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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 14 Jan 2010 12:07:55 -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/14/t1263496111w7ezi9tz20sm2zc.htm/, Retrieved Thu, 31 Oct 2024 23:17:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72182, Retrieved Thu, 31 Oct 2024 23:17:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact296
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] [6590c54be3d1f5d26c781440f79f0ebc] [Current]
- R PD    [Exponential Smoothing] [consumptieprijs r...] [2010-01-26 12:42:30] [bf68df4edce3d2e638b253cf289b9d76]
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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 time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72182&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72182&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72182&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.88008275007892
beta0.141425389189999
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.88008275007892 \tabularnewline
beta & 0.141425389189999 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72182&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.88008275007892[/C][/ROW]
[ROW][C]beta[/C][C]0.141425389189999[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72182&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72182&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.88008275007892
beta0.141425389189999
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132.172.157297008547010.0127029914529908
142.182.18086489286783-0.000864892867825873
152.182.18280093311450-0.00280093311449692
162.182.18268447666828-0.00268447666828431
172.172.17233638533652-0.00233638533651703
182.172.17242050920447-0.00242050920447445
192.182.18671265923205-0.006712659232051
202.172.17722519724388-0.00722519724387816
212.182.176804034330870.00319596566913338
222.172.166785479674920.00321452032507885
232.172.168016686617820.00198331338218116
242.172.17924451807540-0.00924451807539528
252.172.161380274606920.00861972539308375
262.172.17757724228165-0.00757724228164536
272.172.1703879541396-0.000387954139601021
282.172.169723677118030.000276322881972657
292.172.159706188679260.0102938113207376
302.172.17015098561080-0.000150985610804621
312.182.18546342276160-0.00546342276159795
322.182.176707039001380.00329296099862342
332.182.18779466538795-0.00779466538794837
342.182.167739973035080.0122600269649209
352.182.177544491912880.00245550808712158
362.182.18866041584772-0.0086604158477157
372.182.174344095250910.00565590474908717
382.182.18651309827509-0.00651309827509117
392.182.18177765296916-0.00177765296915622
402.182.18045220232528-0.000452202325275319
412.182.171386362503530.00861363749647337
422.182.179282372939830.000717627060168091
432.182.19501273787818-0.0150127378781764
442.192.178004172192090.0119958278079140
452.192.19560661940866-0.00560661940866325
462.192.180340005103160.009659994896841
472.22.186814446927660.0131855530723439
482.22.20751013085986-0.00751013085985663
492.212.197535524983970.0124644750160252
502.212.21669739064261-0.00669739064260844
