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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 27 May 2012 07:08:00 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/27/t13381169242dc1ijgc62np1at.htm/, Retrieved Wed, 08 May 2024 20:22:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167671, Retrieved Wed, 08 May 2024 20:22:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-27 11:08:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
4,95
4,95
4,96
4,93
4,95
4,96
4,97
5,01
5,04
5,07
5,07
5,08
5,07
5,08
5,09
5,09
5,14
5,17
5,17
5,18
5,18
5,18
5,17
5,17
5,18
5,18
5,26
5,26
5,26
5,28
5,28
5,31
5,37
5,42
5,43
5,43
5,44
5,5
5,52
5,55
5,55
5,55
5,55
5,55
5,55
5,55
5,55
5,56
5,57
5,59
5,69
5,73
5,76
5,77
5,77
5,79
5,79
5,79
5,79
5,79




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167671&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167671&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167671&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0767906267090112
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0767906267090112 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167671&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]0.0767906267090112[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167671&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167671&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
beta0.0767906267090112
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
34.964.950.00999999999999979
44.934.96076790626709-0.0307679062670907
54.954.928405219462320.0215947805376846
64.964.950063496193450.00993650380655176
74.974.960826526548050.00917347345195019
85.014.971530963323520.0384690366764762
95.045.01448502475880.0255149752411983
105.075.046444335698040.0235556643019619
115.075.07825318992233-0.0082531899223337
125.085.077619422295850.00238057770415079
135.075.08780222834968-0.0178022283496801
145.085.076435184077890.00356481592210844
155.095.086708928526650.00329107147334717
165.095.09696165196763-0.00696165196763499
175.145.096427062350110.0435729376498895
185.175.14977305553980.0202269444602026
195.175.18132629528131-0.0113262952813056
205.185.18045654196836-0.000456541968362423
215.185.19042148382449-0.0104214838244925
225.185.18962121155037-0.00962121155037199
235.175.18888239268572-0.0188823926857191
245.175.17743240191762-0.00743240191761707
255.185.176861663116410.00313833688358933
265.185.18710265797252-0.00710265797252507
275.265.186557240415510.0734427595844851
285.265.27219695595125-0.0121969559512465
295.265.27126034405981-0.0112603440598082
305.285.27039565518250.00960434481750383
315.285.29113317884016-0.0111331788401623
325.315.290278255059760.0197217449402372
335.375.321792700213520.0482072997864815
345.425.385494568976070.0345054310239279
355.435.43814426264926-0.00814426264926382
365.435.44751885961634-0.0175188596163443
375.445.44617357540718-0.00617357540717745
385.55.455699502682630.0443004973173746
395.525.519101365635150.000898634364852491
405.555.539170372331210.0108296276687936
415.555.57000198622692-0.0200019862269185
425.555.56846602116913-0.0184660211691288
