C][C]-0.0125292011849076[/C][/ROW]
[ROW][C]53[/C][C]2.21[/C][C]2.20012385920931[/C][C]0.00987614079068733[/C][/ROW]
[ROW][C]54[/C][C]2.2[/C][C]2.21201986962930[/C][C]-0.0120198696293019[/C][/ROW]
[ROW][C]55[/C][C]2.21[/C][C]2.19971230855387[/C][C]0.0102876914461292[/C][/ROW]
[ROW][C]56[/C][C]2.21[/C][C]2.2116873280066[/C][C]-0.00168732800659965[/C][/ROW]
[ROW][C]57[/C][C]2.22[/C][C]2.21136339667044[/C][C]0.00863660332956284[/C][/ROW]
[ROW][C]58[/C][C]2.22[/C][C]2.22302144208040[/C][C]-0.00302144208040245[/C][/ROW]
[ROW][C]59[/C][C]2.23[/C][C]2.22244138902231[/C][C]0.00755861097769461[/C][/ROW]
[ROW][C]60[/C][C]2.24[/C][C]2.23389248267094[/C][C]0.00610751732906367[/C][/ROW]
[ROW][C]61[/C][C]2.24[/C][C]2.24506499699020[/C][C]-0.0050649969902028[/C][/ROW]
[ROW][C]62[/C][C]2.25[/C][C]2.24409262455504[/C][C]0.00590737544495878[/C][/ROW]
[ROW][C]63[/C][C]2.25[/C][C]2.25522671586012[/C][C]-0.0052267158601178[/C][/ROW]
[ROW][C]64[/C][C]2.32[/C][C]2.25422329681789[/C][C]0.0657767031821108[/C][/ROW]
[ROW][C]65[/C][C]2.36[/C][C]2.33685103444020[/C][C]0.0231489655597970[/C][/ROW]
[ROW][C]66[/C][C]2.37[/C][C]2.38129514685654[/C][C]-0.0112951468565363[/C][/ROW]
[ROW][C]67[/C][C]2.37[/C][C]2.38912671724530[/C][C]-0.0191267172452965[/C][/ROW]
[ROW][C]68[/C][C]2.37[/C][C]2.38545479154417[/C][C]-0.0154547915441694[/C][/ROW]
[ROW][C]69[/C][C]2.38[/C][C]2.38248779801628[/C][C]-0.00248779801627874[/C][/ROW]
[ROW][C]70[/C][C]2.38[/C][C]2.39201019334643[/C][C]-0.0120101933464318[/C][/ROW]
[ROW][C]71[/C][C]2.41[/C][C]2.38970448991292[/C][C]0.0202955100870787[/C][/ROW]
[ROW][C]72[/C][C]2.42[/C][C]2.42360079915148[/C][C]-0.00360079915148415[/C][/ROW]
[ROW][C]73[/C][C]2.43[/C][C]2.43290952177339[/C][C]-0.00290952177338699[/C][/ROW]
[ROW][C]74[/C][C]2.44[/C][C]2.44235095505017[/C][C]-0.00235095505016591[/C][/ROW]
[ROW][C]75[/C][C]2.44[/C][C]2.45189962133931[/C][C]-0.0118996213393054[/C][/ROW]
[ROW][C]76[/C][C]2.44[/C][C]2.44961514539557[/C][C]-0.00961514539557173[/C][/ROW]
[ROW][C]77[/C][C]2.43[/C][C]2.44776924057849[/C][C]-0.0177692405784886[/C][/ROW]
[ROW][C]78[/C][C]2.43[/C][C]2.43435792172367[/C][C]-0.00435792172367044[/C][/ROW]
[ROW][C]79[/C][C]2.43[/C][C]2.43352129280427[/C][C]-0.00352129280426805[/C][/ROW]
[ROW][C]80[/C][C]2.42[/C][C]2.43284527896544[/C][C]-0.0128452789654396[/C][/ROW]
[ROW][C]81[/C][C]2.42[/C][C]2.42037925673243[/C][C]-0.000379256732432331[/C][/ROW]
[ROW][C]82[/C][C]2.42[/C][C]2.42030644745077[/C][C]-0.000306447450772129[/C][/ROW]
[ROW][C]83[/C][C]2.42[/C][C]2.42024761601325[/C][C]-0.000247616013254515[/C][/ROW]
[ROW][C]84[/C][C]2.42[/C][C]2.42020007896906[/C][C]-0.000200078969055273[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72620&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72620&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
32.142.144.44089209850063e-16
42.152.150
52.152.16-0.00999999999999979
62.162.158080211228080.00191978877192334
72.172.168448770120960.00155122987904299
82.172.17874657349140-0.00874657349140273
92.182.177067416133240.0029325838667571
102.172.18763041029126-0.0176304102912557
112.172.1742457439191-0.00424574391910015
122.182.173430650768670.00656934923133479
132.172.18469182705798-0.0146918270579817
142.182.171871306595490.00812869340451394
152.182.18343184402833-0.00343184402832541
