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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 04 Jun 2009 04:12:59 -0600
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/Jun/04/t1244110510v241o8y96pipoak.htm/, Retrieved Tue, 14 May 2024 00:47:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41573, Retrieved Tue, 14 May 2024 00:47:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2009-06-04 10:12:59] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
5,11
5,11
5,11
5,1
5,1
5,1
5,1
5,1
5,12
5,25
5,26
5,26
5,26
5,26
5,26
5,26
5,29
5,3
5,33
5,33
5,35
5,38
5,38
5,38
5,38
5,38
5,39
5,39
5,4
5,4
5,4
5,4
5,4
5,41
5,41
5,41
5,41
5,41
5,42
5,42
5,42
5,42
5,43
5,43
5,45
5,51
5,51
5,51
5,51
5,51
5,51
5,53
5,53
5,53
5,53
5,52
5,53
5,54
5,54
5,57
5,56
5,57
5,58
5,61
5,66
5,68
5,69
5,7
5,72
5,71
5,69
5,7
5,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41573&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41573&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41573&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0406582087810778
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0406582087810778 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41573&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]0.0406582087810778[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41573&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41573&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
beta0.0406582087810778
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
35.115.110
45.15.11-0.0100000000000007
55.15.099593417912190.000406582087810747
65.15.09960994881160.000390051188397855
75.15.099625807594260.000374192405744544
85.15.099641021587210.000358978412787536
95.125.099655617006470.0203443829935335
105.255.120482783177740.129517216822260
115.265.255748721220040.00425127877995557
125.265.26592157060027-0.00592157060026643
135.265.26568081014649-0.00568081014648847
145.265.26544983858151-0.00544983858150694
155.265.26522825790664-0.00522825790663717
165.265.26501568630511-0.00501568630510718
175.295.264811757484130.0251882425158660
185.35.295835866307170.00416413369282687
195.335.306005172524250.023994827475752
205.335.33698075922942-0.00698075922942287
215.355.336696934063220.0133030659367765
225.385.357237812895510.0227621871044921
235.385.38816328265112-0.00816328265111732
245.385.38783137820075-0.0078313782007493
255.385.38751296839082-0.00751296839081927
265.385.38720750455342-0.00720750455341967
275.395.38691446032850.00308553967150349
285.395.39703991284466-0.00703991284466277
295.45.396753682598420.00324631740157688
305.45.40688567204911-0.00688567204910662
315.45.40660571295734-0.00660571295733625
325.45.40633713650077-0.00633713650076917
335.45.40607947988185-0.00607947988184598
345.415.405832299119530.00416770088046992
355.415.41600175037207-0.0060017503720653
365.415.41575772995239-0.00575772995238566
375.415.41552363096588-0.00552363096587616
385.415.41529905002484-0.00529905002483666
395.425.415083600142590.00491639985741443
405.425.42528349215444-0.00528349215443935
415.425.42506867482733-0.00506867482733053
