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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2011 16:06:57 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/28/t1322514497taq78lnn53pp66o.htm/, Retrieved Thu, 28 Mar 2024 18:08:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148033, Retrieved Thu, 28 Mar 2024 18:08:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMPD    [Exponential Smoothing] [smooting models test] [2011-11-28 21:06:57] [5e0d67387daac495c180286b1f543191] [Current]
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Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8




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=148033&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=148033&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148033&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
alpha0.384309739467462
beta0.0302997010977021
gamma0.742528245786947

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.384309739467462 \tabularnewline
beta & 0.0302997010977021 \tabularnewline
gamma & 0.742528245786947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148033&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]0.384309739467462[/C][/ROW]
[ROW][C]beta[/C][C]0.0302997010977021[/C][/ROW]
[ROW][C]gamma[/C][C]0.742528245786947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148033&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148033&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
alpha0.384309739467462
beta0.0302997010977021
gamma0.742528245786947







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138065.953525641025614.0464743589744
144232.48964526929549.51035473070461
155447.18489965428236.81510034571767
166660.63203309523265.36796690476743
178179.75219285802721.2478071419728
186369.4284651489414-6.42846514894138
19137111.45481516457125.5451848354292
207280.2330770866427-8.23307708664271
2110786.434154148703320.5658458512967
225868.1507494951891-10.1507494951891
233697.1111246530485-61.1111246530485
2452157.233657972123-105.233657972123
257965.429005431777413.5709945682226
267728.444808651510548.5551913484895
275456.1040291621919-2.10402916219191
288464.548851083419.4511489166
294886.4486823494848-38.4486823494848
309656.148591258351439.8514087416486
3183129.905688555298-46.9056885552983
326653.882031955816412.1179680441836
336179.7910982360018-18.7910982360018
345330.602474960697822.3975250393022
353047.4157183788858-17.4157183788858
3674103.30991954801-29.3099195480102
376995.0316879334499-26.0316879334499
385958.39485050423420.605149495765815
394243.4817268439243-1.48172684392433
406561.04234541160143.95765458839864
417049.359861417782720.6401385822173
4210077.094388853560322.9056111464397
4363104.009168236201-41.0091682362014
4410556.636590379907748.3634096200923
458282.1678704778572-0.16787047785725
468159.006644176753621.9933558232464
477557.498750730201417.5012492697986
48102121.816337740838-19.8163377408382
49121119.2379266949141.76207330508561
5098106.336283949771-8.33628394977093
517687.804997816099-11.804997816099
5277104.536951034864-27.5369510348641
536388.6626936587582-25.6626936587582
543799.3843422847504-62.3843422847504
553563.0545018301303-28.0545018301303
562360.4225025745948-37.4225025745948
574028.703314289242711.2966857107573
582918.117730448940810.8822695510592
59378.1950223523656328.8049776476344
605157.8369123668596-6.83691236685961
612068.3032603711942-48.3032603711942
622829.1530913703556-1.15309137035556
63139.488946554592053.51105344540795
642222.785571833592-0.785571833592023
652516.23118573957578.76881426042425
661321.9804002345207-8.98040023452069
671621.0737026562198-5.07370265621981
681322.4633065520694-9.46330655206938
691623.5601075505731-7.56010755057313
70175.1168123377282311.8831876622718
7193.362695500375265.63730449962474
721727.1271879455909-10.1271879455909
732516.65414997711198.34585002288814
741420.7721171731624-6.7721171731624
7580.9572011769203687.04279882307963

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 80 & 65.9535256410256 & 14.0464743589744 \tabularnewline
