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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 29 May 2012 02:28:18 -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/29/t133827293093d2loo9vthrssk.htm/, Retrieved Mon, 29 Apr 2024 21:11:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167916, Retrieved Mon, 29 Apr 2024 21:11:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-29 06:28:18] [57781dd4fd8fc2f3d4652fc8b989af11] [Current]
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Dataseries X:
-6
-3
-2
-5
-11
-11
-11
-10
-14
-8
-9
-5
-1
-2
-5
-4
-6
-2
-2
-2
-2
2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0
-2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167916&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167916&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167916&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.872863233637848
beta0.115842866993129
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.872863233637848 \tabularnewline
beta & 0.115842866993129 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167916&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]0.872863233637848[/C][/ROW]
[ROW][C]beta[/C][C]0.115842866993129[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167916&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167916&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
alpha0.872863233637848
beta0.115842866993129
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3-20-2
4-51.0520435737693-6.0520435737693
5-11-2.04474497086176-8.95525502913824
6-11-8.58115048284771-2.41884951715229
7-11-9.65674986255937-1.34325013744063
8-10-9.9293207996775-0.0706792003224912
9-14-9.09825807947926-4.90174192052074
10-8-12.9796919208384.97969192083798
11-9-7.73246402007005-1.26753597992995
12-5-8.066378540636613.06637854063661
13-1-4.307321615264693.30732161526469
14-2-0.0035345813972758-1.99646541860272
15-5-0.53110080826742-4.46889919173258
16-4-3.66863622336618-0.33136377663382
17-6-3.22817493822464-2.77182506177536
18-2-5.198175616236363.19817561623636
19-2-1.63379873581744-0.36620126418256
20-2-1.21766381845742-0.782336181542582
21-2-1.24386367763507-0.756136322364931
222-1.323651351728183.32365135172818
2312.49372857416382-1.49372857416382
24-81.95515634615814-9.95515634615814
25-1-6.97570051774075.9757005177407
261-1.396865309580042.39686530958004
27-11.30049521271705-2.30049521271705
282-0.3349120862628492.33491208626285
2922.31185180665757-0.31185180665757
3012.61681992029737-1.61681992029737
31-11.61924463341157-2.61924463341157
32-2-0.518155197395554-1.48184480260445
33-2-1.81259724074942-0.187402759250578
34-1-1.99611764254030.996117642540299
35-8-1.04586418436499-6.95413581563501
36-4-7.738261968214763.73826196821476
37-6-4.71966456491369-1.28033543508631
38-3-6.211077410627583.21107741062758
39-3-3.457413089752790.457413089752792
40-7-3.06106979716685-3.93893020283315
41-9-6.90041777375232-2.09958222624768
42-11-9.34656574142853-1.65343425857147
43-13-11.5704745224808-1.42952547751922
44-11-13.74348800018582.74348800018578
45-9-11.99662370689132.99662370689131
46-17-9.72580301746854-7.27419698253146
47-22-17.1555343657338-4.84446563426618
48-25-22.9542905956693-2.04570940433069
49-20-26.51696727701516.51696727701506
50-24-21.946635289215-2.05336471078497
51-24-25.06465692422691.06465692422687
52-22-25.35341934930573.35341934930573
53-19-23.30532427431694.30532427431694
54-18-19.99101361272551.99101361272552
