Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 19 Aug 2009 09:48:41 -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/Aug/19/t1250696958uq78q214238v0l8.htm/, Retrieved Tue, 07 May 2024 09:17:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42957, Retrieved Tue, 07 May 2024 09:17:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Thomas Van den Bo...] [2009-04-22 20:03:59] [29fb2afdd4eca1705c3ee13bfc104084]
- RMPD  [(Partial) Autocorrelation Function] [Thomas Van den Bo...] [2009-08-19 14:06:37] [f85cc8f00ef4b762f0a6fdfddc793773]
- RM        [Exponential Smoothing] [Thomas van den Bo...] [2009-08-19 15:48:41] [50e97696ebad247f45d73cd9926afb25] [Current]
Feedback Forum

Post a new message
Dataseries X:
5.93
5.9
5.9
5.94
5.86
5.92
5.9
5.91
5.84
5.84
5.83
5.82
5.8
5.91
5.92
5.96
5.9
5.92
6.09
6.31
6.25
6.23
6.22
6.19
6.15
6.12
6.13
6.1
6.05
6.07
6.09
6.17
6.12
6.12
6.13
6.19
6.24
6.41
6.5
6.53
6.58
6.53
6.51
6.51
6.49
6.49
6.49
6.53
6.65
6.61
6.52
6.62
6.6
6.61
6.63
6.62
6.6
6.59
6.59
6.52
6.52
6.61
6.59
6.6
6.48
6.53
6.56
6.56
6.49
6.45
6.44
6.43




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=42957&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=42957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42957&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
beta4.7857361519868e-19
gamma0.0425143406904243

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 4.7857361519868e-19 \tabularnewline
gamma & 0.0425143406904243 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42957&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]4.7857361519868e-19[/C][/ROW]
[ROW][C]gamma[/C][C]0.0425143406904243[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42957&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
beta4.7857361519868e-19
gamma0.0425143406904243







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135.85.789638180826160.0103618191738422
145.915.900475510808010.009524489191989
155.925.90138607436680.0186139256331979
165.965.941780144004690.0182198559953131
175.95.882878990749860.0171210092501433
185.925.903727359521470.0162726404785287
196.096.081594838677650.00840516132235436
206.316.120669753457720.189330246542281
216.256.248905948243820.00109405175618171
226.236.26319341225341-0.0331934122534143
236.226.23162127244342-0.0116212724434224
246.196.22247541860107-0.0324754186010647
256.156.17526655614421-0.0252665561442118
266.126.25563038306529-0.135630383065286
276.136.110547292484380.0194527075156152
286.16.15202033872586-0.0520203387258569
296.056.020720300598140.0292796994018572
306.076.05344712527420.0165528747257984
316.096.23530632444558-0.145306324445584
326.176.120669753457720.0493302465422811
336.126.110593597450320.0094064025496765
346.126.13323029168604-0.0132302916860390
356.136.121856337090930.00814366290906676
366.196.132655262586020.0573447374139757
376.246.175266556144210.064733443855788
386.416.346955921645730.063044078354272
396.56.399388974646760.100611025353238
406.536.522443538948870.0075564610511325
416.586.44409003798930.135909962010696
426.536.58245696426719-0.0524569642671864
436.516.70668821413392-0.196688214133925
446.516.54173984835998-0.031739848359984
456.496.446495020805950.0435049791940454
466.496.50312532714703-0.0131253271470317