14 & 42 & 32.4896452692954 & 9.51035473070461 \tabularnewline
15 & 54 & 47.1848996542823 & 6.81510034571767 \tabularnewline
16 & 66 & 60.6320330952326 & 5.36796690476743 \tabularnewline
17 & 81 & 79.7521928580272 & 1.2478071419728 \tabularnewline
18 & 63 & 69.4284651489414 & -6.42846514894138 \tabularnewline
19 & 137 & 111.454815164571 & 25.5451848354292 \tabularnewline
20 & 72 & 80.2330770866427 & -8.23307708664271 \tabularnewline
21 & 107 & 86.4341541487033 & 20.5658458512967 \tabularnewline
22 & 58 & 68.1507494951891 & -10.1507494951891 \tabularnewline
23 & 36 & 97.1111246530485 & -61.1111246530485 \tabularnewline
24 & 52 & 157.233657972123 & -105.233657972123 \tabularnewline
25 & 79 & 65.4290054317774 & 13.5709945682226 \tabularnewline
26 & 77 & 28.4448086515105 & 48.5551913484895 \tabularnewline
27 & 54 & 56.1040291621919 & -2.10402916219191 \tabularnewline
28 & 84 & 64.5488510834 & 19.4511489166 \tabularnewline
29 & 48 & 86.4486823494848 & -38.4486823494848 \tabularnewline
30 & 96 & 56.1485912583514 & 39.8514087416486 \tabularnewline
31 & 83 & 129.905688555298 & -46.9056885552983 \tabularnewline
32 & 66 & 53.8820319558164 & 12.1179680441836 \tabularnewline
33 & 61 & 79.7910982360018 & -18.7910982360018 \tabularnewline
34 & 53 & 30.6024749606978 & 22.3975250393022 \tabularnewline
35 & 30 & 47.4157183788858 & -17.4157183788858 \tabularnewline
36 & 74 & 103.30991954801 & -29.3099195480102 \tabularnewline
37 & 69 & 95.0316879334499 & -26.0316879334499 \tabularnewline
38 & 59 & 58.3948505042342 & 0.605149495765815 \tabularnewline
39 & 42 & 43.4817268439243 & -1.48172684392433 \tabularnewline
40 & 65 & 61.0423454116014 & 3.95765458839864 \tabularnewline
41 & 70 & 49.3598614177827 & 20.6401385822173 \tabularnewline
42 & 100 & 77.0943888535603 & 22.9056111464397 \tabularnewline
43 & 63 & 104.009168236201 & -41.0091682362014 \tabularnewline
44 & 105 & 56.6365903799077 & 48.3634096200923 \tabularnewline
45 & 82 & 82.1678704778572 & -0.16787047785725 \tabularnewline
46 & 81 & 59.0066441767536 & 21.9933558232464 \tabularnewline
47 & 75 & 57.4987507302014 & 17.5012492697986 \tabularnewline
48 & 102 & 121.816337740838 & -19.8163377408382 \tabularnewline
49 & 121 & 119.237926694914 & 1.76207330508561 \tabularnewline
50 & 98 & 106.336283949771 & -8.33628394977093 \tabularnewline
51 & 76 & 87.804997816099 & -11.804997816099 \tabularnewline
52 & 77 & 104.536951034864 & -27.5369510348641 \tabularnewline
53 & 63 & 88.6626936587582 & -25.6626936587582 \tabularnewline
54 & 37 & 99.3843422847504 & -62.3843422847504 \tabularnewline
55 & 35 & 63.0545018301303 & -28.0545018301303 \tabularnewline
56 & 23 & 60.4225025745948 & -37.4225025745948 \tabularnewline
57 & 40 & 28.7033142892427 & 11.2966857107573 \tabularnewline
58 & 29 & 18.1177304489408 & 10.8822695510592 \tabularnewline
59 & 37 & 8.19502235236563 & 28.8049776476344 \tabularnewline
60 & 51 & 57.8369123668596 & -6.83691236685961 \tabularnewline
61 & 20 & 68.3032603711942 & -48.3032603711942 \tabularnewline
62 & 28 & 29.1530913703556 & -1.15309137035556 \tabularnewline
63 & 13 & 9.48894655459205 & 3.51105344540795 \tabularnewline
64 & 22 & 22.785571833592 & -0.785571833592023 \tabularnewline
65 & 25 & 16.2311857395757 & 8.76881426042425 \tabularnewline
66 & 13 & 21.9804002345207 & -8.98040023452069 \tabularnewline
67 & 16 & 21.0737026562198 & -5.07370265621981 \tabularnewline
68 & 13 & 22.4633065520694 & -9.46330655206938 \tabularnewline
69 & 16 & 23.5601075505731 & -7.56010755057313 \tabularnewline
70 & 17 & 5.11681233772823 & 11.8831876622718 \tabularnewline
71 & 9 & 3.36269550037526 & 5.63730449962474 \tabularnewline
72 & 17 & 27.1271879455909 & -10.1271879455909 \tabularnewline
73 & 25 & 16.6541499771119 & 8.34585002288814 \tabularnewline
74 & 14 & 20.7721171731624 & -6.7721171731624 \tabularnewline