512.212.21480470700586-0.00480470700586277
522.22.21303446989610-0.0130344698961022
532.212.194476606099980.0155233939000228
542.22.20886119824393-0.00886119824392839
552.212.21443711580331-0.00443711580331074
562.212.21145312509673-0.00145312509673046
572.222.214912965308420.00508703469158345
582.222.212023800267440.00797619973256358
592.232.218364981281050.01163501871895
602.242.235947151320760.0040528486792426
612.242.24071627656621-0.00071627656620743
622.252.246511648350170.00348835164982564
632.252.25560950174062-0.00560950174061547
642.322.253843194038290.066156805961711
652.362.319960517415670.04003948258433
662.372.367604314532410.00239568546759283
672.372.39962599631797-0.0296259963179746
682.372.38770462924133-0.0177046292413348
692.382.38849640942027-0.00849640942026886
702.382.38315880313578-0.00315880313577521
712.412.387912738820310.0220872611796916
722.422.42285918656155-0.00285918656154527
732.432.429187607139030.00081239286096757
742.442.44523716810679-0.00523716810679264
752.442.45288344771435-0.0128834477143540
762.442.45973471980118-0.0197347198011837
772.432.44285113274165-0.0128511327416478
782.432.428572242670780.00142775732921807
792.432.44492121302189-0.0149212130218905
802.422.43822019328998-0.0182201932899790
812.422.43044763228951-0.0104476322895062
822.422.414575171937470.00542482806253375
832.422.42152153506199-0.00152153506199193
842.422.42137096865162-0.00137096865162478

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.17 & 2.15729700854701 & 0.0127029914529908 \tabularnewline
14 & 2.18 & 2.18086489286783 & -0.000864892867825873 \tabularnewline
15 & 2.18 & 2.18280093311450 & -0.00280093311449692 \tabularnewline
16 & 2.18 & 2.18268447666828 & -0.00268447666828431 \tabularnewline
17 & 2.17 & 2.17233638533652 & -0.00233638533651703 \tabularnewline
18 & 2.17 & 2.17242050920447 & -0.00242050920447445 \tabularnewline
19 & 2.18 & 2.18671265923205 & -0.006712659232051 \tabularnewline
20 & 2.17 & 2.17722519724388 & -0.00722519724387816 \tabularnewline
21 & 2.18 & 2.17680403433087 & 0.00319596566913338 \tabularnewline
22 & 2.17 & 2.16678547967492 & 0.00321452032507885 \tabularnewline
23 & 2.17 & 2.16801668661782 & 0.00198331338218116 \tabularnewline
24 & 2.17 & 2.17924451807540 & -0.00924451807539528 \tabularnewline
25 & 2.17 & 2.16138027460692 & 0.00861972539308375 \tabularnewline
26 & 2.17 & 2.17757724228165 & -0.00757724228164536 \tabularnewline
27 & 2.17 & 2.1703879541396 & -0.000387954139601021 \tabularnewline
28 & 2.17 & 2.16972367711803 & 0.000276322881972657 \tabularnewline
29 & 2.17 & 2.15970618867926 & 0.0102938113207376 \tabularnewline
30 & 2.17 & 2.17015098561080 & -0.000150985610804621 \tabularnewline
31 & 2.18 & 2.18546342276160 & -0.00546342276159795 \tabularnewline
32 & 2.18 & 2.17670703900138 & 0.00329296099862342 \tabularnewline
33 & 2.18 & 2.18779466538795 & -0.00779466538794837 \tabularnewline
34 & 2.18 & 2.16773997303508 & 0.0122600269649209 \tabularnewline
35 & 2.18 & 2.17754449191288 & 0.00245550808712158 \tabularnewline
36 & 2.18 & 2.18866041584772 & -0.0086604158477157 \tabularnewline
37 & 2.18 & 2.17434409525091 & 0.00565590474908717 \tabularnewline