476.496.49106566509476-0.00106566509475581
486.536.491935886646190.0380641133538147
496.656.513642526796560.136357473203437
506.616.76299448628996-0.152994486289963
516.526.59859013475875-0.0785901347587474
526.626.54246641463660.077533585363402
536.66.532702308606060.0672976913939412
546.616.602419599700880.00758040029911644
556.636.78866767321016-0.158667673210159
566.626.66204558976063-0.0420455897606313
576.66.555169010715130.0448309892848693
586.596.61309412147327-0.0230941214732727
596.596.59085196996065-0.000851969960653953
606.526.59173605999623-0.0717360599962289
616.526.503690292365610.0163097076343881
626.616.63107981945155-0.0210798194515460
636.596.59859013475875-0.00859013475874715
646.66.61254647954365-0.0125464795436550
656.486.51301069291345-0.0330106929134448
666.536.48264378709870.0473562129013008
676.566.70668821413392-0.146688214133925
686.566.59186724061025-0.0318672406102536
696.496.49589228894649-0.0058922889464883
706.456.50312532714703-0.0531253271470318
716.446.4511511431484-0.0111511431483962
726.436.44203579997116-0.0120357999711631

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5.8 & 5.78963818082616 & 0.0103618191738422 \tabularnewline
14 & 5.91 & 5.90047551080801 & 0.009524489191989 \tabularnewline
15 & 5.92 & 5.9013860743668 & 0.0186139256331979 \tabularnewline
16 & 5.96 & 5.94178014400469 & 0.0182198559953131 \tabularnewline
17 & 5.9 & 5.88287899074986 & 0.0171210092501433 \tabularnewline
18 & 5.92 & 5.90372735952147 & 0.0162726404785287 \tabularnewline
19 & 6.09 & 6.08159483867765 & 0.00840516132235436 \tabularnewline
20 & 6.31 & 6.12066975345772 & 0.189330246542281 \tabularnewline
21 & 6.25 & 6.24890594824382 & 0.00109405175618171 \tabularnewline
22 & 6.23 & 6.26319341225341 & -0.0331934122534143 \tabularnewline
23 & 6.22 & 6.23162127244342 & -0.0116212724434224 \tabularnewline
24 & 6.19 & 6.22247541860107 & -0.0324754186010647 \tabularnewline
25 & 6.15 & 6.17526655614421 & -0.0252665561442118 \tabularnewline
26 & 6.12 & 6.25563038306529 & -0.135630383065286 \tabularnewline
27 & 6.13 & 6.11054729248438 & 0.0194527075156152 \tabularnewline
28 & 6.1 & 6.15202033872586 & -0.0520203387258569 \tabularnewline
29 & 6.05 & 6.02072030059814 & 0.0292796994018572 \tabularnewline
30 & 6.07 & 6.0534471252742 & 0.0165528747257984 \tabularnewline
31 & 6.09 & 6.23530632444558 & -0.145306324445584 \tabularnewline
32 & 6.17 & 6.12066975345772 & 0.0493302465422811 \tabularnewline
33 & 6.12 & 6.11059359745032 & 0.0094064025496765 \tabularnewline
34 & 6.12 & 6.13323029168604 & -0.0132302916860390 \tabularnewline
35 & 6.13 & 6.12185633709093 & 0.00814366290906676 \tabularnewline
36 & 6.19 & 6.13265526258602 & 0.0573447374139757 \tabularnewline
37 & 6.24 & 6.17526655614421 & 0.064733443855788 \tabularnewline
38 & 6.41 & 6.34695592164573 & 0.063044078354272 \tabularnewline
39 & 6.5 & 6.39938897464676 & 0.100611025353238 \tabularnewline
40 & 6.53 & 6.52244353894887 & 0.0075564610511325 \tabularnewline
41 & 6.58 & 6.4440900379893 & 0.135909962010696 \tabularnewline
42 & 6.53 & 6.58245696426719 & -0.0524569642671864 \tabularnewline
43 & 6.51 & 6.70668821413392 & -0.196688214133925 \tabularnewline
44 & 6.51 & 6.54173984835998 & -0.031739848359984 \tabularnewline