425.425.42486259158796-0.00486259158795743
435.435.424664887323960.00533511267604236
445.435.43488180344901-0.00488180344901057
455.455.434683318065150.0153166819348476
465.515.455306066917090.0546939330829064
475.515.51752982426744-0.00752982426743642
485.515.51722367510029-0.00722367510028565
495.515.51692997340989-0.00692997340989177
505.515.51664821310414-0.0066482131041452
515.515.51637790866774-0.00637790866773535
525.535.516118594325540.0138814056744643
535.535.53668298741562-0.00668298741562356
545.535.536411269118-0.00641126911799805
555.535.53615059839965-0.00615059839964616
565.525.53590052608579-0.0159005260857858
575.535.525254039176460.00474596082354051
585.545.535447001442490.00455299855750901
595.545.54563211820842-0.00563211820842202
605.575.545403126370420.0245968736295765
615.565.57640319119382-0.0164031911938176
625.575.565736266821580.00426373317841744
635.585.575909622575340.00409037742466190
645.615.586075929994660.0239240700053376
655.665.617048639827830.0429513601721663
665.685.668794965197140.0112050348028552
675.695.689250541841560.000749458158442629
685.75.699281013467840.000718986532162624
695.725.709310246172370.0106897538276272
705.715.72974487241531-0.0197448724153144
715.695.7189420812703-0.0289420812702961
725.75.697765348087450.00223465191254935
735.75.70785620503146-0.00785620503146323

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5.11 & 5.11 & 0 \tabularnewline
4 & 5.1 & 5.11 & -0.0100000000000007 \tabularnewline
5 & 5.1 & 5.09959341791219 & 0.000406582087810747 \tabularnewline
6 & 5.1 & 5.0996099488116 & 0.000390051188397855 \tabularnewline
7 & 5.1 & 5.09962580759426 & 0.000374192405744544 \tabularnewline
8 & 5.1 & 5.09964102158721 & 0.000358978412787536 \tabularnewline
9 & 5.12 & 5.09965561700647 & 0.0203443829935335 \tabularnewline
10 & 5.25 & 5.12048278317774 & 0.129517216822260 \tabularnewline
11 & 5.26 & 5.25574872122004 & 0.00425127877995557 \tabularnewline
12 & 5.26 & 5.26592157060027 & -0.00592157060026643 \tabularnewline
13 & 5.26 & 5.26568081014649 & -0.00568081014648847 \tabularnewline
14 & 5.26 & 5.26544983858151 & -0.00544983858150694 \tabularnewline
15 & 5.26 & 5.26522825790664 & -0.00522825790663717 \tabularnewline
16 & 5.26 & 5.26501568630511 & -0.00501568630510718 \tabularnewline
17 & 5.29 & 5.26481175748413 & 0.0251882425158660 \tabularnewline
18 & 5.3 & 5.29583586630717 & 0.00416413369282687 \tabularnewline
19 & 5.33 & 5.30600517252425 & 0.023994827475752 \tabularnewline
20 & 5.33 & 5.33698075922942 & -0.00698075922942287 \tabularnewline
21 & 5.35 & 5.33669693406322 & 0.0133030659367765 \tabularnewline
22 & 5.38 & 5.35723781289551 & 0.0227621871044921 \tabularnewline
23 & 5.38 & 5.38816328265112 & -0.00816328265111732 \tabularnewline
24 & 5.38 & 5.38783137820075 & -0.0078313782007493 \tabularnewline
25 & 5.38 & 5.38751296839082 & -0.00751296839081927 \tabularnewline
26 & 5.38 & 5.38720750455342 & -0.00720750455341967 \tabularnewline
27 & 5.39 & 5.3869144603285 & 0.00308553967150349 \tabularnewline
28 & 5.39 & 5.39703991284466 & -0.00703991284466277 \tabularnewline
