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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 22 May 2012 11:32:12 -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/22/t1337700746gs83yrn6hlut61o.htm/, Retrieved Fri, 03 May 2024 22:30:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167084, Retrieved Fri, 03 May 2024 22:30:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-22 15:32:12] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
13,15
13,47
13,65
13,52
14,13
14,84
15,29
15,51
15,43
15,42
15,56
15,43
15,36
15,18
15,41
15,15
15,21
15,09
15,09
15,5
15,41
15,42
15,47
15,23
15,59
15,22
15,45
15,02
15,5
15,59
15,98
15,76
15,43
15,45
15,32
15,4
15,42
15,54
15,6
15,67
15,61
16,01
16,06
16,15
15,87
15,89
15,73
15,78
16,07
16,2
16,42
16,61
16,89
17,62
17,83
17,94
18,07
17,85
17,86
17,85




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167084&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]1 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=167084&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167084&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.978955537240387
beta0.159772015237894
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.978955537240387 \tabularnewline
beta & 0.159772015237894 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167084&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]0.978955537240387[/C][/ROW]
[ROW][C]beta[/C][C]0.159772015237894[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167084&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167084&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
alpha0.978955537240387
beta0.159772015237894
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
313.6513.79-0.140000000000001
413.5213.9510488669245-0.431048866924499
514.1313.75975361043010.370246389569919
614.8414.41080090859870.429199091401317
715.2915.18669118136320.103308818636771
815.5115.6597078683005-0.149707868300526
915.4315.8616167059255-0.431616705925549
1015.4215.7200402868977-0.300040286897673
1115.5615.6603421208819-0.1003421208819
1215.4315.7804450993385-0.350445099338536
1315.3615.6008953696465-0.240895369646548
1415.1815.4909115821796-0.31091158217963
1515.4115.26375544876840.146244551231581
1615.1515.507008909784-0.357008909783969
1715.2115.20175995237860.00824004762137953
1815.0915.2553623076648-0.165362307664832
1915.0915.1131514071956-0.0231514071956482
2015.515.10653755056550.393462449434489
2115.4115.5693114790636-0.159311479063561
2215.4215.4660264489266-0.0460264489266464
2315.4715.46644344330540.00355655669455679
2415.2315.5159562755523-0.285956275552259
2515.5915.23732258257880.352677417421155
2615.2215.6390450483176-0.419045048317624
2715.4515.21974282312830.230257176871705
2815.0215.4720930623607-0.452093062360692
2915.514.98574101674940.514258983250558
3015.5915.5258397498980.0641602501020486
3115.9815.63534712133290.344652878667084
3215.7616.0733513576731-0.313351357673083
3315.4315.8181875117814-0.388187511781389
3415.4515.42904610656120.0209538934388132
3515.3215.4437133376615-0.123713337661533
3615.415.29740781591140.102592184088596
3715.4215.3886917504210.0313082495789576