75 & 8 & 0.957201176920368 & 7.04279882307963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148033&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]80[/C][C]65.9535256410256[/C][C]14.0464743589744[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]32.4896452692954[/C][C]9.51035473070461[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]47.1848996542823[/C][C]6.81510034571767[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]60.6320330952326[/C][C]5.36796690476743[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]79.7521928580272[/C][C]1.2478071419728[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]69.4284651489414[/C][C]-6.42846514894138[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]111.454815164571[/C][C]25.5451848354292[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]80.2330770866427[/C][C]-8.23307708664271[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]86.4341541487033[/C][C]20.5658458512967[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]68.1507494951891[/C][C]-10.1507494951891[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]97.1111246530485[/C][C]-61.1111246530485[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]157.233657972123[/C][C]-105.233657972123[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]65.4290054317774[/C][C]13.5709945682226[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]28.4448086515105[/C][C]48.5551913484895[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]56.1040291621919[/C][C]-2.10402916219191[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]64.5488510834[/C][C]19.4511489166[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]86.4486823494848[/C][C]-38.4486823494848[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]56.1485912583514[/C][C]39.8514087416486[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]129.905688555298[/C][C]-46.9056885552983[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]53.8820319558164[/C][C]12.1179680441836[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]79.7910982360018[/C][C]-18.7910982360018[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]30.6024749606978[/C][C]22.3975250393022[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]47.4157183788858[/C][C]-17.4157183788858[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]103.30991954801[/C][C]-29.3099195480102[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]95.0316879334499[/C][C]-26.0316879334499[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]58.3948505042342[/C][C]0.605149495765815[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]43.4817268439243[/C][C]-1.48172684392433[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]61.0423454116014[/C][C]3.95765458839864[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]49.3598614177827[/C][C]20.6401385822173[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]77.0943888535603[/C][C]22.9056111464397[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]104.009168236201[/C][C]-41.0091682362014[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]56.6365903799077[/C][C]48.3634096200923[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]82.1678704778572[/C][C]-0.16787047785725[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]59.0066441767536[/C][C]21.9933558232464[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]57.4987507302014[/C][C]17.5012492697986[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]121.816337740838[/C][C]-19.8163377408382[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]119.237926694914[/C][C]1.76207330508561[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]106.336283949771[/C][C]-8.33628394977093[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]87.804997816099[/C][C]-11.804997816099[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]104.536951034864[/C][C]-27.5369510348641[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]88.6626936587582[/C][C]-25.6626936587582[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]99.3843422847504[/C][C]-62.3843422847504[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]63.0545018301303[/C][C]-28.0545018301303[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