29 & 5.4 & 5.39675368259842 & 0.00324631740157688 \tabularnewline
30 & 5.4 & 5.40688567204911 & -0.00688567204910662 \tabularnewline
31 & 5.4 & 5.40660571295734 & -0.00660571295733625 \tabularnewline
32 & 5.4 & 5.40633713650077 & -0.00633713650076917 \tabularnewline
33 & 5.4 & 5.40607947988185 & -0.00607947988184598 \tabularnewline
34 & 5.41 & 5.40583229911953 & 0.00416770088046992 \tabularnewline
35 & 5.41 & 5.41600175037207 & -0.0060017503720653 \tabularnewline
36 & 5.41 & 5.41575772995239 & -0.00575772995238566 \tabularnewline
37 & 5.41 & 5.41552363096588 & -0.00552363096587616 \tabularnewline
38 & 5.41 & 5.41529905002484 & -0.00529905002483666 \tabularnewline
39 & 5.42 & 5.41508360014259 & 0.00491639985741443 \tabularnewline
40 & 5.42 & 5.42528349215444 & -0.00528349215443935 \tabularnewline
41 & 5.42 & 5.42506867482733 & -0.00506867482733053 \tabularnewline
42 & 5.42 & 5.42486259158796 & -0.00486259158795743 \tabularnewline
43 & 5.43 & 5.42466488732396 & 0.00533511267604236 \tabularnewline
44 & 5.43 & 5.43488180344901 & -0.00488180344901057 \tabularnewline
45 & 5.45 & 5.43468331806515 & 0.0153166819348476 \tabularnewline
46 & 5.51 & 5.45530606691709 & 0.0546939330829064 \tabularnewline
47 & 5.51 & 5.51752982426744 & -0.00752982426743642 \tabularnewline
48 & 5.51 & 5.51722367510029 & -0.00722367510028565 \tabularnewline
49 & 5.51 & 5.51692997340989 & -0.00692997340989177 \tabularnewline
50 & 5.51 & 5.51664821310414 & -0.0066482131041452 \tabularnewline
51 & 5.51 & 5.51637790866774 & -0.00637790866773535 \tabularnewline
52 & 5.53 & 5.51611859432554 & 0.0138814056744643 \tabularnewline
53 & 5.53 & 5.53668298741562 & -0.00668298741562356 \tabularnewline
54 & 5.53 & 5.536411269118 & -0.00641126911799805 \tabularnewline
55 & 5.53 & 5.53615059839965 & -0.00615059839964616 \tabularnewline
56 & 5.52 & 5.53590052608579 & -0.0159005260857858 \tabularnewline
57 & 5.53 & 5.52525403917646 & 0.00474596082354051 \tabularnewline
58 & 5.54 & 5.53544700144249 & 0.00455299855750901 \tabularnewline
59 & 5.54 & 5.54563211820842 & -0.00563211820842202 \tabularnewline
60 & 5.57 & 5.54540312637042 & 0.0245968736295765 \tabularnewline
61 & 5.56 & 5.57640319119382 & -0.0164031911938176 \tabularnewline
62 & 5.57 & 5.56573626682158 & 0.00426373317841744 \tabularnewline
63 & 5.58 & 5.57590962257534 & 0.00409037742466190 \tabularnewline
64 & 5.61 & 5.58607592999466 & 0.0239240700053376 \tabularnewline
65 & 5.66 & 5.61704863982783 & 0.0429513601721663 \tabularnewline
66 & 5.68 & 5.66879496519714 & 0.0112050348028552 \tabularnewline
67 & 5.69 & 5.68925054184156 & 0.000749458158442629 \tabularnewline
68 & 5.7 & 5.69928101346784 & 0.000718986532162624 \tabularnewline
69 & 5.72 & 5.70931024617237 & 0.0106897538276272 \tabularnewline
70 & 5.71 & 5.72974487241531 & -0.0197448724153144 \tabularnewline
71 & 5.69 & 5.7189420812703 & -0.0289420812702961 \tabularnewline
72 & 5.7 & 5.69776534808745 & 0.00223465191254935 \tabularnewline
73 & 5.7 & 5.70785620503146 & -0.00785620503146323 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41573&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]5.11[/C][C]5.11[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]5.1[/C][C]5.11[/C][C]-0.0100000000000007[/C][/ROW]