38 & 2.18 & 2.18651309827509 & -0.00651309827509117 \tabularnewline
39 & 2.18 & 2.18177765296916 & -0.00177765296915622 \tabularnewline
40 & 2.18 & 2.18045220232528 & -0.000452202325275319 \tabularnewline
41 & 2.18 & 2.17138636250353 & 0.00861363749647337 \tabularnewline
42 & 2.18 & 2.17928237293983 & 0.000717627060168091 \tabularnewline
43 & 2.18 & 2.19501273787818 & -0.0150127378781764 \tabularnewline
44 & 2.19 & 2.17800417219209 & 0.0119958278079140 \tabularnewline
45 & 2.19 & 2.19560661940866 & -0.00560661940866325 \tabularnewline
46 & 2.19 & 2.18034000510316 & 0.009659994896841 \tabularnewline
47 & 2.2 & 2.18681444692766 & 0.0131855530723439 \tabularnewline
48 & 2.2 & 2.20751013085986 & -0.00751013085985663 \tabularnewline
49 & 2.21 & 2.19753552498397 & 0.0124644750160252 \tabularnewline
50 & 2.21 & 2.21669739064261 & -0.00669739064260844 \tabularnewline
51 & 2.21 & 2.21480470700586 & -0.00480470700586277 \tabularnewline
52 & 2.2 & 2.21303446989610 & -0.0130344698961022 \tabularnewline
53 & 2.21 & 2.19447660609998 & 0.0155233939000228 \tabularnewline
54 & 2.2 & 2.20886119824393 & -0.00886119824392839 \tabularnewline
55 & 2.21 & 2.21443711580331 & -0.00443711580331074 \tabularnewline
56 & 2.21 & 2.21145312509673 & -0.00145312509673046 \tabularnewline
57 & 2.22 & 2.21491296530842 & 0.00508703469158345 \tabularnewline
58 & 2.22 & 2.21202380026744 & 0.00797619973256358 \tabularnewline
59 & 2.23 & 2.21836498128105 & 0.01163501871895 \tabularnewline
60 & 2.24 & 2.23594715132076 & 0.0040528486792426 \tabularnewline
61 & 2.24 & 2.24071627656621 & -0.00071627656620743 \tabularnewline
62 & 2.25 & 2.24651164835017 & 0.00348835164982564 \tabularnewline
63 & 2.25 & 2.25560950174062 & -0.00560950174061547 \tabularnewline
64 & 2.32 & 2.25384319403829 & 0.066156805961711 \tabularnewline
65 & 2.36 & 2.31996051741567 & 0.04003948258433 \tabularnewline
66 & 2.37 & 2.36760431453241 & 0.00239568546759283 \tabularnewline
67 & 2.37 & 2.39962599631797 & -0.0296259963179746 \tabularnewline
68 & 2.37 & 2.38770462924133 & -0.0177046292413348 \tabularnewline
69 & 2.38 & 2.38849640942027 & -0.00849640942026886 \tabularnewline
70 & 2.38 & 2.38315880313578 & -0.00315880313577521 \tabularnewline
71 & 2.41 & 2.38791273882031 & 0.0220872611796916 \tabularnewline
72 & 2.42 & 2.42285918656155 & -0.00285918656154527 \tabularnewline
73 & 2.43 & 2.42918760713903 & 0.00081239286096757 \tabularnewline
74 & 2.44 & 2.44523716810679 & -0.00523716810679264 \tabularnewline
75 & 2.44 & 2.45288344771435 & -0.0128834477143540 \tabularnewline
76 & 2.44 & 2.45973471980118 & -0.0197347198011837 \tabularnewline
77 & 2.43 & 2.44285113274165 & -0.0128511327416478 \tabularnewline
78 & 2.43 & 2.42857224267078 & 0.00142775732921807 \tabularnewline
79 & 2.43 & 2.44492121302189 & -0.0149212130218905 \tabularnewline
80 & 2.42 & 2.43822019328998 & -0.0182201932899790 \tabularnewline
81 & 2.42 & 2.43044763228951 & -0.0104476322895062 \tabularnewline
82 & 2.42 & 2.41457517193747 & 0.00542482806253375 \tabularnewline
83 & 2.42 & 2.42152153506199 & -0.00152153506199193 \tabularnewline
84 & 2.42 & 2.42137096865162 & -0.00137096865162478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72182&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]2.17[/C][C]2.15729700854701[/C][C]0.0127029914529908[/C][/ROW]