3815.5415.41508879641950.124911203580536
3915.615.55265629629520.0473437037048061
4015.6715.62169367710430.0483063228956766
4115.6115.6992289967252-0.0892289967251578
4216.0115.6281670731160.381832926883984
4316.0616.0779762011744-0.0179762011744096
4416.1516.13357831726570.0164216827343076
4515.8716.2254229427325-0.355422942732529
4615.8915.8976566176103-0.00765661761034941
4715.7315.9091404928764-0.179140492876376
4815.7815.72472996833140.0552700316685826
4916.0715.77844169379490.291558306205099
5016.216.10907168091920.0909283190807813
5116.4216.25751590223090.162484097769081
5216.6116.50142413813760.108575861862427
5316.8916.70954092587450.180459074125459
5417.6217.01625373175920.603746268240805
5517.8317.8317776522619-0.00177765226190019
5617.9418.0542425358017-0.114242535801736
5718.0718.1487406582159-0.0787406582159029
5817.8518.2656777376235-0.415677737623501
5917.8617.9877523676153-0.127752367615251
6017.8517.9717114235216-0.121711423521635

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 13.65 & 13.79 & -0.140000000000001 \tabularnewline
4 & 13.52 & 13.9510488669245 & -0.431048866924499 \tabularnewline
5 & 14.13 & 13.7597536104301 & 0.370246389569919 \tabularnewline
6 & 14.84 & 14.4108009085987 & 0.429199091401317 \tabularnewline
7 & 15.29 & 15.1866911813632 & 0.103308818636771 \tabularnewline
8 & 15.51 & 15.6597078683005 & -0.149707868300526 \tabularnewline
9 & 15.43 & 15.8616167059255 & -0.431616705925549 \tabularnewline
10 & 15.42 & 15.7200402868977 & -0.300040286897673 \tabularnewline
11 & 15.56 & 15.6603421208819 & -0.1003421208819 \tabularnewline
12 & 15.43 & 15.7804450993385 & -0.350445099338536 \tabularnewline
13 & 15.36 & 15.6008953696465 & -0.240895369646548 \tabularnewline
14 & 15.18 & 15.4909115821796 & -0.31091158217963 \tabularnewline
15 & 15.41 & 15.2637554487684 & 0.146244551231581 \tabularnewline
16 & 15.15 & 15.507008909784 & -0.357008909783969 \tabularnewline
17 & 15.21 & 15.2017599523786 & 0.00824004762137953 \tabularnewline
18 & 15.09 & 15.2553623076648 & -0.165362307664832 \tabularnewline
19 & 15.09 & 15.1131514071956 & -0.0231514071956482 \tabularnewline
20 & 15.5 & 15.1065375505655 & 0.393462449434489 \tabularnewline
21 & 15.41 & 15.5693114790636 & -0.159311479063561 \tabularnewline
22 & 15.42 & 15.4660264489266 & -0.0460264489266464 \tabularnewline
23 & 15.47 & 15.4664434433054 & 0.00355655669455679 \tabularnewline
24 & 15.23 & 15.5159562755523 & -0.285956275552259 \tabularnewline
25 & 15.59 & 15.2373225825788 & 0.352677417421155 \tabularnewline
26 & 15.22 & 15.6390450483176 & -0.419045048317624 \tabularnewline
27 & 15.45 & 15.2197428231283 & 0.230257176871705 \tabularnewline
28 & 15.02 & 15.4720930623607 & -0.452093062360692 \tabularnewline
29 & 15.5 & 14.9857410167494 & 0.514258983250558 \tabularnewline
30 & 15.59 & 15.525839749898 & 0.0641602501020486 \tabularnewline
31 & 15.98 & 15.6353471213329 & 0.344652878667084 \tabularnewline
32 & 15.76 & 16.0733513576731 & -0.313351357673083 \tabularnewline
33 & 15.43 & 15.8181875117814 & -0.388187511781389 \tabularnewline
34 & 15.45 & 15.4290461065612 & 0.0209538934388132 \tabularnewline