435.555.56704800383073-0.0170480038307295
445.555.56573887693243-0.0157388769324296
455.555.56453027870909-0.0145302787090928
465.555.56341448950076-0.0134144895007644
475.555.56238438244502-0.0123843824450196
485.565.56143337795566-0.00143337795566278
495.575.57132330796414-0.00132330796413527
505.595.581221690316240.00877830968375815
515.695.60189578221830.088104217781698
525.735.708661360317470.0213386396825337
535.765.750299967831810.00970003216819304
545.775.7810448393811-0.0110448393810998
555.775.79019669924312-0.0201966992431242
565.795.788645782050790.00135421794920898
575.795.80874977329581-0.018749773295812
585.795.80730996645377-0.0173099664537748
595.795.80598072328148-0.0159807232814773
605.795.80475355352543-0.0147535535254288

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4.96 & 4.95 & 0.00999999999999979 \tabularnewline
4 & 4.93 & 4.96076790626709 & -0.0307679062670907 \tabularnewline
5 & 4.95 & 4.92840521946232 & 0.0215947805376846 \tabularnewline
6 & 4.96 & 4.95006349619345 & 0.00993650380655176 \tabularnewline
7 & 4.97 & 4.96082652654805 & 0.00917347345195019 \tabularnewline
8 & 5.01 & 4.97153096332352 & 0.0384690366764762 \tabularnewline
9 & 5.04 & 5.0144850247588 & 0.0255149752411983 \tabularnewline
10 & 5.07 & 5.04644433569804 & 0.0235556643019619 \tabularnewline
11 & 5.07 & 5.07825318992233 & -0.0082531899223337 \tabularnewline
12 & 5.08 & 5.07761942229585 & 0.00238057770415079 \tabularnewline
13 & 5.07 & 5.08780222834968 & -0.0178022283496801 \tabularnewline
14 & 5.08 & 5.07643518407789 & 0.00356481592210844 \tabularnewline
15 & 5.09 & 5.08670892852665 & 0.00329107147334717 \tabularnewline
16 & 5.09 & 5.09696165196763 & -0.00696165196763499 \tabularnewline
17 & 5.14 & 5.09642706235011 & 0.0435729376498895 \tabularnewline
18 & 5.17 & 5.1497730555398 & 0.0202269444602026 \tabularnewline
19 & 5.17 & 5.18132629528131 & -0.0113262952813056 \tabularnewline
20 & 5.18 & 5.18045654196836 & -0.000456541968362423 \tabularnewline
21 & 5.18 & 5.19042148382449 & -0.0104214838244925 \tabularnewline
22 & 5.18 & 5.18962121155037 & -0.00962121155037199 \tabularnewline
23 & 5.17 & 5.18888239268572 & -0.0188823926857191 \tabularnewline
24 & 5.17 & 5.17743240191762 & -0.00743240191761707 \tabularnewline
25 & 5.18 & 5.17686166311641 & 0.00313833688358933 \tabularnewline
26 & 5.18 & 5.18710265797252 & -0.00710265797252507 \tabularnewline
27 & 5.26 & 5.18655724041551 & 0.0734427595844851 \tabularnewline
28 & 5.26 & 5.27219695595125 & -0.0121969559512465 \tabularnewline
29 & 5.26 & 5.27126034405981 & -0.0112603440598082 \tabularnewline
30 & 5.28 & 5.2703956551825 & 0.00960434481750383 \tabularnewline
31 & 5.28 & 5.29113317884016 & -0.0111331788401623 \tabularnewline
32 & 5.31 & 5.29027825505976 & 0.0197217449402372 \tabularnewline
33 & 5.37 & 5.32179270021352 & 0.0482072997864815 \tabularnewline
34 & 5.42 & 5.38549456897607 & 0.0345054310239279 \tabularnewline
35 & 5.43 & 5.43814426264926 & -0.00814426264926382 \tabularnewline
36 & 5.43 & 5.44751885961634 & -0.0175188596163443 \tabularnewline
37 & 5.44 & 5.44617357540718 & -0.00617357540717745 \tabularnewline