[ROW][C]14[/C][C]2.18[/C][C]2.18086489286783[/C][C]-0.000864892867825873[/C][/ROW]
[ROW][C]15[/C][C]2.18[/C][C]2.18280093311450[/C][C]-0.00280093311449692[/C][/ROW]
[ROW][C]16[/C][C]2.18[/C][C]2.18268447666828[/C][C]-0.00268447666828431[/C][/ROW]
[ROW][C]17[/C][C]2.17[/C][C]2.17233638533652[/C][C]-0.00233638533651703[/C][/ROW]
[ROW][C]18[/C][C]2.17[/C][C]2.17242050920447[/C][C]-0.00242050920447445[/C][/ROW]
[ROW][C]19[/C][C]2.18[/C][C]2.18671265923205[/C][C]-0.006712659232051[/C][/ROW]
[ROW][C]20[/C][C]2.17[/C][C]2.17722519724388[/C][C]-0.00722519724387816[/C][/ROW]
[ROW][C]21[/C][C]2.18[/C][C]2.17680403433087[/C][C]0.00319596566913338[/C][/ROW]
[ROW][C]22[/C][C]2.17[/C][C]2.16678547967492[/C][C]0.00321452032507885[/C][/ROW]
[ROW][C]23[/C][C]2.17[/C][C]2.16801668661782[/C][C]0.00198331338218116[/C][/ROW]
[ROW][C]24[/C][C]2.17[/C][C]2.17924451807540[/C][C]-0.00924451807539528[/C][/ROW]
[ROW][C]25[/C][C]2.17[/C][C]2.16138027460692[/C][C]0.00861972539308375[/C][/ROW]
[ROW][C]26[/C][C]2.17[/C][C]2.17757724228165[/C][C]-0.00757724228164536[/C][/ROW]
[ROW][C]27[/C][C]2.17[/C][C]2.1703879541396[/C][C]-0.000387954139601021[/C][/ROW]
[ROW][C]28[/C][C]2.17[/C][C]2.16972367711803[/C][C]0.000276322881972657[/C][/ROW]
[ROW][C]29[/C][C]2.17[/C][C]2.15970618867926[/C][C]0.0102938113207376[/C][/ROW]
[ROW][C]30[/C][C]2.17[/C][C]2.17015098561080[/C][C]-0.000150985610804621[/C][/ROW]
[ROW][C]31[/C][C]2.18[/C][C]2.18546342276160[/C][C]-0.00546342276159795[/C][/ROW]
[ROW][C]32[/C][C]2.18[/C][C]2.17670703900138[/C][C]0.00329296099862342[/C][/ROW]
[ROW][C]33[/C][C]2.18[/C][C]2.18779466538795[/C][C]-0.00779466538794837[/C][/ROW]
[ROW][C]34[/C][C]2.18[/C][C]2.16773997303508[/C][C]0.0122600269649209[/C][/ROW]
[ROW][C]35[/C][C]2.18[/C][C]2.17754449191288[/C][C]0.00245550808712158[/C][/ROW]
[ROW][C]36[/C][C]2.18[/C][C]2.18866041584772[/C][C]-0.0086604158477157[/C][/ROW]
[ROW][C]37[/C][C]2.18[/C][C]2.17434409525091[/C][C]0.00565590474908717[/C][/ROW]
[ROW][C]38[/C][C]2.18[/C][C]2.18651309827509[/C][C]-0.00651309827509117[/C][/ROW]
[ROW][C]39[/C][C]2.18[/C][C]2.18177765296916[/C][C]-0.00177765296915622[/C][/ROW]
[ROW][C]40[/C][C]2.18[/C][C]2.18045220232528[/C][C]-0.000452202325275319[/C][/ROW]
[ROW][C]41[/C][C]2.18[/C][C]2.17138636250353[/C][C]0.00861363749647337[/C][/ROW]
[ROW][C]42[/C][C]2.18[/C][C]2.17928237293983[/C][C]0.000717627060168091[/C][/ROW]
[ROW][C]43[/C][C]2.18[/C][C]2.19501273787818[/C][C]-0.0150127378781764[/C][/ROW]
[ROW][C]44[/C][C]2.19[/C][C]2.17800417219209[/C][C]0.0119958278079140[/C][/ROW]
[ROW][C]45[/C][C]2.19[/C][C]2.19560661940866[/C][C]-0.00560661940866325[/C][/ROW]
[ROW][C]46[/C][C]2.19[/C][C]2.18034000510316[/C][C]0.009659994896841[/C][/ROW]
[ROW][C]47[/C][C]2.2[/C][C]2.18681444692766[/C][C]0.0131855530723439[/C][/ROW]
[ROW][C]48[/C][C]2.2[/C][C]2.20751013085986[/C][C]-0.00751013085985663[/C][/ROW]
[ROW][C]49[/C][C]2.21[/C][C]2.19753552498397[/C][C]0.0124644750160252[/C][/ROW]
[ROW][C]50[/C][C]2.21[/C][C]2.21669739064261[/C][C]-0.00669739064260844[/C][/ROW]
[ROW][C]51[/C][C]2.21[/C][C]2.21480470700586[/C][C]-0.00480470700586277[/C][/ROW]