55-17-18.49545833826321.49545833826317
56-11-17.28124180393146.28124180393138
57-11-11.25456320216810.254563202168137
58-12-10.462610619873-1.53738938012697
59-10-11.39024065870621.39024065870619
60-15-9.62187591927427-5.37812408072573
61-15-14.3051768187933-0.69482318120667
62-15-14.9708535827673-0.0291464172326545
63-13-15.05843271336172.05843271336175
64-8-13.11570239198325.11570239198324
65-13-7.98711963044184-5.01288036955816
66-9-12.20628166599913.20628166599908
67-7-8.92703624454981.9270362445498
68-4-6.569544887963092.56954488796309
69-4-3.39141188063348-0.608588119366518
70-2-3.048891702212771.04889170221277
710-1.153559664095511.15355966409551
72-20.94977535145009-2.94977535145009

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & -2 & 0 & -2 \tabularnewline
4 & -5 & 1.0520435737693 & -6.0520435737693 \tabularnewline
5 & -11 & -2.04474497086176 & -8.95525502913824 \tabularnewline
6 & -11 & -8.58115048284771 & -2.41884951715229 \tabularnewline
7 & -11 & -9.65674986255937 & -1.34325013744063 \tabularnewline
8 & -10 & -9.9293207996775 & -0.0706792003224912 \tabularnewline
9 & -14 & -9.09825807947926 & -4.90174192052074 \tabularnewline
10 & -8 & -12.979691920838 & 4.97969192083798 \tabularnewline
11 & -9 & -7.73246402007005 & -1.26753597992995 \tabularnewline
12 & -5 & -8.06637854063661 & 3.06637854063661 \tabularnewline
13 & -1 & -4.30732161526469 & 3.30732161526469 \tabularnewline
14 & -2 & -0.0035345813972758 & -1.99646541860272 \tabularnewline
15 & -5 & -0.53110080826742 & -4.46889919173258 \tabularnewline
16 & -4 & -3.66863622336618 & -0.33136377663382 \tabularnewline
17 & -6 & -3.22817493822464 & -2.77182506177536 \tabularnewline
18 & -2 & -5.19817561623636 & 3.19817561623636 \tabularnewline
19 & -2 & -1.63379873581744 & -0.36620126418256 \tabularnewline
20 & -2 & -1.21766381845742 & -0.782336181542582 \tabularnewline
21 & -2 & -1.24386367763507 & -0.756136322364931 \tabularnewline
22 & 2 & -1.32365135172818 & 3.32365135172818 \tabularnewline
23 & 1 & 2.49372857416382 & -1.49372857416382 \tabularnewline
24 & -8 & 1.95515634615814 & -9.95515634615814 \tabularnewline
25 & -1 & -6.9757005177407 & 5.9757005177407 \tabularnewline
26 & 1 & -1.39686530958004 & 2.39686530958004 \tabularnewline
27 & -1 & 1.30049521271705 & -2.30049521271705 \tabularnewline
28 & 2 & -0.334912086262849 & 2.33491208626285 \tabularnewline
29 & 2 & 2.31185180665757 & -0.31185180665757 \tabularnewline
30 & 1 & 2.61681992029737 & -1.61681992029737 \tabularnewline
31 & -1 & 1.61924463341157 & -2.61924463341157 \tabularnewline
32 & -2 & -0.518155197395554 & -1.48184480260445 \tabularnewline
33 & -2 & -1.81259724074942 & -0.187402759250578 \tabularnewline
34 & -1 & -1.9961176425403 & 0.996117642540299 \tabularnewline
35 & -8 & -1.04586418436499 & -6.95413581563501 \tabularnewline
36 & -4 & -7.73826196821476 & 3.73826196821476 \tabularnewline
37 & -6 & -4.71966456491369 & -1.28033543508631 \tabularnewline
38 & -3 & -6.21107741062758 & 3.21107741062758 \tabularnewline
39 & -3 & -3.45741308975279 & 0.457413089752792 \tabularnewline
40 & -7 & -3.06106979716685 & -3.93893020283315 \tabularnewline
41 & -9 & -6.90041777375232 & -2.09958222624768 \tabularnewline
42 & -11 & -9.34656574142853 & -1.65343425857147 \tabularnewline
43 & -13 & -11.5704745224808 & -1.42952547751922 \tabularnewline
44 & -11 & -13.7434880001858 & 2.74348800018578 \tabularnewline
45 & -9 & -11.9966237068913 & 2.99662370689131 \tabularnewline