38 & 5.5 & 5.45569950268263 & 0.0443004973173746 \tabularnewline
39 & 5.52 & 5.51910136563515 & 0.000898634364852491 \tabularnewline
40 & 5.55 & 5.53917037233121 & 0.0108296276687936 \tabularnewline
41 & 5.55 & 5.57000198622692 & -0.0200019862269185 \tabularnewline
42 & 5.55 & 5.56846602116913 & -0.0184660211691288 \tabularnewline
43 & 5.55 & 5.56704800383073 & -0.0170480038307295 \tabularnewline
44 & 5.55 & 5.56573887693243 & -0.0157388769324296 \tabularnewline
45 & 5.55 & 5.56453027870909 & -0.0145302787090928 \tabularnewline
46 & 5.55 & 5.56341448950076 & -0.0134144895007644 \tabularnewline
47 & 5.55 & 5.56238438244502 & -0.0123843824450196 \tabularnewline
48 & 5.56 & 5.56143337795566 & -0.00143337795566278 \tabularnewline
49 & 5.57 & 5.57132330796414 & -0.00132330796413527 \tabularnewline
50 & 5.59 & 5.58122169031624 & 0.00877830968375815 \tabularnewline
51 & 5.69 & 5.6018957822183 & 0.088104217781698 \tabularnewline
52 & 5.73 & 5.70866136031747 & 0.0213386396825337 \tabularnewline
53 & 5.76 & 5.75029996783181 & 0.00970003216819304 \tabularnewline
54 & 5.77 & 5.7810448393811 & -0.0110448393810998 \tabularnewline
55 & 5.77 & 5.79019669924312 & -0.0201966992431242 \tabularnewline
56 & 5.79 & 5.78864578205079 & 0.00135421794920898 \tabularnewline
57 & 5.79 & 5.80874977329581 & -0.018749773295812 \tabularnewline
58 & 5.79 & 5.80730996645377 & -0.0173099664537748 \tabularnewline
59 & 5.79 & 5.80598072328148 & -0.0159807232814773 \tabularnewline
60 & 5.79 & 5.80475355352543 & -0.0147535535254288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167671&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]4.96[/C][C]4.95[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]4.93[/C][C]4.96076790626709[/C][C]-0.0307679062670907[/C][/ROW]
[ROW][C]5[/C][C]4.95[/C][C]4.92840521946232[/C][C]0.0215947805376846[/C][/ROW]
[ROW][C]6[/C][C]4.96[/C][C]4.95006349619345[/C][C]0.00993650380655176[/C][/ROW]
[ROW][C]7[/C][C]4.97[/C][C]4.96082652654805[/C][C]0.00917347345195019[/C][/ROW]
[ROW][C]8[/C][C]5.01[/C][C]4.97153096332352[/C][C]0.0384690366764762[/C][/ROW]
[ROW][C]9[/C][C]5.04[/C][C]5.0144850247588[/C][C]0.0255149752411983[/C][/ROW]
[ROW][C]10[/C][C]5.07[/C][C]5.04644433569804[/C][C]0.0235556643019619[/C][/ROW]
[ROW][C]11[/C][C]5.07[/C][C]5.07825318992233[/C][C]-0.0082531899223337[/C][/ROW]
[ROW][C]12[/C][C]5.08[/C][C]5.07761942229585[/C][C]0.00238057770415079[/C][/ROW]
[ROW][C]13[/C][C]5.07[/C][C]5.08780222834968[/C][C]-0.0178022283496801[/C][/ROW]
[ROW][C]14[/C][C]5.08[/C][C]5.07643518407789[/C][C]0.00356481592210844[/C][/ROW]
[ROW][C]15[/C][C]5.09[/C][C]5.08670892852665[/C][C]0.00329107147334717[/C][/ROW]
[ROW][C]16[/C][C]5.09[/C][C]5.09696165196763[/C][C]-0.00696165196763499[/C][/ROW]
[ROW][C]17[/C][C]5.14[/C][C]5.09642706235011[/C][C]0.0435729376498895[/C][/ROW]
[ROW][C]18[/C][C]5.17[/C][C]5.1497730555398[/C][C]0.0202269444602026[/C][/ROW]
[ROW][C]19[/C][C]5.17[/C][C]5.18132629528131[/C][C]-0.0113262952813056[/C][/ROW]
[ROW][C]20[/C][C]5.18[/C][C]5.18045654196836[/C][C]-0.000456541968362423[/C][/ROW]
[ROW][C]21[/C][C]5.18[/C][C]5.19042148382449[/C][C]-0.0104214838244925[/C][/ROW]