35 & 15.32 & 15.4437133376615 & -0.123713337661533 \tabularnewline
36 & 15.4 & 15.2974078159114 & 0.102592184088596 \tabularnewline
37 & 15.42 & 15.388691750421 & 0.0313082495789576 \tabularnewline
38 & 15.54 & 15.4150887964195 & 0.124911203580536 \tabularnewline
39 & 15.6 & 15.5526562962952 & 0.0473437037048061 \tabularnewline
40 & 15.67 & 15.6216936771043 & 0.0483063228956766 \tabularnewline
41 & 15.61 & 15.6992289967252 & -0.0892289967251578 \tabularnewline
42 & 16.01 & 15.628167073116 & 0.381832926883984 \tabularnewline
43 & 16.06 & 16.0779762011744 & -0.0179762011744096 \tabularnewline
44 & 16.15 & 16.1335783172657 & 0.0164216827343076 \tabularnewline
45 & 15.87 & 16.2254229427325 & -0.355422942732529 \tabularnewline
46 & 15.89 & 15.8976566176103 & -0.00765661761034941 \tabularnewline
47 & 15.73 & 15.9091404928764 & -0.179140492876376 \tabularnewline
48 & 15.78 & 15.7247299683314 & 0.0552700316685826 \tabularnewline
49 & 16.07 & 15.7784416937949 & 0.291558306205099 \tabularnewline
50 & 16.2 & 16.1090716809192 & 0.0909283190807813 \tabularnewline
51 & 16.42 & 16.2575159022309 & 0.162484097769081 \tabularnewline
52 & 16.61 & 16.5014241381376 & 0.108575861862427 \tabularnewline
53 & 16.89 & 16.7095409258745 & 0.180459074125459 \tabularnewline
54 & 17.62 & 17.0162537317592 & 0.603746268240805 \tabularnewline
55 & 17.83 & 17.8317776522619 & -0.00177765226190019 \tabularnewline
56 & 17.94 & 18.0542425358017 & -0.114242535801736 \tabularnewline
57 & 18.07 & 18.1487406582159 & -0.0787406582159029 \tabularnewline
58 & 17.85 & 18.2656777376235 & -0.415677737623501 \tabularnewline
59 & 17.86 & 17.9877523676153 & -0.127752367615251 \tabularnewline
60 & 17.85 & 17.9717114235216 & -0.121711423521635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167084&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]13.65[/C][C]13.79[/C][C]-0.140000000000001[/C][/ROW]
[ROW][C]4[/C][C]13.52[/C][C]13.9510488669245[/C][C]-0.431048866924499[/C][/ROW]
[ROW][C]5[/C][C]14.13[/C][C]13.7597536104301[/C][C]0.370246389569919[/C][/ROW]
[ROW][C]6[/C][C]14.84[/C][C]14.4108009085987[/C][C]0.429199091401317[/C][/ROW]
[ROW][C]7[/C][C]15.29[/C][C]15.1866911813632[/C][C]0.103308818636771[/C][/ROW]
[ROW][C]8[/C][C]15.51[/C][C]15.6597078683005[/C][C]-0.149707868300526[/C][/ROW]
[ROW][C]9[/C][C]15.43[/C][C]15.8616167059255[/C][C]-0.431616705925549[/C][/ROW]
[ROW][C]10[/C][C]15.42[/C][C]15.7200402868977[/C][C]-0.300040286897673[/C][/ROW]
[ROW][C]11[/C][C]15.56[/C][C]15.6603421208819[/C][C]-0.1003421208819[/C][/ROW]
[ROW][C]12[/C][C]15.43[/C][C]15.7804450993385[/C][C]-0.350445099338536[/C][/ROW]
[ROW][C]13[/C][C]15.36[/C][C]15.6008953696465[/C][C]-0.240895369646548[/C][/ROW]
[ROW][C]14[/C][C]15.18[/C][C]15.4909115821796[/C][C]-0.31091158217963[/C][/ROW]
[ROW][C]15[/C][C]15.41[/C][C]15.2637554487684[/C][C]0.146244551231581[/C][/ROW]
[ROW][C]16[/C][C]15.15[/C][C]15.507008909784[/C][C]-0.357008909783969[/C][/ROW]
[ROW][C]17[/C][C]15.21[/C][C]15.2017599523786[/C][C]0.00824004762137953[/C][/ROW]
[ROW][C]18[/C][C]15.09[/C][C]15.2553623076648[/C][C]-0.165362307664832[/C][/ROW]
[ROW][C]19[/C][C]15.09[/C][C]15.1131514071956[/C][C]-0.0231514071956482[/C][/ROW]