46 & -17 & -9.72580301746854 & -7.27419698253146 \tabularnewline
47 & -22 & -17.1555343657338 & -4.84446563426618 \tabularnewline
48 & -25 & -22.9542905956693 & -2.04570940433069 \tabularnewline
49 & -20 & -26.5169672770151 & 6.51696727701506 \tabularnewline
50 & -24 & -21.946635289215 & -2.05336471078497 \tabularnewline
51 & -24 & -25.0646569242269 & 1.06465692422687 \tabularnewline
52 & -22 & -25.3534193493057 & 3.35341934930573 \tabularnewline
53 & -19 & -23.3053242743169 & 4.30532427431694 \tabularnewline
54 & -18 & -19.9910136127255 & 1.99101361272552 \tabularnewline
55 & -17 & -18.4954583382632 & 1.49545833826317 \tabularnewline
56 & -11 & -17.2812418039314 & 6.28124180393138 \tabularnewline
57 & -11 & -11.2545632021681 & 0.254563202168137 \tabularnewline
58 & -12 & -10.462610619873 & -1.53738938012697 \tabularnewline
59 & -10 & -11.3902406587062 & 1.39024065870619 \tabularnewline
60 & -15 & -9.62187591927427 & -5.37812408072573 \tabularnewline
61 & -15 & -14.3051768187933 & -0.69482318120667 \tabularnewline
62 & -15 & -14.9708535827673 & -0.0291464172326545 \tabularnewline
63 & -13 & -15.0584327133617 & 2.05843271336175 \tabularnewline
64 & -8 & -13.1157023919832 & 5.11570239198324 \tabularnewline
65 & -13 & -7.98711963044184 & -5.01288036955816 \tabularnewline
66 & -9 & -12.2062816659991 & 3.20628166599908 \tabularnewline
67 & -7 & -8.9270362445498 & 1.9270362445498 \tabularnewline
68 & -4 & -6.56954488796309 & 2.56954488796309 \tabularnewline
69 & -4 & -3.39141188063348 & -0.608588119366518 \tabularnewline
70 & -2 & -3.04889170221277 & 1.04889170221277 \tabularnewline
71 & 0 & -1.15355966409551 & 1.15355966409551 \tabularnewline
72 & -2 & 0.94977535145009 & -2.94977535145009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167916&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]-2[/C][C]0[/C][C]-2[/C][/ROW]
[ROW][C]4[/C][C]-5[/C][C]1.0520435737693[/C][C]-6.0520435737693[/C][/ROW]
[ROW][C]5[/C][C]-11[/C][C]-2.04474497086176[/C][C]-8.95525502913824[/C][/ROW]
[ROW][C]6[/C][C]-11[/C][C]-8.58115048284771[/C][C]-2.41884951715229[/C][/ROW]
[ROW][C]7[/C][C]-11[/C][C]-9.65674986255937[/C][C]-1.34325013744063[/C][/ROW]
[ROW][C]8[/C][C]-10[/C][C]-9.9293207996775[/C][C]-0.0706792003224912[/C][/ROW]
[ROW][C]9[/C][C]-14[/C][C]-9.09825807947926[/C][C]-4.90174192052074[/C][/ROW]
[ROW][C]10[/C][C]-8[/C][C]-12.979691920838[/C][C]4.97969192083798[/C][/ROW]
[ROW][C]11[/C][C]-9[/C][C]-7.73246402007005[/C][C]-1.26753597992995[/C][/ROW]
[ROW][C]12[/C][C]-5[/C][C]-8.06637854063661[/C][C]3.06637854063661[/C][/ROW]
[ROW][C]13[/C][C]-1[/C][C]-4.30732161526469[/C][C]3.30732161526469[/C][/ROW]
[ROW][C]14[/C][C]-2[/C][C]-0.0035345813972758[/C][C]-1.99646541860272[/C][/ROW]
[ROW][C]15[/C][C]-5[/C][C]-0.53110080826742[/C][C]-4.46889919173258[/C][/ROW]
[ROW][C]16[/C][C]-4[/C][C]-3.66863622336618[/C][C]-0.33136377663382[/C][/ROW]
[ROW][C]17[/C][C]-6[/C][C]-3.22817493822464[/C][C]-2.77182506177536[/C][/ROW]
[ROW][C]18[/C][C]-2[/C][C]-5.19817561623636[/C][C]3.19817561623636[/C][/ROW]
[ROW][C]19[/C][C]-2[/C][C]-1.63379873581744[/C][C]-0.36620126418256[/C][/ROW]
[ROW][C]20[/C][C]-2[/C][C]-1.21766381845742[/C][C]-0.782336181542582[/C][/ROW]
[ROW][C]21[/C][C]-2[/C][C]-1.24386367763507[/C][C]-0.756136322364931[/C][/ROW]
[ROW][C]22[/C][C]2[/C][C]-1.32365135172818[/C][C]3.32365135172818[/C][/ROW]
[ROW][C]23[/C][C]1[/C][C]2.49372857416382[/C][C]-1.49372857416382[/C][/ROW]
[ROW][C]24[/C][C]-8[/C][C]1.95515634615814[/C][C]-9.95515634615814[/C][/ROW]