]60.4225025745948[/C][C]-37.4225025745948[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]28.7033142892427[/C][C]11.2966857107573[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]18.1177304489408[/C][C]10.8822695510592[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]8.19502235236563[/C][C]28.8049776476344[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]57.8369123668596[/C][C]-6.83691236685961[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]68.3032603711942[/C][C]-48.3032603711942[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]29.1530913703556[/C][C]-1.15309137035556[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]9.48894655459205[/C][C]3.51105344540795[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]22.785571833592[/C][C]-0.785571833592023[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]16.2311857395757[/C][C]8.76881426042425[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]21.9804002345207[/C][C]-8.98040023452069[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]21.0737026562198[/C][C]-5.07370265621981[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]22.4633065520694[/C][C]-9.46330655206938[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]23.5601075505731[/C][C]-7.56010755057313[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]5.11681233772823[/C][C]11.8831876622718[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]3.36269550037526[/C][C]5.63730449962474[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]27.1271879455909[/C][C]-10.1271879455909[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]16.6541499771119[/C][C]8.34585002288814[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]20.7721171731624[/C][C]-6.7721171731624[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]0.957201176920368[/C][C]7.04279882307963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148033&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148033&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
138065.953525641025614.0464743589744
144232.48964526929549.51035473070461
155447.18489965428236.81510034571767
166660.63203309523265.36796690476743
178179.75219285802721.2478071419728
186369.4284651489414-6.42846514894138
19137111.45481516457125.5451848354292
207280.2330770866427-8.23307708664271
2110786.434154148703320.5658458512967
225868.1507494951891-10.1507494951891
233697.1111246530485-61.1111246530485
2452157.233657972123-105.233657972123
257965.429005431777413.5709945682226
267728.444808651510548.5551913484895
275456.1040291621919-2.10402916219191
288464.548851083419.4511489166
294886.4486823494848-38.4486823494848
309656.148591258351439.8514087416486
3183129.905688555298-46.9056885552983
326653.882031955816412.1179680441836
336179.7910982360018-18.7910982360018
345330.602474960697822.3975250393022
353047.4157183788858-17.4157183788858
3674103.30991954801-29.3099195480102
376995.0316879334499-26.0316879334499
385958.39485050423420.605149495765815
394243.4817268439243-1.48172684392433
406561.04234541160143.95765458839864
417049.359861417782720.6401385822173
4210077.094388853560322.9056111464397
4363104.009168236201-41.0091682362014
4410556.636590379907748.3634096200923
458282.1678704778572-0.16787047785725
468159.006644176753621.9933558232464
477557.498750730201417.5012492697986
48102121.816337740838-19.8163377408382
49121119.2379266949141.76207330508561
5098106.336283949771-8.33628394977093
517687.804997816099-11.804997816099
5277104.536951034864-27.5369510348641
536388.6626936587582-25.6626936587582
543799.3843422847504-62.3843422847504
553563.0545018301303-28.0545018301303
562360.4225025745948-37.4225025745948
574028.703314289242711.2966857107573
582918.117730448940810.8822695510592
59378.1950223523656328.8049776476344
605157.8369123668596-6.83691236685961
612068.3032603711942-48.3032603711942
622829.1530913703556-1.15309137035556
63139.488946554592053.51105344540795
642222.785571833592-0.785571833592023
652516.23118573957578.76881426042425
661321.9804002345207-8.98040023452069