162.182.18277300246507-0.00277300246506851
172.172.18224064456537-0.0122406445653733
182.172.169890699365600.000109300634397513
192.182.169911682778670.0100883172213297
202.172.18184842659158-0.0118484265915817
212.182.169573778958030.0104262210419663
222.172.18157539316703-0.0115753931670297
232.172.169353162183760.000646837816236534
242.172.169477341381450.000522658618550054
252.172.169577680796190.000422319203805976
262.172.169658757162760.000341242837242461
272.172.16972426857950.000275731420498637
282.172.169777203188020.000222796811984782
292.172.169819975469820.000180024530177736
302.172.169854536376990.000145463623007380
312.182.169882462320010.0101175376799900
322.182.18182481584377-0.00182481584376548
332.182.18147448974700-0.00147448974699671
342.182.18119141886094-0.00119141886093654
352.182.18096269160575-0.000962691605748134
362.182.18077787515219-0.000777875152194074
372.182.18062853955388-0.000628539553880092
382.182.18050787323606-0.000507873236055278
392.182.18041037230244-0.000410372302441342
402.182.18033158948859-0.000331589488587802
412.182.18026793131088-0.000267931310879987
422.182.18021649415865-0.000216494158652658
432.182.18017493185316-0.000174931853155869
442.192.18014134863240.009858651367598
452.192.19203400145258-0.00203400145258392
462.192.19164351613751-0.00164351613750924
472.22.191327995754780.00867200424521775
482.22.20299283739279-0.00299283739278655
492.212.20241827583050.00758172416949954
502.212.21387380672374-0.00387380672374249
512.212.21313011765846-0.00313011765845861
522.22.21252920118491-0.0125292011849076
532.212.200123859209310.00987614079068733
542.22.21201986962930-0.0120198696293019
552.212.199712308553870.0102876914461292
562.212.2116873280066-0.00168732800659965
572.222.211363396670440.00863660332956284
582.222.22302144208040-0.00302144208040245
592.232.222441389022310.00755861097769461
602.242.233892482670940.00610751732906367
612.242.24506499699020-0.0050649969902028
622.252.244092624555040.00590737544495878
632.252.25522671586012-0.0052267158601178
642.322.254223296817890.0657767031821108
652.362.336851034440200.0231489655597970
662.372.38129514685654-0.0112951468565363
672.372.38912671724530-0.0191267172452965
682.372.38545479154417-0.0154547915441694
692.382.38248779801628-0.00248779801627874
702.382.39201019334643-0.0120101933464318
712.412.389704489912920.0202955100870787
722.422.42360079915148-0.00360079915148415
732.432.43290952177339-0.00290952177338699
742.442.44235095505017-0.00235095505016591
752.442.45189962133931-0.0118996213393054
762.442.44961514539557-0.00961514539557173
772.432.44776924057849-0.0177692405784886
782.432.43435792172367-0.00435792172367044
792.432.43352129280427-0.00352129280426805
802.422.43284527896544-0.0128452789654396
812.422.42037925673243-0.000379256732432331
822.422.42030644745077-0.000306447450772129
832.422.42024761601325-0.000247616013254515
842.422.42020007896906-0.000200078969055273







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
852.420161668033232.398874280249572.44144905581688
862.420323336066452.387202365801232.45344430633167
872.420485004099682.37615735942252.46481264877686
882.420646672132902.365055487424782.47623785684103
892.420808340166132.353676227285312.48794045304695