[ROW][C]52[/C][C]2.2[/C][C]2.21303446989610[/C][C]-0.0130344698961022[/C][/ROW]
[ROW][C]53[/C][C]2.21[/C][C]2.19447660609998[/C][C]0.0155233939000228[/C][/ROW]
[ROW][C]54[/C][C]2.2[/C][C]2.20886119824393[/C][C]-0.00886119824392839[/C][/ROW]
[ROW][C]55[/C][C]2.21[/C][C]2.21443711580331[/C][C]-0.00443711580331074[/C][/ROW]
[ROW][C]56[/C][C]2.21[/C][C]2.21145312509673[/C][C]-0.00145312509673046[/C][/ROW]
[ROW][C]57[/C][C]2.22[/C][C]2.21491296530842[/C][C]0.00508703469158345[/C][/ROW]
[ROW][C]58[/C][C]2.22[/C][C]2.21202380026744[/C][C]0.00797619973256358[/C][/ROW]
[ROW][C]59[/C][C]2.23[/C][C]2.21836498128105[/C][C]0.01163501871895[/C][/ROW]
[ROW][C]60[/C][C]2.24[/C][C]2.23594715132076[/C][C]0.0040528486792426[/C][/ROW]
[ROW][C]61[/C][C]2.24[/C][C]2.24071627656621[/C][C]-0.00071627656620743[/C][/ROW]
[ROW][C]62[/C][C]2.25[/C][C]2.24651164835017[/C][C]0.00348835164982564[/C][/ROW]
[ROW][C]63[/C][C]2.25[/C][C]2.25560950174062[/C][C]-0.00560950174061547[/C][/ROW]
[ROW][C]64[/C][C]2.32[/C][C]2.25384319403829[/C][C]0.066156805961711[/C][/ROW]
[ROW][C]65[/C][C]2.36[/C][C]2.31996051741567[/C][C]0.04003948258433[/C][/ROW]
[ROW][C]66[/C][C]2.37[/C][C]2.36760431453241[/C][C]0.00239568546759283[/C][/ROW]
[ROW][C]67[/C][C]2.37[/C][C]2.39962599631797[/C][C]-0.0296259963179746[/C][/ROW]
[ROW][C]68[/C][C]2.37[/C][C]2.38770462924133[/C][C]-0.0177046292413348[/C][/ROW]
[ROW][C]69[/C][C]2.38[/C][C]2.38849640942027[/C][C]-0.00849640942026886[/C][/ROW]
[ROW][C]70[/C][C]2.38[/C][C]2.38315880313578[/C][C]-0.00315880313577521[/C][/ROW]
[ROW][C]71[/C][C]2.41[/C][C]2.38791273882031[/C][C]0.0220872611796916[/C][/ROW]
[ROW][C]72[/C][C]2.42[/C][C]2.42285918656155[/C][C]-0.00285918656154527[/C][/ROW]
[ROW][C]73[/C][C]2.43[/C][C]2.42918760713903[/C][C]0.00081239286096757[/C][/ROW]
[ROW][C]74[/C][C]2.44[/C][C]2.44523716810679[/C][C]-0.00523716810679264[/C][/ROW]
[ROW][C]75[/C][C]2.44[/C][C]2.45288344771435[/C][C]-0.0128834477143540[/C][/ROW]
[ROW][C]76[/C][C]2.44[/C][C]2.45973471980118[/C][C]-0.0197347198011837[/C][/ROW]
[ROW][C]77[/C][C]2.43[/C][C]2.44285113274165[/C][C]-0.0128511327416478[/C][/ROW]
[ROW][C]78[/C][C]2.43[/C][C]2.42857224267078[/C][C]0.00142775732921807[/C][/ROW]
[ROW][C]79[/C][C]2.43[/C][C]2.44492121302189[/C][C]-0.0149212130218905[/C][/ROW]
[ROW][C]80[/C][C]2.42[/C][C]2.43822019328998[/C][C]-0.0182201932899790[/C][/ROW]
[ROW][C]81[/C][C]2.42[/C][C]2.43044763228951[/C][C]-0.0104476322895062[/C][/ROW]
[ROW][C]82[/C][C]2.42[/C][C]2.41457517193747[/C][C]0.00542482806253375[/C][/ROW]
[ROW][C]83[/C][C]2.42[/C][C]2.42152153506199[/C][C]-0.00152153506199193[/C][/ROW]
[ROW][C]84[/C][C]2.42[/C][C]2.42137096865162[/C][C]-0.00137096865162478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72182&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72182&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
132.172.157297008547010.0127029914529908
142.182.18086489286783-0.000864892867825873
152.182.18280093311450-0.00280093311449692
162.182.18268447666828-0.00268447666828431
172.172.17233638533652-0.00233638533651703
182.172.17242050920447-0.00242050920447445
192.182.18671265923205-0.006712659232051