[ROW][C]22[/C][C]5.18[/C][C]5.18962121155037[/C][C]-0.00962121155037199[/C][/ROW]
[ROW][C]23[/C][C]5.17[/C][C]5.18888239268572[/C][C]-0.0188823926857191[/C][/ROW]
[ROW][C]24[/C][C]5.17[/C][C]5.17743240191762[/C][C]-0.00743240191761707[/C][/ROW]
[ROW][C]25[/C][C]5.18[/C][C]5.17686166311641[/C][C]0.00313833688358933[/C][/ROW]
[ROW][C]26[/C][C]5.18[/C][C]5.18710265797252[/C][C]-0.00710265797252507[/C][/ROW]
[ROW][C]27[/C][C]5.26[/C][C]5.18655724041551[/C][C]0.0734427595844851[/C][/ROW]
[ROW][C]28[/C][C]5.26[/C][C]5.27219695595125[/C][C]-0.0121969559512465[/C][/ROW]
[ROW][C]29[/C][C]5.26[/C][C]5.27126034405981[/C][C]-0.0112603440598082[/C][/ROW]
[ROW][C]30[/C][C]5.28[/C][C]5.2703956551825[/C][C]0.00960434481750383[/C][/ROW]
[ROW][C]31[/C][C]5.28[/C][C]5.29113317884016[/C][C]-0.0111331788401623[/C][/ROW]
[ROW][C]32[/C][C]5.31[/C][C]5.29027825505976[/C][C]0.0197217449402372[/C][/ROW]
[ROW][C]33[/C][C]5.37[/C][C]5.32179270021352[/C][C]0.0482072997864815[/C][/ROW]
[ROW][C]34[/C][C]5.42[/C][C]5.38549456897607[/C][C]0.0345054310239279[/C][/ROW]
[ROW][C]35[/C][C]5.43[/C][C]5.43814426264926[/C][C]-0.00814426264926382[/C][/ROW]
[ROW][C]36[/C][C]5.43[/C][C]5.44751885961634[/C][C]-0.0175188596163443[/C][/ROW]
[ROW][C]37[/C][C]5.44[/C][C]5.44617357540718[/C][C]-0.00617357540717745[/C][/ROW]
[ROW][C]38[/C][C]5.5[/C][C]5.45569950268263[/C][C]0.0443004973173746[/C][/ROW]
[ROW][C]39[/C][C]5.52[/C][C]5.51910136563515[/C][C]0.000898634364852491[/C][/ROW]
[ROW][C]40[/C][C]5.55[/C][C]5.53917037233121[/C][C]0.0108296276687936[/C][/ROW]
[ROW][C]41[/C][C]5.55[/C][C]5.57000198622692[/C][C]-0.0200019862269185[/C][/ROW]
[ROW][C]42[/C][C]5.55[/C][C]5.56846602116913[/C][C]-0.0184660211691288[/C][/ROW]
[ROW][C]43[/C][C]5.55[/C][C]5.56704800383073[/C][C]-0.0170480038307295[/C][/ROW]
[ROW][C]44[/C][C]5.55[/C][C]5.56573887693243[/C][C]-0.0157388769324296[/C][/ROW]
[ROW][C]45[/C][C]5.55[/C][C]5.56453027870909[/C][C]-0.0145302787090928[/C][/ROW]
[ROW][C]46[/C][C]5.55[/C][C]5.56341448950076[/C][C]-0.0134144895007644[/C][/ROW]
[ROW][C]47[/C][C]5.55[/C][C]5.56238438244502[/C][C]-0.0123843824450196[/C][/ROW]
[ROW][C]48[/C][C]5.56[/C][C]5.56143337795566[/C][C]-0.00143337795566278[/C][/ROW]
[ROW][C]49[/C][C]5.57[/C][C]5.57132330796414[/C][C]-0.00132330796413527[/C][/ROW]
[ROW][C]50[/C][C]5.59[/C][C]5.58122169031624[/C][C]0.00877830968375815[/C][/ROW]
[ROW][C]51[/C][C]5.69[/C][C]5.6018957822183[/C][C]0.088104217781698[/C][/ROW]
[ROW][C]52[/C][C]5.73[/C][C]5.70866136031747[/C][C]0.0213386396825337[/C][/ROW]
[ROW][C]53[/C][C]5.76[/C][C]5.75029996783181[/C][C]0.00970003216819304[/C][/ROW]
[ROW][C]54[/C][C]5.77[/C][C]5.7810448393811[/C][C]-0.0110448393810998[/C][/ROW]
[ROW][C]55[/C][C]5.77[/C][C]5.79019669924312[/C][C]-0.0201966992431242[/C][/ROW]
[ROW][C]56[/C][C]5.79[/C][C]5.78864578205079[/C][C]0.00135421794920898[/C][/ROW]
[ROW][C]57[/C][C]5.79[/C][C]5.80874977329581[/C][C]-0.018749773295812[/C][/ROW]
[ROW][C]58[/C][C]5.79[/C][C]5.80730996645377[/C][C]-0.0173099664537748[/C][/ROW]
[ROW][C]59[/C][C]5.79[/C][C]5.80598072328148[/C][C]-0.0159807232814773[/C][/ROW]