[ROW][C]25[/C][C]-1[/C][C]-6.9757005177407[/C][C]5.9757005177407[/C][/ROW]
[ROW][C]26[/C][C]1[/C][C]-1.39686530958004[/C][C]2.39686530958004[/C][/ROW]
[ROW][C]27[/C][C]-1[/C][C]1.30049521271705[/C][C]-2.30049521271705[/C][/ROW]
[ROW][C]28[/C][C]2[/C][C]-0.334912086262849[/C][C]2.33491208626285[/C][/ROW]
[ROW][C]29[/C][C]2[/C][C]2.31185180665757[/C][C]-0.31185180665757[/C][/ROW]
[ROW][C]30[/C][C]1[/C][C]2.61681992029737[/C][C]-1.61681992029737[/C][/ROW]
[ROW][C]31[/C][C]-1[/C][C]1.61924463341157[/C][C]-2.61924463341157[/C][/ROW]
[ROW][C]32[/C][C]-2[/C][C]-0.518155197395554[/C][C]-1.48184480260445[/C][/ROW]
[ROW][C]33[/C][C]-2[/C][C]-1.81259724074942[/C][C]-0.187402759250578[/C][/ROW]
[ROW][C]34[/C][C]-1[/C][C]-1.9961176425403[/C][C]0.996117642540299[/C][/ROW]
[ROW][C]35[/C][C]-8[/C][C]-1.04586418436499[/C][C]-6.95413581563501[/C][/ROW]
[ROW][C]36[/C][C]-4[/C][C]-7.73826196821476[/C][C]3.73826196821476[/C][/ROW]
[ROW][C]37[/C][C]-6[/C][C]-4.71966456491369[/C][C]-1.28033543508631[/C][/ROW]
[ROW][C]38[/C][C]-3[/C][C]-6.21107741062758[/C][C]3.21107741062758[/C][/ROW]
[ROW][C]39[/C][C]-3[/C][C]-3.45741308975279[/C][C]0.457413089752792[/C][/ROW]
[ROW][C]40[/C][C]-7[/C][C]-3.06106979716685[/C][C]-3.93893020283315[/C][/ROW]
[ROW][C]41[/C][C]-9[/C][C]-6.90041777375232[/C][C]-2.09958222624768[/C][/ROW]
[ROW][C]42[/C][C]-11[/C][C]-9.34656574142853[/C][C]-1.65343425857147[/C][/ROW]
[ROW][C]43[/C][C]-13[/C][C]-11.5704745224808[/C][C]-1.42952547751922[/C][/ROW]
[ROW][C]44[/C][C]-11[/C][C]-13.7434880001858[/C][C]2.74348800018578[/C][/ROW]
[ROW][C]45[/C][C]-9[/C][C]-11.9966237068913[/C][C]2.99662370689131[/C][/ROW]
[ROW][C]46[/C][C]-17[/C][C]-9.72580301746854[/C][C]-7.27419698253146[/C][/ROW]
[ROW][C]47[/C][C]-22[/C][C]-17.1555343657338[/C][C]-4.84446563426618[/C][/ROW]
[ROW][C]48[/C][C]-25[/C][C]-22.9542905956693[/C][C]-2.04570940433069[/C][/ROW]
[ROW][C]49[/C][C]-20[/C][C]-26.5169672770151[/C][C]6.51696727701506[/C][/ROW]
[ROW][C]50[/C][C]-24[/C][C]-21.946635289215[/C][C]-2.05336471078497[/C][/ROW]
[ROW][C]51[/C][C]-24[/C][C]-25.0646569242269[/C][C]1.06465692422687[/C][/ROW]
[ROW][C]52[/C][C]-22[/C][C]-25.3534193493057[/C][C]3.35341934930573[/C][/ROW]
[ROW][C]53[/C][C]-19[/C][C]-23.3053242743169[/C][C]4.30532427431694[/C][/ROW]
[ROW][C]54[/C][C]-18[/C][C]-19.9910136127255[/C][C]1.99101361272552[/C][/ROW]
[ROW][C]55[/C][C]-17[/C][C]-18.4954583382632[/C][C]1.49545833826317[/C][/ROW]
[ROW][C]56[/C][C]-11[/C][C]-17.2812418039314[/C][C]6.28124180393138[/C][/ROW]
[ROW][C]57[/C][C]-11[/C][C]-11.2545632021681[/C][C]0.254563202168137[/C][/ROW]
[ROW][C]58[/C][C]-12[/C][C]-10.462610619873[/C][C]-1.53738938012697[/C][/ROW]
[ROW][C]59[/C][C]-10[/C][C]-11.3902406587062[/C][C]1.39024065870619[/C][/ROW]
[ROW][C]60[/C][C]-15[/C][C]-9.62187591927427[/C][C]-5.37812408072573[/C][/ROW]
[ROW][C]61[/C][C]-15[/C][C]-14.3051768187933[/C][C]-0.69482318120667[/C][/ROW]
[ROW][C]62[/C][C]-15[/C][C]-14.9708535827673[/C][C]-0.0291464172326545[/C][/ROW]
[ROW][C]63[/C][C]-13[/C][C]-15.0584327133617[/C][C]2.05843271336175[/C][/ROW]
[ROW][C]64[/C][C]-8[/C][C]-13.1157023919832[/C][C]5.11570239198324[/C][/ROW]
[ROW][C]65[/C][C]-13[/C][C]-7.98711963044184[/C][C]-5.01288036955816[/C][/ROW]
[ROW][C]66[/C][C]-9[/C][C]-12.2062816659991[/C][C]3.20628166599908[/C][/ROW]
[ROW][C]67[/C][C]-7[/C][C]-8.9270362445498[/C][C]1.9270362445498[/C][/ROW]
[ROW][C]68[/C][C]-4[/C][C]-6.56954488796309[/C][C]2.56954488796309[/C][/ROW]