902.420970008199362.341929733180552.50001028321816
912.421131676232582.329776785791392.51248656667377
922.421293344265812.317201192391072.52538549614055
932.421455012299032.304198251287662.53871177331041
942.421616680332262.29076930941842.55246405124612
952.421778348365492.276918974477792.56663772225318
962.421940016398712.262653601749722.58122643104770

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2.42016166803323 & 2.39887428024957 & 2.44144905581688 \tabularnewline
86 & 2.42032333606645 & 2.38720236580123 & 2.45344430633167 \tabularnewline
87 & 2.42048500409968 & 2.3761573594225 & 2.46481264877686 \tabularnewline
88 & 2.42064667213290 & 2.36505548742478 & 2.47623785684103 \tabularnewline
89 & 2.42080834016613 & 2.35367622728531 & 2.48794045304695 \tabularnewline
90 & 2.42097000819936 & 2.34192973318055 & 2.50001028321816 \tabularnewline
91 & 2.42113167623258 & 2.32977678579139 & 2.51248656667377 \tabularnewline
92 & 2.42129334426581 & 2.31720119239107 & 2.52538549614055 \tabularnewline
93 & 2.42145501229903 & 2.30419825128766 & 2.53871177331041 \tabularnewline
94 & 2.42161668033226 & 2.2907693094184 & 2.55246405124612 \tabularnewline
95 & 2.42177834836549 & 2.27691897447779 & 2.56663772225318 \tabularnewline
96 & 2.42194001639871 & 2.26265360174972 & 2.58122643104770 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72620&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]2.42016166803323[/C][C]2.39887428024957[/C][C]2.44144905581688[/C][/ROW]
[ROW][C]86[/C][C]2.42032333606645[/C][C]2.38720236580123[/C][C]2.45344430633167[/C][/ROW]
[ROW][C]87[/C][C]2.42048500409968[/C][C]2.3761573594225[/C][C]2.46481264877686[/C][/ROW]
[ROW][C]88[/C][C]2.42064667213290[/C][C]2.36505548742478[/C][C]2.47623785684103[/C][/ROW]
[ROW][C]89[/C][C]2.42080834016613[/C][C]2.35367622728531[/C][C]2.48794045304695[/C][/ROW]
[ROW][C]90[/C][C]2.42097000819936[/C][C]2.34192973318055[/C][C]2.50001028321816[/C][/ROW]
[ROW][C]91[/C][C]2.42113167623258[/C][C]2.32977678579139[/C][C]2.51248656667377[/C][/ROW]
[ROW][C]92[/C][C]2.42129334426581[/C][C]2.31720119239107[/C][C]2.52538549614055[/C][/ROW]
[ROW][C]93[/C][C]2.42145501229903[/C][C]2.30419825128766[/C][C]2.53871177331041[/C][/ROW]
[ROW][C]94[/C][C]2.42161668033226[/C][C]2.2907693094184[/C][C]2.55246405124612[/C][/ROW]
[ROW][C]95[/C][C]2.42177834836549[/C][C]2.27691897447779[/C][C]2.56663772225318[/C][/ROW]
[ROW][C]96[/C][C]2.42194001639871[/C][C]2.26265360174972[/C][C]2.58122643104770[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72620&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72620&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
852.420161668033232.398874280249572.44144905581688
862.420323336066452.387202365801232.45344430633167
872.420485004099682.37615735942252.46481264877686
882.420646672132902.365055487424782.47623785684103
892.420808340166132.353676227285312.48794045304695
902.420970008199362.341929733180552.50001028321816
912.421131676232582.329776785791392.51248656667377
922.421293344265812.317201192391072.52538549614055
932.421455012299032.304198251287662.53871177331041
942.421616680332262.29076930941842.55246405124612
952.421778348365492.276918974477792.56663772225318
962.421940016398712.262653601749722.58122643104770



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')