202.172.17722519724388-0.00722519724387816
212.182.176804034330870.00319596566913338
222.172.166785479674920.00321452032507885
232.172.168016686617820.00198331338218116
242.172.17924451807540-0.00924451807539528
252.172.161380274606920.00861972539308375
262.172.17757724228165-0.00757724228164536
272.172.1703879541396-0.000387954139601021
282.172.169723677118030.000276322881972657
292.172.159706188679260.0102938113207376
302.172.17015098561080-0.000150985610804621
312.182.18546342276160-0.00546342276159795
322.182.176707039001380.00329296099862342
332.182.18779466538795-0.00779466538794837
342.182.167739973035080.0122600269649209
352.182.177544491912880.00245550808712158
362.182.18866041584772-0.0086604158477157
372.182.174344095250910.00565590474908717
382.182.18651309827509-0.00651309827509117
392.182.18177765296916-0.00177765296915622
402.182.18045220232528-0.000452202325275319
412.182.171386362503530.00861363749647337
422.182.179282372939830.000717627060168091
432.182.19501273787818-0.0150127378781764
442.192.178004172192090.0119958278079140
452.192.19560661940866-0.00560661940866325
462.192.180340005103160.009659994896841
472.22.186814446927660.0131855530723439
482.22.20751013085986-0.00751013085985663
492.212.197535524983970.0124644750160252
502.212.21669739064261-0.00669739064260844
512.212.21480470700586-0.00480470700586277
522.22.21303446989610-0.0130344698961022
532.212.194476606099980.0155233939000228
542.22.20886119824393-0.00886119824392839
552.212.21443711580331-0.00443711580331074
562.212.21145312509673-0.00145312509673046
572.222.214912965308420.00508703469158345
582.222.212023800267440.00797619973256358
592.232.218364981281050.01163501871895
602.242.235947151320760.0040528486792426
612.242.24071627656621-0.00071627656620743
622.252.246511648350170.00348835164982564
632.252.25560950174062-0.00560950174061547
642.322.253843194038290.066156805961711
652.362.319960517415670.04003948258433
662.372.367604314532410.00239568546759283
672.372.39962599631797-0.0296259963179746
682.372.38770462924133-0.0177046292413348
692.382.38849640942027-0.00849640942026886
702.382.38315880313578-0.00315880313577521
712.412.387912738820310.0220872611796916
722.422.42285918656155-0.00285918656154527
732.432.429187607139030.00081239286096757
742.442.44523716810679-0.00523716810679264
752.442.45288344771435-0.0128834477143540
762.442.45973471980118-0.0197347198011837
772.432.44285113274165-0.0128511327416478
782.432.428572242670780.00142775732921807
792.432.44492121302189-0.0149212130218905
802.422.43822019328998-0.0182201932899790
812.422.43044763228951-0.0104476322895062
822.422.414575171937470.00542482806253375
832.422.42152153506199-0.00152153506199193
842.422.42137096865162-0.00137096865162478







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
852.418306852024482.39275607803782.44385762601116
862.421672300185052.385455772177082.45788882819302
872.422418956734122.376117790187552.46872012328069
882.430798851451662.374500069834722.48709763306861
892.425576922471152.359175652473782.49197819246852
902.419387918320892.342688811721942.49608702491984
912.427409653649562.340170596505612.51464871079351