45 & 6.49 & 6.44649502080595 & 0.0435049791940454 \tabularnewline
46 & 6.49 & 6.50312532714703 & -0.0131253271470317 \tabularnewline
47 & 6.49 & 6.49106566509476 & -0.00106566509475581 \tabularnewline
48 & 6.53 & 6.49193588664619 & 0.0380641133538147 \tabularnewline
49 & 6.65 & 6.51364252679656 & 0.136357473203437 \tabularnewline
50 & 6.61 & 6.76299448628996 & -0.152994486289963 \tabularnewline
51 & 6.52 & 6.59859013475875 & -0.0785901347587474 \tabularnewline
52 & 6.62 & 6.5424664146366 & 0.077533585363402 \tabularnewline
53 & 6.6 & 6.53270230860606 & 0.0672976913939412 \tabularnewline
54 & 6.61 & 6.60241959970088 & 0.00758040029911644 \tabularnewline
55 & 6.63 & 6.78866767321016 & -0.158667673210159 \tabularnewline
56 & 6.62 & 6.66204558976063 & -0.0420455897606313 \tabularnewline
57 & 6.6 & 6.55516901071513 & 0.0448309892848693 \tabularnewline
58 & 6.59 & 6.61309412147327 & -0.0230941214732727 \tabularnewline
59 & 6.59 & 6.59085196996065 & -0.000851969960653953 \tabularnewline
60 & 6.52 & 6.59173605999623 & -0.0717360599962289 \tabularnewline
61 & 6.52 & 6.50369029236561 & 0.0163097076343881 \tabularnewline
62 & 6.61 & 6.63107981945155 & -0.0210798194515460 \tabularnewline
63 & 6.59 & 6.59859013475875 & -0.00859013475874715 \tabularnewline
64 & 6.6 & 6.61254647954365 & -0.0125464795436550 \tabularnewline
65 & 6.48 & 6.51301069291345 & -0.0330106929134448 \tabularnewline
66 & 6.53 & 6.4826437870987 & 0.0473562129013008 \tabularnewline
67 & 6.56 & 6.70668821413392 & -0.146688214133925 \tabularnewline
68 & 6.56 & 6.59186724061025 & -0.0318672406102536 \tabularnewline
69 & 6.49 & 6.49589228894649 & -0.0058922889464883 \tabularnewline
70 & 6.45 & 6.50312532714703 & -0.0531253271470318 \tabularnewline
71 & 6.44 & 6.4511511431484 & -0.0111511431483962 \tabularnewline
72 & 6.43 & 6.44203579997116 & -0.0120357999711631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42957&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]5.8[/C][C]5.78963818082616[/C][C]0.0103618191738422[/C][/ROW]
[ROW][C]14[/C][C]5.91[/C][C]5.90047551080801[/C][C]0.009524489191989[/C][/ROW]
[ROW][C]15[/C][C]5.92[/C][C]5.9013860743668[/C][C]0.0186139256331979[/C][/ROW]
[ROW][C]16[/C][C]5.96[/C][C]5.94178014400469[/C][C]0.0182198559953131[/C][/ROW]
[ROW][C]17[/C][C]5.9[/C][C]5.88287899074986[/C][C]0.0171210092501433[/C][/ROW]
[ROW][C]18[/C][C]5.92[/C][C]5.90372735952147[/C][C]0.0162726404785287[/C][/ROW]
[ROW][C]19[/C][C]6.09[/C][C]6.08159483867765[/C][C]0.00840516132235436[/C][/ROW]
[ROW][C]20[/C][C]6.31[/C][C]6.12066975345772[/C][C]0.189330246542281[/C][/ROW]
[ROW][C]21[/C][C]6.25[/C][C]6.24890594824382[/C][C]0.00109405175618171[/C][/ROW]
[ROW][C]22[/C][C]6.23[/C][C]6.26319341225341[/C][C]-0.0331934122534143[/C][/ROW]
[ROW][C]23[/C][C]6.22[/C][C]6.23162127244342[/C][C]-0.0116212724434224[/C][/ROW]
[ROW][C]24[/C][C]6.19[/C][C]6.22247541860107[/C][C]-0.0324754186010647[/C][/ROW]
[ROW][C]25[/C][C]6.15[/C][C]6.17526655614421[/C][C]-0.0252665561442118[/C][/ROW]
[ROW][C]26[/C][C]6.12[/C][C]6.25563038306529[/C][C]-0.135630383065286[/C][/ROW]
[ROW][C]27[/C][C]6.13[/C][C]6.11054729248438[/C][C]0.0194527075156152[/C][/ROW]
[ROW][C]28[/C][C]6.1[/C][C]6.15202033872586[/C][C]-0.0520203387258569[/C][/ROW]