[ROW][C]5[/C][C]5.1[/C][C]5.09959341791219[/C][C]0.000406582087810747[/C][/ROW]
[ROW][C]6[/C][C]5.1[/C][C]5.0996099488116[/C][C]0.000390051188397855[/C][/ROW]
[ROW][C]7[/C][C]5.1[/C][C]5.09962580759426[/C][C]0.000374192405744544[/C][/ROW]
[ROW][C]8[/C][C]5.1[/C][C]5.09964102158721[/C][C]0.000358978412787536[/C][/ROW]
[ROW][C]9[/C][C]5.12[/C][C]5.09965561700647[/C][C]0.0203443829935335[/C][/ROW]
[ROW][C]10[/C][C]5.25[/C][C]5.12048278317774[/C][C]0.129517216822260[/C][/ROW]
[ROW][C]11[/C][C]5.26[/C][C]5.25574872122004[/C][C]0.00425127877995557[/C][/ROW]
[ROW][C]12[/C][C]5.26[/C][C]5.26592157060027[/C][C]-0.00592157060026643[/C][/ROW]
[ROW][C]13[/C][C]5.26[/C][C]5.26568081014649[/C][C]-0.00568081014648847[/C][/ROW]
[ROW][C]14[/C][C]5.26[/C][C]5.26544983858151[/C][C]-0.00544983858150694[/C][/ROW]
[ROW][C]15[/C][C]5.26[/C][C]5.26522825790664[/C][C]-0.00522825790663717[/C][/ROW]
[ROW][C]16[/C][C]5.26[/C][C]5.26501568630511[/C][C]-0.00501568630510718[/C][/ROW]
[ROW][C]17[/C][C]5.29[/C][C]5.26481175748413[/C][C]0.0251882425158660[/C][/ROW]
[ROW][C]18[/C][C]5.3[/C][C]5.29583586630717[/C][C]0.00416413369282687[/C][/ROW]
[ROW][C]19[/C][C]5.33[/C][C]5.30600517252425[/C][C]0.023994827475752[/C][/ROW]
[ROW][C]20[/C][C]5.33[/C][C]5.33698075922942[/C][C]-0.00698075922942287[/C][/ROW]
[ROW][C]21[/C][C]5.35[/C][C]5.33669693406322[/C][C]0.0133030659367765[/C][/ROW]
[ROW][C]22[/C][C]5.38[/C][C]5.35723781289551[/C][C]0.0227621871044921[/C][/ROW]
[ROW][C]23[/C][C]5.38[/C][C]5.38816328265112[/C][C]-0.00816328265111732[/C][/ROW]
[ROW][C]24[/C][C]5.38[/C][C]5.38783137820075[/C][C]-0.0078313782007493[/C][/ROW]
[ROW][C]25[/C][C]5.38[/C][C]5.38751296839082[/C][C]-0.00751296839081927[/C][/ROW]
[ROW][C]26[/C][C]5.38[/C][C]5.38720750455342[/C][C]-0.00720750455341967[/C][/ROW]
[ROW][C]27[/C][C]5.39[/C][C]5.3869144603285[/C][C]0.00308553967150349[/C][/ROW]
[ROW][C]28[/C][C]5.39[/C][C]5.39703991284466[/C][C]-0.00703991284466277[/C][/ROW]
[ROW][C]29[/C][C]5.4[/C][C]5.39675368259842[/C][C]0.00324631740157688[/C][/ROW]
[ROW][C]30[/C][C]5.4[/C][C]5.40688567204911[/C][C]-0.00688567204910662[/C][/ROW]
[ROW][C]31[/C][C]5.4[/C][C]5.40660571295734[/C][C]-0.00660571295733625[/C][/ROW]
[ROW][C]32[/C][C]5.4[/C][C]5.40633713650077[/C][C]-0.00633713650076917[/C][/ROW]
[ROW][C]33[/C][C]5.4[/C][C]5.40607947988185[/C][C]-0.00607947988184598[/C][/ROW]
[ROW][C]34[/C][C]5.41[/C][C]5.40583229911953[/C][C]0.00416770088046992[/C][/ROW]
[ROW][C]35[/C][C]5.41[/C][C]5.41600175037207[/C][C]-0.0060017503720653[/C][/ROW]
[ROW][C]36[/C][C]5.41[/C][C]5.41575772995239[/C][C]-0.00575772995238566[/C][/ROW]
[ROW][C]37[/C][C]5.41[/C][C]5.41552363096588[/C][C]-0.00552363096587616[/C][/ROW]
[ROW][C]38[/C][C]5.41[/C][C]5.41529905002484[/C][C]-0.00529905002483666[/C][/ROW]
[ROW][C]39[/C][C]5.42[/C][C]5.41508360014259[/C][C]0.00491639985741443[/C][/ROW]
[ROW][C]40[/C][C]5.42[/C][C]5.42528349215444[/C][C]-0.00528349215443935[/C][/ROW]
[ROW][C]41[/C][C]5.42[/C][C]5.42506867482733[/C][C]-0.00506867482733053[/C][/ROW]