[ROW][C]69[/C][C]-4[/C][C]-3.39141188063348[/C][C]-0.608588119366518[/C][/ROW]
[ROW][C]70[/C][C]-2[/C][C]-3.04889170221277[/C][C]1.04889170221277[/C][/ROW]
[ROW][C]71[/C][C]0[/C][C]-1.15355966409551[/C][C]1.15355966409551[/C][/ROW]
[ROW][C]72[/C][C]-2[/C][C]0.94977535145009[/C][C]-2.94977535145009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167916&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167916&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
3-20-2
4-51.0520435737693-6.0520435737693
5-11-2.04474497086176-8.95525502913824
6-11-8.58115048284771-2.41884951715229
7-11-9.65674986255937-1.34325013744063
8-10-9.9293207996775-0.0706792003224912
9-14-9.09825807947926-4.90174192052074
10-8-12.9796919208384.97969192083798
11-9-7.73246402007005-1.26753597992995
12-5-8.066378540636613.06637854063661
13-1-4.307321615264693.30732161526469
14-2-0.0035345813972758-1.99646541860272
15-5-0.53110080826742-4.46889919173258
16-4-3.66863622336618-0.33136377663382
17-6-3.22817493822464-2.77182506177536
18-2-5.198175616236363.19817561623636
19-2-1.63379873581744-0.36620126418256
20-2-1.21766381845742-0.782336181542582
21-2-1.24386367763507-0.756136322364931
222-1.323651351728183.32365135172818
2312.49372857416382-1.49372857416382
24-81.95515634615814-9.95515634615814
25-1-6.97570051774075.9757005177407
261-1.396865309580042.39686530958004
27-11.30049521271705-2.30049521271705
282-0.3349120862628492.33491208626285
2922.31185180665757-0.31185180665757
3012.61681992029737-1.61681992029737
31-11.61924463341157-2.61924463341157
32-2-0.518155197395554-1.48184480260445
33-2-1.81259724074942-0.187402759250578
34-1-1.99611764254030.996117642540299
35-8-1.04586418436499-6.95413581563501
36-4-7.738261968214763.73826196821476
37-6-4.71966456491369-1.28033543508631
38-3-6.211077410627583.21107741062758
39-3-3.457413089752790.457413089752792
40-7-3.06106979716685-3.93893020283315
41-9-6.90041777375232-2.09958222624768
42-11-9.34656574142853-1.65343425857147
43-13-11.5704745224808-1.42952547751922
44-11-13.74348800018582.74348800018578
45-9-11.99662370689132.99662370689131
46-17-9.72580301746854-7.27419698253146
47-22-17.1555343657338-4.84446563426618
48-25-22.9542905956693-2.04570940433069
49-20-26.51696727701516.51696727701506
50-24-21.946635289215-2.05336471078497
51-24-25.06465692422691.06465692422687
52-22-25.35341934930573.35341934930573
53-19-23.30532427431694.30532427431694
54-18-19.99101361272551.99101361272552
55-17-18.49545833826321.49545833826317
56-11-17.28124180393146.28124180393138
57-11-11.25456320216810.254563202168137
58-12-10.462610619873-1.53738938012697
59-10-11.39024065870621.39024065870619
60-15-9.62187591927427-5.37812408072573
61-15-14.3051768187933-0.69482318120667
62-15-14.9708535827673-0.0291464172326545
63-13-15.05843271336172.05843271336175
64-8-13.11570239198325.11570239198324
65-13-7.98711963044184-5.01288036955816
66-9-12.20628166599913.20628166599908
67-7-8.92703624454981.9270362445498
68-4-6.569544887963092.56954488796309
69-4-3.39141188063348-0.608588119366518
70-2-3.048891702212771.04889170221277
710-1.153559664095511.15355966409551
72-20.94977535145009-2.94977535145009







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73-0.826806377497968-7.722434649198976.06882189420303
74-0.0286376546740812-9.654484123665119.59720881431695
750.769531068149806-11.380203807963212.9192659442629
761.56769979097369-13.040497222659116.1758968046065