[ROW][C]29[/C][C]6.05[/C][C]6.02072030059814[/C][C]0.0292796994018572[/C][/ROW]
[ROW][C]30[/C][C]6.07[/C][C]6.0534471252742[/C][C]0.0165528747257984[/C][/ROW]
[ROW][C]31[/C][C]6.09[/C][C]6.23530632444558[/C][C]-0.145306324445584[/C][/ROW]
[ROW][C]32[/C][C]6.17[/C][C]6.12066975345772[/C][C]0.0493302465422811[/C][/ROW]
[ROW][C]33[/C][C]6.12[/C][C]6.11059359745032[/C][C]0.0094064025496765[/C][/ROW]
[ROW][C]34[/C][C]6.12[/C][C]6.13323029168604[/C][C]-0.0132302916860390[/C][/ROW]
[ROW][C]35[/C][C]6.13[/C][C]6.12185633709093[/C][C]0.00814366290906676[/C][/ROW]
[ROW][C]36[/C][C]6.19[/C][C]6.13265526258602[/C][C]0.0573447374139757[/C][/ROW]
[ROW][C]37[/C][C]6.24[/C][C]6.17526655614421[/C][C]0.064733443855788[/C][/ROW]
[ROW][C]38[/C][C]6.41[/C][C]6.34695592164573[/C][C]0.063044078354272[/C][/ROW]
[ROW][C]39[/C][C]6.5[/C][C]6.39938897464676[/C][C]0.100611025353238[/C][/ROW]
[ROW][C]40[/C][C]6.53[/C][C]6.52244353894887[/C][C]0.0075564610511325[/C][/ROW]
[ROW][C]41[/C][C]6.58[/C][C]6.4440900379893[/C][C]0.135909962010696[/C][/ROW]
[ROW][C]42[/C][C]6.53[/C][C]6.58245696426719[/C][C]-0.0524569642671864[/C][/ROW]
[ROW][C]43[/C][C]6.51[/C][C]6.70668821413392[/C][C]-0.196688214133925[/C][/ROW]
[ROW][C]44[/C][C]6.51[/C][C]6.54173984835998[/C][C]-0.031739848359984[/C][/ROW]
[ROW][C]45[/C][C]6.49[/C][C]6.44649502080595[/C][C]0.0435049791940454[/C][/ROW]
[ROW][C]46[/C][C]6.49[/C][C]6.50312532714703[/C][C]-0.0131253271470317[/C][/ROW]
[ROW][C]47[/C][C]6.49[/C][C]6.49106566509476[/C][C]-0.00106566509475581[/C][/ROW]
[ROW][C]48[/C][C]6.53[/C][C]6.49193588664619[/C][C]0.0380641133538147[/C][/ROW]
[ROW][C]49[/C][C]6.65[/C][C]6.51364252679656[/C][C]0.136357473203437[/C][/ROW]
[ROW][C]50[/C][C]6.61[/C][C]6.76299448628996[/C][C]-0.152994486289963[/C][/ROW]
[ROW][C]51[/C][C]6.52[/C][C]6.59859013475875[/C][C]-0.0785901347587474[/C][/ROW]
[ROW][C]52[/C][C]6.62[/C][C]6.5424664146366[/C][C]0.077533585363402[/C][/ROW]
[ROW][C]53[/C][C]6.6[/C][C]6.53270230860606[/C][C]0.0672976913939412[/C][/ROW]
[ROW][C]54[/C][C]6.61[/C][C]6.60241959970088[/C][C]0.00758040029911644[/C][/ROW]
[ROW][C]55[/C][C]6.63[/C][C]6.78866767321016[/C][C]-0.158667673210159[/C][/ROW]
[ROW][C]56[/C][C]6.62[/C][C]6.66204558976063[/C][C]-0.0420455897606313[/C][/ROW]
[ROW][C]57[/C][C]6.6[/C][C]6.55516901071513[/C][C]0.0448309892848693[/C][/ROW]
[ROW][C]58[/C][C]6.59[/C][C]6.61309412147327[/C][C]-0.0230941214732727[/C][/ROW]
[ROW][C]59[/C][C]6.59[/C][C]6.59085196996065[/C][C]-0.000851969960653953[/C][/ROW]
[ROW][C]60[/C][C]6.52[/C][C]6.59173605999623[/C][C]-0.0717360599962289[/C][/ROW]
[ROW][C]61[/C][C]6.52[/C][C]6.50369029236561[/C][C]0.0163097076343881[/C][/ROW]
[ROW][C]62[/C][C]6.61[/C][C]6.63107981945155[/C][C]-0.0210798194515460[/C][/ROW]
[ROW][C]63[/C][C]6.59[/C][C]6.59859013475875[/C][C]-0.00859013475874715[/C][/ROW]
[ROW][C]64[/C][C]6.6[/C][C]6.61254647954365[/C][C]-0.0125464795436550[/C][/ROW]
[ROW][C]65[/C][C]6.48[/C][C]6.51301069291345[/C][C]-0.0330106929134448[/C][/ROW]
[ROW][C]66[/C][C]6.53[/C][C]6.4826437870987[/C][C]0.0473562129013008[/C][/ROW]
[ROW][C]67[/C][C]6.56[/C][C]6.70668821413392[/C][C]-0.146688214133925[/C][/ROW]
[ROW][C]68[/C][C]6.56[/C][C]6.59186724061025[/C][C]-0.0318672406102536[/C][/ROW]
[ROW][C]69[/C][C]6.49[/C][C]6.49589228894649[/C][C]-0.0058922889464883[/C][/ROW]