[ROW][C]42[/C][C]5.42[/C][C]5.42486259158796[/C][C]-0.00486259158795743[/C][/ROW]
[ROW][C]43[/C][C]5.43[/C][C]5.42466488732396[/C][C]0.00533511267604236[/C][/ROW]
[ROW][C]44[/C][C]5.43[/C][C]5.43488180344901[/C][C]-0.00488180344901057[/C][/ROW]
[ROW][C]45[/C][C]5.45[/C][C]5.43468331806515[/C][C]0.0153166819348476[/C][/ROW]
[ROW][C]46[/C][C]5.51[/C][C]5.45530606691709[/C][C]0.0546939330829064[/C][/ROW]
[ROW][C]47[/C][C]5.51[/C][C]5.51752982426744[/C][C]-0.00752982426743642[/C][/ROW]
[ROW][C]48[/C][C]5.51[/C][C]5.51722367510029[/C][C]-0.00722367510028565[/C][/ROW]
[ROW][C]49[/C][C]5.51[/C][C]5.51692997340989[/C][C]-0.00692997340989177[/C][/ROW]
[ROW][C]50[/C][C]5.51[/C][C]5.51664821310414[/C][C]-0.0066482131041452[/C][/ROW]
[ROW][C]51[/C][C]5.51[/C][C]5.51637790866774[/C][C]-0.00637790866773535[/C][/ROW]
[ROW][C]52[/C][C]5.53[/C][C]5.51611859432554[/C][C]0.0138814056744643[/C][/ROW]
[ROW][C]53[/C][C]5.53[/C][C]5.53668298741562[/C][C]-0.00668298741562356[/C][/ROW]
[ROW][C]54[/C][C]5.53[/C][C]5.536411269118[/C][C]-0.00641126911799805[/C][/ROW]
[ROW][C]55[/C][C]5.53[/C][C]5.53615059839965[/C][C]-0.00615059839964616[/C][/ROW]
[ROW][C]56[/C][C]5.52[/C][C]5.53590052608579[/C][C]-0.0159005260857858[/C][/ROW]
[ROW][C]57[/C][C]5.53[/C][C]5.52525403917646[/C][C]0.00474596082354051[/C][/ROW]
[ROW][C]58[/C][C]5.54[/C][C]5.53544700144249[/C][C]0.00455299855750901[/C][/ROW]
[ROW][C]59[/C][C]5.54[/C][C]5.54563211820842[/C][C]-0.00563211820842202[/C][/ROW]
[ROW][C]60[/C][C]5.57[/C][C]5.54540312637042[/C][C]0.0245968736295765[/C][/ROW]
[ROW][C]61[/C][C]5.56[/C][C]5.57640319119382[/C][C]-0.0164031911938176[/C][/ROW]
[ROW][C]62[/C][C]5.57[/C][C]5.56573626682158[/C][C]0.00426373317841744[/C][/ROW]
[ROW][C]63[/C][C]5.58[/C][C]5.57590962257534[/C][C]0.00409037742466190[/C][/ROW]
[ROW][C]64[/C][C]5.61[/C][C]5.58607592999466[/C][C]0.0239240700053376[/C][/ROW]
[ROW][C]65[/C][C]5.66[/C][C]5.61704863982783[/C][C]0.0429513601721663[/C][/ROW]
[ROW][C]66[/C][C]5.68[/C][C]5.66879496519714[/C][C]0.0112050348028552[/C][/ROW]
[ROW][C]67[/C][C]5.69[/C][C]5.68925054184156[/C][C]0.000749458158442629[/C][/ROW]
[ROW][C]68[/C][C]5.7[/C][C]5.69928101346784[/C][C]0.000718986532162624[/C][/ROW]
[ROW][C]69[/C][C]5.72[/C][C]5.70931024617237[/C][C]0.0106897538276272[/C][/ROW]
[ROW][C]70[/C][C]5.71[/C][C]5.72974487241531[/C][C]-0.0197448724153144[/C][/ROW]
[ROW][C]71[/C][C]5.69[/C][C]5.7189420812703[/C][C]-0.0289420812702961[/C][/ROW]
[ROW][C]72[/C][C]5.7[/C][C]5.69776534808745[/C][C]0.00223465191254935[/C][/ROW]
[ROW][C]73[/C][C]5.7[/C][C]5.70785620503146[/C][C]-0.00785620503146323[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41573&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41573&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
35.115.110
45.15.11-0.0100000000000007
55.15.099593417912190.000406582087810747
65.15.09960994881160.000390051188397855
75.15.099625807594260.000374192405744544
85.15.099641021587210.000358978412787536
95.125.099655617006470.0203443829935335
105.255.120482783177740.129517216822260
115.265.255748721220040.00425127877995557