922.430191948983172.332145753419542.5282381445468
932.438401542862452.329267723792222.54753536193269
942.433942433659982.31343400040822.55445086691176
952.434921491923002.302749029145362.56709395470063
962.435957418737692.291831605113112.58008323236226

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2.41830685202448 & 2.3927560780378 & 2.44385762601116 \tabularnewline
86 & 2.42167230018505 & 2.38545577217708 & 2.45788882819302 \tabularnewline
87 & 2.42241895673412 & 2.37611779018755 & 2.46872012328069 \tabularnewline
88 & 2.43079885145166 & 2.37450006983472 & 2.48709763306861 \tabularnewline
89 & 2.42557692247115 & 2.35917565247378 & 2.49197819246852 \tabularnewline
90 & 2.41938791832089 & 2.34268881172194 & 2.49608702491984 \tabularnewline
91 & 2.42740965364956 & 2.34017059650561 & 2.51464871079351 \tabularnewline
92 & 2.43019194898317 & 2.33214575341954 & 2.5282381445468 \tabularnewline
93 & 2.43840154286245 & 2.32926772379222 & 2.54753536193269 \tabularnewline
94 & 2.43394243365998 & 2.3134340004082 & 2.55445086691176 \tabularnewline
95 & 2.43492149192300 & 2.30274902914536 & 2.56709395470063 \tabularnewline
96 & 2.43595741873769 & 2.29183160511311 & 2.58008323236226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72182&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]2.41830685202448[/C][C]2.3927560780378[/C][C]2.44385762601116[/C][/ROW]
[ROW][C]86[/C][C]2.42167230018505[/C][C]2.38545577217708[/C][C]2.45788882819302[/C][/ROW]
[ROW][C]87[/C][C]2.42241895673412[/C][C]2.37611779018755[/C][C]2.46872012328069[/C][/ROW]
[ROW][C]88[/C][C]2.43079885145166[/C][C]2.37450006983472[/C][C]2.48709763306861[/C][/ROW]
[ROW][C]89[/C][C]2.42557692247115[/C][C]2.35917565247378[/C][C]2.49197819246852[/C][/ROW]
[ROW][C]90[/C][C]2.41938791832089[/C][C]2.34268881172194[/C][C]2.49608702491984[/C][/ROW]
[ROW][C]91[/C][C]2.42740965364956[/C][C]2.34017059650561[/C][C]2.51464871079351[/C][/ROW]
[ROW][C]92[/C][C]2.43019194898317[/C][C]2.33214575341954[/C][C]2.5282381445468[/C][/ROW]
[ROW][C]93[/C][C]2.43840154286245[/C][C]2.32926772379222[/C][C]2.54753536193269[/C][/ROW]
[ROW][C]94[/C][C]2.43394243365998[/C][C]2.3134340004082[/C][C]2.55445086691176[/C][/ROW]
[ROW][C]95[/C][C]2.43492149192300[/C][C]2.30274902914536[/C][C]2.56709395470063[/C][/ROW]
[ROW][C]96[/C][C]2.43595741873769[/C][C]2.29183160511311[/C][C]2.58008323236226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72182&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72182&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
852.418306852024482.39275607803782.44385762601116
862.421672300185052.385455772177082.45788882819302
872.422418956734122.376117790187552.46872012328069
882.430798851451662.374500069834722.48709763306861
892.425576922471152.359175652473782.49197819246852
902.419387918320892.342688811721942.49608702491984
912.427409653649562.340170596505612.51464871079351
922.430191948983172.332145753419542.5282381445468
932.438401542862452.329267723792222.54753536193269
942.433942433659982.31343400040822.55445086691176
952.434921491923002.302749029145362.56709395470063
962.435957418737692.291831605113112.58008323236226



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