[ROW][C]20[/C][C]15.5[/C][C]15.1065375505655[/C][C]0.393462449434489[/C][/ROW]
[ROW][C]21[/C][C]15.41[/C][C]15.5693114790636[/C][C]-0.159311479063561[/C][/ROW]
[ROW][C]22[/C][C]15.42[/C][C]15.4660264489266[/C][C]-0.0460264489266464[/C][/ROW]
[ROW][C]23[/C][C]15.47[/C][C]15.4664434433054[/C][C]0.00355655669455679[/C][/ROW]
[ROW][C]24[/C][C]15.23[/C][C]15.5159562755523[/C][C]-0.285956275552259[/C][/ROW]
[ROW][C]25[/C][C]15.59[/C][C]15.2373225825788[/C][C]0.352677417421155[/C][/ROW]
[ROW][C]26[/C][C]15.22[/C][C]15.6390450483176[/C][C]-0.419045048317624[/C][/ROW]
[ROW][C]27[/C][C]15.45[/C][C]15.2197428231283[/C][C]0.230257176871705[/C][/ROW]
[ROW][C]28[/C][C]15.02[/C][C]15.4720930623607[/C][C]-0.452093062360692[/C][/ROW]
[ROW][C]29[/C][C]15.5[/C][C]14.9857410167494[/C][C]0.514258983250558[/C][/ROW]
[ROW][C]30[/C][C]15.59[/C][C]15.525839749898[/C][C]0.0641602501020486[/C][/ROW]
[ROW][C]31[/C][C]15.98[/C][C]15.6353471213329[/C][C]0.344652878667084[/C][/ROW]
[ROW][C]32[/C][C]15.76[/C][C]16.0733513576731[/C][C]-0.313351357673083[/C][/ROW]
[ROW][C]33[/C][C]15.43[/C][C]15.8181875117814[/C][C]-0.388187511781389[/C][/ROW]
[ROW][C]34[/C][C]15.45[/C][C]15.4290461065612[/C][C]0.0209538934388132[/C][/ROW]
[ROW][C]35[/C][C]15.32[/C][C]15.4437133376615[/C][C]-0.123713337661533[/C][/ROW]
[ROW][C]36[/C][C]15.4[/C][C]15.2974078159114[/C][C]0.102592184088596[/C][/ROW]
[ROW][C]37[/C][C]15.42[/C][C]15.388691750421[/C][C]0.0313082495789576[/C][/ROW]
[ROW][C]38[/C][C]15.54[/C][C]15.4150887964195[/C][C]0.124911203580536[/C][/ROW]
[ROW][C]39[/C][C]15.6[/C][C]15.5526562962952[/C][C]0.0473437037048061[/C][/ROW]
[ROW][C]40[/C][C]15.67[/C][C]15.6216936771043[/C][C]0.0483063228956766[/C][/ROW]
[ROW][C]41[/C][C]15.61[/C][C]15.6992289967252[/C][C]-0.0892289967251578[/C][/ROW]
[ROW][C]42[/C][C]16.01[/C][C]15.628167073116[/C][C]0.381832926883984[/C][/ROW]
[ROW][C]43[/C][C]16.06[/C][C]16.0779762011744[/C][C]-0.0179762011744096[/C][/ROW]
[ROW][C]44[/C][C]16.15[/C][C]16.1335783172657[/C][C]0.0164216827343076[/C][/ROW]
[ROW][C]45[/C][C]15.87[/C][C]16.2254229427325[/C][C]-0.355422942732529[/C][/ROW]
[ROW][C]46[/C][C]15.89[/C][C]15.8976566176103[/C][C]-0.00765661761034941[/C][/ROW]
[ROW][C]47[/C][C]15.73[/C][C]15.9091404928764[/C][C]-0.179140492876376[/C][/ROW]
[ROW][C]48[/C][C]15.78[/C][C]15.7247299683314[/C][C]0.0552700316685826[/C][/ROW]
[ROW][C]49[/C][C]16.07[/C][C]15.7784416937949[/C][C]0.291558306205099[/C][/ROW]
[ROW][C]50[/C][C]16.2[/C][C]16.1090716809192[/C][C]0.0909283190807813[/C][/ROW]
[ROW][C]51[/C][C]16.42[/C][C]16.2575159022309[/C][C]0.162484097769081[/C][/ROW]
[ROW][C]52[/C][C]16.61[/C][C]16.5014241381376[/C][C]0.108575861862427[/C][/ROW]
[ROW][C]53[/C][C]16.89[/C][C]16.7095409258745[/C][C]0.180459074125459[/C][/ROW]
[ROW][C]54[/C][C]17.62[/C][C]17.0162537317592[/C][C]0.603746268240805[/C][/ROW]
[ROW][C]55[/C][C]17.83[/C][C]17.8317776522619[/C][C]-0.00177765226190019[/C][/ROW]
[ROW][C]56[/C][C]17.94[/C][C]18.0542425358017[/C][C]-0.114242535801736[/C][/ROW]
[ROW][C]57[/C][C]18.07[/C][C]18.1487406582159[/C][C]-0.0787406582159029[/C][/ROW]
[ROW][C]58[/C][C]17.85[/C][C]18.2656777376235[/C][C]-0.415677737623501[/C][/ROW]