125.265.26592157060027-0.00592157060026643
135.265.26568081014649-0.00568081014648847
145.265.26544983858151-0.00544983858150694
155.265.26522825790664-0.00522825790663717
165.265.26501568630511-0.00501568630510718
175.295.264811757484130.0251882425158660
185.35.295835866307170.00416413369282687
195.335.306005172524250.023994827475752
205.335.33698075922942-0.00698075922942287
215.355.336696934063220.0133030659367765
225.385.357237812895510.0227621871044921
235.385.38816328265112-0.00816328265111732
245.385.38783137820075-0.0078313782007493
255.385.38751296839082-0.00751296839081927
265.385.38720750455342-0.00720750455341967
275.395.38691446032850.00308553967150349
285.395.39703991284466-0.00703991284466277
295.45.396753682598420.00324631740157688
305.45.40688567204911-0.00688567204910662
315.45.40660571295734-0.00660571295733625
325.45.40633713650077-0.00633713650076917
335.45.40607947988185-0.00607947988184598
345.415.405832299119530.00416770088046992
355.415.41600175037207-0.0060017503720653
365.415.41575772995239-0.00575772995238566
375.415.41552363096588-0.00552363096587616
385.415.41529905002484-0.00529905002483666
395.425.415083600142590.00491639985741443
405.425.42528349215444-0.00528349215443935
415.425.42506867482733-0.00506867482733053
425.425.42486259158796-0.00486259158795743
435.435.424664887323960.00533511267604236
445.435.43488180344901-0.00488180344901057
455.455.434683318065150.0153166819348476
465.515.455306066917090.0546939330829064
475.515.51752982426744-0.00752982426743642
485.515.51722367510029-0.00722367510028565
495.515.51692997340989-0.00692997340989177
505.515.51664821310414-0.0066482131041452
515.515.51637790866774-0.00637790866773535
525.535.516118594325540.0138814056744643
535.535.53668298741562-0.00668298741562356
545.535.536411269118-0.00641126911799805
555.535.53615059839965-0.00615059839964616
565.525.53590052608579-0.0159005260857858
575.535.525254039176460.00474596082354051
585.545.535447001442490.00455299855750901
595.545.54563211820842-0.00563211820842202
605.575.545403126370420.0245968736295765
615.565.57640319119382-0.0164031911938176
625.575.565736266821580.00426373317841744
635.585.575909622575340.00409037742466190
645.615.586075929994660.0239240700053376
655.665.617048639827830.0429513601721663
665.685.668794965197140.0112050348028552
675.695.689250541841560.000749458158442629
685.75.699281013467840.000718986532162624
695.725.709310246172370.0106897538276272
705.715.72974487241531-0.0197448724153144
715.695.7189420812703-0.0289420812702961
725.75.697765348087450.00223465191254935
735.75.70785620503146-0.00785620503146323







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
745.707536785807075.667857203258315.74721636835583
755.715073571614135.657806028603265.77234111462501
765.72261035742125.651052603736475.79416811110594
775.730147143228275.645870831968325.81442345448822
785.737683929035345.641607238091765.83376061997891
795.74522071484245.637934092655455.85250733702936
805.752757500649475.634661063823165.87085393747579
815.760294286456545.631666982614585.8889215902985
825.767831072263615.628869676593225.90679246793399