[ROW][C]70[/C][C]6.45[/C][C]6.50312532714703[/C][C]-0.0531253271470318[/C][/ROW]
[ROW][C]71[/C][C]6.44[/C][C]6.4511511431484[/C][C]-0.0111511431483962[/C][/ROW]
[ROW][C]72[/C][C]6.43[/C][C]6.44203579997116[/C][C]-0.0120357999711631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42957&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42957&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
135.85.789638180826160.0103618191738422
145.915.900475510808010.009524489191989
155.925.90138607436680.0186139256331979
165.965.941780144004690.0182198559953131
175.95.882878990749860.0171210092501433
185.925.903727359521470.0162726404785287
196.096.081594838677650.00840516132235436
206.316.120669753457720.189330246542281
216.256.248905948243820.00109405175618171
226.236.26319341225341-0.0331934122534143
236.226.23162127244342-0.0116212724434224
246.196.22247541860107-0.0324754186010647
256.156.17526655614421-0.0252665561442118
266.126.25563038306529-0.135630383065286
276.136.110547292484380.0194527075156152
286.16.15202033872586-0.0520203387258569
296.056.020720300598140.0292796994018572
306.076.05344712527420.0165528747257984
316.096.23530632444558-0.145306324445584
326.176.120669753457720.0493302465422811
336.126.110593597450320.0094064025496765
346.126.13323029168604-0.0132302916860390
356.136.121856337090930.00814366290906676
366.196.132655262586020.0573447374139757
376.246.175266556144210.064733443855788
386.416.346955921645730.063044078354272
396.56.399388974646760.100611025353238
406.536.522443538948870.0075564610511325
416.586.44409003798930.135909962010696
426.536.58245696426719-0.0524569642671864
436.516.70668821413392-0.196688214133925
446.516.54173984835998-0.031739848359984
456.496.446495020805950.0435049791940454
466.496.50312532714703-0.0131253271470317
476.496.49106566509476-0.00106566509475581
486.536.491935886646190.0380641133538147
496.656.513642526796560.136357473203437
506.616.76299448628996-0.152994486289963
516.526.59859013475875-0.0785901347587474
526.626.54246641463660.077533585363402
536.66.532702308606060.0672976913939412
546.616.602419599700880.00758040029911644
556.636.78866767321016-0.158667673210159
566.626.66204558976063-0.0420455897606313
576.66.555169010715130.0448309892848693
586.596.61309412147327-0.0230941214732727
596.596.59085196996065-0.000851969960653953
606.526.59173605999623-0.0717360599962289
616.526.503690292365610.0163097076343881
626.616.63107981945155-0.0210798194515460
636.596.59859013475875-0.00859013475874715
646.66.61254647954365-0.0125464795436550
656.486.51301069291345-0.0330106929134448
666.536.48264378709870.0473562129013008
676.566.70668821413392-0.146688214133925
686.566.59186724061025-0.0318672406102536
696.496.49589228894649-0.0058922889464883
706.456.50312532714703-0.0531253271470318
716.446.4511511431484-0.0111511431483962
726.436.44203579997116-0.0120357999711631







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
736.414120182487056.275557287540226.55268307743388
746.523640582127446.326234730931066.72104643332383
756.51257565362476.272038614554076.75311269269533
766.535033576409836.257202381219266.81286477160041
776.44904600060046.142406509982676.75568549121813
786.451747616837246.115776709564356.78771852411013
796.626499613595066.255378217878116.997621009312