[ROW][C]59[/C][C]17.86[/C][C]17.9877523676153[/C][C]-0.127752367615251[/C][/ROW]
[ROW][C]60[/C][C]17.85[/C][C]17.9717114235216[/C][C]-0.121711423521635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167084&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167084&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
313.6513.79-0.140000000000001
413.5213.9510488669245-0.431048866924499
514.1313.75975361043010.370246389569919
614.8414.41080090859870.429199091401317
715.2915.18669118136320.103308818636771
815.5115.6597078683005-0.149707868300526
915.4315.8616167059255-0.431616705925549
1015.4215.7200402868977-0.300040286897673
1115.5615.6603421208819-0.1003421208819
1215.4315.7804450993385-0.350445099338536
1315.3615.6008953696465-0.240895369646548
1415.1815.4909115821796-0.31091158217963
1515.4115.26375544876840.146244551231581
1615.1515.507008909784-0.357008909783969
1715.2115.20175995237860.00824004762137953
1815.0915.2553623076648-0.165362307664832
1915.0915.1131514071956-0.0231514071956482
2015.515.10653755056550.393462449434489
2115.4115.5693114790636-0.159311479063561
2215.4215.4660264489266-0.0460264489266464
2315.4715.46644344330540.00355655669455679
2415.2315.5159562755523-0.285956275552259
2515.5915.23732258257880.352677417421155
2615.2215.6390450483176-0.419045048317624
2715.4515.21974282312830.230257176871705
2815.0215.4720930623607-0.452093062360692
2915.514.98574101674940.514258983250558
3015.5915.5258397498980.0641602501020486
3115.9815.63534712133290.344652878667084
3215.7616.0733513576731-0.313351357673083
3315.4315.8181875117814-0.388187511781389
3415.4515.42904610656120.0209538934388132
3515.3215.4437133376615-0.123713337661533
3615.415.29740781591140.102592184088596
3715.4215.3886917504210.0313082495789576
3815.5415.41508879641950.124911203580536
3915.615.55265629629520.0473437037048061
4015.6715.62169367710430.0483063228956766
4115.6115.6992289967252-0.0892289967251578
4216.0115.6281670731160.381832926883984
4316.0616.0779762011744-0.0179762011744096
4416.1516.13357831726570.0164216827343076
4515.8716.2254229427325-0.355422942732529
4615.8915.8976566176103-0.00765661761034941
4715.7315.9091404928764-0.179140492876376
4815.7815.72472996833140.0552700316685826
4916.0715.77844169379490.291558306205099
5016.216.10907168091920.0909283190807813
5116.4216.25751590223090.162484097769081
5216.6116.50142413813760.108575861862427
5316.8916.70954092587450.180459074125459
5417.6217.01625373175920.603746268240805
5517.8317.8317776522619-0.00177765226190019
5617.9418.0542425358017-0.114242535801736
5718.0718.1487406582159-0.0787406582159029
5817.8518.2656777376235-0.415677737623501
5917.8617.9877523676153-0.127752367615251
6017.8517.9717114235216-0.121711423521635







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6117.942547447979117.434100063422218.4509948325361
6218.032533544438617.263271937948418.8017951509287
6318.12251964089817.111011303284719.1340279785113
6418.212505737357416.961376392202619.4636350825122
6518.302491833816816.808859086158119.7961245814756
6618.392477930276316.651030153656120.1339257068964
6718.482464026735716.486698970002420.478229083469
6818.572450123195116.315261385905720.8296388604845