835.775367858070675.626210784994255.9245249311471
845.782904643877745.623647375100215.94216191265527
855.790441429684815.621146980293975.95973587907565

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 5.70753678580707 & 5.66785720325831 & 5.74721636835583 \tabularnewline
75 & 5.71507357161413 & 5.65780602860326 & 5.77234111462501 \tabularnewline
76 & 5.7226103574212 & 5.65105260373647 & 5.79416811110594 \tabularnewline
77 & 5.73014714322827 & 5.64587083196832 & 5.81442345448822 \tabularnewline
78 & 5.73768392903534 & 5.64160723809176 & 5.83376061997891 \tabularnewline
79 & 5.7452207148424 & 5.63793409265545 & 5.85250733702936 \tabularnewline
80 & 5.75275750064947 & 5.63466106382316 & 5.87085393747579 \tabularnewline
81 & 5.76029428645654 & 5.63166698261458 & 5.8889215902985 \tabularnewline
82 & 5.76783107226361 & 5.62886967659322 & 5.90679246793399 \tabularnewline
83 & 5.77536785807067 & 5.62621078499425 & 5.9245249311471 \tabularnewline
84 & 5.78290464387774 & 5.62364737510021 & 5.94216191265527 \tabularnewline
85 & 5.79044142968481 & 5.62114698029397 & 5.95973587907565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41573&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]74[/C][C]5.70753678580707[/C][C]5.66785720325831[/C][C]5.74721636835583[/C][/ROW]
[ROW][C]75[/C][C]5.71507357161413[/C][C]5.65780602860326[/C][C]5.77234111462501[/C][/ROW]
[ROW][C]76[/C][C]5.7226103574212[/C][C]5.65105260373647[/C][C]5.79416811110594[/C][/ROW]
[ROW][C]77[/C][C]5.73014714322827[/C][C]5.64587083196832[/C][C]5.81442345448822[/C][/ROW]
[ROW][C]78[/C][C]5.73768392903534[/C][C]5.64160723809176[/C][C]5.83376061997891[/C][/ROW]
[ROW][C]79[/C][C]5.7452207148424[/C][C]5.63793409265545[/C][C]5.85250733702936[/C][/ROW]
[ROW][C]80[/C][C]5.75275750064947[/C][C]5.63466106382316[/C][C]5.87085393747579[/C][/ROW]
[ROW][C]81[/C][C]5.76029428645654[/C][C]5.63166698261458[/C][C]5.8889215902985[/C][/ROW]
[ROW][C]82[/C][C]5.76783107226361[/C][C]5.62886967659322[/C][C]5.90679246793399[/C][/ROW]
[ROW][C]83[/C][C]5.77536785807067[/C][C]5.62621078499425[/C][C]5.9245249311471[/C][/ROW]
[ROW][C]84[/C][C]5.78290464387774[/C][C]5.62364737510021[/C][C]5.94216191265527[/C][/ROW]
[ROW][C]85[/C][C]5.79044142968481[/C][C]5.62114698029397[/C][C]5.95973587907565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41573&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41573&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
745.707536785807075.667857203258315.74721636835583
755.715073571614135.657806028603265.77234111462501
765.72261035742125.651052603736475.79416811110594
775.730147143228275.645870831968325.81442345448822
785.737683929035345.641607238091765.83376061997891
795.74522071484245.637934092655455.85250733702936
805.752757500649475.634661063823165.87085393747579
815.760294286456545.631666982614585.8889215902985
825.767831072263615.628869676593225.90679246793399
835.775367858070675.626210784994255.9245249311471
845.782904643877745.623647375100215.94216191265527
855.790441429684815.621146980293975.95973587907565



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