806.658536284913676.261505435684577.05556713414277
816.593240754695546.177241177405927.00924033198517
826.606336793685216.167979461721177.04469412564926
836.60715385271276.14831134936417.06599635606128
846.60885563473971-2.6368126397116115.8545239091910

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 6.41412018248705 & 6.27555728754022 & 6.55268307743388 \tabularnewline
74 & 6.52364058212744 & 6.32623473093106 & 6.72104643332383 \tabularnewline
75 & 6.5125756536247 & 6.27203861455407 & 6.75311269269533 \tabularnewline
76 & 6.53503357640983 & 6.25720238121926 & 6.81286477160041 \tabularnewline
77 & 6.4490460006004 & 6.14240650998267 & 6.75568549121813 \tabularnewline
78 & 6.45174761683724 & 6.11577670956435 & 6.78771852411013 \tabularnewline
79 & 6.62649961359506 & 6.25537821787811 & 6.997621009312 \tabularnewline
80 & 6.65853628491367 & 6.26150543568457 & 7.05556713414277 \tabularnewline
81 & 6.59324075469554 & 6.17724117740592 & 7.00924033198517 \tabularnewline
82 & 6.60633679368521 & 6.16797946172117 & 7.04469412564926 \tabularnewline
83 & 6.6071538527127 & 6.1483113493641 & 7.06599635606128 \tabularnewline
84 & 6.60885563473971 & -2.63681263971161 & 15.8545239091910 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42957&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]73[/C][C]6.41412018248705[/C][C]6.27555728754022[/C][C]6.55268307743388[/C][/ROW]
[ROW][C]74[/C][C]6.52364058212744[/C][C]6.32623473093106[/C][C]6.72104643332383[/C][/ROW]
[ROW][C]75[/C][C]6.5125756536247[/C][C]6.27203861455407[/C][C]6.75311269269533[/C][/ROW]
[ROW][C]76[/C][C]6.53503357640983[/C][C]6.25720238121926[/C][C]6.81286477160041[/C][/ROW]
[ROW][C]77[/C][C]6.4490460006004[/C][C]6.14240650998267[/C][C]6.75568549121813[/C][/ROW]
[ROW][C]78[/C][C]6.45174761683724[/C][C]6.11577670956435[/C][C]6.78771852411013[/C][/ROW]
[ROW][C]79[/C][C]6.62649961359506[/C][C]6.25537821787811[/C][C]6.997621009312[/C][/ROW]
[ROW][C]80[/C][C]6.65853628491367[/C][C]6.26150543568457[/C][C]7.05556713414277[/C][/ROW]
[ROW][C]81[/C][C]6.59324075469554[/C][C]6.17724117740592[/C][C]7.00924033198517[/C][/ROW]
[ROW][C]82[/C][C]6.60633679368521[/C][C]6.16797946172117[/C][C]7.04469412564926[/C][/ROW]
[ROW][C]83[/C][C]6.6071538527127[/C][C]6.1483113493641[/C][C]7.06599635606128[/C][/ROW]
[ROW][C]84[/C][C]6.60885563473971[/C][C]-2.63681263971161[/C][C]15.8545239091910[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42957&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42957&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
736.414120182487056.275557287540226.55268307743388
746.523640582127446.326234730931066.72104643332383
756.51257565362476.272038614554076.75311269269533
766.535033576409836.257202381219266.81286477160041
776.44904600060046.142406509982676.75568549121813
786.451747616837246.115776709564356.78771852411013
796.626499613595066.255378217878116.997621009312
806.658536284913676.261505435684577.05556713414277
816.593240754695546.177241177405927.00924033198517
826.606336793685216.167979461721177.04469412564926
836.60715385271276.14831134936417.06599635606128
846.60885563473971-2.6368126397116115.8545239091910



Parameters (Session):
par1 = 0 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')