772.36586851379758-14.692247628211919.4239846558071
783.16403723662147-16.363586666896322.6916611401392
793.96220595944535-18.069998782246925.9944107011376
804.76037468226924-19.820542641622329.3412920061608
815.55854340509313-21.620690693967632.7377775041538
826.35671212791701-23.473778544285936.1872028001199
837.1548808507409-25.381806716748139.6915684182299
847.95304957356479-27.345911846758143.2520109938877

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & -0.826806377497968 & -7.72243464919897 & 6.06882189420303 \tabularnewline
74 & -0.0286376546740812 & -9.65448412366511 & 9.59720881431695 \tabularnewline
75 & 0.769531068149806 & -11.3802038079632 & 12.9192659442629 \tabularnewline
76 & 1.56769979097369 & -13.0404972226591 & 16.1758968046065 \tabularnewline
77 & 2.36586851379758 & -14.6922476282119 & 19.4239846558071 \tabularnewline
78 & 3.16403723662147 & -16.3635866668963 & 22.6916611401392 \tabularnewline
79 & 3.96220595944535 & -18.0699987822469 & 25.9944107011376 \tabularnewline
80 & 4.76037468226924 & -19.8205426416223 & 29.3412920061608 \tabularnewline
81 & 5.55854340509313 & -21.6206906939676 & 32.7377775041538 \tabularnewline
82 & 6.35671212791701 & -23.4737785442859 & 36.1872028001199 \tabularnewline
83 & 7.1548808507409 & -25.3818067167481 & 39.6915684182299 \tabularnewline
84 & 7.95304957356479 & -27.3459118467581 & 43.2520109938877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167916&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]-0.826806377497968[/C][C]-7.72243464919897[/C][C]6.06882189420303[/C][/ROW]
[ROW][C]74[/C][C]-0.0286376546740812[/C][C]-9.65448412366511[/C][C]9.59720881431695[/C][/ROW]
[ROW][C]75[/C][C]0.769531068149806[/C][C]-11.3802038079632[/C][C]12.9192659442629[/C][/ROW]
[ROW][C]76[/C][C]1.56769979097369[/C][C]-13.0404972226591[/C][C]16.1758968046065[/C][/ROW]
[ROW][C]77[/C][C]2.36586851379758[/C][C]-14.6922476282119[/C][C]19.4239846558071[/C][/ROW]
[ROW][C]78[/C][C]3.16403723662147[/C][C]-16.3635866668963[/C][C]22.6916611401392[/C][/ROW]
[ROW][C]79[/C][C]3.96220595944535[/C][C]-18.0699987822469[/C][C]25.9944107011376[/C][/ROW]
[ROW][C]80[/C][C]4.76037468226924[/C][C]-19.8205426416223[/C][C]29.3412920061608[/C][/ROW]
[ROW][C]81[/C][C]5.55854340509313[/C][C]-21.6206906939676[/C][C]32.7377775041538[/C][/ROW]
[ROW][C]82[/C][C]6.35671212791701[/C][C]-23.4737785442859[/C][C]36.1872028001199[/C][/ROW]
[ROW][C]83[/C][C]7.1548808507409[/C][C]-25.3818067167481[/C][C]39.6915684182299[/C][/ROW]
[ROW][C]84[/C][C]7.95304957356479[/C][C]-27.3459118467581[/C][C]43.2520109938877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167916&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167916&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
73-0.826806377497968-7.722434649198976.06882189420303
74-0.0286376546740812-9.654484123665119.59720881431695
750.769531068149806-11.380203807963212.9192659442629
761.56769979097369-13.040497222659116.1758968046065
772.36586851379758-14.692247628211919.4239846558071
783.16403723662147-16.363586666896322.6916611401392
793.96220595944535-18.069998782246925.9944107011376
804.76037468226924-19.820542641622329.3412920061608
815.55854340509313-21.620690693967632.7377775041538
826.35671212791701-23.473778544285936.1872028001199
837.1548808507409-25.381806716748139.6915684182299
847.95304957356479-27.345911846758143.2520109938877



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=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')