[ROW][C]60[/C][C]5.79[/C][C]5.80475355352543[/C][C]-0.0147535535254288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167671&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167671&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
34.964.950.00999999999999979
44.934.96076790626709-0.0307679062670907
54.954.928405219462320.0215947805376846
64.964.950063496193450.00993650380655176
74.974.960826526548050.00917347345195019
85.014.971530963323520.0384690366764762
95.045.01448502475880.0255149752411983
105.075.046444335698040.0235556643019619
115.075.07825318992233-0.0082531899223337
125.085.077619422295850.00238057770415079
135.075.08780222834968-0.0178022283496801
145.085.076435184077890.00356481592210844
155.095.086708928526650.00329107147334717
165.095.09696165196763-0.00696165196763499
175.145.096427062350110.0435729376498895
185.175.14977305553980.0202269444602026
195.175.18132629528131-0.0113262952813056
205.185.18045654196836-0.000456541968362423
215.185.19042148382449-0.0104214838244925
225.185.18962121155037-0.00962121155037199
235.175.18888239268572-0.0188823926857191
245.175.17743240191762-0.00743240191761707
255.185.176861663116410.00313833688358933
265.185.18710265797252-0.00710265797252507
275.265.186557240415510.0734427595844851
285.265.27219695595125-0.0121969559512465
295.265.27126034405981-0.0112603440598082
305.285.27039565518250.00960434481750383
315.285.29113317884016-0.0111331788401623
325.315.290278255059760.0197217449402372
335.375.321792700213520.0482072997864815
345.425.385494568976070.0345054310239279
355.435.43814426264926-0.00814426264926382
365.435.44751885961634-0.0175188596163443
375.445.44617357540718-0.00617357540717745
385.55.455699502682630.0443004973173746
395.525.519101365635150.000898634364852491
405.555.539170372331210.0108296276687936
415.555.57000198622692-0.0200019862269185
425.555.56846602116913-0.0184660211691288
435.555.56704800383073-0.0170480038307295
445.555.56573887693243-0.0157388769324296
455.555.56453027870909-0.0145302787090928
465.555.56341448950076-0.0134144895007644
475.555.56238438244502-0.0123843824450196
485.565.56143337795566-0.00143337795566278
495.575.57132330796414-0.00132330796413527
505.595.581221690316240.00877830968375815
515.695.60189578221830.088104217781698
525.735.708661360317470.0213386396825337
535.765.750299967831810.00970003216819304
545.775.7810448393811-0.0110448393810998
555.775.79019669924312-0.0201966992431242
565.795.788645782050790.00135421794920898
575.795.80874977329581-0.018749773295812
585.795.80730996645377-0.0173099664537748
595.795.80598072328148-0.0159807232814773
605.795.80475355352543-0.0147535535254288







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
615.803620618904035.757498077770335.84974316003772
625.817241237808055.749463413418465.88501906219765
635.830861856712085.744695027654945.91702868576921
645.844482475616115.741307652875075.94765729835714
655.858103094520135.738604614499165.9776015745411
665.871723713424165.736245527491936.00720189935639
675.885344332328195.734038387795826.03665027686055
685.898964951232215.731864906097456.06606499636697
695.912585570136245.729647777545976.09552336272651