671621.0737026562198-5.07370265621981
681322.4633065520694-9.46330655206938
691623.5601075505731-7.56010755057313
70175.1168123377282311.8831876622718
7193.362695500375265.63730449962474
721727.1271879455909-10.1271879455909
732516.65414997711198.34585002288814
741420.7721171731624-6.7721171731624
7580.9572011769203687.04279882307963







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7613.5643390198893-38.939834658675866.0685126984545
7711.6064628012529-44.863716150227868.0766417527336
785.69591900397162-54.693385974521966.0852239824651
799.9556083492285-54.320335577231274.2315522756882
8011.2764991696405-56.864642040473179.4176403797541
8116.9786142103193-55.014928612436688.9721570330752
8210.5160089149046-65.324018741684186.3560365714933
831.38770573245094-78.298437760667281.0738492255691
8415.7611241951368-67.775291796822999.2975401870965
8517.7256690404371-69.6689038455758105.12024192645
8611.7279548390752-79.5357551627387102.991664840889
870.913368443513928-94.233047967878996.0597848549068

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 13.5643390198893 & -38.9398346586758 & 66.0685126984545 \tabularnewline
77 & 11.6064628012529 & -44.8637161502278 & 68.0766417527336 \tabularnewline
78 & 5.69591900397162 & -54.6933859745219 & 66.0852239824651 \tabularnewline
79 & 9.9556083492285 & -54.3203355772312 & 74.2315522756882 \tabularnewline
80 & 11.2764991696405 & -56.8646420404731 & 79.4176403797541 \tabularnewline
81 & 16.9786142103193 & -55.0149286124366 & 88.9721570330752 \tabularnewline
82 & 10.5160089149046 & -65.3240187416841 & 86.3560365714933 \tabularnewline
83 & 1.38770573245094 & -78.2984377606672 & 81.0738492255691 \tabularnewline
84 & 15.7611241951368 & -67.7752917968229 & 99.2975401870965 \tabularnewline
85 & 17.7256690404371 & -69.6689038455758 & 105.12024192645 \tabularnewline
86 & 11.7279548390752 & -79.5357551627387 & 102.991664840889 \tabularnewline
87 & 0.913368443513928 & -94.2330479678789 & 96.0597848549068 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148033&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]76[/C][C]13.5643390198893[/C][C]-38.9398346586758[/C][C]66.0685126984545[/C][/ROW]
[ROW][C]77[/C][C]11.6064628012529[/C][C]-44.8637161502278[/C][C]68.0766417527336[/C][/ROW]
[ROW][C]78[/C][C]5.69591900397162[/C][C]-54.6933859745219[/C][C]66.0852239824651[/C][/ROW]
[ROW][C]79[/C][C]9.9556083492285[/C][C]-54.3203355772312[/C][C]74.2315522756882[/C][/ROW]
[ROW][C]80[/C][C]11.2764991696405[/C][C]-56.8646420404731[/C][C]79.4176403797541[/C][/ROW]
[ROW][C]81[/C][C]16.9786142103193[/C][C]-55.0149286124366[/C][C]88.9721570330752[/C][/ROW]
[ROW][C]82[/C][C]10.5160089149046[/C][C]-65.3240187416841[/C][C]86.3560365714933[/C][/ROW]
[ROW][C]83[/C][C]1.38770573245094[/C][C]-78.2984377606672[/C][C]81.0738492255691[/C][/ROW]
[ROW][C]84[/C][C]15.7611241951368[/C][C]-67.7752917968229[/C][C]99.2975401870965[/C][/ROW]
[ROW][C]85[/C][C]17.7256690404371[/C][C]-69.6689038455758[/C][C]105.12024192645[/C][/ROW]
[ROW][C]86[/C][C]11.7279548390752[/C][C]-79.5357551627387[/C][C]102.991664840889[/C][/ROW]
[ROW][C]87[/C][C]0.913368443513928[/C][C]-94.2330479678789[/C][C]96.0597848549068[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148033&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148033&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
7613.5643390198893-38.939834658675866.0685126984545
7711.6064628012529-44.863716150227868.0766417527336
785.69591900397162-54.693385974521966.0852239824651
799.9556083492285-54.320335577231274.2315522756882
8011.2764991696405-56.864642040473179.4176403797541
8116.9786142103193-55.014928612436688.9721570330752
8210.5160089149046-65.324018741684186.3560365714933
831.38770573245094-78.298437760667281.0738492255691
8415.7611241951368-67.775291796822999.2975401870965
8517.7256690404371-69.6689038455758105.12024192645
8611.7279548390752-79.5357551627387102.991664840889
870.913368443513928-94.233047967878996.0597848549068



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')