6918.662436219654516.136420055252421.1884523840566
7018.752422316113915.950048864051921.554795768176
7118.842408412573415.756121370888621.9286954542581
7218.932394509032815.554670618409522.310118399656

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 17.9425474479791 & 17.4341000634222 & 18.4509948325361 \tabularnewline
62 & 18.0325335444386 & 17.2632719379484 & 18.8017951509287 \tabularnewline
63 & 18.122519640898 & 17.1110113032847 & 19.1340279785113 \tabularnewline
64 & 18.2125057373574 & 16.9613763922026 & 19.4636350825122 \tabularnewline
65 & 18.3024918338168 & 16.8088590861581 & 19.7961245814756 \tabularnewline
66 & 18.3924779302763 & 16.6510301536561 & 20.1339257068964 \tabularnewline
67 & 18.4824640267357 & 16.4866989700024 & 20.478229083469 \tabularnewline
68 & 18.5724501231951 & 16.3152613859057 & 20.8296388604845 \tabularnewline
69 & 18.6624362196545 & 16.1364200552524 & 21.1884523840566 \tabularnewline
70 & 18.7524223161139 & 15.9500488640519 & 21.554795768176 \tabularnewline
71 & 18.8424084125734 & 15.7561213708886 & 21.9286954542581 \tabularnewline
72 & 18.9323945090328 & 15.5546706184095 & 22.310118399656 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167084&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]17.9425474479791[/C][C]17.4341000634222[/C][C]18.4509948325361[/C][/ROW]
[ROW][C]62[/C][C]18.0325335444386[/C][C]17.2632719379484[/C][C]18.8017951509287[/C][/ROW]
[ROW][C]63[/C][C]18.122519640898[/C][C]17.1110113032847[/C][C]19.1340279785113[/C][/ROW]
[ROW][C]64[/C][C]18.2125057373574[/C][C]16.9613763922026[/C][C]19.4636350825122[/C][/ROW]
[ROW][C]65[/C][C]18.3024918338168[/C][C]16.8088590861581[/C][C]19.7961245814756[/C][/ROW]
[ROW][C]66[/C][C]18.3924779302763[/C][C]16.6510301536561[/C][C]20.1339257068964[/C][/ROW]
[ROW][C]67[/C][C]18.4824640267357[/C][C]16.4866989700024[/C][C]20.478229083469[/C][/ROW]
[ROW][C]68[/C][C]18.5724501231951[/C][C]16.3152613859057[/C][C]20.8296388604845[/C][/ROW]
[ROW][C]69[/C][C]18.6624362196545[/C][C]16.1364200552524[/C][C]21.1884523840566[/C][/ROW]
[ROW][C]70[/C][C]18.7524223161139[/C][C]15.9500488640519[/C][C]21.554795768176[/C][/ROW]
[ROW][C]71[/C][C]18.8424084125734[/C][C]15.7561213708886[/C][C]21.9286954542581[/C][/ROW]
[ROW][C]72[/C][C]18.9323945090328[/C][C]15.5546706184095[/C][C]22.310118399656[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167084&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167084&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
6117.942547447979117.434100063422218.4509948325361
6218.032533544438617.263271937948418.8017951509287
6318.12251964089817.111011303284719.1340279785113
6418.212505737357416.961376392202619.4636350825122
6518.302491833816816.808859086158119.7961245814756
6618.392477930276316.651030153656120.1339257068964
6718.482464026735716.486698970002420.478229083469
6818.572450123195116.315261385905720.8296388604845
6918.662436219654516.136420055252421.1884523840566
7018.752422316113915.950048864051921.554795768176
7118.842408412573415.756121370888621.9286954542581
7218.932394509032815.554670618409522.310118399656



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')