705.926206189040275.727334346219796.12507803186074
715.939826807944295.724887664915956.15476595097263
725.953447426848325.722281252053376.18461360164327

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 5.80362061890403 & 5.75749807777033 & 5.84974316003772 \tabularnewline
62 & 5.81724123780805 & 5.74946341341846 & 5.88501906219765 \tabularnewline
63 & 5.83086185671208 & 5.74469502765494 & 5.91702868576921 \tabularnewline
64 & 5.84448247561611 & 5.74130765287507 & 5.94765729835714 \tabularnewline
65 & 5.85810309452013 & 5.73860461449916 & 5.9776015745411 \tabularnewline
66 & 5.87172371342416 & 5.73624552749193 & 6.00720189935639 \tabularnewline
67 & 5.88534433232819 & 5.73403838779582 & 6.03665027686055 \tabularnewline
68 & 5.89896495123221 & 5.73186490609745 & 6.06606499636697 \tabularnewline
69 & 5.91258557013624 & 5.72964777754597 & 6.09552336272651 \tabularnewline
70 & 5.92620618904027 & 5.72733434621979 & 6.12507803186074 \tabularnewline
71 & 5.93982680794429 & 5.72488766491595 & 6.15476595097263 \tabularnewline
72 & 5.95344742684832 & 5.72228125205337 & 6.18461360164327 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167671&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]61[/C][C]5.80362061890403[/C][C]5.75749807777033[/C][C]5.84974316003772[/C][/ROW]
[ROW][C]62[/C][C]5.81724123780805[/C][C]5.74946341341846[/C][C]5.88501906219765[/C][/ROW]
[ROW][C]63[/C][C]5.83086185671208[/C][C]5.74469502765494[/C][C]5.91702868576921[/C][/ROW]
[ROW][C]64[/C][C]5.84448247561611[/C][C]5.74130765287507[/C][C]5.94765729835714[/C][/ROW]
[ROW][C]65[/C][C]5.85810309452013[/C][C]5.73860461449916[/C][C]5.9776015745411[/C][/ROW]
[ROW][C]66[/C][C]5.87172371342416[/C][C]5.73624552749193[/C][C]6.00720189935639[/C][/ROW]
[ROW][C]67[/C][C]5.88534433232819[/C][C]5.73403838779582[/C][C]6.03665027686055[/C][/ROW]
[ROW][C]68[/C][C]5.89896495123221[/C][C]5.73186490609745[/C][C]6.06606499636697[/C][/ROW]
[ROW][C]69[/C][C]5.91258557013624[/C][C]5.72964777754597[/C][C]6.09552336272651[/C][/ROW]
[ROW][C]70[/C][C]5.92620618904027[/C][C]5.72733434621979[/C][C]6.12507803186074[/C][/ROW]
[ROW][C]71[/C][C]5.93982680794429[/C][C]5.72488766491595[/C][C]6.15476595097263[/C][/ROW]
[ROW][C]72[/C][C]5.95344742684832[/C][C]5.72228125205337[/C][C]6.18461360164327[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167671&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167671&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
615.803620618904035.757498077770335.84974316003772
625.817241237808055.749463413418465.88501906219765
635.830861856712085.744695027654945.91702868576921
645.844482475616115.741307652875075.94765729835714
655.858103094520135.738604614499165.9776015745411
665.871723713424165.736245527491936.00720189935639
675.885344332328195.734038387795826.03665027686055
685.898964951232215.731864906097456.06606499636697
695.912585570136245.729647777545976.09552336272651
705.926206189040275.727334346219796.12507803186074
715.939826807944295.724887664915956.15476595097263
725.953447426848325.722281252053376.18461360164327



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')